Yep. When you don’t have the underlying data you can’t see the obvious lie. So the question is, how much to 20K a year grunts donate vs how much to 180K DC employees donate? Not complicated. https://t.co/iswfcMMsNB
YES P-LANGUAGE IS ODD Why? Because we disambiguate terms where normies retain ambiguity. So learning the terms – and increasing precision and parsimony by doing so – is most of the work.
Why? Because we disambiguate terms where normies retain ambiguity. So learning the terms – and increasing precision and parsimony by doing so – is most of the work.
“Mathematics, by the virtue of consisting of nothing other than positional names, preserves constant relations, since only constant relations are expressible in the grammar of mathematics: the grammar of positional names.”
“The discipline we call computer science is more generally the logic of operations, and is superior in informational density to mathematics in that it is causal and mathematics is merely descriptive.”
In mathematics, at least, for the most part, the means of conducting operations to solve a problem is nearly identical to the means of demonstrating the construction of a solution using existentially possible operations.
We sought to copy mathematics – starting with the Greeks. But we lacked the understanding of why math was so effective at the ascertaining truth of relations: because there is very little difference between the process of theorizing and the process of construction.
FOUNDATIONS OF LOGIC
The foundations of logic like those of mathematics are terribly simple as subsets of reality. But by doubling down in the 19th and 20th centuries all we have found is that we say rather nonsensical terms like ‘the axiom of choice’ or ‘limits’ rather than ‘undecidable without appeal to information provided by existential context’. After all, math is just the discipline of scale-independent measurement, and the deduction that is possible given the precision of constant relations using identical unitary measures. Logic is nothing more than than set operations. Algorithms are nothing more than sequential operations restoring time. Operations are nothing more than algorithms restoring physical transformation, time and cost. etc.
As a consequence, I find most of this kind of terminological discourse … silly hermeneutics. As Poincare stated ‘that isn’t math its philosophy’. Or as I would say, ‘with platonism we depart science and join theology. It may be secular theology in that it is ideal rather than supernatural, but it is theology none the less’.
it is one thing to say ‘by convention in math (or logic or whatever dimension we speak of) we use this colloquialism (half-truth) as a matter of convenience. It is not ‘true’. It is just the best approximation given the brevity we exercise in simplifying our work.
There exists only one possible ‘True’: the most parsimonious and correspondent testimony one can speak in the available language in the given context. Everything else is a convention.
Ergo, if you do not know the operational construction of the terms that you use, you do not know of what you speak. That does not mean you cannot speak truth any more than monkey cannot accidentally type one of the Sonnets.
This is why the operationalist movement in math we call Intuitionism failed.
Anyway. Well-formed (grammatically correct) statements in math may or may not be decidable but our intention is to produce decidable statements. In symbolic logic, well formed (grammatically correct) statements may or may not be decidable. in logic (language), well-formed (grammatically correct) statements are difficult to construct because of the categorical difference between constant relations (ideals in math), constant categories (ideals in formal logic), and inconstant categories (ordinary language). Furthermore, the process of DEDUCTION using premises (or logical summation) limits us to the utility of true statements. Ergo for that purpose statements can only evaluate to true or not-true (including false and undecidable). While for the purpose of INDUCTION (transfer of meaning by seeding free association, or the construction of possibility by the same means) seeks only possibility or impossibility not truth or falsehood.
How can you claim to make a truth proposition and demand precise language when your premises are mere demonstrably falsehoods used by convention?
NUMBERS
“Nouns are names. Numbers are nouns. Numbers evolved as positional names. Numbers are positional names of constant relations. As positional names, they are extensions of ordinary language. Math: the science of measurement by the use of constant relations.”
We use many positional names: none, one, and some, short medium and tall; small, medium, and large; front, middle, and back; right center and left; port and starboard; daughter, mother, and grandmother;
Numbers differ from ordinary nouns only in that we produce them by positional naming. Whereas early positional names varied from one two and many, to base ten, or base twelve, or in the twenties, or sixties, each which increases the demand on the human mind; the decimal system of positional naming
Positional names are produced by a series of consistent operations. We call those series of consistent operations ‘functions’. By analogy we (unfortunately) called all such functions numbers: a convenient fiction.
Because of positional naming all positional names (numbers) are context independent, scale independent, constant relations, descriptively parsimonious and closed to interpretation.
So unlike other nouns (names), they are almost impossible to misinterpret by processes of conflation (adding information), and are impossible to further deflate (removing information).
Any other information we desire to add to the noun,( by which we mean name, positional name, number) must be provided by analogy to a context: application.
Numbers exist as positional names of constant relations. Those constant relations are scale-independent, context-dependent, informationally parsimonious, and nearly impossible to conflate with information that will allow for misinterpretation or deception.
As such, numbers allow us to perform DEDUCTIONS that other names, that lack constant relations, scale independence, context dependence, parsimony, immutability, and incorruptibility do not. Because deduction is possible wherever constant relations, parsimony, immutability, and incorruptibility are present.
As such, numbers serve as a method of verbal reasoning within and beyond the limits of human imagination (cognition), short term memory, and ordinary reason.
Numbers then are simply a very clean set of nouns(positional names), verbs (operations and functions), including tests of positional relations (comparison operators) that allow us to describe, reason and discourse about that which is otherwise beyond our ordinary language, and mental capacity.
As such we distinguish language, reason, and logic from numbers and measurement, and deduction both artificially and practically. Since while they consist of the same processes, the language of numbers, measurements, and deductions is simply more precise than the language of ordinary language, reason, and logic, if for no other reason than it is nearly closed to ignorance, error, bias, wishful thinking, suggestion, obscurantism, deceit, and the fictionalism of superstition, pseudo-rationalism, pseudoscience.
Unfortunately, since to humans, that which allows them to perform such ‘seeming miracles’ that are otherwise beyond comprehension, must be justified, we invented various fictionalisms – primarily idealisms, or what philosophers refer to as platonisms – (mythologies) to explain our actions. To attribute comprehension to that which we did not comprehend. To provide authority by general rule to that which we could only demonstrate through repeated application. So mathematics maintains much of it’s ‘magical language’ and philosophers persist this magical language under the pseudo-rational label of ‘idealism’ or ‘abstraction’. Which roughly translates to “I don’t understand”.
Perhaps more unfortunately, in the 19th century, with the addition of statistics and the application of mathematics to the inconstant relations of heuristic systems: particularly probability, fiat money, economics, finance, banking and commercial and tax accounting, this language no longer retains informational parsimony, and deducibility, and has instead evolved into a pseudoscience under which ignorance, error, bias, wishful thinking, suggestion, obscurantism, and deceit are pervasive.
Math is a very simple thing. It’s just ordinary language with positional names that allow us to give names and describe transformations to, that which is otherwise beyond our ability to imagine and recall, and therefore describe or reason with.
Like everything else, if you make up stories of gods, demons, ghosts and monsters, or ‘abstractions’ or ‘ideals’ you can obscure the very simple causality that we seek to discover through science: the systematic attempt to remove error, bias, wishful thinking, suggestion, obscurantism, fictionalism, and deceit from our language of testimony about the world we perceive, cognate, remember, hypothesize within, act, advocate, negotiate, and cooperate within.
Numbers are positional names of context-independent, scale-independent, informationally parsimonious, constant relations and mathematics consists of the grammar of that language.
In other words, Math is an extension of ordinary language, ordinary reason, and ordinary science: the attempt by which we attempt to obtain information about our world within, above, and below human scale, by the use of rational and physical instrumentation, to eliminate ignorance, error, bias, and deceit from our descriptions, and as a consequence our language, and as a consequence our collective knowledge.
MATH IS SIMPLE
The foundations of mathematics are simple.
The fact that they even phrase the question as such is hysterical. The reason mathematics is so powerful a tool is precisely because its foundations are so trivial. Like discourse on property in ethics and law, it is a word game because no one establishes sufficient limits under which the general term obscures a change in state.
Math is very simple. Correspondence (what remains and what does not), Types, operations, grammar, syntax. Generally we use mathematics for the purpose of scale independence. in other words, we remove the property of scale from the set of correspondences. But we might also pass from physical dimensions to logical dimensions (there are only so many possible physical dimensions). So now we leave dimensional correspondence. In mathematics we remove time correspondence by default, and only add it in when we specifically want to make use of it. In sets we remove temporal and causal correspondence … at least in most cases. So we can add and remove many different correspondences, and work only with reciprocal (self referencing) correspondence (constant relations). But there is nothing magic here at all except for the fields (results) that can be produced by these different definitions as we use them to describe the consequences of using different values in different orders.
But if you say “I want to study the parsimony, limits, and full accounting, of this set of types using this set of operations, with the common grammar and syntax” that is pretty much what someone means when they say ‘foundations’. Most of the time. Sometimes they have no clue.
There is nothing much more difficult here in the ‘foundations’ so to speak. What’s hard in mathematics is holding operations, grammar and syntax constant, what happens as we use different correspondences (dimensions), types, and values in combination with others and yet others, to produce these various kinds of patterns that represent phenomenon that we want to describe. And what mathematicians find beautiful is that there is a bizarre set of regularities (that they call symmetries or some variation thereof), that emerge once you becomes skilled in these models, just like some games become predictable if you see a certain pattern.
But really, math is interesting because by describing regular patterns that produce complex phenomenon, we are able to describe things very accurately that we cannot ‘see’ without math to help us find it.
Its seems mystical. It isn’t. Its just the adult version of mommy saying ‘boo’ to the toddler and the joy he gets from the stimulation. There is nothing magical here. it’s creative, and interesting, but it’s just engineering with cheaper tools at lower risk: paper, pencil, and time.
Simplicity is necessary in mathematics since mathematical symbols and operations itself (state and operators) are necessary to allow us to remember state with sufficient precision that we can conduct comparisons between states.
However, if we restated the foundations of mathematics operationally (constructively – analogous to gears), and we stated the foundations of mathematical deduction negatively, as geometry, we would be able to show that it is convergence between the via-positiva construction, and the via-negative deduction that leads us to truth.
Unfortunately, man discovered (logically so) geometry prior to gears, and as such, we retain the ‘superstitious’ language of geometry (and algebra) of the superstitious era in which both were invented.
Reality has only so many dimensions. By adding and removing dimensions from consideration we simplify the problem of describing the constant relations within it.
Mathematics specializes in the removal of (a) scale, and (b) time, and (c) operations (and arguable (d) morality) from consideration, leaving only identity, quantity, and ratio, to which we add positional naming (numbers). We then construct general rules of arbitrary precision (scale independence) and apply those to reality wherein we must ‘hydrate’ (reconstitute) scale, time, and operations(actions).
So just as philosophy is ‘stuck’ in non contradiction instead of increasing dimensions in order to test theories, mathematics is ‘stuck’ in non-contradiction instead of re-hydrating (restoring dimensions) to justify propositions.
In other words, fancy words like ‘limits’ or ‘non-contradictory’ or ‘axiom of choice’ and various other terms in the field are just nonsense words that prevent the conversion of mathematics from a fictionalism into a science.
UNREASONABLE EFFECTIVENESS? NONSENSE.
The “Unreasonable effectiveness” trope annoys the hell out of me. The only reason this ‘magical mathematics’ nonsense perpetuates, and the average person is still afraid of mathematics, is because it’s taught as a superstition.
Math is trivial. 1 = any unitary measure. By the combination of some number of symbols – in the current case 0123456789, we can create positional names. By adding, subtracting units, and by adding and subtracting sets of units (multiplication and division), we can create positional names (numbers) for an unlimited set of positions. we can create names of positions in an unlimited number of directions (dimensions). We can create positions relative to any other position (relative positions). We can create changes in positions of relative positions. producing numbers, sets, and fields, and topographies (many different fields.
So the fact that math is ‘unreasonable’ is rather ridiculous. It’s people who are unreasonable. Math is TRIVIAL. Deduction in multiple dimensions is hard because we are not well suited to it.
I mean, we have 26 letters, and 44 phonemes in the english language. If we were ‘elegant’ we might increase the 26 to 44 letters, so that english was easier to read. but look at what we can say with those 44 phonemes, 26 characters, and 250K words in some including terms, and maybe 200K words that are not archaic.
There are roughly 100,000 word-families in the English language.
A native English speaking person knows between 10,000 (uneducated) to 20,000 (educated) word families.
A person needs to know 8,000-9,000 word families to enjoy reading a book.
A person with a vocabulary size of 2,500 passive word-families and 2,000 active word-families can speak a language fluently.
Of those we can pretty much COMMUNICATE anything, although in wordy prose, with only 300 words.
Now think of how much MORE you can say in language than you can say in mathematics.
Why should it surprise you that running around with a perfectly scalable yardstick that can measure any distance, allows you to measure and compare anything? It shouldn’t. It’s freaking obvious.
REMOVING MATHEMATICS FROM PHILOSOPHY AND THEOLOGY AND RETURNING IT TO THE SCIENCE OF MEASUREMENT.
In mathematics, construction must be operationally possible (computable), even if the descriptions (proofs) are only deducible.
Others only provide an IDEAL (logical) justification of why cantor is wrong, and not a REAL (scientific and operational) explanation of why he was wrong: that the technique (like gears) demonstrated something valuable: that the rate of production of positional names produces different sized sets regardless of the point of termination (scale or limit). Cantor is one step removed from theology(ideal by design), and speaking in philosophy (ideals), instead of speaking in mathematics (measurement) and science (operations).
The depth of this statement allows us to repair mathematics and return it to a science of measurement, rather than this nonsensical platonism used today – a remnant of the ancient greeks.
—“You’re saying all mathematical statements are true or false but the liar paradox is one example of an ordinary language sentence which hasn’t got a truth-value, right? Well, stated that way, I’d say you’re right about all of that, but are you also saying that the liar sentence expresses a proposition? That might be the part where it starts to get problematic.”—
Good question.
In short, we can ask a question, or we can assert an opinion, conflate the two, or we can speak nonsense. And only humans (so far) can ask, assert, conflate, and fail at all of them. But out of convenience, we subtract from the real to produce the ideal, and speak of the speech as if it can act on its own.
Just to illustrate that the test we are performing (context) limits both what we are saying and what we can say. From the most decidable to the least:
1 – The mathematical category of statements, (tautological) single category. (relative measure)
2 – The ideal category of statements, (logical) multiple categories. (relative meaning)
3 – The operational category of statements (existential possibility)
(sequential possibility )
4 – The correspondent (empirical) category of statements. all categories. ( full correspondence )
5 – The rational category of statements ( an actor making rational choices) (‘praxeological’)
6 – The ‘moral’ category of statements ( test of reciprocity)
7 – The fully accounted category of statements (tests of scope)
8 – The valued (loaded) category of statements. (full correspondence and loaded with subjective value)
9 – The deceptive category of statements (suggestion, obscurantism, fictionalism, and outright lying.
We can speak a statement in any one or more of these (cumulative) contexts.
So for example, statements are not true or false or unknowable, but the people who speak them speak truthfully, falsely, or undecidedly. So performatively (as you have mentioned) only people can make statements.
However, to make our lives easier, we eliminate unnecessary dimensions of existence unused in our scope of inquiry, and we conflate terms across those dimensions of existence, and we very often don’t even understand ourselves what we are saying. (ie; a number consists of a function for producing a positional name, from an ordered series of symbols in some set of dimensions. Or, only people can act and therefore only people can assert, and therefore no assertions are true or false, the person speaking speaks truth or falsehood. etc.)
This matters primarily because no dimensional subset in logic closed without appeal to the consequence dimensional subset. In other words, only reality provides full means of decidability.
Or translated differently, there just as there is little action value in game theory and little action value in more than single regression analysis, there is little value after first-order logic, since decidability is provided by appeal to additional information in additional dimensions rather than its own. Which is, as far as I know, the principal lesson of analytic philosophy and the study of logic, of the 20th century.
Or as I might restate it, we regress into deeper idealism through methodological specialization than is empirically demonstrable in the value returned. Then we export these ‘ideals’ as pseudosciences to the rest of the population. This leading to wonderful consequences like the Copenhagen consensus. Or the many-worlds hypothesis, or String Theory. Or Keynesian economics. Or the (exceedingly frustrating) nonsense the public seems to fascinate over as a substitute for numerology, astrology, magic, and the rigorous hard work required
THE STATE OF MATHEMATICAL ECONOMICS
Understanding advanced mathematics of economics and physics for ordinary people.
The Mengerian revolution, which we call the Marginalist revolution, occurred when the people of the period applied calculus ( the mathematics of “relative motion”) to what had been largely a combination of accounting and algebra.
20th century economics can be seen largely as an attempt to apply the mathematics of relative motion (constant change) from mathematics of constant categories that we use in perfectly constant axiomatic systems, and the relatively constant mathematics of physical systems, to the mathematics of inconstant categories that we find in economics – because things on the market have a multitude of subsequent yet interdependent uses that are determined by ever-changing preferences, demands, availability, and shocks.
Physics is a much harder problem than axiomatic mathematics. Economics is a much harder problem than mathematical physics, and before we head down this road (which I have been thinking about a long time) Sentience (the next dimension of complexity) is a much harder problem than economics.
And there have been questions in the 20th century whether mathematics, as we understand it, can solve the hard problem of economics. But this is, as usual, a problem of misunderstanding the very simple nature of mathematics as the study of constant relations. Most human use of mathematics consists of the study of trivial constant relations such as quantities of objects, physical measurements.
Or changes in state over time. Or relative motion in time. And this constitutes the four dimensions we can conceive of when discussing real-world physical phenomenon. So in our simplistic view of mathematics, we think in terms of small numbers of causal relations. But, it does not reflect the number of POSSIBLE causal relations. In other words, we change from the position of observing a change in state by things humans can observe and act upon, to a causal density higher than humans can observe and act upon, to a causal density such that every act of measurement distorts what humans can observe and act upon, by distorting the causality.
One of our discoveries in mathematical physics, is that as things move along a trajectory, they are affected by high causal density, and change through many different states during that time period. Such that causal density is so high that it is very hard to reduce change in state of many dimensions of constant relations to a trivial value: meaning a measurement or state that we can predict. Instead we fine a range of output constant relations, which we call probabilistic. So that instead of a say, a point as a measurement, we fined a line, or a triangle, or a multi dimensional geometry that the resulting state will fit within.
However, we can, with some work identify what we might call sums or aggregates (which are simple sets of relationships) but what higher mathematicians refer to as patterns, ‘symmetries’ or ‘geometries’. And these patterns refer to a set of constant relations in ‘space’ (on a coordinate system of sorts) that seem to emerge regardless of differences in the causes that produce them.
These patterns, symmetries, or geometries reflect a set of constant relationships that are the product of inconstant causal operations. And when you refer to a ‘number’, a pattern, a symmetry, or a geometry, or what is called a non-euclidian geometry, we are merely talking about the number of dimensions of constant relations we are talking about, and using ‘space’ as the analogy that the human mind is able to grasp.
Unfortunately, mathematics has not ‘reformed’ itself into operational language as have the physical sciences – and remains like the social sciences and philosophy a bastion of archaic language. But we can reduce this archaic language into meaningful operational terms as nothing more than sets of constant relations between measurements, consisting of a dimension per measurement, which we represent as a field (flat), euclidian geometry (possible geometry), or post Euclidian geometry (physically impossible but logically useful) geometry of constant relations.
And more importantly, once we can identify these patterns, symmetries, or geometries that arise from complex causal density consisting of seemingly unrelated causal operations, we have found a constant by which to measure that which is causally dense but consequentially constant.
So think of the current need for reform in economics to refer to and require a transition from the measurement of numeric (trivial) values, to the analysis of (non-trivial) consequent geometries.
These constant states (geometries) constitute the aggregate operations in economies. The unintended but constant consequences of causally dense actions.
Think of it like using fingers to make a shadow puppet. If you put a lot of people together between the light and the shadow, you can form the same pattern in the shadow despite very different combinations of fingers, hands, and arms. But because of the limits of the human anatomy, there are certain patterns more likely to emerge than others.
Now imagine we do that in three dimensions. Now (if you can) four, and so on. At some point we can’t imagine these things. Because we have moved beyond what is possible to that which is only analogous to the possible: a set of constant relations in multiple dimensions.
So economics then can evolve from the study of inputs and outputs without intermediary state which allows prediction, to the study of the consequence of inputs and the range of possible outputs that will likely produce predictability.
in other words, it is possible to define constant relations in economics.
And of course it is possible to define constant relations in sentience.
The same is true for the operations possible by mankind. There are many possible, but there are only so many that produce a condition of natural law: reciprocity.
Like I’ve said. Math isn’t complicated if you understand that it’s nothing more than saying “this stone represents one of our sheep”. And in doing so produce a constant relation. all we do is increase the quantity of constant relations we must measure. And from them deduce what we do not know, but is necessary because of those constant relations.
Math is simple. That’s why it works for just about everything: we can define a correspondence with anything.
As far as I know, all truth refers to testimony and we use the term ‘True’ ‘loosely’ for many purposes – largely ‘consent’. Technically speaking logic gates output charges (1) or not (0).
We equate this to True=On (constant relation) or false=Off (inconstant). We do this to conflate the logically true (constant relations) and logically false (inconstant relations).
We do this DESPITE the fact that all logic is ternary with negative priority (1-False, 2-True, 3-Undecidable), because all premises are contingent. Since all premises are contingent, we cannot claim positives (constructions) are true, only that they are not false.
As a consequence we falsify alternatives leaving truth candidates as possibilities. This is in fact how cognition, communication, testimony, and science function: free association(some relations), hypothesis (meaning), theory(self-tested), “Law”(Market Tested). The only question is how we falsify.
In mathematics, logic, and language not all ideas can be constructed, and must be deduced by creating constructions that permit us to deduce that which we cannot construct (a heptagon being the most rudimentary problem in geometry – it cannot be constructed by ruler and compass).
Nearly all non-trivial constructions cannot be constructed (proven or testified to) they can only be described by the process of elimination.
Mathematics is an extremely simple logic since it consists of only one dimension: position. Models are constructed of just that one relation – but in large numbers. Language consists of many kinds of measurements. And is far harder to test. What we intuit as constant relations may be in our brains, but not in reality.
This isn’t something that’s open to opinion. Words consists of constant relations. There is simply much higher density that simple reductio models in more primitive grammars (logics).
GAIN: OPERATIONS (REAL) VS SETS (IDEAL) – CANTOR AS AN EXAMPLE OF THE PROBLEM IN MATHEMATICS AND BY EXTENSION EVERYTHING.
—”Ok but Cantor’s work is specifically set-theoretic, not analytical. Also, an infinite sum is by definition a sum over a countable set. So cantor’s notions are in fact relevant for this.”—Alex Pareto
Yes it is a sacred cow because people who are (knowingly or unknowingly) mathematical platonists are just as indoctrinated into superstitious nonsense as people who are indoctrinated into platonism proper, and people indoctrinated into theology. They know how to DO what they do (meaning make arguments with the objects, relations, and values of their vocabulary and grammar) but they don’t know how and why what they do functions.
Frequencies are the scientific description and infinities (sizes) the fictional (imaginary) description. The difference is that those of us who work in the sciences, where we CANNOT engage in Platonism, because that is the purpose of science: to prevent such ‘magical’ speech, and instead force us to undrestand the causal relations between reality and our speech.
So in this case a number consists of nothing more than the name of a position. That’s it. Mathematics consists of the vocabulary and grammar of positional names. Nothing more. Period.
We generate positional names by the process of positional naming. We can scientifically describe that process as did Babbage, Turing, and Computer Science (consisting of nothing but addition), with gears, or the positional equivalent of gears (positional names), or the electronic-switch(memory) of positional names, and use these gears to produce positional names and operations on positional names at varying speeds. We can also tell a ‘story’ about those things (a fiction) which is what we do with literary, symbolic, and set mathematics. And then we can tell a fairy tale about sets, as if they are an equivalent to red riding hood.
But no matter what we do, operationally, (scientifically) all we can do is produce a series of positional names faster or slower than another series of positional names.
Ergo, there exists only one name “infinity” for “unknown limit of operations” and different rates (frequencies) by which we generate positional names, using any set of operations with which we produce positional names.
This is why mathematics ‘went off the rails’ into fictionalism despite Poincare’s and others efforts at the beginning of the 20th century. Math is just the use of positional names which have only one property: position, and therefore only ONE constant relation: position.
All logic consists of the study of constant relations, and as such mathematics provides the most commensurable language of constant relations, since it has only ONE constant relation: position.
“Mathematics, by the virtue of consisting of nothing other than positional names, preserves constant relations, since only constant relations are expressible in the grammar of mathematics: the grammar of positional names.”
“The discipline we call computer science is more generally the logic of operations, and is superior in informational density to mathematics in that it is causal and mathematics is merely descriptive.”
In mathematics, at least, for the most part, the means of conducting operations to solve a problem is nearly identical to the means of demonstrating the construction of a solution using existentially possible operations.
We sought to copy mathematics – starting with the Greeks. But we lacked the understanding of why math was so effective at the ascertaining truth of relations: because there is very little difference between the process of theorizing and the process of construction.
FOUNDATIONS OF LOGIC
The foundations of logic like those of mathematics are terribly simple as subsets of reality. But by doubling down in the 19th and 20th centuries all we have found is that we say rather nonsensical terms like ‘the axiom of choice’ or ‘limits’ rather than ‘undecidable without appeal to information provided by existential context’. After all, math is just the discipline of scale-independent measurement, and the deduction that is possible given the precision of constant relations using identical unitary measures. Logic is nothing more than than set operations. Algorithms are nothing more than sequential operations restoring time. Operations are nothing more than algorithms restoring physical transformation, time and cost. etc.
As a consequence, I find most of this kind of terminological discourse … silly hermeneutics. As Poincare stated ‘that isn’t math its philosophy’. Or as I would say, ‘with platonism we depart science and join theology. It may be secular theology in that it is ideal rather than supernatural, but it is theology none the less’.
it is one thing to say ‘by convention in math (or logic or whatever dimension we speak of) we use this colloquialism (half-truth) as a matter of convenience. It is not ‘true’. It is just the best approximation given the brevity we exercise in simplifying our work.
There exists only one possible ‘True’: the most parsimonious and correspondent testimony one can speak in the available language in the given context. Everything else is a convention.
Ergo, if you do not know the operational construction of the terms that you use, you do not know of what you speak. That does not mean you cannot speak truth any more than monkey cannot accidentally type one of the Sonnets.
This is why the operationalist movement in math we call Intuitionism failed.
Anyway. Well-formed (grammatically correct) statements in math may or may not be decidable but our intention is to produce decidable statements. In symbolic logic, well formed (grammatically correct) statements may or may not be decidable. in logic (language), well-formed (grammatically correct) statements are difficult to construct because of the categorical difference between constant relations (ideals in math), constant categories (ideals in formal logic), and inconstant categories (ordinary language). Furthermore, the process of DEDUCTION using premises (or logical summation) limits us to the utility of true statements. Ergo for that purpose statements can only evaluate to true or not-true (including false and undecidable). While for the purpose of INDUCTION (transfer of meaning by seeding free association, or the construction of possibility by the same means) seeks only possibility or impossibility not truth or falsehood.
How can you claim to make a truth proposition and demand precise language when your premises are mere demonstrably falsehoods used by convention?
NUMBERS
“Nouns are names. Numbers are nouns. Numbers evolved as positional names. Numbers are positional names of constant relations. As positional names, they are extensions of ordinary language. Math: the science of measurement by the use of constant relations.”
We use many positional names: none, one, and some, short medium and tall; small, medium, and large; front, middle, and back; right center and left; port and starboard; daughter, mother, and grandmother;
Numbers differ from ordinary nouns only in that we produce them by positional naming. Whereas early positional names varied from one two and many, to base ten, or base twelve, or in the twenties, or sixties, each which increases the demand on the human mind; the decimal system of positional naming
Positional names are produced by a series of consistent operations. We call those series of consistent operations ‘functions’. By analogy we (unfortunately) called all such functions numbers: a convenient fiction.
Because of positional naming all positional names (numbers) are context independent, scale independent, constant relations, descriptively parsimonious and closed to interpretation.
So unlike other nouns (names), they are almost impossible to misinterpret by processes of conflation (adding information), and are impossible to further deflate (removing information).
Any other information we desire to add to the noun,( by which we mean name, positional name, number) must be provided by analogy to a context: application.
Numbers exist as positional names of constant relations. Those constant relations are scale-independent, context-dependent, informationally parsimonious, and nearly impossible to conflate with information that will allow for misinterpretation or deception.
As such, numbers allow us to perform DEDUCTIONS that other names, that lack constant relations, scale independence, context dependence, parsimony, immutability, and incorruptibility do not. Because deduction is possible wherever constant relations, parsimony, immutability, and incorruptibility are present.
As such, numbers serve as a method of verbal reasoning within and beyond the limits of human imagination (cognition), short term memory, and ordinary reason.
Numbers then are simply a very clean set of nouns(positional names), verbs (operations and functions), including tests of positional relations (comparison operators) that allow us to describe, reason and discourse about that which is otherwise beyond our ordinary language, and mental capacity.
As such we distinguish language, reason, and logic from numbers and measurement, and deduction both artificially and practically. Since while they consist of the same processes, the language of numbers, measurements, and deductions is simply more precise than the language of ordinary language, reason, and logic, if for no other reason than it is nearly closed to ignorance, error, bias, wishful thinking, suggestion, obscurantism, deceit, and the fictionalism of superstition, pseudo-rationalism, pseudoscience.
Unfortunately, since to humans, that which allows them to perform such ‘seeming miracles’ that are otherwise beyond comprehension, must be justified, we invented various fictionalisms – primarily idealisms, or what philosophers refer to as platonisms – (mythologies) to explain our actions. To attribute comprehension to that which we did not comprehend. To provide authority by general rule to that which we could only demonstrate through repeated application. So mathematics maintains much of it’s ‘magical language’ and philosophers persist this magical language under the pseudo-rational label of ‘idealism’ or ‘abstraction’. Which roughly translates to “I don’t understand”.
Perhaps more unfortunately, in the 19th century, with the addition of statistics and the application of mathematics to the inconstant relations of heuristic systems: particularly probability, fiat money, economics, finance, banking and commercial and tax accounting, this language no longer retains informational parsimony, and deducibility, and has instead evolved into a pseudoscience under which ignorance, error, bias, wishful thinking, suggestion, obscurantism, and deceit are pervasive.
Math is a very simple thing. It’s just ordinary language with positional names that allow us to give names and describe transformations to, that which is otherwise beyond our ability to imagine and recall, and therefore describe or reason with.
Like everything else, if you make up stories of gods, demons, ghosts and monsters, or ‘abstractions’ or ‘ideals’ you can obscure the very simple causality that we seek to discover through science: the systematic attempt to remove error, bias, wishful thinking, suggestion, obscurantism, fictionalism, and deceit from our language of testimony about the world we perceive, cognate, remember, hypothesize within, act, advocate, negotiate, and cooperate within.
Numbers are positional names of context-independent, scale-independent, informationally parsimonious, constant relations and mathematics consists of the grammar of that language.
In other words, Math is an extension of ordinary language, ordinary reason, and ordinary science: the attempt by which we attempt to obtain information about our world within, above, and below human scale, by the use of rational and physical instrumentation, to eliminate ignorance, error, bias, and deceit from our descriptions, and as a consequence our language, and as a consequence our collective knowledge.
MATH IS SIMPLE
The foundations of mathematics are simple.
The fact that they even phrase the question as such is hysterical. The reason mathematics is so powerful a tool is precisely because its foundations are so trivial. Like discourse on property in ethics and law, it is a word game because no one establishes sufficient limits under which the general term obscures a change in state.
Math is very simple. Correspondence (what remains and what does not), Types, operations, grammar, syntax. Generally we use mathematics for the purpose of scale independence. in other words, we remove the property of scale from the set of correspondences. But we might also pass from physical dimensions to logical dimensions (there are only so many possible physical dimensions). So now we leave dimensional correspondence. In mathematics we remove time correspondence by default, and only add it in when we specifically want to make use of it. In sets we remove temporal and causal correspondence … at least in most cases. So we can add and remove many different correspondences, and work only with reciprocal (self referencing) correspondence (constant relations). But there is nothing magic here at all except for the fields (results) that can be produced by these different definitions as we use them to describe the consequences of using different values in different orders.
But if you say “I want to study the parsimony, limits, and full accounting, of this set of types using this set of operations, with the common grammar and syntax” that is pretty much what someone means when they say ‘foundations’. Most of the time. Sometimes they have no clue.
There is nothing much more difficult here in the ‘foundations’ so to speak. What’s hard in mathematics is holding operations, grammar and syntax constant, what happens as we use different correspondences (dimensions), types, and values in combination with others and yet others, to produce these various kinds of patterns that represent phenomenon that we want to describe. And what mathematicians find beautiful is that there is a bizarre set of regularities (that they call symmetries or some variation thereof), that emerge once you becomes skilled in these models, just like some games become predictable if you see a certain pattern.
But really, math is interesting because by describing regular patterns that produce complex phenomenon, we are able to describe things very accurately that we cannot ‘see’ without math to help us find it.
Its seems mystical. It isn’t. Its just the adult version of mommy saying ‘boo’ to the toddler and the joy he gets from the stimulation. There is nothing magical here. it’s creative, and interesting, but it’s just engineering with cheaper tools at lower risk: paper, pencil, and time.
Simplicity is necessary in mathematics since mathematical symbols and operations itself (state and operators) are necessary to allow us to remember state with sufficient precision that we can conduct comparisons between states.
However, if we restated the foundations of mathematics operationally (constructively – analogous to gears), and we stated the foundations of mathematical deduction negatively, as geometry, we would be able to show that it is convergence between the via-positiva construction, and the via-negative deduction that leads us to truth.
Unfortunately, man discovered (logically so) geometry prior to gears, and as such, we retain the ‘superstitious’ language of geometry (and algebra) of the superstitious era in which both were invented.
Reality has only so many dimensions. By adding and removing dimensions from consideration we simplify the problem of describing the constant relations within it.
Mathematics specializes in the removal of (a) scale, and (b) time, and (c) operations (and arguable (d) morality) from consideration, leaving only identity, quantity, and ratio, to which we add positional naming (numbers). We then construct general rules of arbitrary precision (scale independence) and apply those to reality wherein we must ‘hydrate’ (reconstitute) scale, time, and operations(actions).
So just as philosophy is ‘stuck’ in non contradiction instead of increasing dimensions in order to test theories, mathematics is ‘stuck’ in non-contradiction instead of re-hydrating (restoring dimensions) to justify propositions.
In other words, fancy words like ‘limits’ or ‘non-contradictory’ or ‘axiom of choice’ and various other terms in the field are just nonsense words that prevent the conversion of mathematics from a fictionalism into a science.
UNREASONABLE EFFECTIVENESS? NONSENSE.
The “Unreasonable effectiveness” trope annoys the hell out of me. The only reason this ‘magical mathematics’ nonsense perpetuates, and the average person is still afraid of mathematics, is because it’s taught as a superstition.
Math is trivial. 1 = any unitary measure. By the combination of some number of symbols – in the current case 0123456789, we can create positional names. By adding, subtracting units, and by adding and subtracting sets of units (multiplication and division), we can create positional names (numbers) for an unlimited set of positions. we can create names of positions in an unlimited number of directions (dimensions). We can create positions relative to any other position (relative positions). We can create changes in positions of relative positions. producing numbers, sets, and fields, and topographies (many different fields.
So the fact that math is ‘unreasonable’ is rather ridiculous. It’s people who are unreasonable. Math is TRIVIAL. Deduction in multiple dimensions is hard because we are not well suited to it.
I mean, we have 26 letters, and 44 phonemes in the english language. If we were ‘elegant’ we might increase the 26 to 44 letters, so that english was easier to read. but look at what we can say with those 44 phonemes, 26 characters, and 250K words in some including terms, and maybe 200K words that are not archaic.
There are roughly 100,000 word-families in the English language.
A native English speaking person knows between 10,000 (uneducated) to 20,000 (educated) word families.
A person needs to know 8,000-9,000 word families to enjoy reading a book.
A person with a vocabulary size of 2,500 passive word-families and 2,000 active word-families can speak a language fluently.
Of those we can pretty much COMMUNICATE anything, although in wordy prose, with only 300 words.
Now think of how much MORE you can say in language than you can say in mathematics.
Why should it surprise you that running around with a perfectly scalable yardstick that can measure any distance, allows you to measure and compare anything? It shouldn’t. It’s freaking obvious.
REMOVING MATHEMATICS FROM PHILOSOPHY AND THEOLOGY AND RETURNING IT TO THE SCIENCE OF MEASUREMENT.
In mathematics, construction must be operationally possible (computable), even if the descriptions (proofs) are only deducible.
Others only provide an IDEAL (logical) justification of why cantor is wrong, and not a REAL (scientific and operational) explanation of why he was wrong: that the technique (like gears) demonstrated something valuable: that the rate of production of positional names produces different sized sets regardless of the point of termination (scale or limit). Cantor is one step removed from theology(ideal by design), and speaking in philosophy (ideals), instead of speaking in mathematics (measurement) and science (operations).
The depth of this statement allows us to repair mathematics and return it to a science of measurement, rather than this nonsensical platonism used today – a remnant of the ancient greeks.
—“You’re saying all mathematical statements are true or false but the liar paradox is one example of an ordinary language sentence which hasn’t got a truth-value, right? Well, stated that way, I’d say you’re right about all of that, but are you also saying that the liar sentence expresses a proposition? That might be the part where it starts to get problematic.”—
Good question.
In short, we can ask a question, or we can assert an opinion, conflate the two, or we can speak nonsense. And only humans (so far) can ask, assert, conflate, and fail at all of them. But out of convenience, we subtract from the real to produce the ideal, and speak of the speech as if it can act on its own.
Just to illustrate that the test we are performing (context) limits both what we are saying and what we can say. From the most decidable to the least:
1 – The mathematical category of statements, (tautological) single category. (relative measure)
2 – The ideal category of statements, (logical) multiple categories. (relative meaning)
3 – The operational category of statements (existential possibility)
(sequential possibility )
4 – The correspondent (empirical) category of statements. all categories. ( full correspondence )
5 – The rational category of statements ( an actor making rational choices) (‘praxeological’)
6 – The ‘moral’ category of statements ( test of reciprocity)
7 – The fully accounted category of statements (tests of scope)
8 – The valued (loaded) category of statements. (full correspondence and loaded with subjective value)
9 – The deceptive category of statements (suggestion, obscurantism, fictionalism, and outright lying.
We can speak a statement in any one or more of these (cumulative) contexts.
So for example, statements are not true or false or unknowable, but the people who speak them speak truthfully, falsely, or undecidedly. So performatively (as you have mentioned) only people can make statements.
However, to make our lives easier, we eliminate unnecessary dimensions of existence unused in our scope of inquiry, and we conflate terms across those dimensions of existence, and we very often don’t even understand ourselves what we are saying. (ie; a number consists of a function for producing a positional name, from an ordered series of symbols in some set of dimensions. Or, only people can act and therefore only people can assert, and therefore no assertions are true or false, the person speaking speaks truth or falsehood. etc.)
This matters primarily because no dimensional subset in logic closed without appeal to the consequence dimensional subset. In other words, only reality provides full means of decidability.
Or translated differently, there just as there is little action value in game theory and little action value in more than single regression analysis, there is little value after first-order logic, since decidability is provided by appeal to additional information in additional dimensions rather than its own. Which is, as far as I know, the principal lesson of analytic philosophy and the study of logic, of the 20th century.
Or as I might restate it, we regress into deeper idealism through methodological specialization than is empirically demonstrable in the value returned. Then we export these ‘ideals’ as pseudosciences to the rest of the population. This leading to wonderful consequences like the Copenhagen consensus. Or the many-worlds hypothesis, or String Theory. Or Keynesian economics. Or the (exceedingly frustrating) nonsense the public seems to fascinate over as a substitute for numerology, astrology, magic, and the rigorous hard work required
THE STATE OF MATHEMATICAL ECONOMICS
Understanding advanced mathematics of economics and physics for ordinary people.
The Mengerian revolution, which we call the Marginalist revolution, occurred when the people of the period applied calculus ( the mathematics of “relative motion”) to what had been largely a combination of accounting and algebra.
20th century economics can be seen largely as an attempt to apply the mathematics of relative motion (constant change) from mathematics of constant categories that we use in perfectly constant axiomatic systems, and the relatively constant mathematics of physical systems, to the mathematics of inconstant categories that we find in economics – because things on the market have a multitude of subsequent yet interdependent uses that are determined by ever-changing preferences, demands, availability, and shocks.
Physics is a much harder problem than axiomatic mathematics. Economics is a much harder problem than mathematical physics, and before we head down this road (which I have been thinking about a long time) Sentience (the next dimension of complexity) is a much harder problem than economics.
And there have been questions in the 20th century whether mathematics, as we understand it, can solve the hard problem of economics. But this is, as usual, a problem of misunderstanding the very simple nature of mathematics as the study of constant relations. Most human use of mathematics consists of the study of trivial constant relations such as quantities of objects, physical measurements.
Or changes in state over time. Or relative motion in time. And this constitutes the four dimensions we can conceive of when discussing real-world physical phenomenon. So in our simplistic view of mathematics, we think in terms of small numbers of causal relations. But, it does not reflect the number of POSSIBLE causal relations. In other words, we change from the position of observing a change in state by things humans can observe and act upon, to a causal density higher than humans can observe and act upon, to a causal density such that every act of measurement distorts what humans can observe and act upon, by distorting the causality.
One of our discoveries in mathematical physics, is that as things move along a trajectory, they are affected by high causal density, and change through many different states during that time period. Such that causal density is so high that it is very hard to reduce change in state of many dimensions of constant relations to a trivial value: meaning a measurement or state that we can predict. Instead we fine a range of output constant relations, which we call probabilistic. So that instead of a say, a point as a measurement, we fined a line, or a triangle, or a multi dimensional geometry that the resulting state will fit within.
However, we can, with some work identify what we might call sums or aggregates (which are simple sets of relationships) but what higher mathematicians refer to as patterns, ‘symmetries’ or ‘geometries’. And these patterns refer to a set of constant relations in ‘space’ (on a coordinate system of sorts) that seem to emerge regardless of differences in the causes that produce them.
These patterns, symmetries, or geometries reflect a set of constant relationships that are the product of inconstant causal operations. And when you refer to a ‘number’, a pattern, a symmetry, or a geometry, or what is called a non-euclidian geometry, we are merely talking about the number of dimensions of constant relations we are talking about, and using ‘space’ as the analogy that the human mind is able to grasp.
Unfortunately, mathematics has not ‘reformed’ itself into operational language as have the physical sciences – and remains like the social sciences and philosophy a bastion of archaic language. But we can reduce this archaic language into meaningful operational terms as nothing more than sets of constant relations between measurements, consisting of a dimension per measurement, which we represent as a field (flat), euclidian geometry (possible geometry), or post Euclidian geometry (physically impossible but logically useful) geometry of constant relations.
And more importantly, once we can identify these patterns, symmetries, or geometries that arise from complex causal density consisting of seemingly unrelated causal operations, we have found a constant by which to measure that which is causally dense but consequentially constant.
So think of the current need for reform in economics to refer to and require a transition from the measurement of numeric (trivial) values, to the analysis of (non-trivial) consequent geometries.
These constant states (geometries) constitute the aggregate operations in economies. The unintended but constant consequences of causally dense actions.
Think of it like using fingers to make a shadow puppet. If you put a lot of people together between the light and the shadow, you can form the same pattern in the shadow despite very different combinations of fingers, hands, and arms. But because of the limits of the human anatomy, there are certain patterns more likely to emerge than others.
Now imagine we do that in three dimensions. Now (if you can) four, and so on. At some point we can’t imagine these things. Because we have moved beyond what is possible to that which is only analogous to the possible: a set of constant relations in multiple dimensions.
So economics then can evolve from the study of inputs and outputs without intermediary state which allows prediction, to the study of the consequence of inputs and the range of possible outputs that will likely produce predictability.
in other words, it is possible to define constant relations in economics.
And of course it is possible to define constant relations in sentience.
The same is true for the operations possible by mankind. There are many possible, but there are only so many that produce a condition of natural law: reciprocity.
Like I’ve said. Math isn’t complicated if you understand that it’s nothing more than saying “this stone represents one of our sheep”. And in doing so produce a constant relation. all we do is increase the quantity of constant relations we must measure. And from them deduce what we do not know, but is necessary because of those constant relations.
Math is simple. That’s why it works for just about everything: we can define a correspondence with anything.
As far as I know, all truth refers to testimony and we use the term ‘True’ ‘loosely’ for many purposes – largely ‘consent’. Technically speaking logic gates output charges (1) or not (0).
We equate this to True=On (constant relation) or false=Off (inconstant). We do this to conflate the logically true (constant relations) and logically false (inconstant relations).
We do this DESPITE the fact that all logic is ternary with negative priority (1-False, 2-True, 3-Undecidable), because all premises are contingent. Since all premises are contingent, we cannot claim positives (constructions) are true, only that they are not false.
As a consequence we falsify alternatives leaving truth candidates as possibilities. This is in fact how cognition, communication, testimony, and science function: free association(some relations), hypothesis (meaning), theory(self-tested), “Law”(Market Tested). The only question is how we falsify.
In mathematics, logic, and language not all ideas can be constructed, and must be deduced by creating constructions that permit us to deduce that which we cannot construct (a heptagon being the most rudimentary problem in geometry – it cannot be constructed by ruler and compass).
Nearly all non-trivial constructions cannot be constructed (proven or testified to) they can only be described by the process of elimination.
Mathematics is an extremely simple logic since it consists of only one dimension: position. Models are constructed of just that one relation – but in large numbers. Language consists of many kinds of measurements. And is far harder to test. What we intuit as constant relations may be in our brains, but not in reality.
This isn’t something that’s open to opinion. Words consists of constant relations. There is simply much higher density that simple reductio models in more primitive grammars (logics).
GAIN: OPERATIONS (REAL) VS SETS (IDEAL) – CANTOR AS AN EXAMPLE OF THE PROBLEM IN MATHEMATICS AND BY EXTENSION EVERYTHING.
—”Ok but Cantor’s work is specifically set-theoretic, not analytical. Also, an infinite sum is by definition a sum over a countable set. So cantor’s notions are in fact relevant for this.”—Alex Pareto
Yes it is a sacred cow because people who are (knowingly or unknowingly) mathematical platonists are just as indoctrinated into superstitious nonsense as people who are indoctrinated into platonism proper, and people indoctrinated into theology. They know how to DO what they do (meaning make arguments with the objects, relations, and values of their vocabulary and grammar) but they don’t know how and why what they do functions.
Frequencies are the scientific description and infinities (sizes) the fictional (imaginary) description. The difference is that those of us who work in the sciences, where we CANNOT engage in Platonism, because that is the purpose of science: to prevent such ‘magical’ speech, and instead force us to undrestand the causal relations between reality and our speech.
So in this case a number consists of nothing more than the name of a position. That’s it. Mathematics consists of the vocabulary and grammar of positional names. Nothing more. Period.
We generate positional names by the process of positional naming. We can scientifically describe that process as did Babbage, Turing, and Computer Science (consisting of nothing but addition), with gears, or the positional equivalent of gears (positional names), or the electronic-switch(memory) of positional names, and use these gears to produce positional names and operations on positional names at varying speeds. We can also tell a ‘story’ about those things (a fiction) which is what we do with literary, symbolic, and set mathematics. And then we can tell a fairy tale about sets, as if they are an equivalent to red riding hood.
But no matter what we do, operationally, (scientifically) all we can do is produce a series of positional names faster or slower than another series of positional names.
Ergo, there exists only one name “infinity” for “unknown limit of operations” and different rates (frequencies) by which we generate positional names, using any set of operations with which we produce positional names.
This is why mathematics ‘went off the rails’ into fictionalism despite Poincare’s and others efforts at the beginning of the 20th century. Math is just the use of positional names which have only one property: position, and therefore only ONE constant relation: position.
All logic consists of the study of constant relations, and as such mathematics provides the most commensurable language of constant relations, since it has only ONE constant relation: position.
Science: A Warranty of Due Diligence
SCIENCE: The use of logical and physical instrumentation for the purpose of eliminating ignorance, error, bias, wishful thinking, suggestion and obscurantism, Fictionalism and deceit from our free-associations by the systematic deflation and attempted falsification (survival) from criticism in eight dimensions of actionable reality: categorical, logical, empirical, operational, rational, reciprocal, fully accounted including scope and limits – and coherent across those dimensions.
Science is a moral discipline wherein we criticize our ideas, so that we can speak them truthfully:
— We test our categories using differences to eliminate conflation.
— We test our reasoning with logic for internal consistency.
— We test our observations with external correspondence.
— We test the existence of our premises with operations.
— We test the rationality and volition of choice through sympathy
— We test the reciprocity and volition of choice through changes in capital
— We test the scope of our theory with falsifications.
Once we have tested our theories by these means, then we can say that we speak truthfully – and as such do no harm.
The central argument regarding truth:
1) That in order to cooperate, humans evolved sympathy for intent – and are marginally indifferent in their judgment of intentions. This allows us to sympathetically test most human incentives if subject to the same stimuli (information). It is also why juries can functions, since this sympathetic testing of intentions is the criteria by which juries render decisions.
2) That however, we cannot sympathize with the first principles of the physical universe – the equivalent of intentions. So while we intuit and can test man’s intentions, we cannot measure and test the universe’s first principles. As such, the best we can do is testify to observations and measurements of those phenomenon until at some point we know those first principles – if that is ever possible.
3) But our observations must also be reduced to stimuli that can be sympathetically tested by others, and insulated from our deception, bias and error.
4) We call this process ‘science’, but the practice of science is little more than a set of moral rules that instruct us as to how to eliminate deception, bias and error. The scientific method then, is merely a moral discipline: the means by which we struggle to speak the truth, as truthfully as we may possibly accomplish given the frailty of our reason.
5) That giving witness to one’s observations, is testable by reproduction of a set of operational definitions. That operational definitions produce the equivalent of names, just as positional numbering provides quantities with names. Such names are insulated from deception, distraction, loading, framing and overloading. Theories are not. While we cannot demonstrate the absolute parsimony of a theory (that we know of), we can demonstrate that we truthfully conveyed our observations. In other words, we can testify truthfully to an ordered set of facts, even if we cannot testify truthfully to parsimony of a theory.
6) That it is possible to state instead that all outputs of scientific investigation are truthful, if they are truthfully represented – where ‘scientific investigation” refers to the use of the scientific method, regardless of field of inquiry. But that we seek the most parsimonious statement of a theory, and we can never know that we have obtained it, we can only develop consensus that we cannot cause it to fail. This is, as far as I know, the best non-platonic description of truth available. Everything else is a linguistic contrivance for one purpose or another – possibly to obscure ignorance, and possibly to load ideas with moral motivation. Scientists load their contrivance of truth, and mathematicians load their contrivance of numbers, limits, and a dozen other things – most of which obscure linguistic ‘cheats’ to give authority to that which is necessary for the construction of general rules. (ie: the problem of arbitrary precision).
7) That Popper did no investigation into science or the history of science prior to making his argument, and that as yet, we do not have a systematic account of the history of science. However, what history we do have, both distant and recent, is that science operates by criticism upon failure, where failure is demonstrated by via overextension of the theory.
8) The reason for overextension rather than criticism as the operational preference being that it is economically inefficient (expensive) to pursue criticism rather than to extend a theory to its point of failure then criticize it. And as far as we know, this is how science functions in practice, and must work, because it is how all human endeavors must work. Because while a small number of scientists may seek the ‘truth’ (or whatever a Platonist means by it), what scientists try to do is solve problems – i.e. to manufacture recipes for useful cognition.
9) Popper’s advice was merely moral given that the scope of inquiry in all human fields had surpassed that of human scale, where tests are subjectively verifiable. (I think this is an important insight because it occurred in all fields.) Einstein for example, operationalized observations (relative simultaneity for example) over very great distances approaching the speed of light using Lorenz transformations. And as Bridgman demonstrated, the reason Einstein’s work was novel was because prior generations had NOT been operationalizing statements ,and as such, more than a generation and perhaps two were lost to failure of what should have been an obvious solution. (See the problem of length, which I tend to refer to often as the best example.) I addressed this in a previous post, and what popper did was give us good advice, and while he made an argument that appears logical, like most rational arguments, unsupported by data, it is not clear he was correct, and in fact, it appears that he was not. The question is not a rational but empirical one. (Note: I seek to codify this moral insight into law. Thus ending all deception by not only Fictionalism, but all other means.)
10) Popper unlike Misesian Pseudoscience, or Rothbardian Immoral Verbalisms, was engaged in a moral attempt both in politics and in science, and perhaps in science as a vehicle for politics, to prevent the pseudoscientific use of science – particularly by fascist and communists, to use the findings of science as a replacement for divine authority by which to command man. What popper did, particularly with his Platonism, was to remove the ability for the findings of science to be used as justification for the removal of human choice. Popper, Mises, and Hayek were responsible for undermining pseudoscientific authoritarianism. Of the three Popper is perhaps less articulate (possibly to obscure his objective), but certainly not wrong, so to speak. While Mises’ appeal to authoritarianism (which is part and parcel of his Jewish culture) was entirely pseudoscientific, by claiming that economics was deductive rather than empirical, and justifying it under a priorism, instead of as I’ve stated, understanding that he was merely trying to apply operationalism to economic activity, which would merely demonstrate that Keynesian economics was immoral and deterministic, not unscientific.
11) But Popper, Mises, Hayek, Bridgman and Brouwer, did not find a solution to restoring the western aristocratic conditions for public speech. They too were a lost in Platonism a bit. Bridgman and Brouwer did understand that something was wrong, and were very close, but they could not make the moral argument. We have had a century now of attacks by verbal contrivance and we can demonstrate the destruction of our civilization by way of it. So the moral argument is no longer one of undemonstrated results. WE have the results. And we have a generation of men, myself included, trying to repair it.
One must speak truthfully, because no other truth is knowable. Intellectual products that are brought to market must be warrantied just as are all other products that are brought to market, and the warranty that you can provide is operational definitions (recipes, experience), not theories (psychologism, projections). And if you are not willing to stand behind your product then you should not bring it to market. Because you have no right to subject others to harm.
Intellectuals produce ideas (myself included), that is our product. We are paid in measly terms most of the time, for our product, but that is what we do. But it is no different from serving too-hot coffee or selling dangerous ladders, or manufacturing defective gas tanks – intellectuals do plenty of harm in history. Perhaps the most harm of all. Between Abraham, Paul of Tarsus and the Byzantine Emperors, Mohammed and his real author,; Marx, Boaz, and Freud, it is hard to envision any worse catastrophe perpetrated by man.
THEREFORE:
Why is it that the informational commons, and by consequence the political and normative commons, are not – in an age of information – as subject to warranty and liability as pollution or harm to physical commons, life, body, and private property?
Truthfulness – testimony that has been subject to due diligence – is a non trivial cost. And economists are too happy (as it appears all social scientists have been) to produce defective products for personal gains, without the warranty that all other products have been subject to.
Why is it that free speech is not limited to free truthful speech? After all, the cost of producing truthful scientific testimony under due diligence and warranty is much higher than the cost of producing untruthful pseudoscientific testimony without due diligence or warranty. Doesn’t mere free speech without warranty of due diligence of truthfulness construct an impossibility under which the production of high cost truth and the production of low cost fantasy, bias, error and deceit must eventually win?
There is a great difference between the terms “empirical” (observable and measurable) and “scientific” of which empirical criticism is but a minor subset of the criterion necessary for the production of warranty of due diligence against fantasy, bias, error, and deceit.
We have had a century of economists running with intellectual scissors, causing inter-temporal externalities of profound consequence. And the Cosmopolitan (freshwater) rationalist’s justification of priors is only more visible than the mainstream Anglo empirical (Saltwater), justification of priors under the pseudoscience of Rawlsian Justificationism – itself a fascinating example of the logically impossible, yet pervasively persuasive.
So just as all enlightenment adaptations were plagued with errors – Anglo, French, German and Jewish – both freshwater and saltwater economics are plagued with pseudoscience. The freshwater try to justify objective morality, by argumentative construction (pseudoscience), and the saltwater try to justify immorality by intentionally failing to account for profound normative, institutional, civilizational, and genetic consequences (pseudoscience).
So it’s one thing for all of us to point the finger of the accusation of pseudoscience one place or another. But it is quite another to realize that the minute you draw the lens of truth upon either freshwater or saltwater economics, you will discover that both are pseudosciences that merely confirm ideological priors.
INNOVATION IN SCIENCE, EPISTEMOLOGY, AND TRUTH
In the last century intellectuals tried and failed to complete the scientific method and thereby create a test of non-falseness like we do in law. They couldn’t do it.
What I’ve done, because I’ve been lucky enough to spend most of my life working with “computable” systems – meaning that which is existentially possible to construct through a series of operations is supply the habits of strict operational construction with requirements for existential possibility, to the scientific method, and complete what those thinkers failed to discover.
KARL POPPER
Popper applied Jewish critique, (criticism), to science, as “falsificationism”. Meaning, the way to avoid pseudoscience is to require that a statement be falsifiable.
He did this because pseudoscience was rapidly expanding under the popularity of authoritarian socialism, as much as because he was simply interested in philosophy. He was trying to preserve intellectual cosmopolitanism (Jewish diasporism), and this culminated in his work “The Open Society” which is what Soros uses as his ‘plan’.
Now, in his efforts to correct science, he developed a set of ideas that I will try to reduce to these:
1) Falsification (critique, criticism) vs. Justificationism (excuses)
2) Critical Rationalism: we can know what is false but not what is true.
3) Critical Preference: we cannot know which theory is more likely true. there is no method of decidability.
4) Verisimilitude through Problem->Theory->Test
5) That science, by verisimilitude (markets), is conducted as a MORAL (social, normative) process, and that scientific discovery was accomplished by moral means.
BUT THIS IS THE PROBLEMUnempirical: his statements are logical not empirical, and he never did any research, nor has any been formally done.
Costs: he, like most philosophers, continues the Aristotelian tradition of ignoring costs. Costs provide us with information about which theories we can afford to pursue. Historically then, we can empirically demonstrate that man uses costs as methods of decidability.
Decidability: Costs provide decidability, for the simple reason that just as we pursue the least cost methods of research, nature evolves using the least cost method of evolution. It’s only humans that can choose to do the expensive thing and take a risk. Nature can’t do that. Nature is tightly deterministic. Man is only loosely deterministic. Because all of us guess a future and see if we can achieve it.
Falsification: Falsification is not very precise, and he did not see the dimensions. So he did not restate the scientific method as a series of dimensional tests equal to the dimensional tests of mathematics. So categories(identity), math(relations), logic (words/membership), operations (costs/existence), morality (choice/cooperation), and scope (full accounting) were each methods of falsification, that a scientific statement would have to pass. (Rather than the competition between consistency, correspondence, completeness, and coherence.)
Verisimilitude: (Rather than Markets.) Because costs do determine the progress of our investigations, our knowledge evolves just as organisms evolve, planets evolve, solar systems, galaxies, and the universe. What differs is the cost of inquiry in each culture. White people happen to have the lowest cost of inquiry because they have a high trust civilization where the norm of truth is highly defended as (nearly sacred) public property.
Physical absence vs Social presence of first causes. Unable to distinguish between the problem of instrumentation in the physical sciences in the absence of knowledge of first causes (‘nature’s choice’), versus the problem of subjective instrumentation in the social sciences, in the presence of first causes (sympathetic choice)
The Epistemological Cycle …
Problem -> Theory -> Test
… is incomplete.
The complete epistemological cycle is:
Perception(Chaotic) ->
…Opportunity (Free Association) ->
……Hypothesis (way-finding) ->
………Criticism(individual investment) ->
…………Theory (outputs a recipe/opportunity narrative) ->
……………Social Criticism (market investment) ->
………………Law (exhaustion – return on investment) ->
…………………Survival (Perfect Parsimony – incorporation into norms) ->
……………………Tautology ( invisible – assumed world structure )
This long chain that represents the evolutionary survival of ideas, can be broken into these sections:
1 – Perception -> free association(searching) -> identity (opportunity)
2 – Question (Problem)
3 – Iterative Criticism ( Survival!!! )
………..way-finding (criticism) / Hypothesis.
Way-finding is a form of criticizing an idea.
………..criticism / theory / personal use
………..testing / law / general use
………..recognition / survival / universal use
………..identity / tautology / integration into world view.
The Continuous Recursive Disambiguation (falsification) of our free associations.
IMMANUEL KANT
3) A Priori: Or, “independent of observation.”
There are three dimensions to claims of an a priori truth claim:
i) A priori vs. A posteriori,
ii) Analytic vs. Synthetic, and
iii) Necessity vs. Contingency
Therefore we can produce at least the following spectrum of a priori claims.
(a) Analytic A Priori: tautological: “2+2=4 and all deductions thereof.”
(b) Synthetic A Priori : “Increasing money increases inflation.”
(c) Necessary Synthetic A Priori: “Childless women will have no grandchildren.”
(d) Contingent Synthetic A Priori: “all other things being equal, as a general trend, increasing demand will increase supply, although we cannot know the composition of that supply in advance, we can identify it from recorded evidence.”
This produces a an ordered spectrum of declining precision:
(a) Identity(categorical consistency) – Analytic A Priori
(b) Logical:(internal consistency) – Nec. Synthetic a priori
(c) Empirical: (external consistency) – Gen. Synth. a priori
(d) Existential: (operational consistency) – Cont. Synth. a priori
Which corresponds to the testable dimensions of numbers (ideals)
(a) identity (numbers)
(b) logical (sets)
(c) empirical (ratios)
(d) existential (constructible)
Which corresponds to dimensions of physical reality
(a) point
(b) line
(c) shape
(d) object
(e) time (change)
(f) relative change
Which corresponds to a subset of the dimensions of actionable reality , the full set of which we express in fully express in Testimonialism as:
(a) Identity(categorical consistency)(point)
(b) Logical:(internal consistency)(line)
(c) Empirical: (external consistency)(shape)
(d) Existential: (operational consistency)
(e) Volitional: (rational choice of rational actor)(change)(time)
(f) Reciprocal: ( rational exchange between actors) (relative change)
Which together account for the totality of actionable reality (by man) that we currently know of (and its quite hard to imagine anything else is possible).
The test of speech then consists of dimensional deflation and spoken conflation into parsimonious testimony:
1 – Identity tests categories – differences (deflation)
2 – Logic tests internal consistency – membership (deflation)
3 – Empirical actions test correspondence – measurement (deflation)
4 – Operational Language tests existential possibility (deflation)
5 – Rational action tests incentives – rational choice consistency (deflation)
6 – Reciprocity tests moral – rational exchange consistency (deflation)
7 – Full accounting and limits test scope consistency. (deflation)
8 – Narrative by analogy to perception describes reality – coherence (total consistency) (conflation)
Reality is explained by narrative, and the narrative survives falsification by identity, logic, action, reason, reciprocity, and scope.
We test statements about the world by deflating each dimension and testing each for consistency.
Each sub dimension can only be tested by use of the next dimension.
The only native skill we possess is the test of “differences”. Because our brains use samples of inputs in combination with memory to predict results and alert us through new stimulation to the differences.
Our brains sample senses, provide certain services, the hierarchical (distilled) result of which are combined (conflated) through memory and backward propagation into ‘experience’.
It turns out that except in rare cases we ‘experience’ a fairly accurate model of the physical world – but an absurdly inaccurate model of the social world, and completely nonsensical model of our personal value to that world. All of which are precisely what is necessary to survive as sentient (feeling of changes in state) and conscious (self aware) life form when possessed of uncomfortable knowledge in a universe of consistent risk.
This is a simple way of explaining Hume, Kant, and the Phenomenologists.
DEDUCTIBILITY FROM A-PRIORI PROPOSITIONS
Ergo, while one can claim the tautological truth (the Analytic A Priori), and one can claim the ideal(logical) truth (the Necessary Synthetic A Priori), one cannot ever know the non-tautological(identity, The Synthetic A Priori), non-ideal(Contingent Synthetic A Priori ) truth, because we rarely possess sufficient information to do so. As such there is a vast difference between an a priori rule of thumb, and a …..
What does this mean? It means that we can deduce from Analytic A Priori and Necessary Synthetic A Priori, but we cannot deduce from General Synthetic A Priori, or Contingent Synthetic A Priori Statements because we cannot know if such deductions are true (for specific cases).
So the problem with making a priori claims in economics is that you can say statements about statements but not about consequences in reality. You can only say ‘all other things being equal’, we should observe this effect. You cannot say, “we will always observe this effect’. Or even that the effect will appear in the given circumstance. Why? Because we don’t always observe such effects, and economics is rife with examples, the most commonly cited being unemployment does not necessarily increase, and prices are sticky – and for good reason.
The innovation that Menger brought to the table was to bring the principle of relative change from calculus to economics. The principle contribution of Hayek was to transform the use of materials to the use of information as the model for all social phenomenon. The principle contribution of Popper was to bring the information model to philosophy, and in particular the philosophy of science and to model scientific investigation on a market. This followed the transition in physics from the use of electromagnetic fields to that of information. Which then brought physics and mathematics into full correspondence.
What Hayek and popper and the Classicals and the Keynesians all missed and Brouwer in math, Bridgman in physics, and Mises in economics, and the entire analytic and continental movements missed was that man cannot make truth claims.
For example, we did not think the ideas of time(velocity of change), length(distance), and space(volume) varied. Einstein’s discovery was the same as Mises’, Brouwer’s and Bridgman’s: that all our pretense of axioms are false. If our idea of length and time can be false, every other idea that is obvious to our senses and reason can be false.
The difference between economics and physics is in
(a) volition vs. determinism
(b) reciprocity vs. transformation
(c) sympathetic testing of rational choice vs. entropy.
In simplest terms I translated Hoppe’s “Kantian Justificationism” into Anglo scientific terms, and in doing so completed the scientific method, uniting science, philosophy, morality, and law. Its uniting these fields by explaining the proper function of Praxeology that is the innovation.
The primary difference is that I show that you can’t produce a libertarian commune so to speak, and instead have to produce a full scale political order under ‘natural law of reciprocity’ where property rights apply to any demonstrated investment no matter how abstract. Otherwise demand for authority increases, or retaliation increases, or trust and economic velocity decreases, and competitiveness decreases, with all instances of differences not resolvable under law.
Therefore you cannot ‘exit’ to create a condition of liberty, you must conquer and hold territory in the market for territories against all possible competition. And this requires you produce an economy capable of producing the means of doing so. And that economy will always look something like a parliamentary monarchy but with purely empirical natural law.
In other words, you can only get liberty by permission and you can only get sovereignty by force.
So, while you cannot obtain borderland European liberty or separatist, ghetto, and borderland Jewish ‘liberty’, and if you want a condition of Anglo-Saxon liberty for the individual, it’s only possible if you create sovereignty in fact for the polity.
And the only way to create sovereignty and liberty is using (a) a militia, (b)natural law of reciprocity, (c) the markets that are made necessary by the natural law of reciprocity, (d) including the markets for association, cooperation, production, reproduction, commons production, polity production. And in order to do so you must produce a competitive market between the family(church/school), the commons (houses for each class), and judiciary (monarchy, judiciary, military).
In other words, by restoring the pre-revolutionary path, of Christian monarchies, and converting from mere common law, to strictly constructed judge discovered, law. And eliminating the parliament’s ability to create legislation and regulation – limiting them to contracts of the commons. And transforming the treasury into a purely empirical insurer of last resort for whom regulation is merely a matter of actuarial calculation.
GETTING TO THAT DIFFERENCE
(undone)
COMPLETING THE SCIENTIFIC METHOD
Properly understood, the Scientific method, at least as practiced in the physical sciences, if extended to include tests of volition, reciprocity, and full accounting, serves as nothing more than a warranty of due diligence upon our speech about the world.
In other words, the scientific method demands due diligence in the distribution of information just as we demand due diligence in the market for goods and services, and claims about goods and services, by force of involuntary warranty.
THE SCIENTIFIC (UNIVERSAL EPISTEMOLOGICAL) METHOD
“DEFLATION“, DEFLATIONARY (de–conflate)
(undone)
“DIMENSION”
(1) We can make:
(a) statements about experiences(metaphysical), or
(b) statements about statements(ideal), or
(c) statements about existential properties(existential/real), or
(d) statements about existential cause and effect(change).
(e) statements about volition
“CLOSURE”
(2) No test of any dimension can be completed without appeal to the subsequent dimension. (i.e. Gödel. this is profoundly important. no dimension can provide a self-test.) Ergo, all speech is deflationary.
“CRITICAL RATIONALISM”
(3) All descriptive propositions of existential cause and effect (change) are contingent.
“CRITICAL PREFERENCE”
(4) The only method of decidability between two or more non-false cause and effect propositions(change) is cost. This is a clarification of Occam’s razor. And appears to be true, for the simple reason that nature cannot but choose the least cost method, and man generally chooses the least cost method – even if we cannot know the full causal density of his considerations.
“FALSIFICATION”
(0) The purpose of the scientific method is to eliminate ignorance, error, bias, wishful thinking, suggestion, obscurantism, Fictionalism, and deceit from our statements about reality.
DUE DILIGENCE AGAINST IGNORANCE, ERROR, BIAS, DECEIT
(5) The only method of making a truth claim is to perform due diligence in each dimension of reality (a ‘premise’ of the consequential dimension) applicable to the cause and effect phenomenon. (i.e. physical world can’t engage in rational choice, or voluntary exchanges)
Again, those dimensions are:
(a) Identity(categorical consistency)(point)
(b) Logical:(internal consistency)(line)
(c) Empirical: (external consistency)(shape)
(d) Existential: (operational consistency)(object)
(e) Volitional: (rational choice of rational actor)(change)
(f) Reciprocal: ( rational exchange between rational actors)(changes)
(g) Limited: (Limits: At what points does the description fail?)
(h) Fully Accounted: (Have all costs and consequences been accounted for – defense against cherry picking and special pleading.)
DARWINIAN SURVIVAL OF IDEAS
(6) All propositions (facts, propositions, theories) must survive the markets for criticism at the observer-mental-testing, observer-action testing, market application testing, and market survival testing. In other words, the universal epistemological method follows this lifecycle:
(a) observation
(b) Free association (F -> observation)
(c) test of reasonability (F -> free association )
(d) Hypothesis
(e) Perform Due Diligence (a-h) above. (F -> free association )
(f) Theory
(g) Publish to the market for application
(h) Survival in the market for application(F ->observation – of failures )
(i) Law
(j) Survival in the market for refutation (F-> observation – of failures)
(k) Habituation into metaphysical assumptionsSPECIAL CASES
7) This epistemological process is universally applicable despite the fact that various results can be identified with it. Because just as we find prime numbers largely by trial and error we find special cases of statements by trial and error. But when we find these statements we have to ask ourselves what is it we are finding?
(a) Sensations: statements about experiences(metaphysical), or
(b) Logic(analytic): statements about statements(ideal), or
(c) Fact: statements about existential properties(existential/real), or
(d) Theory(Synthetic): statements about existential cause and effect(change).
(e) Morality: statements about volition
(f) Testimony: statements about the fully accounted change in state of a given instance of the statement we are making (I have a credit card report that shows John Doe, on 1/1/2018 at 4:06:32 exchanged $2.00 for a Hershey’s candy bar at Don’s newspaper stand then existing on 225th and Main in Cityname.”)
EXAMPLES
The most common special cases that we find are those that are impossible to contradict at the same dimension. (a,b,c,d,e) above.
(a) Sense(Metaphysics): we cannot sense a ball is green and red all over at the same time.
(b) Logic: If I issue credit on fractional reserves, I will increase the supply of money.
(c) Fact: The differences between commodity money and note money include but are not limited to: liquidity, demand, exchange fee or interest gain, portability(weight/volume), reserve risk, vendor risk.
(d) Theory: All other things being equal, if we increase the supply of money, prices will eventually increase accordingly and lower the purchasing power of payments against debts.
(e) Morality: All other things being equal, when we force majoritarian decisions on the polity by using representative democracy, we create a monopoly out of the market for the commons, and eliminate the possibility of cooperating on means even if we pursue different ends.
“ECONOMIC LEVERS”
Polities can generally use this series of levers to affect the economy.
-Near Term-
(a) Monetary Policy
(b) Fiscal Policy (Spending)
-Medium Term-
(c) Trade Policy (import export policies, foreign trade policies)
(d) Regulatory/Legislative Policy (also includes price controls etc)
(e) Immigration-Deportation policy / Expand military, WPA etc.
-Long Term-
(f) Human Capital Policy (Education policy)
(g) Institutional Policy (laws, regulations, bureaucracies, institutions, banks)
(h) Strategic (military) Policy
Science: A Warranty of Due Diligence
SCIENCE: The use of logical and physical instrumentation for the purpose of eliminating ignorance, error, bias, wishful thinking, suggestion and obscurantism, Fictionalism and deceit from our free-associations by the systematic deflation and attempted falsification (survival) from criticism in eight dimensions of actionable reality: categorical, logical, empirical, operational, rational, reciprocal, fully accounted including scope and limits – and coherent across those dimensions.
Science is a moral discipline wherein we criticize our ideas, so that we can speak them truthfully:
— We test our categories using differences to eliminate conflation.
— We test our reasoning with logic for internal consistency.
— We test our observations with external correspondence.
— We test the existence of our premises with operations.
— We test the rationality and volition of choice through sympathy
— We test the reciprocity and volition of choice through changes in capital
— We test the scope of our theory with falsifications.
Once we have tested our theories by these means, then we can say that we speak truthfully – and as such do no harm.
The central argument regarding truth:
1) That in order to cooperate, humans evolved sympathy for intent – and are marginally indifferent in their judgment of intentions. This allows us to sympathetically test most human incentives if subject to the same stimuli (information). It is also why juries can functions, since this sympathetic testing of intentions is the criteria by which juries render decisions.
2) That however, we cannot sympathize with the first principles of the physical universe – the equivalent of intentions. So while we intuit and can test man’s intentions, we cannot measure and test the universe’s first principles. As such, the best we can do is testify to observations and measurements of those phenomenon until at some point we know those first principles – if that is ever possible.
3) But our observations must also be reduced to stimuli that can be sympathetically tested by others, and insulated from our deception, bias and error.
4) We call this process ‘science’, but the practice of science is little more than a set of moral rules that instruct us as to how to eliminate deception, bias and error. The scientific method then, is merely a moral discipline: the means by which we struggle to speak the truth, as truthfully as we may possibly accomplish given the frailty of our reason.
5) That giving witness to one’s observations, is testable by reproduction of a set of operational definitions. That operational definitions produce the equivalent of names, just as positional numbering provides quantities with names. Such names are insulated from deception, distraction, loading, framing and overloading. Theories are not. While we cannot demonstrate the absolute parsimony of a theory (that we know of), we can demonstrate that we truthfully conveyed our observations. In other words, we can testify truthfully to an ordered set of facts, even if we cannot testify truthfully to parsimony of a theory.
6) That it is possible to state instead that all outputs of scientific investigation are truthful, if they are truthfully represented – where ‘scientific investigation” refers to the use of the scientific method, regardless of field of inquiry. But that we seek the most parsimonious statement of a theory, and we can never know that we have obtained it, we can only develop consensus that we cannot cause it to fail. This is, as far as I know, the best non-platonic description of truth available. Everything else is a linguistic contrivance for one purpose or another – possibly to obscure ignorance, and possibly to load ideas with moral motivation. Scientists load their contrivance of truth, and mathematicians load their contrivance of numbers, limits, and a dozen other things – most of which obscure linguistic ‘cheats’ to give authority to that which is necessary for the construction of general rules. (ie: the problem of arbitrary precision).
7) That Popper did no investigation into science or the history of science prior to making his argument, and that as yet, we do not have a systematic account of the history of science. However, what history we do have, both distant and recent, is that science operates by criticism upon failure, where failure is demonstrated by via overextension of the theory.
8) The reason for overextension rather than criticism as the operational preference being that it is economically inefficient (expensive) to pursue criticism rather than to extend a theory to its point of failure then criticize it. And as far as we know, this is how science functions in practice, and must work, because it is how all human endeavors must work. Because while a small number of scientists may seek the ‘truth’ (or whatever a Platonist means by it), what scientists try to do is solve problems – i.e. to manufacture recipes for useful cognition.
9) Popper’s advice was merely moral given that the scope of inquiry in all human fields had surpassed that of human scale, where tests are subjectively verifiable. (I think this is an important insight because it occurred in all fields.) Einstein for example, operationalized observations (relative simultaneity for example) over very great distances approaching the speed of light using Lorenz transformations. And as Bridgman demonstrated, the reason Einstein’s work was novel was because prior generations had NOT been operationalizing statements ,and as such, more than a generation and perhaps two were lost to failure of what should have been an obvious solution. (See the problem of length, which I tend to refer to often as the best example.) I addressed this in a previous post, and what popper did was give us good advice, and while he made an argument that appears logical, like most rational arguments, unsupported by data, it is not clear he was correct, and in fact, it appears that he was not. The question is not a rational but empirical one. (Note: I seek to codify this moral insight into law. Thus ending all deception by not only Fictionalism, but all other means.)
10) Popper unlike Misesian Pseudoscience, or Rothbardian Immoral Verbalisms, was engaged in a moral attempt both in politics and in science, and perhaps in science as a vehicle for politics, to prevent the pseudoscientific use of science – particularly by fascist and communists, to use the findings of science as a replacement for divine authority by which to command man. What popper did, particularly with his Platonism, was to remove the ability for the findings of science to be used as justification for the removal of human choice. Popper, Mises, and Hayek were responsible for undermining pseudoscientific authoritarianism. Of the three Popper is perhaps less articulate (possibly to obscure his objective), but certainly not wrong, so to speak. While Mises’ appeal to authoritarianism (which is part and parcel of his Jewish culture) was entirely pseudoscientific, by claiming that economics was deductive rather than empirical, and justifying it under a priorism, instead of as I’ve stated, understanding that he was merely trying to apply operationalism to economic activity, which would merely demonstrate that Keynesian economics was immoral and deterministic, not unscientific.
11) But Popper, Mises, Hayek, Bridgman and Brouwer, did not find a solution to restoring the western aristocratic conditions for public speech. They too were a lost in Platonism a bit. Bridgman and Brouwer did understand that something was wrong, and were very close, but they could not make the moral argument. We have had a century now of attacks by verbal contrivance and we can demonstrate the destruction of our civilization by way of it. So the moral argument is no longer one of undemonstrated results. WE have the results. And we have a generation of men, myself included, trying to repair it.
One must speak truthfully, because no other truth is knowable. Intellectual products that are brought to market must be warrantied just as are all other products that are brought to market, and the warranty that you can provide is operational definitions (recipes, experience), not theories (psychologism, projections). And if you are not willing to stand behind your product then you should not bring it to market. Because you have no right to subject others to harm.
Intellectuals produce ideas (myself included), that is our product. We are paid in measly terms most of the time, for our product, but that is what we do. But it is no different from serving too-hot coffee or selling dangerous ladders, or manufacturing defective gas tanks – intellectuals do plenty of harm in history. Perhaps the most harm of all. Between Abraham, Paul of Tarsus and the Byzantine Emperors, Mohammed and his real author,; Marx, Boaz, and Freud, it is hard to envision any worse catastrophe perpetrated by man.
THEREFORE:
Why is it that the informational commons, and by consequence the political and normative commons, are not – in an age of information – as subject to warranty and liability as pollution or harm to physical commons, life, body, and private property?
Truthfulness – testimony that has been subject to due diligence – is a non trivial cost. And economists are too happy (as it appears all social scientists have been) to produce defective products for personal gains, without the warranty that all other products have been subject to.
Why is it that free speech is not limited to free truthful speech? After all, the cost of producing truthful scientific testimony under due diligence and warranty is much higher than the cost of producing untruthful pseudoscientific testimony without due diligence or warranty. Doesn’t mere free speech without warranty of due diligence of truthfulness construct an impossibility under which the production of high cost truth and the production of low cost fantasy, bias, error and deceit must eventually win?
There is a great difference between the terms “empirical” (observable and measurable) and “scientific” of which empirical criticism is but a minor subset of the criterion necessary for the production of warranty of due diligence against fantasy, bias, error, and deceit.
We have had a century of economists running with intellectual scissors, causing inter-temporal externalities of profound consequence. And the Cosmopolitan (freshwater) rationalist’s justification of priors is only more visible than the mainstream Anglo empirical (Saltwater), justification of priors under the pseudoscience of Rawlsian Justificationism – itself a fascinating example of the logically impossible, yet pervasively persuasive.
So just as all enlightenment adaptations were plagued with errors – Anglo, French, German and Jewish – both freshwater and saltwater economics are plagued with pseudoscience. The freshwater try to justify objective morality, by argumentative construction (pseudoscience), and the saltwater try to justify immorality by intentionally failing to account for profound normative, institutional, civilizational, and genetic consequences (pseudoscience).
So it’s one thing for all of us to point the finger of the accusation of pseudoscience one place or another. But it is quite another to realize that the minute you draw the lens of truth upon either freshwater or saltwater economics, you will discover that both are pseudosciences that merely confirm ideological priors.
INNOVATION IN SCIENCE, EPISTEMOLOGY, AND TRUTH
In the last century intellectuals tried and failed to complete the scientific method and thereby create a test of non-falseness like we do in law. They couldn’t do it.
What I’ve done, because I’ve been lucky enough to spend most of my life working with “computable” systems – meaning that which is existentially possible to construct through a series of operations is supply the habits of strict operational construction with requirements for existential possibility, to the scientific method, and complete what those thinkers failed to discover.
KARL POPPER
Popper applied Jewish critique, (criticism), to science, as “falsificationism”. Meaning, the way to avoid pseudoscience is to require that a statement be falsifiable.
He did this because pseudoscience was rapidly expanding under the popularity of authoritarian socialism, as much as because he was simply interested in philosophy. He was trying to preserve intellectual cosmopolitanism (Jewish diasporism), and this culminated in his work “The Open Society” which is what Soros uses as his ‘plan’.
Now, in his efforts to correct science, he developed a set of ideas that I will try to reduce to these:
1) Falsification (critique, criticism) vs. Justificationism (excuses)
2) Critical Rationalism: we can know what is false but not what is true.
3) Critical Preference: we cannot know which theory is more likely true. there is no method of decidability.
4) Verisimilitude through Problem->Theory->Test
5) That science, by verisimilitude (markets), is conducted as a MORAL (social, normative) process, and that scientific discovery was accomplished by moral means.
BUT THIS IS THE PROBLEMUnempirical: his statements are logical not empirical, and he never did any research, nor has any been formally done.
Costs: he, like most philosophers, continues the Aristotelian tradition of ignoring costs. Costs provide us with information about which theories we can afford to pursue. Historically then, we can empirically demonstrate that man uses costs as methods of decidability.
Decidability: Costs provide decidability, for the simple reason that just as we pursue the least cost methods of research, nature evolves using the least cost method of evolution. It’s only humans that can choose to do the expensive thing and take a risk. Nature can’t do that. Nature is tightly deterministic. Man is only loosely deterministic. Because all of us guess a future and see if we can achieve it.
Falsification: Falsification is not very precise, and he did not see the dimensions. So he did not restate the scientific method as a series of dimensional tests equal to the dimensional tests of mathematics. So categories(identity), math(relations), logic (words/membership), operations (costs/existence), morality (choice/cooperation), and scope (full accounting) were each methods of falsification, that a scientific statement would have to pass. (Rather than the competition between consistency, correspondence, completeness, and coherence.)
Verisimilitude: (Rather than Markets.) Because costs do determine the progress of our investigations, our knowledge evolves just as organisms evolve, planets evolve, solar systems, galaxies, and the universe. What differs is the cost of inquiry in each culture. White people happen to have the lowest cost of inquiry because they have a high trust civilization where the norm of truth is highly defended as (nearly sacred) public property.
Physical absence vs Social presence of first causes. Unable to distinguish between the problem of instrumentation in the physical sciences in the absence of knowledge of first causes (‘nature’s choice’), versus the problem of subjective instrumentation in the social sciences, in the presence of first causes (sympathetic choice)
The Epistemological Cycle …
Problem -> Theory -> Test
… is incomplete.
The complete epistemological cycle is:
Perception(Chaotic) ->
…Opportunity (Free Association) ->
……Hypothesis (way-finding) ->
………Criticism(individual investment) ->
…………Theory (outputs a recipe/opportunity narrative) ->
……………Social Criticism (market investment) ->
………………Law (exhaustion – return on investment) ->
…………………Survival (Perfect Parsimony – incorporation into norms) ->
……………………Tautology ( invisible – assumed world structure )
This long chain that represents the evolutionary survival of ideas, can be broken into these sections:
1 – Perception -> free association(searching) -> identity (opportunity)
2 – Question (Problem)
3 – Iterative Criticism ( Survival!!! )
………..way-finding (criticism) / Hypothesis.
Way-finding is a form of criticizing an idea.
………..criticism / theory / personal use
………..testing / law / general use
………..recognition / survival / universal use
………..identity / tautology / integration into world view.
The Continuous Recursive Disambiguation (falsification) of our free associations.
IMMANUEL KANT
3) A Priori: Or, “independent of observation.”
There are three dimensions to claims of an a priori truth claim:
i) A priori vs. A posteriori,
ii) Analytic vs. Synthetic, and
iii) Necessity vs. Contingency
Therefore we can produce at least the following spectrum of a priori claims.
(a) Analytic A Priori: tautological: “2+2=4 and all deductions thereof.”
(b) Synthetic A Priori : “Increasing money increases inflation.”
(c) Necessary Synthetic A Priori: “Childless women will have no grandchildren.”
(d) Contingent Synthetic A Priori: “all other things being equal, as a general trend, increasing demand will increase supply, although we cannot know the composition of that supply in advance, we can identify it from recorded evidence.”
This produces a an ordered spectrum of declining precision:
(a) Identity(categorical consistency) – Analytic A Priori
(b) Logical:(internal consistency) – Nec. Synthetic a priori
(c) Empirical: (external consistency) – Gen. Synth. a priori
(d) Existential: (operational consistency) – Cont. Synth. a priori
Which corresponds to the testable dimensions of numbers (ideals)
(a) identity (numbers)
(b) logical (sets)
(c) empirical (ratios)
(d) existential (constructible)
Which corresponds to dimensions of physical reality
(a) point
(b) line
(c) shape
(d) object
(e) time (change)
(f) relative change
Which corresponds to a subset of the dimensions of actionable reality , the full set of which we express in fully express in Testimonialism as:
(a) Identity(categorical consistency)(point)
(b) Logical:(internal consistency)(line)
(c) Empirical: (external consistency)(shape)
(d) Existential: (operational consistency)
(e) Volitional: (rational choice of rational actor)(change)(time)
(f) Reciprocal: ( rational exchange between actors) (relative change)
Which together account for the totality of actionable reality (by man) that we currently know of (and its quite hard to imagine anything else is possible).
The test of speech then consists of dimensional deflation and spoken conflation into parsimonious testimony:
1 – Identity tests categories – differences (deflation)
2 – Logic tests internal consistency – membership (deflation)
3 – Empirical actions test correspondence – measurement (deflation)
4 – Operational Language tests existential possibility (deflation)
5 – Rational action tests incentives – rational choice consistency (deflation)
6 – Reciprocity tests moral – rational exchange consistency (deflation)
7 – Full accounting and limits test scope consistency. (deflation)
8 – Narrative by analogy to perception describes reality – coherence (total consistency) (conflation)
Reality is explained by narrative, and the narrative survives falsification by identity, logic, action, reason, reciprocity, and scope.
We test statements about the world by deflating each dimension and testing each for consistency.
Each sub dimension can only be tested by use of the next dimension.
The only native skill we possess is the test of “differences”. Because our brains use samples of inputs in combination with memory to predict results and alert us through new stimulation to the differences.
Our brains sample senses, provide certain services, the hierarchical (distilled) result of which are combined (conflated) through memory and backward propagation into ‘experience’.
It turns out that except in rare cases we ‘experience’ a fairly accurate model of the physical world – but an absurdly inaccurate model of the social world, and completely nonsensical model of our personal value to that world. All of which are precisely what is necessary to survive as sentient (feeling of changes in state) and conscious (self aware) life form when possessed of uncomfortable knowledge in a universe of consistent risk.
This is a simple way of explaining Hume, Kant, and the Phenomenologists.
DEDUCTIBILITY FROM A-PRIORI PROPOSITIONS
Ergo, while one can claim the tautological truth (the Analytic A Priori), and one can claim the ideal(logical) truth (the Necessary Synthetic A Priori), one cannot ever know the non-tautological(identity, The Synthetic A Priori), non-ideal(Contingent Synthetic A Priori ) truth, because we rarely possess sufficient information to do so. As such there is a vast difference between an a priori rule of thumb, and a …..
What does this mean? It means that we can deduce from Analytic A Priori and Necessary Synthetic A Priori, but we cannot deduce from General Synthetic A Priori, or Contingent Synthetic A Priori Statements because we cannot know if such deductions are true (for specific cases).
So the problem with making a priori claims in economics is that you can say statements about statements but not about consequences in reality. You can only say ‘all other things being equal’, we should observe this effect. You cannot say, “we will always observe this effect’. Or even that the effect will appear in the given circumstance. Why? Because we don’t always observe such effects, and economics is rife with examples, the most commonly cited being unemployment does not necessarily increase, and prices are sticky – and for good reason.
The innovation that Menger brought to the table was to bring the principle of relative change from calculus to economics. The principle contribution of Hayek was to transform the use of materials to the use of information as the model for all social phenomenon. The principle contribution of Popper was to bring the information model to philosophy, and in particular the philosophy of science and to model scientific investigation on a market. This followed the transition in physics from the use of electromagnetic fields to that of information. Which then brought physics and mathematics into full correspondence.
What Hayek and popper and the Classicals and the Keynesians all missed and Brouwer in math, Bridgman in physics, and Mises in economics, and the entire analytic and continental movements missed was that man cannot make truth claims.
For example, we did not think the ideas of time(velocity of change), length(distance), and space(volume) varied. Einstein’s discovery was the same as Mises’, Brouwer’s and Bridgman’s: that all our pretense of axioms are false. If our idea of length and time can be false, every other idea that is obvious to our senses and reason can be false.
The difference between economics and physics is in
(a) volition vs. determinism
(b) reciprocity vs. transformation
(c) sympathetic testing of rational choice vs. entropy.
In simplest terms I translated Hoppe’s “Kantian Justificationism” into Anglo scientific terms, and in doing so completed the scientific method, uniting science, philosophy, morality, and law. Its uniting these fields by explaining the proper function of Praxeology that is the innovation.
The primary difference is that I show that you can’t produce a libertarian commune so to speak, and instead have to produce a full scale political order under ‘natural law of reciprocity’ where property rights apply to any demonstrated investment no matter how abstract. Otherwise demand for authority increases, or retaliation increases, or trust and economic velocity decreases, and competitiveness decreases, with all instances of differences not resolvable under law.
Therefore you cannot ‘exit’ to create a condition of liberty, you must conquer and hold territory in the market for territories against all possible competition. And this requires you produce an economy capable of producing the means of doing so. And that economy will always look something like a parliamentary monarchy but with purely empirical natural law.
In other words, you can only get liberty by permission and you can only get sovereignty by force.
So, while you cannot obtain borderland European liberty or separatist, ghetto, and borderland Jewish ‘liberty’, and if you want a condition of Anglo-Saxon liberty for the individual, it’s only possible if you create sovereignty in fact for the polity.
And the only way to create sovereignty and liberty is using (a) a militia, (b)natural law of reciprocity, (c) the markets that are made necessary by the natural law of reciprocity, (d) including the markets for association, cooperation, production, reproduction, commons production, polity production. And in order to do so you must produce a competitive market between the family(church/school), the commons (houses for each class), and judiciary (monarchy, judiciary, military).
In other words, by restoring the pre-revolutionary path, of Christian monarchies, and converting from mere common law, to strictly constructed judge discovered, law. And eliminating the parliament’s ability to create legislation and regulation – limiting them to contracts of the commons. And transforming the treasury into a purely empirical insurer of last resort for whom regulation is merely a matter of actuarial calculation.
GETTING TO THAT DIFFERENCE
(undone)
COMPLETING THE SCIENTIFIC METHOD
Properly understood, the Scientific method, at least as practiced in the physical sciences, if extended to include tests of volition, reciprocity, and full accounting, serves as nothing more than a warranty of due diligence upon our speech about the world.
In other words, the scientific method demands due diligence in the distribution of information just as we demand due diligence in the market for goods and services, and claims about goods and services, by force of involuntary warranty.
THE SCIENTIFIC (UNIVERSAL EPISTEMOLOGICAL) METHOD
“DEFLATION“, DEFLATIONARY (de–conflate)
(undone)
“DIMENSION”
(1) We can make:
(a) statements about experiences(metaphysical), or
(b) statements about statements(ideal), or
(c) statements about existential properties(existential/real), or
(d) statements about existential cause and effect(change).
(e) statements about volition
“CLOSURE”
(2) No test of any dimension can be completed without appeal to the subsequent dimension. (i.e. Gödel. this is profoundly important. no dimension can provide a self-test.) Ergo, all speech is deflationary.
“CRITICAL RATIONALISM”
(3) All descriptive propositions of existential cause and effect (change) are contingent.
“CRITICAL PREFERENCE”
(4) The only method of decidability between two or more non-false cause and effect propositions(change) is cost. This is a clarification of Occam’s razor. And appears to be true, for the simple reason that nature cannot but choose the least cost method, and man generally chooses the least cost method – even if we cannot know the full causal density of his considerations.
“FALSIFICATION”
(0) The purpose of the scientific method is to eliminate ignorance, error, bias, wishful thinking, suggestion, obscurantism, Fictionalism, and deceit from our statements about reality.
DUE DILIGENCE AGAINST IGNORANCE, ERROR, BIAS, DECEIT
(5) The only method of making a truth claim is to perform due diligence in each dimension of reality (a ‘premise’ of the consequential dimension) applicable to the cause and effect phenomenon. (i.e. physical world can’t engage in rational choice, or voluntary exchanges)
Again, those dimensions are:
(a) Identity(categorical consistency)(point)
(b) Logical:(internal consistency)(line)
(c) Empirical: (external consistency)(shape)
(d) Existential: (operational consistency)(object)
(e) Volitional: (rational choice of rational actor)(change)
(f) Reciprocal: ( rational exchange between rational actors)(changes)
(g) Limited: (Limits: At what points does the description fail?)
(h) Fully Accounted: (Have all costs and consequences been accounted for – defense against cherry picking and special pleading.)
DARWINIAN SURVIVAL OF IDEAS
(6) All propositions (facts, propositions, theories) must survive the markets for criticism at the observer-mental-testing, observer-action testing, market application testing, and market survival testing. In other words, the universal epistemological method follows this lifecycle:
(a) observation
(b) Free association (F -> observation)
(c) test of reasonability (F -> free association )
(d) Hypothesis
(e) Perform Due Diligence (a-h) above. (F -> free association )
(f) Theory
(g) Publish to the market for application
(h) Survival in the market for application(F ->observation – of failures )
(i) Law
(j) Survival in the market for refutation (F-> observation – of failures)
(k) Habituation into metaphysical assumptionsSPECIAL CASES
7) This epistemological process is universally applicable despite the fact that various results can be identified with it. Because just as we find prime numbers largely by trial and error we find special cases of statements by trial and error. But when we find these statements we have to ask ourselves what is it we are finding?
(a) Sensations: statements about experiences(metaphysical), or
(b) Logic(analytic): statements about statements(ideal), or
(c) Fact: statements about existential properties(existential/real), or
(d) Theory(Synthetic): statements about existential cause and effect(change).
(e) Morality: statements about volition
(f) Testimony: statements about the fully accounted change in state of a given instance of the statement we are making (I have a credit card report that shows John Doe, on 1/1/2018 at 4:06:32 exchanged $2.00 for a Hershey’s candy bar at Don’s newspaper stand then existing on 225th and Main in Cityname.”)
EXAMPLES
The most common special cases that we find are those that are impossible to contradict at the same dimension. (a,b,c,d,e) above.
(a) Sense(Metaphysics): we cannot sense a ball is green and red all over at the same time.
(b) Logic: If I issue credit on fractional reserves, I will increase the supply of money.
(c) Fact: The differences between commodity money and note money include but are not limited to: liquidity, demand, exchange fee or interest gain, portability(weight/volume), reserve risk, vendor risk.
(d) Theory: All other things being equal, if we increase the supply of money, prices will eventually increase accordingly and lower the purchasing power of payments against debts.
(e) Morality: All other things being equal, when we force majoritarian decisions on the polity by using representative democracy, we create a monopoly out of the market for the commons, and eliminate the possibility of cooperating on means even if we pursue different ends.
“ECONOMIC LEVERS”
Polities can generally use this series of levers to affect the economy.
-Near Term-
(a) Monetary Policy
(b) Fiscal Policy (Spending)
-Medium Term-
(c) Trade Policy (import export policies, foreign trade policies)
(d) Regulatory/Legislative Policy (also includes price controls etc)
(e) Immigration-Deportation policy / Expand military, WPA etc.
-Long Term-
(f) Human Capital Policy (Education policy)
(g) Institutional Policy (laws, regulations, bureaucracies, institutions, banks)
(h) Strategic (military) Policy
Now that we have completed our journey through creating Dimensions of Decidability using Deflation, Operationalization, Serialization, and Competition, we can:
Discover and enumerate the Dimensions extant in our Language.
Discover how those dimensions can be combined into Grammars of Decidability.
Discover how those grammars can be organized into a spectrum that covers every niche of human communication from physical, perceptual, emotional, intellectual, and imaginary – as well as deception.
Discover that our set of grammars illustrate a hierarchy of patterns in the physical universe – and that our understanding of that pattern and our grammars are very nearly complete.
Discover that our Language consists of :
Continuous Recursive Disambiguation in Real Time (Serial Speech)
Using Some Set of Analogies to Experience (Words)
Resulting in Transactions (Sentences)
That produce Contracts for Meaning (Stories)
Within some Set of Dimensions (Physical, Experiential, Imaginary)
And that opportunity for Deception (Frauds, Fictions, Fictionalisms) is ever-present.
But by limiting our speech (prose) to Operational Grammar ( using constant relations between reality, perceptions, cognition, actions, and consequences), or what we traditionally call “Testimony”, all statements are both objectively and subjectively testable, thereby providing extremely limited opportunity for error, bias, and deceit.
And by performing Due Diligence, for consistency, correspondence, existential possibility, rationality of choice, reciprocity, completeness and coherence;
We force a Competition for Coherence by which we expose our ignorance and can Warranty our speech is as free of error, bias, and deceit as is possible given our current language knowledge.
Geometry of Decidability
(…)
(the via negativa pzzle pcs)
Dimensions Present in our Vocabulary
Next, we can examine our vocabulary and organize the terms into a series of categories.
|WORD| > Name(Noun) > Action(Verb) > Relations > Agreements > Noise Words > Code Words.
And within each category of word we find multiple dimensions.
|Name(Noun)| : Proper(Person > Thing > Place > Idea > Perception(sense) > Emotion(value)) > Common (categorical) > Compound > Pronoun > Clarifier (Determiner/Measure) > Property(adjective) >
|State| State > Event > Action > Experience > Thought
|Person| First > Second > Third > Abstract
|Gender| Female < Young Female < Neutral > Young Male > Male.
|Possession|- Possession (‘s – “apostrophe s” in English) (“Can Own”) > (“Can be owned”) > (Cannot be owned”)
|Temporality| Always Been > Has been > is Currently > Will Be > Will Always Be.
|Gain or Loss| Gain < Neutral > Loss
|Decidability| Incommensurable > Undecidable > Preferable > Good > True.
|Relations| Relation (Preposition/Postposition) > Link (Conjunction > Copula ) >
|Agreements| Agreement(yes-no) >
|Noise Words| Noise Words(Expletives etc.) >
|Code Words| code-words(acronyms etc.)What Can We Learn From Those Dimensions?
A great deal:
Limited Scales Measurement: We tend to consider only a scale of five, in any dimension which mirrors the accuracy of survey responses: a 1-5 scale is about as accurate as one can get, with 1-3 1-5, 1-7 appearing frequently and with a 1-10 scale ratings always reducible to a 1-5 scale with finer graduation to the high end and lower granulation to the low end. This 3,5,7 scale shows up in nearly all aspects of cognition, such as the number of objects we can independently visualize or numbers one can recall. Usually in the seven plus or minus two range.
Limited Dimensions To Describe References: There are about as many dimensions in both nouns and verbs: seven. While there are about fourteen dimensions between nouns and verbs, the only complex relationships are:
State
Perception (Experience)
Relations
But these three sets provide a large set of sensory dimensions for describing our references.
State, Perception, and Relation function as Weights and Measures: ( … )
Dimensions of Negotiation: Other than Perception and Relations, the number of dimensions is surprisingly small. And nearly all can be categorized as necessities of
Negotiation and
Possession, and
Weights and Measures.
Dimensions of Possession: Our language contains an extraordinary dedication of dimensions to possession. Given the dimensions above, please note the following:
Person, Gender, and Possession are dimensions in our Nouns.
Ownership, Permissibility, and Gain or Loss are dimensions in our Verbs.
The degree of Warranty of our meaning is implied not stated.
As we will see later, this emphasis on possession, ownership, and property is necessary for both cooperation and ‘calculation’, and function as the basis of ethics and morality, and our valuation of changes in state of possessions (or interests) the origin of our emotional responses. We are, whether we like it or not, acquisition machines, using language to negotiate cooperation because of the far higher returns on a division of labor than are possibly by individual action.
A Change In Paradigm (Ontology)
Justification an self and knowledge
versus
Contract and others and trade and consent.
Note: For those who have experience with Taxonomies of vocabulary, this categorization is significantly different from Roget’s – and somewhat dehumanizing.
Words: Measurements and Collections of Measurements (Weights and Measures)The Contractual Constitution of Meaning (Words, Phrases, Sentences)The Experiential: The Dimensions of Perception (Experience)
Now, how can we DESCRIBE the universe? With dimensions consisting of constant relations.
Now, we are going to make frequent use of these terms ‘dimension’ and ‘dimensions’. And the most simple constant relation we know of is mathematics: the study of positional relations:
0-Point (Referent)(Identity, anchor referent)(quantity)
1-Line (Distance)(Relations)
2-Area (Ideal)(Sets)
3-Object (Ideal Object) (Space)
4-Time (Velocity) (Change)
5 – N – Pure Relations (Concepts/Categories)
6 – N vs. N’ Relations, (Forces) (Equilibria)
7 – N vs. N’ Intermediate Relations, (Symmetries)
8 – N vs N’ relations between symmetries (Paradigms)
9 – (N vs N’)’ recursive hierarchies of symmetries ad infinitum. (Reality)
And we have mathematical techniques for such dimensions.
0 – Correspondence (referents, identity)
1 – Positional names, Arithmetic, Accounting. (counting)
2 – Mathematics and algebra (Ratios)
3 – Geometry (Space)
4 – Calculus, Finance, Economics. (Change)
5 – Algebraic Geometry (Math of sets of constant relations)
6 – Physics (equilibration)
7 – Lie Groups, (Symmetries, Externalities, Future of Economics)
(8 – Grammars)
(9 – Paradigms) (stories) (Semantics)
(10 – Fictions)
(11 – Ideals )
(12 – Dreams)
And that we have discovered mathematical techniques for the preservation of constant relations in increasing layers of complexity ….
The Dimensions of RelationsDimensions of Meaning: Geometry of Thought, Speech, and Argument
(try to explain)
(how the mathematical dimensions and the verbal dimension and paradigms and stories…. It’s all dimensions)
From any given point, there are an infinite number of vectors.
All thoughts can be represented geometrically.
But like Mandelbrot’s Fractals, they are not calculable by man, only computable by machines.
However, the underlying symmetries (shapes) will be consistent across contexts, for the simple reason that grammars are consistent across contexts (paradigms).
THE DIMENSIONAL GRAMMARS
The Periodic Table Of Speech
|GRAMMARS| Deflationary Grammars < Ordinary Grammars > Inflationary Grammars.Grammars: Overcoming the Problem of Human Scale (necessary because of computational limitations)
Use of external resources to render commensurable that which is beyond our abilities.
Deflationary Grammars (decidable)
Logic of Differences (identity)
The Logic of Continuous Relations, Logic of Sets (categories)
The Logic of Counting: Counting, Arithmetic, Accounting.
The Logic of Positional Relations (measurement): Mathematics (all of it), Equilibrium mathematics (constant relations)
The Logic of Algorithms – Computers, simulations (automation)
The Logic of Transformations: Physics, chemistry, biology, sentience, reason (transformations)
The Logic of Reciprocity, Law, Contract (cooperation) and Economics
The Logic of Science: Science, Reporting, Testimony (testimony)
Ordinary Grammars (practical)
So we can at least include these Ordinary Language grammars.
Formal or Written
Ordinary Conversational (in the commons)
Idiomatic Varies by Region, class, discipline, and occupation.
Inflationary Grammars (meaningful)
Narration
Story (grammar of stories)
Fiction (grammar of fiction)
Deception Grammars (Under, over, and false loading)
Pseudoscience ( conflation of magic and technology)
Psuedo-rationalism (Pilpul and Critique), (Justificationism en Closure)
Pseudo-mythology (conflation of history and myth as well as wisdom and law, as well as real and supernatural)
Occult (experiential Fiction)
The Periodic Table of Grammars
(Poster Size)
Figure 1 The Periodic Table of GrammarsNote: The table is too large for inclusion in this book, in any readable form, but is available online at https://propertarianinstitute.com/grammars where you can download a PDF version, or order a poster online.
Reorganizing Our Categories of Language
Semantics Are Limited by and Subordinate To Grammars
Now Let’s Look at the Rest of Communication
Now, Just as mathematics consists in the study of constant relations, at increasing numbers of dimensions, we can perform the same analysis for all other forms of communication. And we will see how all our grammars are organized by the very same means – the organization of constant relations. And then how some deflate relations, so me preserve relations, some inflate relations, some conflate relations. And as such we will see how we use these various grammars to communicate the entire spectrum of reality from the existential to the imaginary.
Language – all same enough that they reflect a common set of abilities and limits of the human brain. SVO, SOV, VSO, but in all cases we describe states of subjects or changes in states of subjects, and we combine this little stories into ever increasingly complex sentences, paragraphs and stories, and we weave these stories into paradigms and then into networks of paradigms, and those networks of paradigms and stories provide us with context, and that content lessens the computational cost of composing stories, paragraphs, sentences, phrases, and sub-stories consisting of descriptions of state or changes in state – and attach to those stories some value or other. And therefore assist us in making decisions from the most casual and unconscious to the most deliberative and calculative.
Context and Precision: Ordinary language varies from formal, meaning low context and high precision, to common to idiomatic, meaning high context low precision. The lower the precision the higher the context the more suggestion is created by the speaker and the more substitution is required of the audience.
Dialects. Within languages we create Dialects – regional, class, and occupational. These vary in paradigms, vocabulary, values, morphology and phonology, but most often preserve the same syntax: rules of sentence construction.
Across these dialects, and across all languages and dialects, we have produced various technological variations in grammar (paradigm?), meaning rules of word and sentence construction, which in turn limit the vocabulary, the paradigm, the logic within the paradigm, and the grammar and syntax of statements, sentences, paragraphs, arguments, stories and ever increasing stories within the paradigm.
And Speech itself consists of a hierarchical repetition of increasing complexity:
|Speech| Word > Phrase > Clause > Sentence(Subject + Predicate=Story) > Paragraph(story) > Grammar of Science > Grammar of Narrative > Grammar of Stories(Story) > Grammar of Story > Story, “all the way up”.Organizing Language
So we can organize (or rather we have no choice but to organize) something like a hierarchy such as:
1 – Universal Grammar: recursively limited differences, similarities in all available dimensions.
7 – Idioms and expletives etc.
Anglo Analytic deflationary and scientific as a reformation of law versus continental conflationary and philosophical as a reformation of religion.
Deflationary Literature Markets versus Conflationary Literature Monopolies
( … )
Meaning (Grammars of Meaning?)
THE ART OF SUGGESTION
The Two Faces of Suggestion
( … )
The transfer of knowledge is dependent upon at least ten “supply demand” curves. Such that the contract (exchange) of knowledge is a function of the costs involved in an exchange. In other words, some communication is low cost and some is worthwhile, and some is very costly, and some is prohibitively costly, and some is simply impossible no matter what is done. So transfer of knowledge is one of the most complex human endeavors in no small part because of high causal density with diverse means of increasing costs.
|LEARNING| Learns through inference (145+) < Learns through Suggestion(135+) < Learns through Illustration (125+) < Learns through Explanation (115+) < Learns through Teaching (105+) < Learns through Training (95+) < Learns through Immersion (85+) < Learning challenged (85-)
ie: Cost—>+
This (large) set of causal relations, illustrates the difficulty in the range of communication problems Suggesting > Communicating(illustrate) > Explaining > Teaching > Training(Repetition). And illustrates why it’s simply false to say that if one cannot understand it, one cannot explain it. Instead, it is, that all other causal axis being equal, one should be able to explain a phenomenon to a peer. But as the difference in peerage increases the problem of communication even if all participants are intellectually honest
The Grammars
We use different words for pretentious purposes – largely we don’t know better. So let’s clear up the difference between a religion, an ideology, a philosophy, a logic and a science.
The NARRATIVES
(STORY/CHANGE IN STATE/TRANSACTION)
|NARRATIVE(Story)| Name > Change in State > Description > History (Recipe) > Idealism(Substitution) > Fiction(suggestion) > Myth > Supernatural > Occult > Free Association.WarfareWar is a scientific not emotional process. It is only the men at the bottom who need inspiration. And it is the foot-soldier at the bottom whose tenacity most determines a battle. So the relationship between the top and the bottom is necessary, and this is why non-martial polities cannot compete with martial polities – we fight together even if we conceptualize differently.
Wisdom Literature
(… )
Religion
A Religion provides mindfulness – which is increasingly necessary outside of the simplicity of tribal life of hunter gatherers. Mindfulness increases trust and our ability to cooperate peacefully in larger and larger numbers. A religion provides not only decidability on social interactions, but mindfulness so that we can cope with stresses of all kinds in an increasingly uncertain world. A religion relies on an internally coherent set of rules, myths, rituals, and festivals, but its neither logical nor empirical.
Mythology
( … )
Doctrines (Laws)
( … )
Oath
( … )
Costs (Rituals)
( … )
Feast
( … )
Festivals
( … )
– A RELIGION consists of any set of ideas of justification which require belief in, testimony to, or action according to, one or more falsehoods as a cost of inclusion and use.
1) A religion consists of a set of myths and rules the purpose of which is to resist outsiders, and to set limits on behavior or to be treated as an outsider and deprived of opportunity and insurance of the in-group. Hence most religions evolve with the weak, who have no means of competition except resistance and exclusion.
Theology
Belief
A Belief, or a Set of Beliefs provides an individual or group with a strategy for achieving personal objectives, a set of methods of decidability, and a moral defense (rationalization ) for our behavior if we are criticized.
Mythology
(…) Myth – (INTERTEMPORAL) Wisdom Literature (in my opinion the proper forum for teaching wisdom) – Inflationary vocabulary, grammar, and reality.
Ideology
An Ideology provides an emotional incentive to act in favor of political change under democracy. An ideology provides political decidability for interest groups. An ideology relies upon correspondence with a prejudice, shared by a group with self-perceived common interests. It need not be either rational nor empirical, since the purpose of ideology, like religion, is to make logical and empirical criticism impossible – or at least too costly to prosecute.
– AN IDEOLOGY consist of any set of ideas that agitate, motivate, or inspire achievement of political ends under majoritarian (monopoly) democracy. An ideology need not be internally consistent externally correspondent, or existentially possible. It need only motivate individuals to act in furtherance of policy.
2) An ideology consists of a set of ideas the purpose of which is to excite subclasses to act under democracy to obtain political power. Ideologies are used to obtain followers. Likewise followers, follow ideologies. Hence most ideologies if not all ideologies are lower and working class ideologies, and most followers from the lower and working classes.
Philosophy
3) A philosophical system provides criteria for making judgments in the pursuit of preferences. Philosophies are used to obtain peers. Likewise peers seek philosophies with which to pursue preferences together with their peers. hence all philosophies are class philosophies, and most philosophies are middle class philosophies.
A Philosophy provides a coherent JUSTIFICATIONARY system of decidability within a domain of interest. Philosophy relies upon tests of internal consistency we call logical grammars. A Philosophy need be internally consistent, non contradictory, coherent, even if only marginally correspondent to reality. A philosophy answers the questions of preference and good.
In practice it is very hard to claim that philosophy has practiced the pursuit of truth. (more harm appears to have been done by novelists, philosophers an prophets than good, and more good by historians and scientists than harm. We can easily claim that philosophy has practiced the pursuit of choice and decidability. But if we claim philosophy has sought to produce truth we would have a harder time demarcating between science and philosophy. And my understanding of the point of demarcation between science and philosophy is the difference between choice and decidability – or rather the preferable and the good versus the true.
And as you will discover, my understanding is that the velocity of human existential transcendence – meaning the development of human agency both physical, emotional, and intellectual, and both individual and cooperative – is dependent upon the difference between the decidable truth and the practiced falsehoods.
As such I separate the grammars, from the operations, from the testimonies, from the fictions. Meaning that I separate logical grammars of testimony, from operational recipes such as the sciences, from wisdom literature such as histories, from the literature of persuasion and conflict we call philosophies, fictions, and religions.
In this sense while I have combined philosophy, law, science, logic, and grammar into a single commensurable language, you will find that I frequently criticize those who have done all the damage to this world, with little contribution to the good of it. And in that sense I will come across as an anti-philosopher of sorts who has appropriated some of the content of philosophy while excoriating vast categories of it, as dishonest, manipulative, and harmful to man.
– A PHILOSOPHY consists of any set of internally consistent ideas of decidability which justify pursuit of personal preferences or group goods.
And so:
If we define philosophy (positive and literary) as the search for methods of decidability within a domain of preference, and
If we define truth (negative and descriptive) as the search for methods of decidability across all domains regardless of preference.
Then:
We find that positive or literary philosophy(fiction or philosophy) informs, suggestsopportunities, and justifies preferences for the purpose of forming cooperation and alliances between individuals and groups.
We find that negative or juridical philosophy(truth or law) decides, states limits, and discounts preferences, for the purpose of resolving conflicts between individuals and groups.
The Natural Law of Reciprocity, is a negative, descriptive, juridical science, not a fictional literature.
Literature
A Fiction (Story)
Now, you wouldn’t assume that there exists a formal grammar to the structure of narratives but there is. And it consists of just ‘changes in state, all the way up.’ Just as reality consists of changes in state of dimensions.
And if we look at Fiction (Stories) we see many permutations of changes in state: nothing more than sequences of changes in state. (re: Vonnegut). And only three endings: Happy, Unhappy, and Tragedy.
|ENDINGS| Happy > Unhappy > Tragedy
And only six paths to combine to achieve those endings:
1) “Rags to Riches” (rise – a rise in happiness),
2) “Tragedy”, or “riches to rags” (fall – a fall in happiness),
3) “Man in a hole” (fall–rise),
4) “Icarus” (rise–fall),
5) “Cinderella” (rise–fall–rise)
6) “Oedipus” (fall–rise–fall)
|PLOTS | Fall-Rise-Fall < Fall-Rise < Fall < |STATE| > Rise > Rise-Fall > Rise-Fall-Rise.
And a number of ( … )
So our language consists of not much more than the names (references) and changes in state of some set of marginally indifferent constant relations, using some combination of physical, emotional, and intellectual senses.
And we can create increasingly complex words that themselves constitute micro-paradigms. And in doing so weave together extraordinarily complex sets of categories, relations, changes in state – where one of those changes in state is our ‘value’ – generally expressed as an emotional response.
A History
SPEECH
A Story
A Chapter
A Sentence
A Phrase
A Word
A Sound
A Narrative (Story, Recipe)
A Description (Story) Present
A Testimony (story) past.
A Narration
( … )
A Description
( … )
Testimony
A Testimony provides a warranty of due diligence against ignorance, error, bias, wishful thinking, suggestion, obscurantism, Fictionalism, and deceit. A testimony answers questions of liability against falsehood.
Only sentient beings can make truth claims because only sentient beings can give testimony.
All truth claims can and must exist as testimony.
A truth claim can be false (disagreeable)
Testimonial or Complete Science – operationalism.
Ordinary Language
( … )
Traditions
A Traditional OrderofHabits (or group evolutionary strategy) provides a group with an evolutionary strategy necessary for survival and in the world and competition against others with different strategies. They consist at least, in a portfolio of metaphysical value judgments and carriers (users) of these habits rarely if ever understand or are even aware of, alternatives to these prejudices.
Norms
A Normative Order of Habits provides a group with means of preserving the traditional order within the current demographic, social, economic, political, and military context. This set of habits need not be understood, coherent, rationally articulated but merely practiced. They consist, at least, in manners, ethics, morals, and laws.
– MARKET, TRADITION, NORM, HABIT consist of … (Demonstrated results…)
Laws: Commands, Legislations
5) A legal system provides a means of resolving differences so that a group can cooperate in the production of generations, goods and services. Legal systems are used to rule others. But require strength to enforce. Hence most legal systems are the product of the upper classes that rule by force, and make use of scientific, philosophical, ideological, and religious systems to speak to classes while ruling them with law and violence.
Natural Law
( … )
(Record of conflicts settled…)
– NATURAL LAW of RECIPROCITY (Tort), was produced scientifically (empirically) by trial and error, through the resolution of disputes across personal preferences, group goods, norms, traditions, and intuitions, cumulating always and everywhere that decidability is provided by property, and property consists in the demonstrated investment of human action or inaction anything whether genetic, material, behavioral, or informational.
A Discipline or Field of Study (Network of Paradigms)
4) A scientific system provides for making truthful (true) statements for the description of operations (transformations instate). Scientific systems are used to decide, create, invent, and to provide power over nature and man. Hence, science . Hence science is a largely professional or upper middle class philosophy.
A specialization in the division of labor in the market for the production of knowledge. (usually a difference in operations and scale)
A Demonstration (reality)
A Recipe (protocol…)
An Action
An Input, Output
Science
A Paradigm in Science or ‘-ism’ in Philosophy, provides a system of decidability in an area of exploration, investigation, and research. Either a network of theories or justifications that are used to make decisions in pursuit of research. Wherever possible I choose the scientific term because it is less likely to have been inflated and conflated. And I have chosen the term paradigm for that reason.
An Hypothesis
A Theory(Story, Opportunity, Search Algorithm) – A Test (Warranty) against Impossibility
A theory of possibility by falsification
A Law
Science, Physical Science, or Empiricism (deflation) of imagination, but absent operations.
(Search for Laws(avgs) and Operations(causes))
A Science provides a CRITICAL means of decidability across all domains regardless of convention, interest or preference (Philosophy, Norm, Religion, or Ideology). A Science relies in the very least, upon tests of:
Categorical consistency, i.e. all differences
Internal (logical) consistency, i.e. all logics (Deflationary Grammars)
External (empirical) consistency, and (Correlative)
Existential (operational) consistency,
Under Propertarianism (Testimonialism) it must also include tests of
Rational consistency (rational choice), and
Reciprocal consistency (reciprocity of rational choice).
And we require limits.
Scope consistency (full accounting),
Parsimony (Deflation), and
Commensurable Consistency(Coherence).
– A SCIENCE consists of any set of ideas that provide decidability independent of personal preference or group goods, by the systematic elimination of ignorance, error, bias, wishful thinking, suggestion, obscurantism, Fictionalism, and deceit, by the use of measurement and record of actions – demonstrations versus words.
Algorithms, Accounting, Mathematics, and Logic
Algorithms (Processes)
A Simulation (program)
An Algorithm (Procedure)
A Calculation (transformation of inputs into outputs) but with deduction.
Accounting (Transactions)
A Balance Sheet
An Income Statement
A General Ledger
A Ledger
A Journal
An Entry
An inventory item.
Mathematics (Measurements)
A Model (mathematic)
A Computation (lacking deduction) (information is closed)
A Formula
– MATHEMATICS consists of a deflationary grammar of decidability consisting purely of competition between positional names under the preservation of ratios providing a single axis of decidability: position, but in N dimensions, providing commensurability between any set of positional relations of any number of dimensions.
The Logics (words)
A Proposition
An Axiom
A Statement
A Proof (Operations, Cost, Recipe) – A Test (Warranty) of Possibility
A proof of possibility by construction.
( … )
A proof of internal consistency
( … )
– A LOGIC consists of any deflationary grammar of decidability that assists in the falsification by competition of one or more constant relations between states. (Note that one proves nothing logically other than internal consistency, because all premises of external correspondence are forever contingent.)
The Logics. We use the word logic ‘loosely’, I have to get across the difference between the multiple uses of the term:
The Rationalisms (Justificationisms)
A Justification
A Statement
An Argument
Rationalism is often contrasted with empiricism.
The empiricist view holds that all ideas come to us a posterior through experience; either through the external senses or through such inner sensations as pain and gratification. The empiricist essentially believes that knowledge is based on or derived directly from experience.
The rationalist believes we come to knowledge a priori – through the use of logic – and is thus independent of sensory experience.
Rationalism consists of adopting one of these three claims
The Intuition/Deduction Thesis,
The Innate Knowledge Thesis, or
The Innate Concept Thesis.
In addition, rationalists can choose to adopt the claims of Indispensability of Reason and or the Superiority of Reason – although one can be a rationalist without adopting either thesis.
Logic (formal grammar of decidability) Logic, via-positiva, consists of the use of deflation, organization, and competition to test the survivability of statements) which ( scientifically), consists in the preservation of constant relations in the differences in dimensions available to human action, perception, and experience. Those constant relations are possible because of a deterministic (non-random) universe – at least at various scales. Conversely, via-negativa, we can say that the function of logic is to eliminate ignorance, error, bias, assumption of knowledge, wishful thinking, suggestion, obscurantism, and deceit from our free associations.
Which I’m sure is a mouthful.
A logic requires at least:
The assumption of deterministic Universe (constant relations) within the scope(limits) of the context.
Constant Referents (Names)
A competition between the properties, relation and values two or more referents.
Preservation of Constant relations by grammar
Commensurability (or network of commensurability) of referents
Transformation Operators
Comparison operators
At least ternary logic || Incomparable > Undecidable > Contingent > True(not false) > False (highest certainty is falsehood)
For proofs, only Binary Logic: Unknown or False > True for purpose of deduction. Note that falsehood has greater certainty than truth.
Arbitrary(Normative) or Descriptive(Necessary)?
Is a logic – a means of preserving constant relations – Axiomatic and Arbitrary in a Meaningful Paradigm,? Or is it Natural Law and Correspondent in an Existential Paradigm?
If descriptive, what dimensions of reality can we identify?
Logic of Differences (logic proper)
Logic of Categories of Constant Relations (cumulative differences) (identity)
Logic of Constant Positional Relations (mathematics)
Logic of Physical (Natural) Operations (changes in state/time)
Logic (Operations) of Physical Human Action
Logic (Operations) of Incentives using Property in Toto
Logic (Operations) of Cooperation using Reciprocity
Logic (Operations) of Contingent Relations(Language)
Logic (Operations) Of Testimony given all of the above. (coherence, scope, limits, parsimony)
A Formal Logic. (I’m going to define formal logic as a dimensionally limited grammar – a grammar which limits vocabulary by limiting semantics).
Formallogic consists of the study of inference with purely formal content. An inference possesses a purely formal content if it can be expressed as a particular application of a wholly abstract rule, that is, a rule that is not about any particular thing or property. In many definitions of logic, logical inference and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuances of natural language.
We can identify at least two uses of formal logic:
The construction of discursive proof (or possibility of construction) or disproof about the world using the logic of internal consistency through exclusive reliance on argumentative closure. Mathematics, Law, and Norms rely upon justificationary reasoning. (Science, like evolution, does not. It relies on survivability whether we can explain the causes or not).
Philosophical Logic, Rationalism or Justificationism: The use of Textualism (interpretation) for the interpretation of scripture and law (Pilpul, Interpretation). Generally the attempt at closure rather than appeal to the next higher dimension where there is more information. Non contradiction can be seen as a variation of the liar’s paradox.
To interpret legal precedent or legislation without return to the legislature or judge of record – in which case, again, the construction of said sentences constituted a failure of the authors to produce grammatically complete sentences – or the attempt by prosecutor, defense, and judge to create new law.
To interpret Scripture or other Wisdom Literature under the pretext that it consists of law, history, or science, or any kind of truth – in which case, like interpreting the law, we see only a failure of the authors to produce grammatically complete sentences, open to current knowledge, and we seek to create what is not there.
To construct deceptions by appeals to authority by making use of the ignorance of the audience, the malice of the interpreter, and, once again, the failure of the authors to produce grammatically complete sentences (and paragraphs).
Much of our time will be spent falsifying and replacing the ….
Symboliclogic consists of the study of symbolic abstractions that capture the formal features of logical inference. Symbolic logic is often divided into two main branches: propositional logic and predicate logic. We can think of modal and propositional logic as …..Mathematicallogic consists in of extension of symbolic logic into other areas, in particular to the study of model theory, proof theory, set theory, and recursion theory.”—A Turing, Programmatic, or Algorithmic Logic: The addition of control structure differentiates programmatic logic from mathematical logic. As a consequence the problem of closure increases by the addition of the halting problem.
Logic of Language: The study of the rules of language, the rules of logic and the rules of grammar, and how grammar and syntax function to produce logical statements for the simple reason that what we think of as logic – differences, within a sentence – is reasonably intuitive to us, even if that logic fails us in the comprehension of arguments (and deceits).
Syntax is the study of sentences and their structure, and the constructions within sentences. Syntax tells us what goes where in a sentence. Grammar is the general term referring to the set of rules in a given language including syntax , morphology, phonology, while syntax studies sentence structures.
My preference would be to improve clarity, by redefining grammar as phonology(sounds) and morphology (words), and Syntax for Sentences. So that I could speak of Vocabulary and Syntax. (hmmm….) Because a language consists of vocabulary consisting of morphology and phonology, organized into sentences through syntax. (hmmm….)
Modal Logic – we can think of as the symbolic logic of grammar – qualification or refinement. I think of it as the logic of verb properties.To discover the operations and therefore universal grammar of human beings through analysis of language. In this sense, the study of such grammars constitutes an investigatory cognitive science.
I rely on cognitive science, (neural networks and the structure of the brain) for most of my work. And so I see logic as nothing more than our ability to determine differences. But when those differences are organized into a language we develop this wonderful thing called grammar: the organization of the flow of information between individuals according to predictable rules.
Language is an interesting problem because it’s serialized and very parsimonious and informationally dense, even if it can easily informationally imprecise, ranging from burdensome low context and high precision, to lazy high context and low precision. Yet our minds produce a continuous stream of possibilities that we must transform into that which can be communicated serially in speech.
Investigation of the brain: The use of language to study of cognitive ability of the human brain – and perhaps all brains, given the vocabulary, and the grammatical and syntactical rules the speaker is capable of.
Investigation of reality: The use of language, including semantics (meaning), vocabulary , grammar, phonology, morphology and syntax to investigate reality. This is the ‘verbal’ and primacy of reason strategy. And it is in contrast with the scientific and engineering investigation of reality, by investigation of actions.
As we will see later on when we discuss the table of grammars, the various disciplines all have produced deflated vocabularies, deflationary grammar, and syntax that identifiably if not predictably reflect reality. Conversely, there exist some disciplines that reflect only fictions. And not surprisingly, those fictions exist largely in the pseudosciences we refer to as social science. So as an empirical judgment it is very hard to suggest that these grammars are fictional or arbitrary, and very difficult to deny that our language – at least Germanic languages – reflect and therefore allow us to represent the various dimensions of reality.
As a side note, I was fairly hostile to the philosophy of language producing any result until I’d read kripke. And I have found that language does reflect reality – because cognitive science, analysis of language, and physical science have shown me so. But because I am principally concerned with the elimination of error, bias, and especially deceit, leaving us only truthful voluntary cooperation and exchange, I remain hostile to it for empirical reasons. Which is the next topic (empirical differences).
Empirical difference between the two …..
Informal Logic: The use of Vocabulary, Grammar, Logic(Logic Cognitive Bias, and Fallacy), Correspondence, Ethics, Morality and Rhetoric for the production and falsification of arguments.
–“Informallogic is the study of natural language arguments. The study of fallacies is an important branch of informal logic. Since much informal argument is not strictly speaking deductive – on some conceptions of logic, informal logic is not logic at all.”—
Type
Situation
Arguers’ Goal
Dialogue Goal
Discovery
Need for Explanation
Find a Hypothesis
Test a Hypo-
thesis
Information
Need Information
Acquire Info
Exchange Info
Education
Transfer Info
Shared Understanding
Justification
Need to Have Proof
Verify Evidence
Prove Hypothesis
Deliberation
Practical Choice
Fit Goals and Actions
Decide Action
Persuasion
Conflict of Opinion
Persuade Other Party
Resolve Issue
Negotiation
Search for common Interests
Secure Interests
Settle Issue
Prosecution
Conflict in Fact
Expose the other Party
Cessation, Punishment or restitution
Testimony
Warranty of Due Diligence against conflict
Obtain and preserve unearned premium or discount
Elimination of retaliation, punishment, restitution via truth
Deception
Reciprocity, Conflict, Punishment Avoidance
Fraud
Deceive via falsehood
Distribution
Undermine Opponents interests
Poisoning the well
Opportunity for increase in conflict
Eristic
Avoid argument
Attack an Opponent, or interests
Preserve Conflict
Table 1 Table of Dialog Conditions and Goals
Closure
The Problem of Closure: There Isn’t Any.
Closure. Close or Not Closed (Open). The question of closure. Given a set S, grammar G, and set of operations O, all operations O in that grammar G, upon that set S, will produce a member of that set S in grammar G. In formal logic, it refers to that output set that can be deduced from the given input set. For reasons I won’t go into here, very few systems of operations and values are closed. In fact, only the most reductive (simple) systems can be.
Closure is important for at least these six reasons.
that arguments or proofs in any simple system (sets, grammar, and operations) must be solved by appeal to a containing system (sets, grammar, and operations) – or rather system using more information than available in the current system. You will see me use the problem of closure to explain testimonial truth, and to undermine philosophical rationalism, just as we have undermined theological rationalism.
That closure creates one form of symmetry (shape), but that all sets of operations on all sets produce symmetries because of the variations in the sets, and variations in the possible combinations of operations.
Language is not closed. I hate this non operational term, but “discrete infinity” refers to the property of such things as language to produce an infinite set of discrete sound combinations – at least within sets of paradigmatic assumptions about the world.
That the mind is able to identify symmetries, and produce paradigms, of ever increasing scales, as long as those scales are reducible – even if thru training – to an analogy to experience that are commensurable within our senses, and where we can compare differences and therefore make decisions with.
As such while the set of operations possible within the physical universe is limited, there is no limit to what man can understand through the creating of disciplines (paradigms) of commensurability.
And the principle problem in our development is limiting the difference between our cognitive biases and the state of our knowledge, and those symmetry’s for which we can produce paradigms that are possible and or useful within the universe. But otherwise our ability to understand and manipulate the universe is limited only by our ability to develop means of harnessing the energy to take actions that produce transformations.
Knowledge is never closed because of the cognitive window of action at any given scale of knowledge. As such, Language is never closed. It may be true that we can know the full set of operations possible in the existing universe at each cumulative scale. But, assuming we possess the ability to harness increasing scales of energy, then what we might be able to construct in this universe through though physical, intuitionistic, rational, calculative, and computational means is …. As far as I can tell, not closed.
What is closed, and what is measurable, is the information necessary to cause change in state in the human mind. I am not quite sure, but Nassim Taleb seems to have been struggling to discover this value, although, like me, he has finally come around to warranty rather than measurement – and I think the search is futile at any scale other than the one he has already produced (meaning, logarithmic or big, and therefore economically impossible) if for no other reason than the information sets available to us are not sufficient. Yet when we develop general artificial intelligence we will develop some measure or other of that information. If I had another life to live I might work on that problem. It’s interesting.
So while the volume of information necessary for humans to identify opportunities for changes in state may remain constant, the use of increasingly complex concepts preserves that ability regardless of scale. More on this later.
As such, it is not clear that we will experience any ‘limit’ to cognition as long as – like every other scale of the universe – new symmetries (meaning objects of consideration) never cease to emerge.
THE PATTERN
Fields, Symmetries, and Generations
Given a six sided die, and the single operation “roll the die”, we can produce a noisy distribution of :
1(x1), 2(x1), 3(x1), 4(x1), 5(x1), 6(x1).
Given two six sided dice, and the single operation “roll the dice and sum the results”, we can produce a noisy distribution of:
2(x1), 3(x2), 4(x3), 5(x4), 6(x5), 7(x6), 8(x5), 9(x4),
10(x3), 11(x2), 12(x1).
The difference between the one-die and two-die distributions is that while the results of rolling one die are equidistributed between 1 and 6, with two dice the results of rolling can produce more combinations that sum to 7 than there are that sum to 2 and 12, and therefor the results are normally distributed: in a bell curve.
We can produce the same results with logic instead of numbers: For example, we can take the two words “Even” and “Odd”, and define two operations: “addition” and “multiplication”. Then apply the operations to all pairs:
Even + Even = Even,
Even + Odd = Odd + Even = Odd,
Odd + Odd = Even,
Even x Even = Even x Odd = Odd x Even = Even,
Odd x Odd = Odd.
(… geometric, scalar vectors … from every point, infinite points….)
And we can produce the same set of results with any grammatically correct operations on a set, given the operations possible on the set; including the set of Ordinary Language using ordinary language grammar. Although, unlike our simple examples using dice, the set of combinations of ordinary language is not closed, and so the number of combinations is infinite.
So any grammar applied to a set, allows us to produce a distribution of results, and a density (frequency) of results.
In mathematics this result set is called a ‘field’. A field consists of all the possible results of a set of operations on a set’s members, that are selected from the range of possible operations on those set members.
So in any set of results there will be a range of very dense, less dense, sparse, and empty spaces in the set’s distribution.
Constructability
Now those ‘holes’ in the distribution are notconstructible with the set and operations available to us. So, not everything can be described using the set with the available operations in every grammar. Conversely, we can create a set of operations describing those symmetries (patterns), whether we are referring to holes or densities.
There are things we cannot say then. But by and large, nearly anything we can say that consists of constant relations between existence, perception, cognition, and action, is possible to say – if we possess the knowledge. And conversely: that which does not consist of constant relations between existence, perception, cognition, and action can be said but not said constructively: meaning operationally. So that is why people resort to those terms that are not operational: to compensate for your lack of knowledge, to compensate for their lack of knowledge, to levy pretense of knowledge when they do not possess it, or to deceive despite possessing that knowledge.
Deducibility
|Estimating| Description > Deduction > Induction > Abduction > Guessing > Free Association.
In fact, the virtue of fields is that they assist us in finding those symmetries – albeit with a lot of work. That’s because some results are neither constructible or deducible from a construction, except by via-negativa trial and error.
(Limits of Deduction)
Symmetries as Externalities
In most if not all of these sets, we will discover symmetries (patterns), including patterns of density and patterns of emptiness, and then patterns of relations between those patterns.
These holes and densities consist of the consequences of the operations we performed on the set of references we’ve chosen. So, for example, when we make purchases with money, and observe the resulting financial and economic data, there are patterns within the consequences of the operation we call ‘exchange’ of the set ‘goods and services’. Those consequences appear as patterns in the financial and economic data – as a pattern of holes, distributions, and densities, that we call price, volume, profit, and loss.
And so for the sake of discussion, I’m going to adopt the term externalities from the discipline of economics to describe those unintended or accidental patterns that emerge from the operations we call ‘transactions’ on the set of ‘goods, services and information’. Meaning that Externalities consist of Symmetries produced by our economic cooperation.
It’s these externalities (for example, losses, and profits) that as a consequence determine the behavior of businesses, then industries, then markets – not the individual transactions.
The Natural World: Generations of Operations
At this moment we do not yet understand the fundamental Forces of the universe. But we have discovered a set of the fundamental Particles that those forces produce. And, of those particles that have mass, we have a fairly deep understanding of the Elements (Matter) in the periodic table of elements, that those particles that have mass produce. We have at least scratched the surface of the Molecules that those elements can combine produce. We have barely scratched the surface of the Organic Molecules that those elements can produce. We have only recently begun to understand how those molecules construct organs of Life. We increasingly understand how RNA and DNA construct life forms, although the complexity of that process is so vast that we can spot only correlations not yet operations. It is questionable how much we understand of sentience and consciousness or speech processing, but an understanding of reason, calculation and computation are available through introspection.
Universe > Forces > Particles > Elements > Molecules > Organic Molecules > Life(cells) > Sentience > Consciousness > Speech > Reason > Calculation > Computation
And
Assumptions (Metaphysics) > Psychology (Acquisition) > Sociology(Cooperation) > ( Norms > Traditions > Laws) > Markets > Informal Institutions > Politics(formal institutions) > Education(Religion) > Group Strategy(War)
At each stage of complexity, some set of possible operations produces potentials (densities) for yet another set of possible operations, as well as weaker distributions and holes that do not provide opportunities for yet another set of operations. So for the sake of our discussion we’re going to refer to each stage as an Operational Generation.
Operational Generations as Disciplines
The various Sciences (disciplines) mirror these Operational Generations. Each discipline seeks to discover the operations and sets (objects, states) that complete the grammar of the discipline. (Categories, properties, relations, values, and Operations, and Externalities (Symmetries)).
Commensurability Across Grammars
Unfortunately, some of these disciplines are very old – like mathematics – and some are quite new – like genetics. Some are fairly scientific (chemistry most of all) and some are merely storytelling if not outright deceits (psychology and sociology). In mathematics we find archaic (supernatural) terms left over from Mathematical Platonism. In the sciences we use awkward non-operational names for phenomenon and processes – often peoples names. In economics we use the term ‘rents and rent-seeking’ for what is a form of parasitism or corruption. In psychology and sociology the terms are by and large no better than fairy tale fictions with no basis in science whatsoever.
By converting the terminology in each discipline to purely operational prose, we create commensurability across disciplines. And with that commensurability we can rapidly improve the ease of learning them. We can identify that which they claim to understand but do not. And identify what they claim that is outright false.
OPERATIONAL GRAMMAR
Operational grammar leaves holes.
Operations
Language
Continuous recursive disambiguation resulting in a series of transactions, culminating in a contract for meaning.
Convergence
In this era, as in prior eras, the world has been converging on common weights and measures: the common languages of science, of technology, of business, of contract of accounting rules, a common trade law – at least at the international level of cooperation. The current financial system of fiat money, central banks, and reserves, allows relative commensurability of worldwide trade.
However, those convergences tend to occur both within and across commercial and legal fields, but only within fields – thereby preserving incommensurability of language across all fields. And within fields they converge on old habits that preserve obscurant language.
SOME OF OUR MODELS ARE WRONG:
THEY ARE DISCONTIGUOUS WITH REALITY
Metaphysics
Logic
MathematicsPsychology (acquisitionism)Sociology (propertarianism)Economics Law (Natural law of reciprocity)Politics (the production of commons)Strategy (group competitive strategy)Religion ( production of commensurability)
EXPLANATION
Current knowledge ….. my understanding…..
Constant vs contingent vs inconsistent vs non-relations.
Recursive Continuous Disambiguation vs Scale of Set of Constant Relations(density)
Cumulation of association vs falsification of associations
Computational efficiency.
State Persistence vs breadth search, vs depth search
We cannot know the intelligence of distant ancestors.
Planning a series of steps in sequence must emerge – which requires recursion.
Consciousness must emerge, meaning, the ability to compare states.
Cooperation must emerge, meaning, the ability to empathize with intent.
At some point we must develop sufficient computational ability to manipulate our bodies in some way that allows for unambiguous communication, or a means of continuous disambiguation, that is fast enough for one another to make use of in real time, and easy enough for one another to retain.
And at some point, given sufficient computational ability, memory, and state persistence independent of recursion, language must emerge.
At some point the value of such communication much be such that the cost of it is offset by the rewards of it.
And we should see a cliff in history where there is a dramatic change when we did develop those abilities. And we do see it – rather recently.
But language requires a system of measurement. The system of measurement is limited by our senses. And as such meaning refers to a set of measurements, eventually reducible to analogies to human experience.
So while semantic content (measurements) must vary from species to species, grammar (continuous recursive disambiguation) should be universal in the sense that it varies predictably with computational abilities.
We can understand a child, a person with 60IQ, 70IQ and so on, up to 200+ IQ. But as far as I can tell the set of measurements (basis of semantics) remain the same, and all that changes is the scope of the state persisted, the depth of recursion, and the density and distance of relations, and the ability to model (forecast). In other words, simple people are in fact simply ‘more simple’ in the density of content of their semantics, use of grammar, and models (Stories) that they can construct with them.
So universal grammar as a set of computational minimums and efficiencies, should always exist, and human universal grammar as universal grammar limited to human measurements (semantics), does exist. And any organism with sufficient computational (neural) capacity, should develop some means of communication using some variation of universal grammar, and some sense-perception – action dependent semantics.
Now that we have completed our journey through creating Dimensions of Decidability using Deflation, Operationalization, Serialization, and Competition, we can:
Discover and enumerate the Dimensions extant in our Language.
Discover how those dimensions can be combined into Grammars of Decidability.
Discover how those grammars can be organized into a spectrum that covers every niche of human communication from physical, perceptual, emotional, intellectual, and imaginary – as well as deception.
Discover that our set of grammars illustrate a hierarchy of patterns in the physical universe – and that our understanding of that pattern and our grammars are very nearly complete.
Discover that our Language consists of :
Continuous Recursive Disambiguation in Real Time (Serial Speech)
Using Some Set of Analogies to Experience (Words)
Resulting in Transactions (Sentences)
That produce Contracts for Meaning (Stories)
Within some Set of Dimensions (Physical, Experiential, Imaginary)
And that opportunity for Deception (Frauds, Fictions, Fictionalisms) is ever-present.
But by limiting our speech (prose) to Operational Grammar ( using constant relations between reality, perceptions, cognition, actions, and consequences), or what we traditionally call “Testimony”, all statements are both objectively and subjectively testable, thereby providing extremely limited opportunity for error, bias, and deceit.
And by performing Due Diligence, for consistency, correspondence, existential possibility, rationality of choice, reciprocity, completeness and coherence;
We force a Competition for Coherence by which we expose our ignorance and can Warranty our speech is as free of error, bias, and deceit as is possible given our current language knowledge.
Geometry of Decidability
(…)
(the via negativa pzzle pcs)
Dimensions Present in our Vocabulary
Next, we can examine our vocabulary and organize the terms into a series of categories.
|WORD| > Name(Noun) > Action(Verb) > Relations > Agreements > Noise Words > Code Words.
And within each category of word we find multiple dimensions.
|Name(Noun)| : Proper(Person > Thing > Place > Idea > Perception(sense) > Emotion(value)) > Common (categorical) > Compound > Pronoun > Clarifier (Determiner/Measure) > Property(adjective) >
|State| State > Event > Action > Experience > Thought
|Person| First > Second > Third > Abstract
|Gender| Female < Young Female < Neutral > Young Male > Male.
|Possession|- Possession (‘s – “apostrophe s” in English) (“Can Own”) > (“Can be owned”) > (Cannot be owned”)
|Temporality| Always Been > Has been > is Currently > Will Be > Will Always Be.
|Gain or Loss| Gain < Neutral > Loss
|Decidability| Incommensurable > Undecidable > Preferable > Good > True.
|Relations| Relation (Preposition/Postposition) > Link (Conjunction > Copula ) >
|Agreements| Agreement(yes-no) >
|Noise Words| Noise Words(Expletives etc.) >
|Code Words| code-words(acronyms etc.)What Can We Learn From Those Dimensions?
A great deal:
Limited Scales Measurement: We tend to consider only a scale of five, in any dimension which mirrors the accuracy of survey responses: a 1-5 scale is about as accurate as one can get, with 1-3 1-5, 1-7 appearing frequently and with a 1-10 scale ratings always reducible to a 1-5 scale with finer graduation to the high end and lower granulation to the low end. This 3,5,7 scale shows up in nearly all aspects of cognition, such as the number of objects we can independently visualize or numbers one can recall. Usually in the seven plus or minus two range.
Limited Dimensions To Describe References: There are about as many dimensions in both nouns and verbs: seven. While there are about fourteen dimensions between nouns and verbs, the only complex relationships are:
State
Perception (Experience)
Relations
But these three sets provide a large set of sensory dimensions for describing our references.
State, Perception, and Relation function as Weights and Measures: ( … )
Dimensions of Negotiation: Other than Perception and Relations, the number of dimensions is surprisingly small. And nearly all can be categorized as necessities of
Negotiation and
Possession, and
Weights and Measures.
Dimensions of Possession: Our language contains an extraordinary dedication of dimensions to possession. Given the dimensions above, please note the following:
Person, Gender, and Possession are dimensions in our Nouns.
Ownership, Permissibility, and Gain or Loss are dimensions in our Verbs.
The degree of Warranty of our meaning is implied not stated.
As we will see later, this emphasis on possession, ownership, and property is necessary for both cooperation and ‘calculation’, and function as the basis of ethics and morality, and our valuation of changes in state of possessions (or interests) the origin of our emotional responses. We are, whether we like it or not, acquisition machines, using language to negotiate cooperation because of the far higher returns on a division of labor than are possibly by individual action.
A Change In Paradigm (Ontology)
Justification an self and knowledge
versus
Contract and others and trade and consent.
Note: For those who have experience with Taxonomies of vocabulary, this categorization is significantly different from Roget’s – and somewhat dehumanizing.
Words: Measurements and Collections of Measurements (Weights and Measures)The Contractual Constitution of Meaning (Words, Phrases, Sentences)The Experiential: The Dimensions of Perception (Experience)
Now, how can we DESCRIBE the universe? With dimensions consisting of constant relations.
Now, we are going to make frequent use of these terms ‘dimension’ and ‘dimensions’. And the most simple constant relation we know of is mathematics: the study of positional relations:
0-Point (Referent)(Identity, anchor referent)(quantity)
1-Line (Distance)(Relations)
2-Area (Ideal)(Sets)
3-Object (Ideal Object) (Space)
4-Time (Velocity) (Change)
5 – N – Pure Relations (Concepts/Categories)
6 – N vs. N’ Relations, (Forces) (Equilibria)
7 – N vs. N’ Intermediate Relations, (Symmetries)
8 – N vs N’ relations between symmetries (Paradigms)
9 – (N vs N’)’ recursive hierarchies of symmetries ad infinitum. (Reality)
And we have mathematical techniques for such dimensions.
0 – Correspondence (referents, identity)
1 – Positional names, Arithmetic, Accounting. (counting)
2 – Mathematics and algebra (Ratios)
3 – Geometry (Space)
4 – Calculus, Finance, Economics. (Change)
5 – Algebraic Geometry (Math of sets of constant relations)
6 – Physics (equilibration)
7 – Lie Groups, (Symmetries, Externalities, Future of Economics)
(8 – Grammars)
(9 – Paradigms) (stories) (Semantics)
(10 – Fictions)
(11 – Ideals )
(12 – Dreams)
And that we have discovered mathematical techniques for the preservation of constant relations in increasing layers of complexity ….
The Dimensions of RelationsDimensions of Meaning: Geometry of Thought, Speech, and Argument
(try to explain)
(how the mathematical dimensions and the verbal dimension and paradigms and stories…. It’s all dimensions)
From any given point, there are an infinite number of vectors.
All thoughts can be represented geometrically.
But like Mandelbrot’s Fractals, they are not calculable by man, only computable by machines.
However, the underlying symmetries (shapes) will be consistent across contexts, for the simple reason that grammars are consistent across contexts (paradigms).
THE DIMENSIONAL GRAMMARS
The Periodic Table Of Speech
|GRAMMARS| Deflationary Grammars < Ordinary Grammars > Inflationary Grammars.Grammars: Overcoming the Problem of Human Scale (necessary because of computational limitations)
Use of external resources to render commensurable that which is beyond our abilities.
Deflationary Grammars (decidable)
Logic of Differences (identity)
The Logic of Continuous Relations, Logic of Sets (categories)
The Logic of Counting: Counting, Arithmetic, Accounting.
The Logic of Positional Relations (measurement): Mathematics (all of it), Equilibrium mathematics (constant relations)
The Logic of Algorithms – Computers, simulations (automation)
The Logic of Transformations: Physics, chemistry, biology, sentience, reason (transformations)
The Logic of Reciprocity, Law, Contract (cooperation) and Economics
The Logic of Science: Science, Reporting, Testimony (testimony)
Ordinary Grammars (practical)
So we can at least include these Ordinary Language grammars.
Formal or Written
Ordinary Conversational (in the commons)
Idiomatic Varies by Region, class, discipline, and occupation.
Inflationary Grammars (meaningful)
Narration
Story (grammar of stories)
Fiction (grammar of fiction)
Deception Grammars (Under, over, and false loading)
Pseudoscience ( conflation of magic and technology)
Psuedo-rationalism (Pilpul and Critique), (Justificationism en Closure)
Pseudo-mythology (conflation of history and myth as well as wisdom and law, as well as real and supernatural)
Occult (experiential Fiction)
The Periodic Table of Grammars
(Poster Size)
Figure 1 The Periodic Table of GrammarsNote: The table is too large for inclusion in this book, in any readable form, but is available online at https://propertarianinstitute.com/grammars where you can download a PDF version, or order a poster online.
Reorganizing Our Categories of Language
Semantics Are Limited by and Subordinate To Grammars
Now Let’s Look at the Rest of Communication
Now, Just as mathematics consists in the study of constant relations, at increasing numbers of dimensions, we can perform the same analysis for all other forms of communication. And we will see how all our grammars are organized by the very same means – the organization of constant relations. And then how some deflate relations, so me preserve relations, some inflate relations, some conflate relations. And as such we will see how we use these various grammars to communicate the entire spectrum of reality from the existential to the imaginary.
Language – all same enough that they reflect a common set of abilities and limits of the human brain. SVO, SOV, VSO, but in all cases we describe states of subjects or changes in states of subjects, and we combine this little stories into ever increasingly complex sentences, paragraphs and stories, and we weave these stories into paradigms and then into networks of paradigms, and those networks of paradigms and stories provide us with context, and that content lessens the computational cost of composing stories, paragraphs, sentences, phrases, and sub-stories consisting of descriptions of state or changes in state – and attach to those stories some value or other. And therefore assist us in making decisions from the most casual and unconscious to the most deliberative and calculative.
Context and Precision: Ordinary language varies from formal, meaning low context and high precision, to common to idiomatic, meaning high context low precision. The lower the precision the higher the context the more suggestion is created by the speaker and the more substitution is required of the audience.
Dialects. Within languages we create Dialects – regional, class, and occupational. These vary in paradigms, vocabulary, values, morphology and phonology, but most often preserve the same syntax: rules of sentence construction.
Across these dialects, and across all languages and dialects, we have produced various technological variations in grammar (paradigm?), meaning rules of word and sentence construction, which in turn limit the vocabulary, the paradigm, the logic within the paradigm, and the grammar and syntax of statements, sentences, paragraphs, arguments, stories and ever increasing stories within the paradigm.
And Speech itself consists of a hierarchical repetition of increasing complexity:
|Speech| Word > Phrase > Clause > Sentence(Subject + Predicate=Story) > Paragraph(story) > Grammar of Science > Grammar of Narrative > Grammar of Stories(Story) > Grammar of Story > Story, “all the way up”.Organizing Language
So we can organize (or rather we have no choice but to organize) something like a hierarchy such as:
1 – Universal Grammar: recursively limited differences, similarities in all available dimensions.
7 – Idioms and expletives etc.
Anglo Analytic deflationary and scientific as a reformation of law versus continental conflationary and philosophical as a reformation of religion.
Deflationary Literature Markets versus Conflationary Literature Monopolies
( … )
Meaning (Grammars of Meaning?)
THE ART OF SUGGESTION
The Two Faces of Suggestion
( … )
The transfer of knowledge is dependent upon at least ten “supply demand” curves. Such that the contract (exchange) of knowledge is a function of the costs involved in an exchange. In other words, some communication is low cost and some is worthwhile, and some is very costly, and some is prohibitively costly, and some is simply impossible no matter what is done. So transfer of knowledge is one of the most complex human endeavors in no small part because of high causal density with diverse means of increasing costs.
|LEARNING| Learns through inference (145+) < Learns through Suggestion(135+) < Learns through Illustration (125+) < Learns through Explanation (115+) < Learns through Teaching (105+) < Learns through Training (95+) < Learns through Immersion (85+) < Learning challenged (85-)
ie: Cost—>+
This (large) set of causal relations, illustrates the difficulty in the range of communication problems Suggesting > Communicating(illustrate) > Explaining > Teaching > Training(Repetition). And illustrates why it’s simply false to say that if one cannot understand it, one cannot explain it. Instead, it is, that all other causal axis being equal, one should be able to explain a phenomenon to a peer. But as the difference in peerage increases the problem of communication even if all participants are intellectually honest
The Grammars
We use different words for pretentious purposes – largely we don’t know better. So let’s clear up the difference between a religion, an ideology, a philosophy, a logic and a science.
The NARRATIVES
(STORY/CHANGE IN STATE/TRANSACTION)
|NARRATIVE(Story)| Name > Change in State > Description > History (Recipe) > Idealism(Substitution) > Fiction(suggestion) > Myth > Supernatural > Occult > Free Association.WarfareWar is a scientific not emotional process. It is only the men at the bottom who need inspiration. And it is the foot-soldier at the bottom whose tenacity most determines a battle. So the relationship between the top and the bottom is necessary, and this is why non-martial polities cannot compete with martial polities – we fight together even if we conceptualize differently.
Wisdom Literature
(… )
Religion
A Religion provides mindfulness – which is increasingly necessary outside of the simplicity of tribal life of hunter gatherers. Mindfulness increases trust and our ability to cooperate peacefully in larger and larger numbers. A religion provides not only decidability on social interactions, but mindfulness so that we can cope with stresses of all kinds in an increasingly uncertain world. A religion relies on an internally coherent set of rules, myths, rituals, and festivals, but its neither logical nor empirical.
Mythology
( … )
Doctrines (Laws)
( … )
Oath
( … )
Costs (Rituals)
( … )
Feast
( … )
Festivals
( … )
– A RELIGION consists of any set of ideas of justification which require belief in, testimony to, or action according to, one or more falsehoods as a cost of inclusion and use.
1) A religion consists of a set of myths and rules the purpose of which is to resist outsiders, and to set limits on behavior or to be treated as an outsider and deprived of opportunity and insurance of the in-group. Hence most religions evolve with the weak, who have no means of competition except resistance and exclusion.
Theology
Belief
A Belief, or a Set of Beliefs provides an individual or group with a strategy for achieving personal objectives, a set of methods of decidability, and a moral defense (rationalization ) for our behavior if we are criticized.
Mythology
(…) Myth – (INTERTEMPORAL) Wisdom Literature (in my opinion the proper forum for teaching wisdom) – Inflationary vocabulary, grammar, and reality.
Ideology
An Ideology provides an emotional incentive to act in favor of political change under democracy. An ideology provides political decidability for interest groups. An ideology relies upon correspondence with a prejudice, shared by a group with self-perceived common interests. It need not be either rational nor empirical, since the purpose of ideology, like religion, is to make logical and empirical criticism impossible – or at least too costly to prosecute.
– AN IDEOLOGY consist of any set of ideas that agitate, motivate, or inspire achievement of political ends under majoritarian (monopoly) democracy. An ideology need not be internally consistent externally correspondent, or existentially possible. It need only motivate individuals to act in furtherance of policy.
2) An ideology consists of a set of ideas the purpose of which is to excite subclasses to act under democracy to obtain political power. Ideologies are used to obtain followers. Likewise followers, follow ideologies. Hence most ideologies if not all ideologies are lower and working class ideologies, and most followers from the lower and working classes.
Philosophy
3) A philosophical system provides criteria for making judgments in the pursuit of preferences. Philosophies are used to obtain peers. Likewise peers seek philosophies with which to pursue preferences together with their peers. hence all philosophies are class philosophies, and most philosophies are middle class philosophies.
A Philosophy provides a coherent JUSTIFICATIONARY system of decidability within a domain of interest. Philosophy relies upon tests of internal consistency we call logical grammars. A Philosophy need be internally consistent, non contradictory, coherent, even if only marginally correspondent to reality. A philosophy answers the questions of preference and good.
In practice it is very hard to claim that philosophy has practiced the pursuit of truth. (more harm appears to have been done by novelists, philosophers an prophets than good, and more good by historians and scientists than harm. We can easily claim that philosophy has practiced the pursuit of choice and decidability. But if we claim philosophy has sought to produce truth we would have a harder time demarcating between science and philosophy. And my understanding of the point of demarcation between science and philosophy is the difference between choice and decidability – or rather the preferable and the good versus the true.
And as you will discover, my understanding is that the velocity of human existential transcendence – meaning the development of human agency both physical, emotional, and intellectual, and both individual and cooperative – is dependent upon the difference between the decidable truth and the practiced falsehoods.
As such I separate the grammars, from the operations, from the testimonies, from the fictions. Meaning that I separate logical grammars of testimony, from operational recipes such as the sciences, from wisdom literature such as histories, from the literature of persuasion and conflict we call philosophies, fictions, and religions.
In this sense while I have combined philosophy, law, science, logic, and grammar into a single commensurable language, you will find that I frequently criticize those who have done all the damage to this world, with little contribution to the good of it. And in that sense I will come across as an anti-philosopher of sorts who has appropriated some of the content of philosophy while excoriating vast categories of it, as dishonest, manipulative, and harmful to man.
– A PHILOSOPHY consists of any set of internally consistent ideas of decidability which justify pursuit of personal preferences or group goods.
And so:
If we define philosophy (positive and literary) as the search for methods of decidability within a domain of preference, and
If we define truth (negative and descriptive) as the search for methods of decidability across all domains regardless of preference.
Then:
We find that positive or literary philosophy(fiction or philosophy) informs, suggestsopportunities, and justifies preferences for the purpose of forming cooperation and alliances between individuals and groups.
We find that negative or juridical philosophy(truth or law) decides, states limits, and discounts preferences, for the purpose of resolving conflicts between individuals and groups.
The Natural Law of Reciprocity, is a negative, descriptive, juridical science, not a fictional literature.
Literature
A Fiction (Story)
Now, you wouldn’t assume that there exists a formal grammar to the structure of narratives but there is. And it consists of just ‘changes in state, all the way up.’ Just as reality consists of changes in state of dimensions.
And if we look at Fiction (Stories) we see many permutations of changes in state: nothing more than sequences of changes in state. (re: Vonnegut). And only three endings: Happy, Unhappy, and Tragedy.
|ENDINGS| Happy > Unhappy > Tragedy
And only six paths to combine to achieve those endings:
1) “Rags to Riches” (rise – a rise in happiness),
2) “Tragedy”, or “riches to rags” (fall – a fall in happiness),
3) “Man in a hole” (fall–rise),
4) “Icarus” (rise–fall),
5) “Cinderella” (rise–fall–rise)
6) “Oedipus” (fall–rise–fall)
|PLOTS | Fall-Rise-Fall < Fall-Rise < Fall < |STATE| > Rise > Rise-Fall > Rise-Fall-Rise.
And a number of ( … )
So our language consists of not much more than the names (references) and changes in state of some set of marginally indifferent constant relations, using some combination of physical, emotional, and intellectual senses.
And we can create increasingly complex words that themselves constitute micro-paradigms. And in doing so weave together extraordinarily complex sets of categories, relations, changes in state – where one of those changes in state is our ‘value’ – generally expressed as an emotional response.
A History
SPEECH
A Story
A Chapter
A Sentence
A Phrase
A Word
A Sound
A Narrative (Story, Recipe)
A Description (Story) Present
A Testimony (story) past.
A Narration
( … )
A Description
( … )
Testimony
A Testimony provides a warranty of due diligence against ignorance, error, bias, wishful thinking, suggestion, obscurantism, Fictionalism, and deceit. A testimony answers questions of liability against falsehood.
Only sentient beings can make truth claims because only sentient beings can give testimony.
All truth claims can and must exist as testimony.
A truth claim can be false (disagreeable)
Testimonial or Complete Science – operationalism.
Ordinary Language
( … )
Traditions
A Traditional OrderofHabits (or group evolutionary strategy) provides a group with an evolutionary strategy necessary for survival and in the world and competition against others with different strategies. They consist at least, in a portfolio of metaphysical value judgments and carriers (users) of these habits rarely if ever understand or are even aware of, alternatives to these prejudices.
Norms
A Normative Order of Habits provides a group with means of preserving the traditional order within the current demographic, social, economic, political, and military context. This set of habits need not be understood, coherent, rationally articulated but merely practiced. They consist, at least, in manners, ethics, morals, and laws.
– MARKET, TRADITION, NORM, HABIT consist of … (Demonstrated results…)
Laws: Commands, Legislations
5) A legal system provides a means of resolving differences so that a group can cooperate in the production of generations, goods and services. Legal systems are used to rule others. But require strength to enforce. Hence most legal systems are the product of the upper classes that rule by force, and make use of scientific, philosophical, ideological, and religious systems to speak to classes while ruling them with law and violence.
Natural Law
( … )
(Record of conflicts settled…)
– NATURAL LAW of RECIPROCITY (Tort), was produced scientifically (empirically) by trial and error, through the resolution of disputes across personal preferences, group goods, norms, traditions, and intuitions, cumulating always and everywhere that decidability is provided by property, and property consists in the demonstrated investment of human action or inaction anything whether genetic, material, behavioral, or informational.
A Discipline or Field of Study (Network of Paradigms)
4) A scientific system provides for making truthful (true) statements for the description of operations (transformations instate). Scientific systems are used to decide, create, invent, and to provide power over nature and man. Hence, science . Hence science is a largely professional or upper middle class philosophy.
A specialization in the division of labor in the market for the production of knowledge. (usually a difference in operations and scale)
A Demonstration (reality)
A Recipe (protocol…)
An Action
An Input, Output
Science
A Paradigm in Science or ‘-ism’ in Philosophy, provides a system of decidability in an area of exploration, investigation, and research. Either a network of theories or justifications that are used to make decisions in pursuit of research. Wherever possible I choose the scientific term because it is less likely to have been inflated and conflated. And I have chosen the term paradigm for that reason.
An Hypothesis
A Theory(Story, Opportunity, Search Algorithm) – A Test (Warranty) against Impossibility
A theory of possibility by falsification
A Law
Science, Physical Science, or Empiricism (deflation) of imagination, but absent operations.
(Search for Laws(avgs) and Operations(causes))
A Science provides a CRITICAL means of decidability across all domains regardless of convention, interest or preference (Philosophy, Norm, Religion, or Ideology). A Science relies in the very least, upon tests of:
Categorical consistency, i.e. all differences
Internal (logical) consistency, i.e. all logics (Deflationary Grammars)
External (empirical) consistency, and (Correlative)
Existential (operational) consistency,
Under Propertarianism (Testimonialism) it must also include tests of
Rational consistency (rational choice), and
Reciprocal consistency (reciprocity of rational choice).
And we require limits.
Scope consistency (full accounting),
Parsimony (Deflation), and
Commensurable Consistency(Coherence).
– A SCIENCE consists of any set of ideas that provide decidability independent of personal preference or group goods, by the systematic elimination of ignorance, error, bias, wishful thinking, suggestion, obscurantism, Fictionalism, and deceit, by the use of measurement and record of actions – demonstrations versus words.
Algorithms, Accounting, Mathematics, and Logic
Algorithms (Processes)
A Simulation (program)
An Algorithm (Procedure)
A Calculation (transformation of inputs into outputs) but with deduction.
Accounting (Transactions)
A Balance Sheet
An Income Statement
A General Ledger
A Ledger
A Journal
An Entry
An inventory item.
Mathematics (Measurements)
A Model (mathematic)
A Computation (lacking deduction) (information is closed)
A Formula
– MATHEMATICS consists of a deflationary grammar of decidability consisting purely of competition between positional names under the preservation of ratios providing a single axis of decidability: position, but in N dimensions, providing commensurability between any set of positional relations of any number of dimensions.
The Logics (words)
A Proposition
An Axiom
A Statement
A Proof (Operations, Cost, Recipe) – A Test (Warranty) of Possibility
A proof of possibility by construction.
( … )
A proof of internal consistency
( … )
– A LOGIC consists of any deflationary grammar of decidability that assists in the falsification by competition of one or more constant relations between states. (Note that one proves nothing logically other than internal consistency, because all premises of external correspondence are forever contingent.)
The Logics. We use the word logic ‘loosely’, I have to get across the difference between the multiple uses of the term:
The Rationalisms (Justificationisms)
A Justification
A Statement
An Argument
Rationalism is often contrasted with empiricism.
The empiricist view holds that all ideas come to us a posterior through experience; either through the external senses or through such inner sensations as pain and gratification. The empiricist essentially believes that knowledge is based on or derived directly from experience.
The rationalist believes we come to knowledge a priori – through the use of logic – and is thus independent of sensory experience.
Rationalism consists of adopting one of these three claims
The Intuition/Deduction Thesis,
The Innate Knowledge Thesis, or
The Innate Concept Thesis.
In addition, rationalists can choose to adopt the claims of Indispensability of Reason and or the Superiority of Reason – although one can be a rationalist without adopting either thesis.
Logic (formal grammar of decidability) Logic, via-positiva, consists of the use of deflation, organization, and competition to test the survivability of statements) which ( scientifically), consists in the preservation of constant relations in the differences in dimensions available to human action, perception, and experience. Those constant relations are possible because of a deterministic (non-random) universe – at least at various scales. Conversely, via-negativa, we can say that the function of logic is to eliminate ignorance, error, bias, assumption of knowledge, wishful thinking, suggestion, obscurantism, and deceit from our free associations.
Which I’m sure is a mouthful.
A logic requires at least:
The assumption of deterministic Universe (constant relations) within the scope(limits) of the context.
Constant Referents (Names)
A competition between the properties, relation and values two or more referents.
Preservation of Constant relations by grammar
Commensurability (or network of commensurability) of referents
Transformation Operators
Comparison operators
At least ternary logic || Incomparable > Undecidable > Contingent > True(not false) > False (highest certainty is falsehood)
For proofs, only Binary Logic: Unknown or False > True for purpose of deduction. Note that falsehood has greater certainty than truth.
Arbitrary(Normative) or Descriptive(Necessary)?
Is a logic – a means of preserving constant relations – Axiomatic and Arbitrary in a Meaningful Paradigm,? Or is it Natural Law and Correspondent in an Existential Paradigm?
If descriptive, what dimensions of reality can we identify?
Logic of Differences (logic proper)
Logic of Categories of Constant Relations (cumulative differences) (identity)
Logic of Constant Positional Relations (mathematics)
Logic of Physical (Natural) Operations (changes in state/time)
Logic (Operations) of Physical Human Action
Logic (Operations) of Incentives using Property in Toto
Logic (Operations) of Cooperation using Reciprocity
Logic (Operations) of Contingent Relations(Language)
Logic (Operations) Of Testimony given all of the above. (coherence, scope, limits, parsimony)
A Formal Logic. (I’m going to define formal logic as a dimensionally limited grammar – a grammar which limits vocabulary by limiting semantics).
Formallogic consists of the study of inference with purely formal content. An inference possesses a purely formal content if it can be expressed as a particular application of a wholly abstract rule, that is, a rule that is not about any particular thing or property. In many definitions of logic, logical inference and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuances of natural language.
We can identify at least two uses of formal logic:
The construction of discursive proof (or possibility of construction) or disproof about the world using the logic of internal consistency through exclusive reliance on argumentative closure. Mathematics, Law, and Norms rely upon justificationary reasoning. (Science, like evolution, does not. It relies on survivability whether we can explain the causes or not).
Philosophical Logic, Rationalism or Justificationism: The use of Textualism (interpretation) for the interpretation of scripture and law (Pilpul, Interpretation). Generally the attempt at closure rather than appeal to the next higher dimension where there is more information. Non contradiction can be seen as a variation of the liar’s paradox.
To interpret legal precedent or legislation without return to the legislature or judge of record – in which case, again, the construction of said sentences constituted a failure of the authors to produce grammatically complete sentences – or the attempt by prosecutor, defense, and judge to create new law.
To interpret Scripture or other Wisdom Literature under the pretext that it consists of law, history, or science, or any kind of truth – in which case, like interpreting the law, we see only a failure of the authors to produce grammatically complete sentences, open to current knowledge, and we seek to create what is not there.
To construct deceptions by appeals to authority by making use of the ignorance of the audience, the malice of the interpreter, and, once again, the failure of the authors to produce grammatically complete sentences (and paragraphs).
Much of our time will be spent falsifying and replacing the ….
Symboliclogic consists of the study of symbolic abstractions that capture the formal features of logical inference. Symbolic logic is often divided into two main branches: propositional logic and predicate logic. We can think of modal and propositional logic as …..Mathematicallogic consists in of extension of symbolic logic into other areas, in particular to the study of model theory, proof theory, set theory, and recursion theory.”—A Turing, Programmatic, or Algorithmic Logic: The addition of control structure differentiates programmatic logic from mathematical logic. As a consequence the problem of closure increases by the addition of the halting problem.
Logic of Language: The study of the rules of language, the rules of logic and the rules of grammar, and how grammar and syntax function to produce logical statements for the simple reason that what we think of as logic – differences, within a sentence – is reasonably intuitive to us, even if that logic fails us in the comprehension of arguments (and deceits).
Syntax is the study of sentences and their structure, and the constructions within sentences. Syntax tells us what goes where in a sentence. Grammar is the general term referring to the set of rules in a given language including syntax , morphology, phonology, while syntax studies sentence structures.
My preference would be to improve clarity, by redefining grammar as phonology(sounds) and morphology (words), and Syntax for Sentences. So that I could speak of Vocabulary and Syntax. (hmmm….) Because a language consists of vocabulary consisting of morphology and phonology, organized into sentences through syntax. (hmmm….)
Modal Logic – we can think of as the symbolic logic of grammar – qualification or refinement. I think of it as the logic of verb properties.To discover the operations and therefore universal grammar of human beings through analysis of language. In this sense, the study of such grammars constitutes an investigatory cognitive science.
I rely on cognitive science, (neural networks and the structure of the brain) for most of my work. And so I see logic as nothing more than our ability to determine differences. But when those differences are organized into a language we develop this wonderful thing called grammar: the organization of the flow of information between individuals according to predictable rules.
Language is an interesting problem because it’s serialized and very parsimonious and informationally dense, even if it can easily informationally imprecise, ranging from burdensome low context and high precision, to lazy high context and low precision. Yet our minds produce a continuous stream of possibilities that we must transform into that which can be communicated serially in speech.
Investigation of the brain: The use of language to study of cognitive ability of the human brain – and perhaps all brains, given the vocabulary, and the grammatical and syntactical rules the speaker is capable of.
Investigation of reality: The use of language, including semantics (meaning), vocabulary , grammar, phonology, morphology and syntax to investigate reality. This is the ‘verbal’ and primacy of reason strategy. And it is in contrast with the scientific and engineering investigation of reality, by investigation of actions.
As we will see later on when we discuss the table of grammars, the various disciplines all have produced deflated vocabularies, deflationary grammar, and syntax that identifiably if not predictably reflect reality. Conversely, there exist some disciplines that reflect only fictions. And not surprisingly, those fictions exist largely in the pseudosciences we refer to as social science. So as an empirical judgment it is very hard to suggest that these grammars are fictional or arbitrary, and very difficult to deny that our language – at least Germanic languages – reflect and therefore allow us to represent the various dimensions of reality.
As a side note, I was fairly hostile to the philosophy of language producing any result until I’d read kripke. And I have found that language does reflect reality – because cognitive science, analysis of language, and physical science have shown me so. But because I am principally concerned with the elimination of error, bias, and especially deceit, leaving us only truthful voluntary cooperation and exchange, I remain hostile to it for empirical reasons. Which is the next topic (empirical differences).
Empirical difference between the two …..
Informal Logic: The use of Vocabulary, Grammar, Logic(Logic Cognitive Bias, and Fallacy), Correspondence, Ethics, Morality and Rhetoric for the production and falsification of arguments.
–“Informallogic is the study of natural language arguments. The study of fallacies is an important branch of informal logic. Since much informal argument is not strictly speaking deductive – on some conceptions of logic, informal logic is not logic at all.”—
Type
Situation
Arguers’ Goal
Dialogue Goal
Discovery
Need for Explanation
Find a Hypothesis
Test a Hypo-
thesis
Information
Need Information
Acquire Info
Exchange Info
Education
Transfer Info
Shared Understanding
Justification
Need to Have Proof
Verify Evidence
Prove Hypothesis
Deliberation
Practical Choice
Fit Goals and Actions
Decide Action
Persuasion
Conflict of Opinion
Persuade Other Party
Resolve Issue
Negotiation
Search for common Interests
Secure Interests
Settle Issue
Prosecution
Conflict in Fact
Expose the other Party
Cessation, Punishment or restitution
Testimony
Warranty of Due Diligence against conflict
Obtain and preserve unearned premium or discount
Elimination of retaliation, punishment, restitution via truth
Deception
Reciprocity, Conflict, Punishment Avoidance
Fraud
Deceive via falsehood
Distribution
Undermine Opponents interests
Poisoning the well
Opportunity for increase in conflict
Eristic
Avoid argument
Attack an Opponent, or interests
Preserve Conflict
Table 1 Table of Dialog Conditions and Goals
Closure
The Problem of Closure: There Isn’t Any.
Closure. Close or Not Closed (Open). The question of closure. Given a set S, grammar G, and set of operations O, all operations O in that grammar G, upon that set S, will produce a member of that set S in grammar G. In formal logic, it refers to that output set that can be deduced from the given input set. For reasons I won’t go into here, very few systems of operations and values are closed. In fact, only the most reductive (simple) systems can be.
Closure is important for at least these six reasons.
that arguments or proofs in any simple system (sets, grammar, and operations) must be solved by appeal to a containing system (sets, grammar, and operations) – or rather system using more information than available in the current system. You will see me use the problem of closure to explain testimonial truth, and to undermine philosophical rationalism, just as we have undermined theological rationalism.
That closure creates one form of symmetry (shape), but that all sets of operations on all sets produce symmetries because of the variations in the sets, and variations in the possible combinations of operations.
Language is not closed. I hate this non operational term, but “discrete infinity” refers to the property of such things as language to produce an infinite set of discrete sound combinations – at least within sets of paradigmatic assumptions about the world.
That the mind is able to identify symmetries, and produce paradigms, of ever increasing scales, as long as those scales are reducible – even if thru training – to an analogy to experience that are commensurable within our senses, and where we can compare differences and therefore make decisions with.
As such while the set of operations possible within the physical universe is limited, there is no limit to what man can understand through the creating of disciplines (paradigms) of commensurability.
And the principle problem in our development is limiting the difference between our cognitive biases and the state of our knowledge, and those symmetry’s for which we can produce paradigms that are possible and or useful within the universe. But otherwise our ability to understand and manipulate the universe is limited only by our ability to develop means of harnessing the energy to take actions that produce transformations.
Knowledge is never closed because of the cognitive window of action at any given scale of knowledge. As such, Language is never closed. It may be true that we can know the full set of operations possible in the existing universe at each cumulative scale. But, assuming we possess the ability to harness increasing scales of energy, then what we might be able to construct in this universe through though physical, intuitionistic, rational, calculative, and computational means is …. As far as I can tell, not closed.
What is closed, and what is measurable, is the information necessary to cause change in state in the human mind. I am not quite sure, but Nassim Taleb seems to have been struggling to discover this value, although, like me, he has finally come around to warranty rather than measurement – and I think the search is futile at any scale other than the one he has already produced (meaning, logarithmic or big, and therefore economically impossible) if for no other reason than the information sets available to us are not sufficient. Yet when we develop general artificial intelligence we will develop some measure or other of that information. If I had another life to live I might work on that problem. It’s interesting.
So while the volume of information necessary for humans to identify opportunities for changes in state may remain constant, the use of increasingly complex concepts preserves that ability regardless of scale. More on this later.
As such, it is not clear that we will experience any ‘limit’ to cognition as long as – like every other scale of the universe – new symmetries (meaning objects of consideration) never cease to emerge.
THE PATTERN
Fields, Symmetries, and Generations
Given a six sided die, and the single operation “roll the die”, we can produce a noisy distribution of :
1(x1), 2(x1), 3(x1), 4(x1), 5(x1), 6(x1).
Given two six sided dice, and the single operation “roll the dice and sum the results”, we can produce a noisy distribution of:
2(x1), 3(x2), 4(x3), 5(x4), 6(x5), 7(x6), 8(x5), 9(x4),
10(x3), 11(x2), 12(x1).
The difference between the one-die and two-die distributions is that while the results of rolling one die are equidistributed between 1 and 6, with two dice the results of rolling can produce more combinations that sum to 7 than there are that sum to 2 and 12, and therefor the results are normally distributed: in a bell curve.
We can produce the same results with logic instead of numbers: For example, we can take the two words “Even” and “Odd”, and define two operations: “addition” and “multiplication”. Then apply the operations to all pairs:
Even + Even = Even,
Even + Odd = Odd + Even = Odd,
Odd + Odd = Even,
Even x Even = Even x Odd = Odd x Even = Even,
Odd x Odd = Odd.
(… geometric, scalar vectors … from every point, infinite points….)
And we can produce the same set of results with any grammatically correct operations on a set, given the operations possible on the set; including the set of Ordinary Language using ordinary language grammar. Although, unlike our simple examples using dice, the set of combinations of ordinary language is not closed, and so the number of combinations is infinite.
So any grammar applied to a set, allows us to produce a distribution of results, and a density (frequency) of results.
In mathematics this result set is called a ‘field’. A field consists of all the possible results of a set of operations on a set’s members, that are selected from the range of possible operations on those set members.
So in any set of results there will be a range of very dense, less dense, sparse, and empty spaces in the set’s distribution.
Constructability
Now those ‘holes’ in the distribution are notconstructible with the set and operations available to us. So, not everything can be described using the set with the available operations in every grammar. Conversely, we can create a set of operations describing those symmetries (patterns), whether we are referring to holes or densities.
There are things we cannot say then. But by and large, nearly anything we can say that consists of constant relations between existence, perception, cognition, and action, is possible to say – if we possess the knowledge. And conversely: that which does not consist of constant relations between existence, perception, cognition, and action can be said but not said constructively: meaning operationally. So that is why people resort to those terms that are not operational: to compensate for your lack of knowledge, to compensate for their lack of knowledge, to levy pretense of knowledge when they do not possess it, or to deceive despite possessing that knowledge.
Deducibility
|Estimating| Description > Deduction > Induction > Abduction > Guessing > Free Association.
In fact, the virtue of fields is that they assist us in finding those symmetries – albeit with a lot of work. That’s because some results are neither constructible or deducible from a construction, except by via-negativa trial and error.
(Limits of Deduction)
Symmetries as Externalities
In most if not all of these sets, we will discover symmetries (patterns), including patterns of density and patterns of emptiness, and then patterns of relations between those patterns.
These holes and densities consist of the consequences of the operations we performed on the set of references we’ve chosen. So, for example, when we make purchases with money, and observe the resulting financial and economic data, there are patterns within the consequences of the operation we call ‘exchange’ of the set ‘goods and services’. Those consequences appear as patterns in the financial and economic data – as a pattern of holes, distributions, and densities, that we call price, volume, profit, and loss.
And so for the sake of discussion, I’m going to adopt the term externalities from the discipline of economics to describe those unintended or accidental patterns that emerge from the operations we call ‘transactions’ on the set of ‘goods, services and information’. Meaning that Externalities consist of Symmetries produced by our economic cooperation.
It’s these externalities (for example, losses, and profits) that as a consequence determine the behavior of businesses, then industries, then markets – not the individual transactions.
The Natural World: Generations of Operations
At this moment we do not yet understand the fundamental Forces of the universe. But we have discovered a set of the fundamental Particles that those forces produce. And, of those particles that have mass, we have a fairly deep understanding of the Elements (Matter) in the periodic table of elements, that those particles that have mass produce. We have at least scratched the surface of the Molecules that those elements can combine produce. We have barely scratched the surface of the Organic Molecules that those elements can produce. We have only recently begun to understand how those molecules construct organs of Life. We increasingly understand how RNA and DNA construct life forms, although the complexity of that process is so vast that we can spot only correlations not yet operations. It is questionable how much we understand of sentience and consciousness or speech processing, but an understanding of reason, calculation and computation are available through introspection.
Universe > Forces > Particles > Elements > Molecules > Organic Molecules > Life(cells) > Sentience > Consciousness > Speech > Reason > Calculation > Computation
And
Assumptions (Metaphysics) > Psychology (Acquisition) > Sociology(Cooperation) > ( Norms > Traditions > Laws) > Markets > Informal Institutions > Politics(formal institutions) > Education(Religion) > Group Strategy(War)
At each stage of complexity, some set of possible operations produces potentials (densities) for yet another set of possible operations, as well as weaker distributions and holes that do not provide opportunities for yet another set of operations. So for the sake of our discussion we’re going to refer to each stage as an Operational Generation.
Operational Generations as Disciplines
The various Sciences (disciplines) mirror these Operational Generations. Each discipline seeks to discover the operations and sets (objects, states) that complete the grammar of the discipline. (Categories, properties, relations, values, and Operations, and Externalities (Symmetries)).
Commensurability Across Grammars
Unfortunately, some of these disciplines are very old – like mathematics – and some are quite new – like genetics. Some are fairly scientific (chemistry most of all) and some are merely storytelling if not outright deceits (psychology and sociology). In mathematics we find archaic (supernatural) terms left over from Mathematical Platonism. In the sciences we use awkward non-operational names for phenomenon and processes – often peoples names. In economics we use the term ‘rents and rent-seeking’ for what is a form of parasitism or corruption. In psychology and sociology the terms are by and large no better than fairy tale fictions with no basis in science whatsoever.
By converting the terminology in each discipline to purely operational prose, we create commensurability across disciplines. And with that commensurability we can rapidly improve the ease of learning them. We can identify that which they claim to understand but do not. And identify what they claim that is outright false.
OPERATIONAL GRAMMAR
Operational grammar leaves holes.
Operations
Language
Continuous recursive disambiguation resulting in a series of transactions, culminating in a contract for meaning.
Convergence
In this era, as in prior eras, the world has been converging on common weights and measures: the common languages of science, of technology, of business, of contract of accounting rules, a common trade law – at least at the international level of cooperation. The current financial system of fiat money, central banks, and reserves, allows relative commensurability of worldwide trade.
However, those convergences tend to occur both within and across commercial and legal fields, but only within fields – thereby preserving incommensurability of language across all fields. And within fields they converge on old habits that preserve obscurant language.
SOME OF OUR MODELS ARE WRONG:
THEY ARE DISCONTIGUOUS WITH REALITY
Metaphysics
Logic
MathematicsPsychology (acquisitionism)Sociology (propertarianism)Economics Law (Natural law of reciprocity)Politics (the production of commons)Strategy (group competitive strategy)Religion ( production of commensurability)
EXPLANATION
Current knowledge ….. my understanding…..
Constant vs contingent vs inconsistent vs non-relations.
Recursive Continuous Disambiguation vs Scale of Set of Constant Relations(density)
Cumulation of association vs falsification of associations
Computational efficiency.
State Persistence vs breadth search, vs depth search
We cannot know the intelligence of distant ancestors.
Planning a series of steps in sequence must emerge – which requires recursion.
Consciousness must emerge, meaning, the ability to compare states.
Cooperation must emerge, meaning, the ability to empathize with intent.
At some point we must develop sufficient computational ability to manipulate our bodies in some way that allows for unambiguous communication, or a means of continuous disambiguation, that is fast enough for one another to make use of in real time, and easy enough for one another to retain.
And at some point, given sufficient computational ability, memory, and state persistence independent of recursion, language must emerge.
At some point the value of such communication much be such that the cost of it is offset by the rewards of it.
And we should see a cliff in history where there is a dramatic change when we did develop those abilities. And we do see it – rather recently.
But language requires a system of measurement. The system of measurement is limited by our senses. And as such meaning refers to a set of measurements, eventually reducible to analogies to human experience.
So while semantic content (measurements) must vary from species to species, grammar (continuous recursive disambiguation) should be universal in the sense that it varies predictably with computational abilities.
We can understand a child, a person with 60IQ, 70IQ and so on, up to 200+ IQ. But as far as I can tell the set of measurements (basis of semantics) remain the same, and all that changes is the scope of the state persisted, the depth of recursion, and the density and distance of relations, and the ability to model (forecast). In other words, simple people are in fact simply ‘more simple’ in the density of content of their semantics, use of grammar, and models (Stories) that they can construct with them.
So universal grammar as a set of computational minimums and efficiencies, should always exist, and human universal grammar as universal grammar limited to human measurements (semantics), does exist. And any organism with sufficient computational (neural) capacity, should develop some means of communication using some variation of universal grammar, and some sense-perception – action dependent semantics.
