All Questions
Tagged with philosophy soft-question
251
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4
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0
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(When) are recursive "definitions" definitions?
This is a "soft" question, but I'm greatly interested in canvassing opinions on it. I don't know whether there is anything like a consensus on the answer. Under what conditions (if any) are ...
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4
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Proof by Contradiction: "Bad Form" or "Finest Weapon"? Reconciling Perspectives [duplicate]
G.H. Hardy famously described proof by contradiction as "one of a mathematician's finest weapons." However, I've encountered claims that some schools of thought consider proof by ...
1
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0
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120
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Are quasi-sets (and therefore Schrödinger logic(s)) studied by mathematicians or are they purely in the domain of philosophers?
Context:
I'm a fan of different kinds of logic. I'm conflicted about whether different logics actually exist beyond, say, a philosophical oddity.
The Question:
Are quasi-sets (and therefore ...
- 45.7k
3
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2
answers
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Creating larger structures from smaller ones without an explicit construction
I'm asking this question as a replacement for my previous one, which I admit isn't clear, and which I am voting to close. Hopefully I'll be clearer now.
Admittedly, I'm not sure if this question ...
- 585
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Finitists reject the Axiom of Infinity - are there groups who reject the others?
I've seen rejections of the Axiom of Infinity. This is called finitism. Some ultrafinitists even add the negation of the Axiom of Infinity. Definitely doable.
I've seen rejections of the Axiom of ...
- 351
2
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1
answer
100
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Why is it important to prove that some particular set is a vector space as opposed to just asserting such objects exist?
In Axler's Linear Algebra Done Right Example 1.24, we are asked to prove that the set of all functions from some set S to the set of real (or complex) numbers is a vector space.
I proved this by using ...
user1281086
5
votes
1
answer
154
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Is there a mathematical notion of "why"?
Is there a mathematical notion of "why"? That is, are there reasons behind the truth of certain mathematical statements? Personally, my belief is that true mathematical statements just are ...
- 21.4k
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What makes one proof different from another one? [duplicate]
There are around 370 different ways to prove the Pythagorean Theorem, but what does that exactly mean? For instance, if your proof states that $x^2+y^2=z^2$, I could construct a different one by ...
- 33
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1
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223
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What is the purpose of mathematical research? [closed]
This is a bit of a soft and philosophical question, but what is the purpose of mathematical research? It seems to me that there is no end goal of mathematical research, because everything can be ...
- 21.4k
2
votes
2
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115
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(Soft Question) Real World Modeling as Understood Through Pure Math
This question is necessarily vague; I'm not looking for an answer so much as I'm checking to see if this is something that has been thought about/discussed before, and if there are any resources out ...
- 2,221
2
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110
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Is expression and its result is the same thing?
So, $\frac{1}{2}$ and $0.5$ are just two different ways to address the same object which is rational number $\frac{1}{2}$.
What about more complex expressions? Like $\{a, b\} \cap \{b, c\}$ is just ...
- 37
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1
answer
80
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How do proofs of program termination depend on strength of logical systems?
I'm looking for clarifying insights on the following topic. While there can be no general proof strategy to show that terminating Turing programs do, indeed, terminate, some specific programs can be ...
- 41
1
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2
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304
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On the Consistency of Non-Euclidean Geometry
I've recently found a really old "Philosophy of Math" book in my University library, and in the book it says that the it has been proven that :
if non-euclidean geometry is inconsistent, ...
- 77
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13
answers
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Does the epsilon-delta definition of limits truly capture our intuitive understanding of limits?
I've been delving into the concept of limits and the Epsilon-Delta definition. The most basic definition, as I understand it, states that for every real number $\epsilon \gt 0$, there exists a real ...
- 287
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133
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Is a line/line segment not a composition of points?
At exactly 3:00 in this video, William Lane Craig states that a line is not a composition of points: a line is logically prior to any points that you specify on it. To assume that a line is a ...
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