Speakpigeon wrote: ↑Mon Sep 14, 2020 8:14 pm
So what I actually said isn't at all what you claim I said.

I didn't "claim" you said anything. I quoted you saying it. Are you having memory problems?

Click the little blue arrow at the end of "Speakpigeon wrote: ↑" <--- right here, to convince yourself that you actually said the thing you insist you didn't say.

Speakpigeon wrote: ↑Mon Sep 14, 2020 8:14 pm
This is also fallacious. I would accept that all the

formal models you know are mathematical, but then you are ignorant of those which are no mathematical. Which confirms you are ignorant.

And I would accept that all the

FORMAL models you know are

FORMAL.

That's why they are called

FORMAL languages.

FORMALISM is the philosophical position equivalent to "syntax is semantics", so from the view-point of a

FORMALIST there is no difference between Logic and Mathematics.

Speakpigeon wrote: ↑Mon Sep 14, 2020 8:14 pm
This is also fallacious. Mathematicians outside mathematical logic use their logical sense to prove theorems, and so, no, mathematics doesn't rest on first-order logic. Mathematics rests on logic, i.e. the logic of mathematicians's logical sense.

If you can't even be bothered to read the first paragraph of a Wikipedia article you aren't just wasting your time, you are wasting mine too.

https://en.wikipedia.org/wiki/First-order_logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists" is a quantifier, while x is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic.

Speakpigeon wrote: ↑Mon Sep 14, 2020 8:14 pm
They also don't use the material implication to prove theorems. In fact, most of them are barely able to explain the difference between material implication and logical implication. You yourself would be unable to explain the difference.

This is also fallacious because first-order logic is not logic. Mathematics rest on logic, not first-order logic.

The meaning of the symbol "⇒" is entirely grammatical/syntactic. The rules of the FORMAL language determine what "⇒" means.

The rules determine whether A ⇒ B is a permissible thing to say. Outside of the rules of the language "⇒" means nothing.

That is why

Proof theory is 100% syntactic.

FORMALISMS are about FORM. It's right in the name.

Speakpigeon wrote: ↑Mon Sep 14, 2020 8:14 pm
And where is the proof that predicate logic is a correct model of logic?

This sentence is incoherent. In order to arrive at a "correct model of logic", then you are necessarily appealing to

Metalogic.

Logic concerns the truths that may be derived using a logical system; metalogic concerns the truths that may be derived about the languages and systems that are used to express truths.

The basic objects of metalogical study are formal languages, formal systems, and their interpretations. The study of interpretation of formal systems is the branch of mathematical logic that is known as model theory, and the study of deductive systems is the branch that is known as proof theory.

Proof theory is Mathematical.

Model theory is Mathematical.

Seeming as you are objecting to the use of Mathematics on your quest, what sort of proof-system or model-system do you have in mind when you demand a "provably correct model of logic"?

Any non-idiot (and you clearly don't fit in that category) knows the implications of Godel. Any system that can prove itself correct is incorrect.

Speakpigeon wrote: ↑Mon Sep 14, 2020 8:14 pm
Well, exactly nowhere, because predicate logic is, loosely, based on propositional logic and proposition logic is false logic.

Which notions to "truth" and "falsity" are you appealing to here?

In the FORMAL sense truth is just "⊤" and falsity is just "⊥". Is just symbols.

Speakpigeon wrote: ↑Mon Sep 14, 2020 8:14 pm
You obviously don't know, which only confirms you know very little about logic. You probably know a LOT about predicate logic, but nothing about logic that any idiot on the street wouldn't know.

You want to give lessons, but you are ignorant.

EB

Look, I know what I know. Little or a lot. I know some stuff about FORMAL languages such as Logic and Mathematics. The most powerful FORMAL languages are called

Unrestricted grammars. They are equivalent to Turing machines. Computers.

And I am a computer scientist. Or something. Telling you about the science of logic. You even

recognized my expertise.

Your OP asks an answered question, but you don't like the answer. I can't do much more for you.