Theme: Decidability

THE PRETENSE OF PROOF

(from elsewhere, against demand for proof)

I don’t know if I mean to target anyone with this criticism, so much as almost anyone who vastly overstates and possibly misrepresents what it is possible to accomplish with the formal logics (meaning deflationary grammars of constant relations, and their representation using symbols in general rules), versus the inherent human capacity that is a byproduct of recursive hierarchies of neural relations, that we call ‘logic’: the test of constant relations between states (in any single or set of dimensions).

I think this disconnect we face, is not lack of knowledge of the logics, but between people trained in rational (verbal) logic inherited from mathematics, law, justificationary philosophy, and scriptural interpretation of meaning) and people trained in the sciences (testimony of truth regardless of semantic reference), and a public not trained, but environmentally exposed to the semantics of both, and as such conflating them, – and therefore everyone talks past each other.

1- Reason (a human capacity of deliberate ‘calculation’),

2 – logic (the human capacity that makes reason possible),

3 – Logics (deflationary grammars) are not synonyms.

They refer to the biological ability to determine differences at ever increasing scales of relations(logic), the use of our ability to make use of logic in decisions of all scales (‘reason’), and the the discipline by which we create and use deflationary grammars to study the general rules that vary between different sets of constant relations.

So few logicians make the bridge between how scientific speech provides tests of truth (testimony that’s consistent, correspondent, operational(existential), moral(reciprocal), fully-accounted, and coherent by survival) – meaning ever contingent theories; and logic as he we it provides a test of internal consistency across axioms (propositions that are declared). In other words, the difference between truthful testimony about the universe given forever contingent knowledge, about speech itself.

Nor is it obvious that for anyone to make a truth claim requires the statement consist of incomplete knowledge – otherwise we are not testifying to the due diligence of our reason, but merely stating a tautology.

In other words, as far as I know you cannot prove any non trivial statement (which is why logic is not used outside of training people in the discipline of analysis) and the entire world operates on scientific speech, not the formal logics – whose application is extremely limited just as game theory is extremely limited – because knowledge is always too fractional, and relations in in minds too elastic, to make use of either.

We make proofs of internal consistency (not truth – we use “true” by analogy in math as we do in construction ‘plumb and true’) And we can create proos of internal consistency in mathematics because the relations of positions are by necessity constant – they cannot be otherwise.

I mean, mathematics consists in the logic of POSITIONAL relations. Numbers exist of nothing but positional names. In that sense, they are the only perfect information set of any complexity we humans work with, and of any scale. Which is why they are so useful to us: our tests of truth consist in the search for constant relations. If expressed in positional relations (as numbers) we are nearly guaranteed of the preservation of constant relations.

Unfortunately the semantics and grammar of the constant relations of positional names cannot always be applied to some categories (such as economics) due to the substitution of properties of categories we measure, and measurement of more granular transactions is beyond our current technical ability.

All speech relies upon grammar (rules of continuous disambiguation), and unfortunately because ordinary language grammar and semantics include fictions, fictionalisms, and the purely experiential and non-rational (unlimited), we tend to separate semantics(networks recursive references to sensory relations) and grammar.

Whereas the we apply logical reasoning (tests of constant relations) in everything from languages of the disciplines, legal and contractual, to the algorithmic, to mathematics, to ‘the logics’, and each consists of a deflationary grammar (a more constrained set of rules of continuous disambiguation) which also consists in a deflationary semantics (in other words, semantics of any deflationary language are demonstrably bound by grammar).

And as such, the deflationary grammars allow us to limit semantic content to a subset of the constant relations we are capable of perceiving and remembering, recalling, and comparing, by analogy to sense-experience – thereby making testable comparisons possible within the limits of human perception.

In my experience Logic (Formal logic) is almost never used to make an assertion of truth proper, (as is science) but as a means of falsifying the assertions of others.

In this sense, like pilpul, religious scripture, and law, it serves as a means of preventing non-conformity in arbitrary relations (justification, scripture, norm, and law), while science consist largely of an effort to circumvent the failings of logic ( interpretation of scriptural, philosophical, moral, legal prose of arbitrary relations) by limiting us to a grammar and semantics that consist exclusively of continuous relations with reality – not just continuous relations between written or spoken words (textualism).

And to no small degree it certainly appears that philosophical logic can neither join mathematics, nor join the sciences, and serves little other purpose than training us to falsify language – not to demonstrate truths (statements about reality).

We use logic to falsify inference between propositions. And that is its’ function. We *can* use logic like any of the formal deflationary grammars, to discover what we cannot articulate, and because we cannot articulate it,we learn we do not understand it.

So we can use logic ‘against’ (to test) our thoughts about our thoughts, the way we can use empirical tests against our thoughts about the universe.

Conversely we make arguments in science to falsify non correspondence with reality. And that which survives does so.

One can positively construct a proof given perfect knowledge (Axioms – Positional Names are perfect knowledge and mathematics axiomatic, meaning declarable) where one applies tests of constant relations to falsify the correspondence between statements.

Whereas one cannot do so under contingent knowledge whose constant relations are not provided by declaration (definition).

Instead since we never know if any non trivial statement (premise, proposition) is false, then we can only seek to falsify inferences from it.

Or stated differently, logic of ordinary language (imperfect knowledge) serves only as a means of determining inconstancy of relations between propositions – not truth (consistency, correspondence, existence, morality, and coherence) between our statements and reality.

Asking for proofs is the same category of error in logic that we call ‘mathiness’ in economics. Math-envy. It’s one of the reasons in almost any general proposition describing a distribution, one cannot achieve greater precision than a single regression analysis.

We are forever limited because our knowledge is always continent, because the set of constant relations that provide commensurability (coherence) in the semantics of our languages, is subject to reorganization (albeit it appears, greater parsimony) as knowledge (and therefore paradigm: the set of constant relations within a domain) change.

So it’s a kind of “fraud or pseudoscience”, to demand a proof of an asserted truthful statement about the world – it can’t be done other than for the reductio ad absurdum.

And I generally find people who conflate the study of logic for the purpose of studying logic (grammars of constant relations) itself, by the construction of proofs, pretenders to knowledge and wisdom when they ask for proofs rather than use logic for it’s only possible purpose, which is to demonstrate the failure of constant relations in claims of constant relations about the world. It is just a continuation of the invention of that great deceit we call scripturalism, and the technique used to justify it ‘pilpul’.

Instead, statements either survive criticism of consistency (internal consistence), correspondence, existential possibility (constant existential relations in operational grammar and semantics), morality(reciprocity), fully accounting (avoiding cherry picking), and coherence (constant relations across all those dimensions.

If a statement survives such falsification then it is a truth candidate. If not it is not. But one does not construct a proof of anything that is not complete, axiomatic, and declared. On only tests statements as if they were complete, axiomatic, and declared. To say otherwise is to claim that which is demonstrably false.

Criticism serves as a market like any other – by Internal criticism, demonstration criticism, market criticism, and ultimate survival.

But demands for warranty of perfect information are a kind of fraudulent argument. It is a common kind of fraud. A logical violation in and of itself. But that does not stop it from being a widespread exercise in dominance expression and silencing non-conformity rather than whether speech is false or survives falsification.

if you cannot explain something in operational language either you do not understand it (which does not mean a carpenter cannot use a drill without understanding the electric motor), or you are trying to preserve a deception, whether a deception by convention, or a deception by overstating the veracity of one’s system and units of measure.

One does not prove an argument. One puts for a theory, informs others as to its method of construction, and asks them to falsify whether it it is consistent, correspondent, existentially possible, reciprocal, fully accounted and coherent. Either it survives or does not. However, one might pull a statement out of think air, provide no justification, and such a statement could survive (and often does) all attempts at falsification.

But NO DIMENSION IS CLOSED. That’s the lesson of the 20th century’s exercise in attempting to merge mathematics and language. The logics (other than the trivial_ are not closed, and therefore the test of correspondence defeats the test of consistency, just as the test of operational grammar defeats the test of correspondence, just as the test of reciprocity defeats the tests of correspondence, just as coherence defeats all. The only test of truth is science: falsification in each dimension of action possibly by man. The rest is pretense. So a great deal of ‘contradiction is not as such contradiction but merely appeal to the next dimension (correspondence) rather than dependence upon the impossible completeness of the underlying propositions that an argument is built from. I find this the most common error of people trained in philosophy, logic and rhetoric, – even mathematics – but not trained in the hard sciences. (Albeit the criticism works both directions.)

Ergo, just as pseudoscience exists, peudorationalism exists, and the pretense that we can justify rather than falsify a statement is endemic.

Yet, what we CAN do with justification is make arbitrary ordinary language statements just as we can express arbitrary mathematical statements and test whether they are internally consistent across states (statements).

But there exist no non-arbitrary true statements, only truthful statements about arbitrary statements. Hence why philosophers and theologians rely on rationalism: because one can (as we see in numerology, astrology, philosophy, and theology) anything at all.

Justification tells us little other than to suspect the speaker of deceit or fraud.

A scientist (falsificationist), like science itself, evolved both in the ancient world (reason) and in the early modern (empiricism), and currently in the later modern, as a means of falsifying the frauds made possible by justification in each of those eras. Specifically those of the Germans and French (Rousseau, Kant, Hegel) and most importantly those of the Marxists (pseudoscience and pseudorationalism), Boazians (pseudoscience), Freudians (Pseudoscience), Cantorians (pseudoscience, but artful), postmoderns (outright denial and deceit as an attack on truth), and every group in between that took advantage of the ability to overload the very limited ability for humans to test constant relations in other tha trivial causal density.

Humans are only capable of cognition and therefore arguments in N dimensions (listed above), and truth propositions (theories) must be tested in each of those dimensions without appeal to closure in any, before we can warranty due diligence on our parts, that we do not engage in ignorance, error, bias, wishful thinking, suggestion, suggestion, obscurantism, fictionalism (pseudoscience, pseudo-rationalism, pseudo-historicism/myth), or outright lying.

Curt Doolittle

The Propertarian Institute

Kiev, Ukraine