Are all mathematically true statements provable?

>>8758816
Please don't bait the intuitionistic logic fags, they already have a hard life, being autists

>>8758816
No, but I can't prove it

>>8758816
How do you know a statement is true if it can't be proven?

>>8758917
You don't.

>>8758917
Can't play the game without the rules

>>8758917
muh models

>He thinks Logic itself is without-a-doubt true

No

Counter example: "This statement can't be proven true"

it's true, but it can't be proven true, because then it'd be false

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>>8758816
You literally put the image of the guy who proved that no. gr8b8m8

>>8758917
Pythagorean theorem represented with rocks will always be true before humans do it,

If unproven statements aren't true, are you claiming that we have proven everything there is to be proven?

>>8758917
it's a gut feeling

>>8759449
and I took the b8. feelsbadman

No. Some of them are even outright incongruous to reality.

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>>8758837

>>8759451
I never said that. I said we don't know whether something is true or not if there is no proof.

>>8758917
>>8758816
define truth

>>8760222
https://plato.stanford.edu/entries/tarski-truth/

>>8760232
okay so it is just slapping the word truth on something that is not truth by essence. Glad to hear there is no truth in math nor logic.

>>8760243
Hey, blame reality.

>>8760249
preferring fantasies over reality would be nihilistic, better blame people's fantasy

>>8760222
Define define.

>>8760222
Define bait.

>>8760222
A series of arguments based on evidence and logic.

For example:
The appendix and the wisdom tooth is the reason why we think humans evolved.

The expansion of the universe is why we think the Big Bang happened.

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>>8758917
this guys just writing gibberish, r-right?

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>>8758917

This: >>8759033

Instead of saying
>The Gödel sentence is true but unprovable"
say
>The Gödel sentence can neither be proven true nor false
and you got a statement that still mind bending, but removed from the "true, from a point of view outisde of proof theory" spiel

And, in any case, the value of Gödels theorem is to show that a theory involving basic arithmetic can't be proven consistent using another theory that also has basic arithmetic build into it. E.g. implying you can't prove the consistency of any set theory with a weaker theory.

https://en.m.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

literally /thread/

>>8760421
>appendix and the wisdom tooth is the reason why we think humans evolved
Wrong. A wave function satisfying the developing of perturbations due to decreasing local energy is why humans evolved.


>expansion of universe is why BB happened
Wrong. Isotropy and nonzero CMB (cosmic background radiation) is.

>>8760421
Hello /sci/, I need your help as I'm a 83 IQ brainlet and discovered arithmetics a couple of days ago.
We have [math]N_p=\frac{p^p-1}{p-1}[/math] and we find that [math]N_p\equiv1\mod p^2-p[/math] and that if [math] l [/math] is a prime divisor of [math] N_p [/math], then it doesn't divide [math] p^2-p [/math]. How the fuck does this lead to [math] l\equiv1\mod p [/math]

Thanks in advance.

>>8760803
>how the fuck
If you are accustomed to using emotions as a tool for solving problems, you are not suited for science. Try economics, engineering, or labor.

>>8758917
Take the continuum hypothesis.
It's been proven that you can't prove neither the hypothesis nor its contradiction.
Yet either the hypothesis or its contradiction must be true, so whichever is is true but not provable.

>>8758917
watch
>this statement cannot be disproved.

>>8762472
This thread is about mathematics, not English.

Fucking moron.

>>8762353
>It's been proven that you can't prove

>>8760222
Trips have you cornered, OP. Checkmate, game and set, ready, match

>>8762353
>Yet either the hypothesis or its contradiction must be true
says the undergrad

>>8762353
>Yet either the hypothesis or its contradiction must be true,

nope. both are *inaccessible* from the usual set of acioms and either could be chosen as an additional axiom without upsetting consistency. how does it feel to claim that adding the "false" one to a set of axioms preserves consistency?

>>8760275
State the meaning of.

>>8758816
Iff you insist on a formal system

>>8762744
found the engineer

>>8762776
Intuitionism is a mental illness.

>>8763984
Intuitionism has nothing to do with it.

>>8760818
autism

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Yes but how well can they be proven is the question. There are usually more than one way to prove something, especially with regards to mathematics and geometry.

>>8762472
Yes it can

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>>8758816

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maybe