Scott Mayers wrote: ↑Wed Feb 20, 2019 5:31 am
You don't appear to understand.

You seem to self-identify as somebody who "understands logic" and you sound like you have spent a considerable amount of time studying the Aristotelian religion.

So I am literally setting on a quest to prove to you that your life and identity are an error. The odds are against me...

Scott Mayers wrote: ↑Wed Feb 20, 2019 5:31 am
"First Order Logic" deals with the underlying logic of Propositions (statements or claims THAT can be answered with yes/no or some form of binary assignment, Predicates, an extension of propositions that include quantification (All, Some, None, etc) and to connected instances of terms withing propositions, Boolean algebra, which CAN extend to muli-valued systems (3 or more valued logics), and Set theory.

1. Any proposition that can be answered with a binary assignment is a decision problem.

2. First Order Logic is provably UNDECIDABLE.

So, literally - your proposition "First Order Logic deals with yes/no statements/questions" is false!

First Order Logic CAN NOT answer yes/no questions! Because it is undecidable.

There is a fundamental incompatibility here (I consider type theory - you consider set theory foundational) but I'll ignore it for now unless it causes more errors.

Scott Mayers wrote: ↑Wed Feb 20, 2019 5:31 am
Propositional and Predicate Calculii ARE proven complete and does 'decide' all possible combinations of any domain within it.

Completeness and decidability are unrelated criterions! First order logic is complete BUT undecidable!

Completeness deals with the deductive power of the system. Yes - First Order logic is complete.

Also you have left the contingency door wide open by saying "any domain within it". What is the boundary/domain of FOL?

Is it universal or context-specific? Rhetorical question. FOL is a Type-1 (context sensitive) grammar in the Chomsky hierarchy.

So a far more important question is "In what context does FOL fall apart?". The answer is self-evident: decision-making!

IF THE PREMISES ARE TRUE.

First order logic falls apart the moment you ask this question: Are the premises true?

Decision problem! FOL assumes truth is a given. It is not.

The part your brain mis-calculates is that you mistake "completeness" for "universality".

A first order logic which accepts "1+1=2" as true is a different system to a first order logic which accepts the premise "1+1=10" as true.

Both systems will be consistent and complete! The theorems of the first system will APPEAR to contradict the theorems of the other.

So for first order logic to be of any use all interlocutors have to agree on the truth-value of the premises. This leads to infinite regress.

Are the premises true? God exists.

Scott Mayers wrote: ↑Wed Feb 20, 2019 5:31 am
What Godel, Turing, and others were doing had to do with how all logics are proved on meta-level.

It's not meta. It's (whatever the antonym of meta is). You are pre-supposing foundationalism. Logic as a point of departure.

Logic is synthesized. The synthesis of logic is "reason" or "thought" or whatever else you wish to call it.

Metaphysics IS logic. So Choose your logic wisely.

https://philpapers.org/archive/ALVLIM-3.pdf
Scott Mayers wrote: ↑Wed Feb 20, 2019 5:31 am
Can you prove all mathematically complex systems beginning with these first-order types that ignore any 'contradictory' allowances.

Yes. Curry-Howard isomorphism. Proofs are programs.

http://www4.di.uminho.pt/~mjf/pub/SFV-C ... rd-2up.pdf
You have to abandon set theory and the law of excluded middle and adopt Type theory.

Scott Mayers wrote: ↑Wed Feb 20, 2019 5:31 am
"First Order Logic" deals with the underlying logic of Propositions

FOL doesn't do that. Because it's undecidable.