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/sci/ - Science & Math

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2958049 No.2958049 [Reply] [Original]

Hey /sci/.

Today my philosophy teacher suddenly started talking about prime numbers and argued that a proof by contradiction isn't enough to prove that there are an infinite amount of primes. According to him there are some mathematicians who think that proof by contradiction in general is flawed. Yeah I know, he's not even a mathematician but this still got me interested and so I tried googling but didn't really find anything of relevance.

What do you think /sci/? Is this some wannabe-wise -philosopher's bullshit again?

Pic not related

>> No.2958056

http://en.wikipedia.org/wiki/Constructivism_%28mathematics%29

>> No.2958051

i hate proof by contradiction

>> No.2958067

As far as the mathematics goes, they are somewhat inelegant, but they are proofs nonetheless. The logic is sound.

Personally, I have no problem with them.

>> No.2958071

he's a retard. the proof is correct.

>> No.2958085

>>2958056
Reductio presupposes platonism.

>> No.2958096

>>2958049

Your professor should expand on what he's attempting to explain, imo. He's talking about certain mathematicians denying the "law of the excluded middle." Some logicians and mathematicians believe in the soundness of it; others disagree with it. Proofs by contradiction are built upon this notion.

In general, the law of excluded middle means this:
If it's not T, then it's F. If it's not F, it's T.

This is how proofs via contradiction works.

Primes are infinite? Suppose they're NOT infinite(not T); suppose they're finite(F). But, there's a flaw! So, they must be infinite(T).

>> No.2958107

> philosophy
Of course it's bullshit. Those people do nothing but spout bullshit. Name one worthwhile thing a philosopher has given us in the last hundred years, or the last thousand years.

Fucking nothing.

>> No.2958115

>>2958107

Democracy
Capitalism
Universities
Party politics

>> No.2958118

>>2958107

once you grow up a bit, and get out of high school, you'll stop having disdain for other disciplines.

To be a true academic means you cannot believe yours is superior.

>> No.2958122

>>2958118

>To be a true academic means you cannot believe yours is superior.

NUH UH I'VE PASSED ALL MY 9TH GRADE MATHS TESTS SO FAR I'VE GOT A JOB AT NASA LINED UP AFTER MY SCHOLARSHIP AT MIT THANKS

>> No.2959427

Proof by contradiction works well when the categories are mutually exclusive and exhaustive of the possibilities.

EX: infinite, finite,
even, odd
negative, 0, positive

>>2958051
>>2958096

only works when the above condition is met.

>> No.2959450

>>2958107

w-what?

decartes-coordinate plane
leibniz- calculus
godel - incompleteness
russell and whitehead - principia mathematica
frege - a fucking definition of numbers

these are all things which are important.

>> No.2959476

Does your philosphy teacher know that there are heaps of different proofs for the infinitude of primes?

I know that wasn't your point, but fuck. He should know what he's talking about.

>> No.2959539

the proof goes like this: if there are only finitely many primes, then we can construct this number (product of all primes + 1) which is strictly greater than all of the primes so far and also not divisible by any of them.

So if this fucktard of a philosopher piece of shit turdface wants to have a finite amount of primes then our whole system of integer arithmetic must be fundamentally flawed (i.e. contradictory).
Either this or the assumption of a finite amount of primes is wrong.

Your philosophy teacher doesn't understand shit. How he ever got to teach a class in anything is totally amazing.

>> No.2959548

>>2958118
I mean, I'd agree that hating on physicists or chemists or even economists or psychologists is stupid (guess what my major is) and I can't overstate my appreciation for philosophy itself but the majority of people who do study philosophy are pretentious pseudo-intellectual douches who aren't contributing anything to the world at all and think they're way smarter than they are because they ask inane and asinine questions with a fucking smug smile on their faces.

>> No.2959550
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2959550

>In philosophy class today
>talking about God and shit
>talk about how God doesn't want bad shit to happen, people choose to live in dangerous places and bring natural disasters upon themselves
>Teacher says "The people of Pompeii didn't know about the laws of thermodynamics and when the volcano was going to go off."
>mfw

>> No.2959587

Yes there is a possibility of both

>> No.2959686

>>2958107
Oh wow you're going to get owned.

You're so dumb so I'm going to name one; Descartes, he invented the coordinate system.