The Godel-sentence G is proven true in a meta-theory that is ordinary arithmetic. It is not at all controversial that in plain arithmetic the Godel-sentence is true.
It is completely a confused notion that G is false. — TonesInDeepFreeze
The poster said that G is untrue. Now he says he did not say it is false. — TonesInDeepFreeze
What a seriously risible argument the poster makes! Really, the poster is as hopelessly ignorant, confused and irrational as they come. I've seen some that are more dishonest, but the poster ranks fairly high in dishonesty too, as just witnessed that he touts a Wikipedia article that actually shows the OPPOSITE of his own claim! — TonesInDeepFreeze
Truth preservation is: If the premises are true then the conclusion is true. And that is PROVABLY upheld by classical logic. — TonesInDeepFreeze
Every expression of language X that is {true on the basis of its meaning} can only be verified as true on the basis of a connection to this meaning. — PL Olcott
The poster has to be bot. — TonesInDeepFreeze
The poster lies that I believe that PA proves G or it proves ~G. It is the opposite. PA proves neither G nor ~G. That is the very statement of incompleteness. — TonesInDeepFreeze
Whatever else the poster thinks he is doing, he claimed that classical logic is not truth preserving. I explained why that is false. The poster still refuses to understand the matter. — TonesInDeepFreeze
I am precisely focused on the central point from which this discussion is pursuant: — TonesInDeepFreeze
This isn't a particularly productive discussion. — fdrake
It is exactly your fault, Olcott. By my count through at least 450 posts in good will and good faith made in an attempt to gain any clarity about what you are talking about, you have dodged, evaded, and avoided every attempt, content to make and repeat nonsense claims, and when pressed to change the subject.It is not my fault.... — PL Olcott
It is exactly your fault, Olcott. By my count through at least 450 posts in good will and good faith made in an attempt to gain any clarity about what you are talking about, you have dodged, evaded, and avoided every attempt, content to make and repeat nonsense claims, and when pressed to change the subject.
Not a good look for you, and to my way of thinking making it impossible to have any respect for you. Sympathy? Maybe. Respect - which also implies trust - no. — tim wood
I agree.This isn't a particularly productive discussion. — fdrake
Every expression of language x that is {true on the basis of its meaning}
can only be verified as true on the basis of a connection to this meaning.
This does enable a True(L, x) predicate to be defined where L is a formal
language of a formal system. — PL Olcott
In mathematics, do you think there can be true, but unprovable statements? — ssu
I've not made any ad hominem attacks. Please understand that just repeating the same thing will get tempers to rise. Always true to really think what the other one is trying to say.When I provide a simple yes/no answer all that I get is ad hominem attacks
without anyone even looking at what I said. — PL Olcott
But we do! We can give an indirect proof.True and unprovable never means EXACTLY what it says:
We know that X is true and have no way what-so-ever to know
that X is true yet we know it is true anyway, as if by majick. — PL Olcott
But we do! We can give an indirect proof. — ssu
Then is never really was literally unprovable.
True yet cannot possibly be proved in any way what-so-ever
does not allow indirect proof. — PL Olcott
So how can you prove this? Well, you prove it by reductio ad absurdum. So let's assume the opposite is true and hence statement S is provable and then go and prove that this cannot be. . Did you give a direct proof? No. You didn't prove S. You proved that not-S is false. — ssu
In mathematics, do you think there can be true, but unprovable statements? — ssu
Truth-maker making it true means that there's a proof that it is true? Sorry, with negative self reference you can easily do that.There cannot possibly be any expression of language that is true and does not have a truth-maker making it true. — PL Olcott
What do you mean by this? Again, the ability to give a direct proof and something to be true are two different things.When it is said that G is true and unprovable it never means EXACTLY what it says. — PL Olcott
When it is said that G is true and unprovable it never means EXACTLY what it says.
— PL Olcott
What do you mean by this? Again, the ability to give a direct proof and something to be true are two different things. — ssu
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.