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Questions tagged [philosophy]

Questions involving philosophy of mathematics. Please consider if Philosophy Stack Exchange is a better site to post your question.

The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts.

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Do complex numbers really exist?

Complex numbers involve the square root of negative one, and most non-mathematicians find it hard to accept that such a number is meaningful. In contrast, they feel that real numbers have an obvious and intuitive meaning. What's the best way to…
Neil Mayhew
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Is mathematics one big tautology?

Is mathematics one big tautology? Let me put the question in clearer terms: Mathematics is a deductive system; it works by starting with arbitrary axioms, and deriving therefrom "new" properties through the process of deduction. As such, it would…
Coffee_Table
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How do I convince someone that $1+1=2$ may not necessarily be true?

Me and my friend were arguing over this "fact" that we all know and hold dear. However, I do know that $1+1=2$ is an axiom. That is why I beg to differ. Neither of us have the required mathematical knowledge to convince each other. And that is why,…
Aces12345
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Can a coin with an unknown bias be treated as fair?

This morning, I wanted to flip a coin to make a decision but only had an SD card: Given that I don't know the bias of this SD card, would flipping it be considered a "fair toss"? I thought if I'm just as likely to assign an outcome to one side as…
Andrew Cheong
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How far can one get in analysis without leaving $\mathbb{Q}$?

Suppose you're trying to teach analysis to a stubborn algebraist who refuses to acknowledge the existence of any characteristic $0$ field other than $\mathbb{Q}$. How ugly are things going to get for him? The algebraist argues that the real numbers…
Alexander Gruber
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Is 10 closer to infinity than 1?

This may be considered a philosophical question but is the number "10" closer to infinity than the number "1"?
termsofservice
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Is math built on assumptions?

I just came across this statement when I was lecturing a student on math and strictly speaking I used: Assuming that the value of $x$ equals , ... One of my students just rose and asked me: Why do we assume so much in math? Is math…
Anz Joy
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How is a system of axioms different from a system of beliefs?

Other ways to put it: Is there any faith required in the adoption of a system of axioms? How is a given system of axioms accepted or rejected if not based on blind faith?
Gabriel
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What is "ultrafinitism" and why do people believe it?

I know there's something called "ultrafinitism" which is a very radical form of constructivism that I've heard said means people don't believe that really large integers actually exist. Could someone make this a little bit more precise? Are there…
Noah Snyder
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Is mathematics just a bunch of nested empty sets?

When in high school I used to see mathematical objects as ideal objects whose existence is independent of us. But when I learned set theory, I discovered that all mathematical objects I was studying were sets, for example: $ 0 = \emptyset $ What…
Vinicius L. Deloi
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In what sense are math axioms true?

Say I am explaining to a kid, $A +B$ is the same as $B+A$ for natural numbers. The kid asks: why? Well, it's an axiom. It's called commutativity (which is not even true for most groups). How do I "prove" the axioms? I can say, look, there are $3$…
user4951
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Does mathematics require axioms?

I just read this whole article: http://web.maths.unsw.edu.au/~norman/papers/SetTheory.pdf which is also discussed over here: Infinite sets don't exist!? However, the paragraph which I found most interesting is not really discussed there. I think…
Kasper
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Infinite sets don't exist!?

Has anyone read this article? This accomplished mathematician gives his opinion on why he doesn't think infinite sets exist, and claims that axioms are nonsense. I don't disagree with his arguments, but with my limited knowledge of axiomatic set…
Nicolas Bourbaki
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Why do we not have to prove definitions?

I am a beginning level math student and I read recently (in a book written by a Ph. D in Mathematical Education) that mathematical definitions do not get "proven." As in they can't be proven. Why not? It seems like some definitions should have a…
Zduff
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I need mathematical proof that the distance from zero to 1 is the equal to the distance from 1 to 2

I didn't know how to phrase the question properly so I am going to explain how this came about. I know Math is a very rigorous subject and there are proofs for everything we know and use. In fact, I am sure that if there was anything that we…
Anonymous
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