Working Through The Logic

Enjoy.

anirban.metal wrote:

I'll share whatever I know about logic.

Hello Anirban, great post.

I'm going to go into one aspect of what you bring up here - I'll be able to give some indications of what I wish to do with logic.

Quote :

We've got classical logic and intuitionistic logic, which varies in that in intuitionistic logic the law of excluded middle and the principle of double negation are not tautologies, and reductio ad absurdum fails to remain a valid approach to construct proofs as a consequence. All proofs are required to be constructive as in if one is arguing the existence of something, then an algorithm for it's construction should be implicit in the proof.

Logic unfortunately, like the rest of mathematics, is based on the same Hilbert like axiomatic system. We have to take certain propositions for granted, as an example, modus ponens ({Px →Qx, Px} ⊢ Qx). Or the formula

∀ x : (Px → Qx) → (∀ x : Px → ∀ x : Qx)

has to be treated as a logical axiom. One could argue about their validity in a metalanguage, but I have never attempted it.

The axiomatization of a logical system can be done in multiple ways (as in one could ad libitum choose different sets of axioms but end up with the same logic).

A good property which we desire of any logic to have is completeness and soundness, which establish that one can syntactically derive a proof of a proposition if and only if it's a semantically valid sentence.

After sufficient amount of bootstrapping, we get fancy meta theorems like the deduction theorem, reductio ad absurdum etc.

Value Ontology as we use it here has use of intuitionistic logic, that is to say that the notion of Truth is shifted from the outcome of the formula, to the mechanism of the formula itself.

The process, the way by which data is gathered into coherence, into a logical 'object', is that very 'object', prior to its specific content. The object, or 'logical inevitability' is thus presumed, or postulated empty and a priori as a necessary outcome, before the relevant data sets are led into that outcome.

We do this because in all cases of representation of knowledge, the 'object' is brought into being arbitrarily, haphazardly, and 'accidentally' almost - simply because there is no other way of representing.

But VO replaces 'object' and 'truth' and 'result' and 'fixed value' and 'Constant' and more with 'self-valuing', meaning an active agent, that enters into our logical faculties and processes as an active element, to which we respond - the formula is the axiomatic but truth to which the mind gives further substance.

The work of constructing a formal logic is predominantly problematized by the fact that 'self-valuing' is the only 'empty' value - there aren't any variables except direct derivatives such as 'valency' - thus the process is changed and the concept 'variable' has taken on an entirely different meaning - after all, being itself is now a variable, whereas only Being as Logically Soundly Spoken is axiomatic, fixed, and operative.

I am not schooled in the terms of formal logic but all the more in its application, due to an early background in theoretical astrophysics, which is a field that posits, simply by observing reality, a lot of logical conundrums that, within themselves, contain proper logical propositions, that have not been yet derived, or made. Reality gives birth to logic, and value ontology is a logic without any presumptions of values, or constants, except the entirely unavoidable epistemic axiom that a statement of fact is itself a phenomenon, which' ground does not need have anything to do with the ground to the fact it states.

It is a logic to contextualize logical formula and logically arrived-at truths within a logic about logic, or a logic about statements. It thus potentiates logical processes, as the very mechanism of its logic assembles all other types of logics and semantic substances its own context.

Obviously this method is entirely unconventional and 'rogue' -
it does not give a shit about line around concepts or languages.



Welcome to Before the Light, anyway,
a bit belated but certainly meant.


FC