You are still conflating justification with truth, and consequently ascribing views to both of us that we did not state and do not hold. — aletheist
I would say it's the toes.
But seriously speaking, other things are necessary than just the lack of known counterexamples. So I say this is a false assessement of my stand, please disregard the quote by TheMadFool that attributes this to me.
Now I am not confident that @aletheist claim is properly written, either.
So I refuse to make a statement on a potential Strawman. — god must be atheist
No, justification is about why someone believes a proposition, while truth is about whether that proposition represents reality. Besides, if justification were necessary for truth, then only justified beliefs could be true, which is not the case.Do you think justification is necessary for truth? — TheMadFool
No, he did not say that, either. He said that an absence of counterexamples can be taken as justification for a belief; proof is a stronger form of justification.You say that if a claim doesn't have a counterexample it can be taken as proof. — TheMadFool
Besides, if justification were necessary for truth, then only justified beliefs could be true, which is not the case. — aletheist
Lots of people believe things without justification that happen to be true. That is why the standard modern definition of knowledge is justified true belief, not merely true belief.Can you name one unjustified truth? — TheMadFool
Nuancing science is what mostly happens, rather than "revolutions" or even "falsifying" (unless the proposition had been very narrow). — Fine Doubter
I read in Knowles that Anselm (and I type from memory) translated "necessarius" as "admissible" and not "compelling". (However he spoiled everything by attempting a so-called "ontological proof" which I am told Descartes swallowed.) — Fine Doubter
Lots of people believe things without justification that happen to be true. That is why the standard modern definition of knowledge is justified true belief, not merely true belief. — aletheist
. I really adore ifs and I really adore buts - I think they are so firm and reliable. — Fine Doubter
Isn't true but unprovable a contradiction? — TheMadFool
The proof for the diagonal lemma itself is also purely syntactic. — alcontali
Like "Colorless green ideas sleep furiously"? No meaning? I though proofs need to be meaningful. — TheMadFool
No. Consider Goldbach's conjecture(GC):Every even integer greater than 2 can be expressed as the sum of two primes.Isn't true but unprovable a contradiction? — TheMadFool
But it demonstrates that conceptually, propositions can be true but unprovable. — Relativist
Unprovable in the system, but provable outside the system. — tim wood
That's not true.Goldbach's Conjecture is not "semantically empty": all the terms and relations are well defined (prime number, even number, sum). If true and unprovable, it is because the formal system of peano arithmetic is incomplete. That's what Godel's incompleteness theorem is all about: incompleteness = there are unprovable true statements in the formal system.if I can't prove a proposition in a given system x, that proposition can't belong to that system. — TheMadFool
Godel's Incompleteness theorem is about formal mathematical systems. It has no metaphysical implications. Similary, the uncertainty principle of Quantum Mechanics has no relation to the uncertainty various metaphysical claims.I can form the grammatically correct sentence "the uncertainty principle is true" with words that occur in theism in statements like " it is true there's no uncertainty regarding god's existence", "god commands us to live by the moral principles he laid out". The uncertainty principle is a fact in quantum physics, a totally different system to theism and insofar as theism is concerned, the sentence "the uncertainty principle is true" is meaningless. — TheMadFool
Take a look at Un's pot just above yours and follow the link. — tim wood
The mapping works because no two formulas will ever end up with the same Gödel number. — Quanta article
“The formula with Gödel number sub(y, y, 17) cannot be proved” — is sure to translate into a formula with a unique Gödel number. Let’s call it n.
Now, one last round of substitution: Gödel creates a new formula by substituting the number n anywhere there’s a y in the previous formula. His new formula reads, “The formula with Gödel number sub(n, n, 17) cannot be proved.” Let’s call this new formula G.
Naturally, G has a Gödel number. What’s its value? Lo and behold, it must be sub(n, n, 17). By definition, sub(n, n, 17) is the Gödel number of the formula that results from taking the formula with Gödel number n and substituting n anywhere there’s a symbol with Gödel number 17. And G is exactly this formula! Because of the uniqueness of prime factorization, we now see that the formula G is talking about is none other than G itself. — Quanta article
So what do you think is happening here? Do you think that Godel's argument fails? Or do you think that you need to do more to understand it?
One choice leads to understanding. The other, to psychoceramics. — Banno
What's your point Madfool? — tim wood
Unprovable in the system, but provable outside the system. — tim wood
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