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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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Is a proof still valid if only the writer understands it?

Say that there is some conjecture that someone has just proved. Let's assume that this proof is correct--that it is based on deductive reasoning and reaches the desired conclusion. However, if he/she is the only person (in the world) that…
beep-boop
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What is(are) the reason(s) for defining things in the following way?

In this answer it is written that, In modern mathematics, there's a tendency to define things in terms of what they do rather than in terms of what they are. My questions are, What is(are) the philosophical and mathematical reason(s) for doing…
user170039
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What is more important in Mathematics, Theorems or its Proofs?

Felix Klein once said, Mathematics has been advanced most by those who are distinguished more for intuition than for rigorous methods of proof. Till now I thought the opposite. I thought that it is the rigorous methods of proof that requires more…
William Hilbert
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What are the most important questions or areas of study in the philosophy of mathematics?

This question is intended to complement What mathematical questions or areas have philosophical implications outside of mathematics?
Casebash
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What exactly is real number?

This question may sound philosophy, but it has been bothering me for a very long time, therefore I have to ask it here. The story goes back when my first time reading Apostol's Calculus, then I had learned what real number is by the way Apostol…
Shing
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Is there an online Q/A forum for the philosophy of mathematical practice?

Certain philosophers of mathematics are interested in aspects of the philosophy of mathematical practice. Mathematicians, perhaps, would be interested in philosophy that may affect their day to day work, as is noted near the end of Gowers's article…
Jon Bannon
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Logic as subset of mathematics and mathematics as subset of logic

Is logic a subset of mathematics or is mathematics a subset of logic? I have heard the former view, but is there any argument for the latter?
vanattab
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How much math does one need to know to do philosophy of math?

I'm looking for advice from mathematicians who also study philosophy of math (PoM). Due to interest I'd like to study PoM as a hobby, but I'm worried if I don't understand math well enough from a pure math perspective I will make errors in reasoning…
Epistechne
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How many instances of some mathematical object (e.g. an integer) are there?

My question is simple: How many instances of a particular mathematical object are there and what's the reason for it? One? Two? Infinite? Undefined? For example, how many instances of the integer "1" are there? Is the first "1" in the equation "1 +…
Ruperrrt
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What is characteristic (function, polynomial, etc)?

My question is - what's the nature of characteristic functions, equations and so on? Am I right in understanding that this is just the general term for naming "ways" to find some invariants of some object? Or is there some other meaning?
hmax
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What is a "trivial implication"?

This is a philosophical question. Most often when a certain axiom or proposition implies another proposition, this implication is not trivial, or "immediate". That is, you need a proof consisting of some number of steps to reach the second…
user56834
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Are there any situations where you can only memorize rather than understand?

I realize that you should understand theorems, equations etc. rather than just memorizing them, but are there any circumstances where memorizing in necessary? (I have always considered math a logical subject, where every fact can be deducted using…
user26649
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Are "proofs" that are contingent upon physical reality valid?

Consider the following statement: Let $P$ be any polygon and let $A$ be a point inside of $P$. Then there exists at least one side of $P$ such that the perpendicular from $A$ to said side touches the side within $P$. Now consider the following…
arshajii
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How Do You Know If Mathematical Definition Matches Up With Reality?

This is probably one of the biggest question I have when learning some mathematics. I always wonder if I have a concept in my head lets say continuity. Lets I want this concept to be able to characterize a function that has "no breaks"; it is…
Kamster
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Truth of Fundamental Theorem of Arithmetic beyond some large number

Let $n$ be a ridiculously large number, e.g., $$\displaystyle23^{23^{23^{23^{23^{23^{23^{23^{23^{23^{23^{23^{23}}}}}}}}}}}}+5$$ which cannot be explicitly written down provided the size of the universe. Can a Prime factorization of $n$ still be…
Maazul
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