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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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Are numbers real, in a metaphysical sense?

I live and work with numbers almost all the time and have done so for most of my 77 years. I can almost feel them. But it is only almost. I have to believe, contra Plato, that they and moreover all of mathematics is unreal in a metaphysical sense. …
Stephen Meskin
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Finitistic objections to the current mathematical model

I recently read this pdf: Warning Signs of a Possible Collapse of Contemporary Mathematics, and I'm having some trouble understanding the issues it raises. The author says that the consistency of Peano Arithmetic cannot be proved within the system,…
Abel
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Logical 0, binary 0, decimal 0: are they the same?

Logical 0, binary 0, decimal 0: are they all the same in mathematics? A programming language might treat them differently, but is 0 just 0? No matter whether it is logical, binary, decimal, hexadecimal.
Quora Feans
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Is it possible for us to know something to be true without actually proving it?

I know, proof is the most crucial part of mathematics, it makes all the things be rigorous and keeps mathematics from contradiction. In real life, there's things that we know to be true, for sure. Such as in physics, objects with opposite charges…
JSCB
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About mathematics and the physical world

Suppose it is proven that in the physical universe all magnitudes are finite: there are no infinitely long magnitudes. there are no infinitely small magnitudes. Then: Would we get a mathematic contradiction? If we assume this to be true, then:…
Jose Antonio Martin H
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Basic atoms in mathematics

Given the concepts '1', 'set' and 'sum' (and maybe 'point' for geometry), can you build the whole mathematics upon then? If not, what other basic atoms would you need?
Quora Feans
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Is platonism assumed when writing down formal theories?

When one for example define a formal theory like ZFC, or even a formal theory of arithmetic, now such theories has infinitely many strings of symbols, that serve as its axioms, theorems etc.. Now proofs can be understood as collections of those…
Zuhair
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What is the deep meaning of this quotes acording to Sir David Hilbert logics?

One of the famous mathematician David Hilbert quotes: “Wir müssen wissen. Wir werden wissen." (We must know. We will know.) What is the deep meaning of this quotes acording to Sir David Hilbert logics ?
jasmine
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Do all mathematical and logical axiomatic systems implicitly ground natural numbers?

Maybe this question is more suitable for Philsophy SE, but I want to hear mathematicians' opinions. Suppose that we have an axiomatic system $\mathcal{A}$ with axioms $A_1, A_2, A_3,\dots,A_n,\dots$ Notice that this at least implicitly grounds…
God bless
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Is i an integer? If so, i/1, which is i, is rational. 1 is an integer, at least.

There's this maths joke, where $i$ says to $π$, "get rational!" while $π$ says to $i$, "get real!" (I like to say that $e$ says to the both of them, "join me, and we will absolutely be one!" (don't forget that $abs(-1) = 1$, and if needed, look at…
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the way we do it or the way it should be done

in the preface to one of his works Sir Bertrand Russell writes: .. in mathematics the greatest degree of self-evidence is usually not to be found quite at the beginning, but at some later point .. isn't it the contrary .. is it not at the very…
Matt
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Adding zero, multiplying times one... are they mathematical operations?

I saw a mathematician explain how the number 1 is not considered a prime number despite it fitting the traditional definition for a prime number; it is a natural number that can be divided by 1 and by itself yielding a natural number as a result.…
Carvo Loco
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Error in Introduction to Mathematical Philosophy

Is this an error in the text or am I reading incorrectly. What am I missing? Introduction to Mathematical Philosophy Page 18 Definition of Number “A relation is said to be “one-one” when, if $x$ has the relation in question to $y$, no other term…
user3042631
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Where does the importance of math come from?

It is a somewhat philosophical question. I personally believe that the importance of math is due to its usefulness and lots of applications. Mathematics is used in everywhere nowadays; as Ian Stewart said in his book Letters to a young…
Henry
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Sheafs appearing in philosophy?

I apologize in advance if I make mistakes in the following construction. I have very recently been introduced to the concept of a sheaf. I am currently a mathematics major and philosophy minor and have found certain concepts in mathematics to be…
Taylor
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