Anonymous at Sat, 27 Jul 2024 10:23:47 UTC No. 16298720

>>16298717
>Is intuitionism wrong?
No, and it's intuitively obvious why not.

Anonymous at Sat, 27 Jul 2024 10:27:31 UTC No. 16298726

>>16298717
Maybe I'm misunderstanding the discussion but it sounds like since we can't explain gravity that gravity doesn't exist.

Anonymous at Sat, 27 Jul 2024 10:31:57 UTC No. 16298733

>>16298720
>>16298726
"Intuininist" is the name for certain dudes like Brouwer.
> https://en.wikipedia.org/wiki/Intuitionistic_logic

They basically claim that the principle of the exluded middle cannot be hold because there are certain sentences we cannot show a prove or a disprove.
I mean, this whole thing is based on the idea that "x is true" = "x is proven" or at least CAN BE PROVEN.

Gravity is not a talking point here. More prime numbers or the succession of the number pi.

Anonymous at Sat, 27 Jul 2024 11:29:08 UTC No. 16298783

>>16298717
>We already know that there are certain true statements, which cannot be proven
No we don't.

Anonymous at Sat, 27 Jul 2024 11:33:42 UTC No. 16298788

>>16298783
>No we don't.
What about the Continuums Hypothesis?
After the work of Gödel und Cohen, we know that this statement cannot be proven or disproven in the stndard set theory.
Either the theory is true or false. If the statement is true, then we have a instance of a statement which is true and cannot be proven.
In the case of the falsehood of the statement, the negation would be true like the orginal statement.
In any ways, there is, at least, one statement which is true and cannot be proven.

Anonymous at Sat, 27 Jul 2024 11:34:42 UTC No. 16298789

>>16298783
>>16298788
Not to talk about the AoC, which seems harsh arbitrarily to me.

Anonymous at Sat, 27 Jul 2024 11:40:10 UTC No. 16298795

>>16298788
>Either the theory is true or false
Why? The statement is "there is no cardinality between that of the reals and the naturals". Why do you think this statement has a truth value independent of the axioms you choose?

Anonymous at Sat, 27 Jul 2024 11:47:40 UTC No. 16298803

>>16298795
Otherwiese, we would just bald identify true with "proven within a given axiom system".
But Gödel and Tarski show us, as far as I catch the point, that this doesn't be true. There are statements which are true but cannot be proven.
You cannot define "truth" with only formal means.

Therfor, I guess, any theory or "philosophy" which implies that any true statement can be proven is false. In the same strict sense in which theories or "philosophies" are false that denied that anything is true at all.

Anonymous at Sat, 27 Jul 2024 11:50:42 UTC No. 16298810

>>16298717
>How could this asstertation be hold in the light of the discouveries of Kurt Gödel and Tarski and even Heisenberg?
The incompleteness theorem precisely asserts that "truth" is a meaningless concept and that the only well-defined notion is instead provability in a given formal system. An alternative way to phrase this is that "truth (in a given metatheory" is just the lifting of "provability (in a given object theory)" into the meta-meta-theory.

Anonymous at Sat, 27 Jul 2024 12:03:33 UTC No. 16298821

>>16298803
No, Godel and Tarski just produce proofs of some statements. To interpret those statements as saying something about the limits of formal systems requires you to make additional metaphysical assumptions.

Anonymous at Sat, 27 Jul 2024 12:25:20 UTC No. 16298832

This was literally explained and solved 2400 years ago by Plato. If your shitty university taught you some actual history of science instead of LGBT feminism you wouldn't need to ask such stupid questions.

Anonymous at Sat, 27 Jul 2024 12:50:01 UTC No. 16298845

>>16298803
>But Gödel and Tarski show us, as far as I catch the point, that this doesn't be true. There are statements which are true but cannot be proven.
Given that Tarski's theorem is popularly known as "the undefinability of truth", I'm curious how you used that to arrive at the conclusion that true statements exist.

Anonymous at Sat, 27 Jul 2024 13:38:29 UTC No. 16298886

>>16298845
YOu can't define truth WITHIN a given formal system.
Doesn't mean there is no true at all. Tarski developed a thoery about "snow has fallen" is true iff snow has fallen.

You can define "is proven" within a formal system. So, Truth must be something different than just proves.

>>16298821
I don't make any assumptions. I just see where the facts guide me.

>>16298810
Explaine more.

Anonymous at Sat, 27 Jul 2024 13:40:26 UTC No. 16298888

>>16298832
> This was literally explained and solved 2400 years ago by Plato.

Where, how?
Platon cannot know Gödel nor Heisenberg.

Anonymous at Sat, 27 Jul 2024 13:45:47 UTC No. 16298892

>>16298888
In Plato's Republic. He didn't need to know Gödel. After all, OP doesn't know Gödel either. But Plato knew epistemology. Epistemology seems to be secret/forbidden knowledge nowadays.

Anonymous at Sat, 27 Jul 2024 13:48:10 UTC No. 16298894

>>16298892
Can you explain how exactly Plato answered OP's question or can you only continue to posture and wank yourself?

Anonymous at Sat, 27 Jul 2024 14:52:17 UTC No. 16298975

>>16298886
>YOu can't define truth WITHIN a given formal system.
>Doesn't mean there is no true at all. Tarski developed a thoery about "snow has fallen" is true iff snow has fallen.
If snow has fallen, then the fact that snow has fallen is proof (in the metalanguage) that the statement "snow has fallen" is true, so this example on its own isn't enough to refute intuitionism.

In fact, Gödel's theorems have been formally proved in intuitionistic logic, which has a higher standard of truth than "ordinary"/classical logic, meaning that every true statement of intuitionistic logic is also a true statement of classical logic. So if "intuitionism is wrong" is a true statement, then you will not be able to prove it using classical logic without making your own system inconsistent as well.

Anonymous at Sat, 27 Jul 2024 15:00:37 UTC No. 16298991

>>16298894
Have you heard of the analogy of the line?

Anonymous at Sat, 27 Jul 2024 15:21:18 UTC No. 16299011

>>16298991
Present your argument in full and get it subjected to critique or gtfo.

Anonymous at Sat, 27 Jul 2024 15:40:00 UTC No. 16299021

>>16299011
Oh, it's not my argument. It's Plato's argument. You ought to read him, or at least that part of his work, before we can talk about it.

Anonymous at Sat, 27 Jul 2024 15:43:11 UTC No. 16299026

>>16299021
We're not talking about it. You present it, I critique it. You failed to present it, so I can only assume you have nothing of worth to say about it.

Anonymous at Sat, 27 Jul 2024 15:49:02 UTC No. 16299035

>>16299026
You are begging for either spoon feeding or bottom spanking. I will give you neither. I expect you to be mature enough to read a Wikipedia article on your own.

Anonymous at Sat, 27 Jul 2024 15:54:23 UTC No. 16299042

>>16299035
I stopped expecting anything from you quite a while ago.

Anonymous at Sat, 27 Jul 2024 15:58:27 UTC No. 16299048

NTA but you do need to read Plato though. Gödel "discovered" nothing that even the Pre-Socratics did not already confront

Anonymous at Sat, 27 Jul 2024 16:00:08 UTC No. 16299053

>>16299048
Are you aware that if you said something like that in a scholarly environment, you would lose all credibility whatsoever?

Anonymous at Sat, 27 Jul 2024 16:02:23 UTC No. 16299056

>>16299053
And that's a good thing. I do not wish to be associated with toxic narrow minded midwits.

Anonymous at Sat, 27 Jul 2024 16:05:36 UTC No. 16299061

>>16299056
That says a lot about you

Anonymous at Sat, 27 Jul 2024 16:13:32 UTC No. 16299077

>>16299053
you're asking a philosophy question on a science board. go post it again on /lit/ and see what happens

Anonymous at Sat, 27 Jul 2024 16:22:05 UTC No. 16299087

>>16299077
I don't think any serious philosopher would accept the statement "Gödel "discovered" nothing that even the Pre-Socratics did not already confront".
/lit/ might though

Anonymous at Sat, 27 Jul 2024 16:25:13 UTC No. 16299088

>>16299087
>serious
>philosophy
Does this juxtaposition prove the excluded middle?

Anonymous at Sat, 27 Jul 2024 17:53:54 UTC No. 16299189

>>16299077
>>16299087
Logic is both, "philosophy" (as long as we accept that disciplin teached on universities as philosophy, I know, this is controverse) and mathematics, and computer science and linguistics, too.

>>16298810
Lets assume we have a statement p like the Continuums Hypothesis.
Lets say, we just declare this statemet as neither true nor false but choise a pseudo-truthvalue called "basically undecidable".

So, we have a logic with 3 different truthvalues: true, false and "basically undecidable".
No, we need to define a negation ¬. I suggest we choice the Gödel-Negation for ¬ which means: "false if true, otherwise true".

In this case, we still get the resulte that :
¬ (p & ¬p)
¬p v ¬¬p | de Morgan
¬p v p | Double negation

Double negation isn't valid in intuitionism, I'm aware. I think, with the given definition, is not that of a problem.

My point is still, truth is something different as evidence since statements that are true and cannot be proven exist.

t. OP, yes, I'm a fag.

Anonymous at Sat, 27 Jul 2024 22:42:17 UTC No. 16299591

>>16298717
>So, "x is true" means the same as "there is a prove for x".
>How could this asstertation be hold in the light of the discouveries of Kurt Gödel and Tarski and even Heisenberg?
because "there is a prove for x" is different from "there is a prove for x from this specific set of recursively enumerable axioms"