Curt Doolittle

Theme: Decidability

  • MORE ON MATHEMATICAL PLATONISM (For me. Pls ignore.) “Famously, Tarski (1936) pr

    MORE ON MATHEMATICAL PLATONISM

    (For me. Pls ignore.)

    “Famously, Tarski (1936) proved that no classical formal language could contain its own truth predicate, due to Liar’s paradox. As such, if we want to include a truth predicate, we are committed to a hierarchy of languages. Moreover, if consisting only of formal languages, this hierarchy does not collapse: at no level will a language Lm provide a truth predicate for a language Ln, where n ≥ m.”

    CD: Yes, but I can see that this is starting to go south already, confusing sets with semantics…

    “If one is not committed to strict formalism, there are far less

    problems with Tarskian truth. In particular, the hierarchy of

    languages can be collapsed. There are two ways of doing this. One

    can either move from formal to informal languages – where Tarski’s

    undefinability result does not hold in the strict sense – at some

    point in the hierarchy, or one can hold some level in the hierarchy

    to be of the language-to-world type. Philosophically these two

    strategies are largely equivalent, since we seem to have no way of

    describing the world outside language. This makes the job a lot

    easier for the non-formalist. Rather than try to explain a

    problematic relation between mathematical languages and mathematical reality, we can concentrate on characterizing the

    connection between our formal and pre-formal mathematical

    languages.”

    “What proof is to formal mathematics, truth is to pre-formal. We

    deal with mathematical proofs syntactically, but at the same time

    we as human beings think about them semantically.

    CD: Yes.

    “We cannot deny pre-formal thinking, and its need for semantical truth. However, this alone is not enough to show a substantial difference between truth and proof. Even though the existence of pre-formal mathematics cannot be reasonably contested, there is always the possibility that when it comes to truth, it is essentially superfluous; whatever we can achieve with truth, we could also achieve with proof alone.”

    CD: First, there is a very great difference between truth and proof if mathematics is platonistic and set based. But if it is marginally indifferent and non-platonic then there is no difference. So that’s my concern. But the question I have is, what externalities are produced? It’s a moral question. I know that’s hard to grasp. But a biologist who plays with viruses and a mathematician that teaches platonism both export risks onto others.

    “The second problem that the lack of reference causes for

    formalism is one that does not require semantical arguments, or

    indeed any sophisticated philosophical devices.”

    CD: I do not see that as a problem. Nor do I see the need for, or desire for, formalism.

    “It could be plausibly claimed that human thinking as we know it could not exist without some mathematical knowledge.

    CD: yes, this is correct. But the reason is not stated here.

    “But if mathematics has absolutely no reference, what reason do we have for picking one theory over another? It must be remembered here that this reference does not have to mean anything resembling a Platonic universe of mathematical ideas. Simply put, if we believe that 2 + 2 = 4 rather than 2 + 2 = 3, we must believe in some kind of reference. (It must be noted that I do not mean to use “some” as a hedge word here. My point throughout this work is that the relevant dichotomy is reference against no reference, rather than no reference against Platonist reference.)”

    CD: Yes, but if you wrote the argument as human actions in operational language you would not have this problem – which is purely linguistic. And obscurely so.

    Source date (UTC): 2013-09-26 14:25:00 UTC

  • What Are The Biggest Unsolved Intellectual Problems In The World Today?

    1) If we are to supply money to the economy, how do we know how much? When are we causing more distortion than good?
    2) There is something wrong with the standard model.  What is the theory of the universe? The theory of ‘everything’?
    3) What is the human population load bearing capacity of the planet? What is the next malthusian limit?
    4) Is our progress since the industrial revolution little more than capturing hydrocarbons?  And if so, what happens when they’re gone?
    5) Our anti-bacterial technology is losing effectiveness, and we still have not found an anti-viral solution.
    6) Is Modern Monetary Theory possible, or will it produce perpetual, and destabilizing inflation?
    7) We still have not solved the mind-body problem to everyone’s satisfaction. What is the answer?
    8) What’s ‘after democracy’?  Because democracy apparently has very hard limits to where it will function, and seems to be of limited use outside of a small number of countries.
    9) Is diversity really a good?  It doesn’t look like it.  And how do we solve that?
    10) The problem of transhumanism: what does this mean for us?
    11) The problem of the technological singularity.
    12) What will happen if we have fully taken advantage of industrialization and we have half of the world’s population permanently poor and living in slums?

    https://www.quora.com/What-are-the-biggest-unsolved-intellectual-problems-in-the-world-today

  • What Are The Biggest Unsolved Intellectual Problems In The World Today?

    1) If we are to supply money to the economy, how do we know how much? When are we causing more distortion than good?
    2) There is something wrong with the standard model.  What is the theory of the universe? The theory of ‘everything’?
    3) What is the human population load bearing capacity of the planet? What is the next malthusian limit?
    4) Is our progress since the industrial revolution little more than capturing hydrocarbons?  And if so, what happens when they’re gone?
    5) Our anti-bacterial technology is losing effectiveness, and we still have not found an anti-viral solution.
    6) Is Modern Monetary Theory possible, or will it produce perpetual, and destabilizing inflation?
    7) We still have not solved the mind-body problem to everyone’s satisfaction. What is the answer?
    8) What’s ‘after democracy’?  Because democracy apparently has very hard limits to where it will function, and seems to be of limited use outside of a small number of countries.
    9) Is diversity really a good?  It doesn’t look like it.  And how do we solve that?
    10) The problem of transhumanism: what does this mean for us?
    11) The problem of the technological singularity.
    12) What will happen if we have fully taken advantage of industrialization and we have half of the world’s population permanently poor and living in slums?

    https://www.quora.com/What-are-the-biggest-unsolved-intellectual-problems-in-the-world-today

  • As far as I know, current set theory is still in conflict with finitism but neit

    As far as I know, current set theory is still in conflict with finitism but neither argument is provable. We can only prove that finitism has no answer to set theory.

    As far as I know, infinity is not a measurement, and not rational concept – it is a purely platonic concept.

    As far as I know there is nothing that we can knowingly (scientifically) demonstrate is infinite – very large, unmeasurable, inestimable, but not infinite unless we discuss actions.

    As far as I understand, most of the problem with these discussion is metaphysical: confusing the platonic INSTRUMENTS, with physical MEASUREMENTS.

    For purpose of INSTRUMENTATION, (deduction) we (arguably, foolishly) rely on infinitudes of various kinds. But for purpose of measurement, we cannot actually perform any infinite measure because I cannot take an infinite measure, nor can I infinitely repeat a series of measures.

    That mathematical DEDUCTION uses the same symbols as arithmetic measurement is confusing. We must deduce many measurements because direct measurement is impractical. That is largely, the value of both geometry (fixed measurement) and calculus(relative measurement). But there still is a metaphysical difference between measurements (real) and deductions (unreal) despite the fact that mathematical deductions are much more trustworthy than linguistic deductions, because they are less open to variance, because numbers are, more uniquely identifiable, less loaded and more precisely ordered than linguistic statements.

    If infinite sets are not possible except platonically, then we are merely engaging yet again in another conversation about the number of angels that may dance on heads of pins. There is quite an argument going on that Cantor is playing a parlor game, and that between Cantor, Marx, Russell and Freud, is an unconscious conspiracy to replace religious mysticism with logical platonism. (I am one of the people who thinks this.)

    It is necessary for us to make practical use of infinitudes because in practice, in engineering, in physics, distance from any event reduces all effects to a relative constant. Therefore, in practice, while the .99999… does not equal 1 EVER, we can create no measurement that can distinguish between the two. So the platonic concept .9999…. is equal to the measurement 1. Even if the point on any line represented by .9999… never equals 1. EVER, unless we change the meaning of .999999… (Which is really what set theorists do.)

    However, one of the most convenient tricks in any discourse is to confuse the ideal, the platonic, practical, and the real. And unless you know which set of concepts are being used for which purpose its pretty easy to fall into the trap of confusing platonic idealism, with pragmatic platonism, with pragmatic instrumentalism, measurements, and objective reality in real time.

    I suspect my suspicions will be confirmed. And that these silly arguments to logical authority are little more than modern scripture.

    The only platonic test is articulating something in Operational Language open to observation.

    But at least I know why modern scripture is necessary: to preserve moral relativism. (Yes, that’s what I think)

    Source date (UTC): 2013-08-06 07:31:00 UTC

  • SETS AND NONSENSE : THE PERCEPTION OF INFINITE SEMANTICALLY MEANINGFUL SETS IS A

    SETS AND NONSENSE : THE PERCEPTION OF INFINITE SEMANTICALLY MEANINGFUL SETS IS A COGNITIVE BIAS

    I have been working with computers for a long time.

    Computers are very good with sets of things and teaching you how to work with them. Relational databases are even better at teaching you the algebra of sets than programming languages. Compilers are very good at teaching you about semantics.

    And trying to write games that have some semblance of intelligence not immediately deducible as trivial dumb patterns. Or writing software that can produce reasonably articulate legal arguments from limited data. Or trying to represent semantic clouds of related terms teaches you something very basic about language:

    That there are actually very few sentences that are not nonsense compared to the number of sentences that are sensible.

    If one accumulates knowledge from many different disciplines, it becomes rapidly apparent that the number of concepts shared by these domains is limited and that the perception of vast knowledge is an illusory artifact of disciplinary methodological loading – most of which is erroneous and caused by ignorance of these greater patterns, or various forms of social and normative loading, or the natural brevity that emerges in any population over time. Worse, no small part of current language consists of loading meant to signal social position or create priestly mysticism to preserve status cues.

    One of our cognitive biases is to assume when we discover something new,

    Mystical statements were not false if they achieved the purpose of getting non-kin to treat each other as kin.

    They may have been allegorical but they were not false. They produced the desired outcome of uniting disunited people by getting them to extend kin-trust to non-kin.

    The externality produced by that allegory was pretty dangerous it turned out. But until trade became pervasive, the need to extend trust in order to trade and operate a division of labor was insufficient to produce the level of trust that religion did.

    We did not become enlightened because we wanted to, but because trade required that we did. And morality could be enforced by trade and credit rather than religion which threatens ostracization and death, and law which threatens punishment. Instead the ability to consume, compete for status and mates or feel the pressure of degrading status made very granular control of moral behavior possible – for nearly everyone, at very low cost, and producing a virtuous cycle of declining prices.

    While we might create very vast and highly loaded languages, the fact of the matter, is that all language is allegory to experience. There is little or nothing that cannot be expressed with a thousand words. The primary challenge is that complexity using that limited vocabulary overwhelms short term memory. So loading using complex words. Like symbols or measurements, allows us to stuff ideas into short term memory and create faster “meaning” in each other’s minds, in the three second window of our processing cycle for those who are already familiar with the topic.

    In this sense, while we use complex words with heavy loading for brevity and status signaling, the concepts that we can convey require analogy to experience, and analogy to experience requires few words.

    Where am I going with this?

    The number if meaningful sentences is fairly small. The number if meaningful narratives has been known to be small for some time.

    The need to restate narratives in the current context is high.

    But the number of theories active at any time is quite small. With the illusion of large numbers a cognitive bias, and most theories merely justifications for preferences masquerading as theories.

    There just aren’t that many theories. And thats in no small part because we are very good at killing theories.

    We are super predators after all.

    Source date (UTC): 2013-08-04 11:02:00 UTC

  • What Are Some Problems People Will Be Surprised Mathematics Can’t Solve?

    I am not sure that there are problems mathematics cannot illustrate.  That seems unlikely.  I think there are LOGICAL problems with number theory that cannot necessarily be solved with certainty.  Math is  a pretty good way of describing the physical world.  It is a pretty good way of describing complex relations.  But that is different from saying that math can express everything about itself.  And that is probably the fundamental question that we would like to solve, but may not be able to.

    Jack Thompson below, asks the metaphysical question whether real numbers exist, and the answer is one of definitions not of existence.  No, real numbers are platonic entities. Natural numbers exist in nature.  All else is a product of mind. And even natural numbers are names for the act of counting. Everything else an act of calculating ratios.  🙂

    https://www.quora.com/What-are-some-problems-people-will-be-surprised-mathematics-cant-solve

  • What Are Some Problems People Will Be Surprised Mathematics Can’t Solve?

    I am not sure that there are problems mathematics cannot illustrate.  That seems unlikely.  I think there are LOGICAL problems with number theory that cannot necessarily be solved with certainty.  Math is  a pretty good way of describing the physical world.  It is a pretty good way of describing complex relations.  But that is different from saying that math can express everything about itself.  And that is probably the fundamental question that we would like to solve, but may not be able to.

    Jack Thompson below, asks the metaphysical question whether real numbers exist, and the answer is one of definitions not of existence.  No, real numbers are platonic entities. Natural numbers exist in nature.  All else is a product of mind. And even natural numbers are names for the act of counting. Everything else an act of calculating ratios.  🙂

    https://www.quora.com/What-are-some-problems-people-will-be-surprised-mathematics-cant-solve

  • (PERSONAL: NOTE: EDITED FOR CLARIFICATION) Someone smarter than I am will have t

    (PERSONAL: NOTE: EDITED FOR CLARIFICATION)

    Someone smarter than I am will have to take on the burden of creating a symbolic logic of action in disequilibrium. But I suspect that we already have it, in the scientific method. And that the attempts to conjoin formal logic of certainty with critical rationalism in science are operationally distinct fields.

    That isn’t saying it’s not possible. Its saying that we haven’t done it, and that Quine’s criticism of Popper is false.

    On the other hand, it is entirely possible that I don’t understand something, since I don’t have a lot of respect for formal logic as having application to actions. And, as a political economist, and philosopher of action, my priorities are different. SInce I don’t respect it, I haven’t spent much time studying it.

    It reminds me of war games and chess. They are, to some degree Ludic fallacies. Wars are won by precisely those criteria that war games and chess present as constants: informational asymmetry: deception, misinformation, and incomplete information, combined with differences in velocity and the concentration of forces. I gave up on both those enterprises for the same reason: as structured they are puzzles not problems.

    There is a difference between puzzles and problems. I view formal logic as an interesting puzzle, but political economy as a material problem.

    This is just a preference after all. I’m not making a moral argument. I’m simply taking the position that the physical sciences and formal logic are easier to solve than economic problems. The universe equilibrates. But human beings are RED QUEENS: we are always trying to outrun it by outwitting it, and that means we must seek to create disequilibria.

    That is a different way of saying that we must constantly battle ‘the dark forces of time and ignorance’ in order to stay alive on the universe’s treadmill by seeking and creating disequliibria both with nature and with each other.

    Certainty then, in any sense, despite the ease that would bring to our minds, by obviating the constant need for problem solving, would in fact, result in our extinction.

    Source date (UTC): 2013-07-14 11:17:00 UTC

  • More on Hoppe (et all) vs Popper (from elsewhere)

    [H]oppe would argue (and has) that the following statements are not possible to contradict – that they are falsifiable, but that is impossible in any circumstances for them be false. 1) increases in the minimum wage increase unemployment. 2) increases in the supply of money cause increases in prices. 3) democracy is simply a slow process of adopting communism. Any circumstance under which any of these statements is false, is a statement of time and externality, not of the scope of the statement itself. And this is why his argument is correct (true) within the framework of action: Any change in the description of circumstances would mean a change in the meaning of the terms minium wage, unemployment, and externality. Any change in the meaning of newtonian gravity would mean a change in the concept of gravity that is open to direct experience. (In other words, as Popper advices elsewhere, our problem lies in our concept of measurement and the calculus of measurement.) So, correctly stated, ACTION has a higher standard of temporal truth than does SCIENCE, and science a higher standard of inter-temporal truth, because science is discovery (the patterns will not change), and ACTION is invention because the pattern of relations are EXPECTED to change, yet we must act in real time to outwit the dark forces of time and ignorance. Within the context of ACTION, the Newtonian theory of gravity is sufficiently precise for the actions to which it need be applied. It is insufficiently precise for larger and smaller relations. But for the scope of action it describes (direct experience), it is in fact, ‘true’. The error was made by those who attempted to extend it into different domains (where tools are needed to experience gravitational effects. Tools expand our perceptions, so we must extend our concepts with our tools. And, it does not mean that any of these concepts likely to be falsified, even though they are falsifiable. It means that the scope of the statement does not require further precision than the statement contains. (The argument, for example, that there is no real reason for this apple not to fall through the table top. It’s just that the chance of such an event occurring requires a time frame many times greater than the existence of the known universe.) For the purpose of action in real time, this statement is true. This is the difference between Humean and Popperian scientific criticism of induction, and the utility of induction for the purpose of taking action. It is also why Popper is ‘weak’ in that he maintains analytical philosophy’s attachment to the metaphysical problem – rather than fully moving into Naturalism. This ‘halfway’ postion is why he’s open to criticism. The mistake in widespread application of the arguments against induction derives from the failure to treating philosophy as a symbolic language for the manipulation of the natural world that exists in our heads, and giving priority to science rather than the phenomenon of experience that we gain from constant bombardment of our short term memory by stimuli both direct and reflected from our memories. So, Hoppe is correct I think, just inarticulate, because he makes a similar error to Popper by confusing domains, even though he is correct because he uses a theory of action. Popper is wrong, I think, because he maintains the language of the metaphysical error – truth independent of action. It’s only by contrasting these types of arguments that we can see the errors in each. ie: we must subject theories to external tests, not those which are proscribed by the philosopher, or constrained by the language of the philosopher. [I] would agree that the mind body problem exists. However, evidence is, that the physical sciences are solving this, and that the philosophical program has been distracted by solving it. Philosophy is a language for transforming external information into perceptions. It is in fact, a system of measurement and calculation. But measurements and calculations must come from outside of us – if only because our internal ‘tools’ are not precise enough to self-analyze, and because we are prone to a pretty significant array of cognitive biases – and philosophy, as well as all other forms of measurement and calculation, must help us overcome those perceptual biases and errors. Our ability to perceive, remember, and calculate (categorize, compare and manipulate) the world is actually incredibly weak. But with language to form networks of perception and calculation with others so that we can perceive more than we can on our own. Writing to store those perceptions and judgements for later consumption. Philosophy to test and manipulate objects, properties and relations (calculate). Tools for extending our perception. And measurements for transforming the output of those tools into sensations that we can perceive, and compare, we can compensate for our inherent weakness. That is: we have incredibly scary-good associative memories, but terrible short term memories, and the ability to grasp only three to five concepts at a time, on perhaps two axis. And while that is good for throwing stones and spears, it is notoriously terrible for understanding the flow, pool and eddy that most of the universe consists of, under Mandelbrotian fractal complexity, to us which appears as kaleidic uncertainty: … “magic”. This means that the problem is in the scope of our statements in the context of our necessary actions. Not a problem with induction per se. But instead, a problem of induction when the scope of the problem is greater than the scope of action we attribute to it. Again, this is because philosophy is still trying to cure itself of the disease of the metaphysical problem. Religions die hard. The criticism I’m levying is that popper is trapped in his era of philosophy (analytical proper) and Hoppe is not (action proper) probably stands. Hoppe’s argumentation ethic probably doesn’t stand. Hoppe’s criticism of popper’s recommendation that we experiment with policy despite the fact that economic statements such as the example he’s given, are open to experimentation, is in fact, a criticism that Popper is an advocate of the error of positivism. Or something like that. I am not done experimenting with this line of argument obviously. The point being that deduction, induction, and abduction are simply statements about the amount of information we lack. I have covered a very complex set of ideas here, and done the best I an in a short space. I hope it’s added some clarity. Perhaps it is just confusing.

  • Reading: On Law As A Problem Of Calculation, Coordination, And Dispute Resolution, In The Face Of Necessary Ignorance And Diversity Of Interest

    common law const

    [T]he common law depends upon experience (scientific evidence), not logic or reason (untested theory), and is relatively impervious to authoritarian influence. In any reading list on Law, I don’t necessarily want to communicate the history of law, so much as emphasize the pervasive problems of the social cognitive biases: a) False Consensus bias, b) the Illusion of Asymmetric Insight, c) Projection Bias, d) Trait Ascription Bias, e) the Illusion of Transparency, that are largely the product of the introduction of women into the voting pool, and their alliance with, and support of, marginal male groups who can obtain power by the use of the near universalism of these female cognitive biases, because these cognitive biases suit the reproductive strategies of females in our prehistoric, pre-agrarian phase of development. 1) Bastiat’s The Law 2) Epstein’s Simple Rules For A Complex World 3) Hayek’s The Constitution of Liberty (as well as Hayek and Popper on knowledge) 4) Oliver Wendell Holmes’ The Common Law 4) Milsen’s A Natural History of The Common Law CLUES TO ADAPTING TO THE 21ST CENTURY 1) Jonathan Haidt’s The Righteous Mind (Believe it or not), my interpretation of Johnson’s Three Methods Of Coercion (see my site), and Perhaps Arnold’ Kling’s pamphlet “The Tree Languages Of Politics”. In particular I love kling’s metaphors both in the Three Languages, and in his “Recalculation” description of recessions. These are both accurate categorical descriptions but they are not sufficiently causally descriptions. Haidt solves the problem of the three languages. I think in my works I’ve sufficiently combined these different perspectives and using Haidt and property rights, I’ve unified these systems into causal relations. (Which new, and is why people have trouble understanding what I’m trying to get across at present.) 2/2) I want to add here Rothbard’s Ethics of Private Property. But since his moral code is incomplete (and therefore false), and his definition of property incomplete, because he was creating an ethic of rebellion not one of civilization, I’ll just have to wait until I finish my own work on propertarianism which corrects those errors. Without this understanding of the relationship between group size (individualism), reproductive strategy, morality, and property it is impossible to adapt the common law to the complex heterogeneous society, because it relies, at least in the arguments of Melvin Eisenberg and perhaps Holmes, relies on assumptions about society, and norms that cannot survive moral scrutiny in our heterogeneous social order. 3) Epstein’s How the Progressives Rewrote the Constitution. The canonical history of how the feminist, progressive, liberal, socialist, and communist movement was able to effectively destroy the rule of law under the constitution. 4) Barnett’s Restoring The Lost Constitution (I don’t believe that this is possible or advisable, and instead that we must create an institutional framework that supports a diversity of genetic strategies. But his analysis of what the constitution actually said, is exceptional, and therefore it is a prescription for how to articulate the rules of future institutions.) CAVEAT [I] don’t really want to spend a lot of my time with the law. I always feel that I’m slumming and need a shower afterward. But as an institution that we both require for calculative purposes, and an institution that must adapt to contemporary diversity and heterogeneity by expanding the concepts of morality and property. To do so, it’s necessary to articulate the impact on the system of common law, which shall remain the means of contract-making and dispute resolution under any more diverse propertarian model. FALURE OF CALCULATIVE INSTITUTIONS TO FACILITATE DIVERSITY OF INTERESTS, AND THEREFORE INCENTIVES AND CALCULATION Civilizations fail because their institutions can no longer calculate cooperation and the user of resources. (ie: Jarred Diamond is wrong. and I’m not so sure about Fukuyama’s and Acemoglu’s analyses have identified this problem correctly as one of property rights.) MORE DETAIL For more detail see Kinsella’s excellent list at mises.org which also addresses the historical development of the common law. In particular Tulluck’s criticism of the method of dispute resolution. A criticism I think is solved by Hoppe’s privatization and insurance model. Hopefully this was helpful to others. Cheers