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/sci/ - Science & Math

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10306202 No.10306202 [Reply] [Original]

Why do some people believe in proof by contradiction?

>> No.10306222

it's just as valid as any other proof

>> No.10306243

>>10306202
Because in some cases it is perfectly valid.
What you'll discover as you experience proving things is that different methods of proof have different weights in different cases.
What may not be able to be proved by contradiction in one case, may be able in another.
The solution being not to rule of a method of proof until you have determined it to be invalid in your case.

>> No.10306479

>>10306202
Proof built upon logic of course it's true tard

>> No.10306908

>>10306202
Because the axiom of choice is true

>> No.10306916

>>10306202
why do some people not?

>> No.10306917

>>10306202
because the principle of noncontradiction is a fundamental part of logic
[eqn]\left(A\implies B\land \lnot B \right)\implies \lnot A[/eqn]

>> No.10306990

>>10306917
But this doesn't imply proof by contradiction,
only proof by negation (see here for the difference http://math.andrej.com/2010/03/29/proof-of-negation-and-proof-by-contradiction/ ).

A proof by contradiction (¬¬A implies A) needs the law of excluded middle, which can be derived by the axiom of choice, which is something some people don't accept.

>> No.10306998

>>10306202
Do married bachelors exist, dumbass?

>> No.10307023

>>10306202

Food is good for you but some food is bad for you?

>> No.10307921

>>10306908
Kek

>> No.10307945

>>10306202
Because dialetheists wnd intuitionists are wrong.

>> No.10307949

Platonism is right and intuitionism is nigger bullshit

>> No.10307961

>>10306202
Why do some people believe in anything at all?

>>10306479
Why do you believe in logic?

>>10306908
Why do you believe in the axiom of choice?

>>10306998
My father is a married bachelor. His marriage is registered in one country but not in another country in which he lives.

>> No.10308008

>>10307961
>Why do some people believe in anything at all?
Because they’re not nihilistic retards.

>Why do you believe in logic?
Because logic strictly adheres to fundamental truths in reality. If there is a deviation between what works logically and what is observed in reality, it indicates there is a mistake in our understanding of one or both.

>My father is a married bachelor. His marriage is registered in one country but not in another country in which he lives.

When he’s in one country, he’s A and not B, when he’s in another, he’s B but not A. That does not contradict the idea that he can’t be A and B at the same time.

>> No.10308030

>>10308008
>Because they’re not nihilistic retards.
So just because it makes you feel better about yourself to believe that you know shit about the world?

>Because logic strictly adheres to fundamental truths in reality. If there is a deviation between what works logically and what is observed in reality, it indicates there is a mistake in our understanding of one or both.
There is no compelling evidence that the universe will always obey the same laws at any given time and place. The uniformity of Nature is merely a postulate. And even if that were the case, there is no evidence that our senses and our intellect can adequately discover and understand those laws. Most science consists in throwing shit at the wall while hoping that it sticks.

>When he’s in one country, he’s A and not B, when he’s in another, he’s B but not A. That does not contradict the idea that he can’t be A and B at the same time.
He doesn't magically disappear from the registers of those countries as he crosses the borders. He is a bachelor while being married.

>> No.10308085

>>10308030
>He is a bachelor while being married.
Only because your definitions of married and bachelor are inaccurate/incomplete.

>> No.10308102

>>10308030
I don’t reject nihilism to feel better about myself, I do it because it nihilism leads to the sort of trivial argumentation of isolating segments of statements instead of confronting a broader summary of thought.

The whole
>[quote]
>Why...?
>[quote]
>But...
>[quote]
>Why...?

Is a time wasting exercise that doesn’t actually seek to make a point or find an answer to a question. It’s just arguing for the sake of arguing. You aren’t condridicting anything in a meaningful sense, just trying to contradict the limitations of language.

>> No.10308622

>>10308102
>a time wasting exercise that doesn’t actually seek to make a point or find an answer to a question.
You're assuming that there is a point to be made or an answer to be found. You're free to do so (you're free to do whatever the fuck you want), but you shouldn't expect other people to hold onto your same beliefs.

>just trying to contradict the limitations of language.
Natural languages are inherently inconsistent because of their self-reference. That's why nearly every discussion is either circle-jerking or shit-flinging; that's also why wars exist and that's a good thing.

>> No.10310022

>>10306202
law of excluded middle