Questions tagged [philosophy]

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

779 questions
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The language of mathematics is not absolute

I know that all the representation,the symbols,equations all this is a sort of expressing some universal fact mathematically. Understanding the universe doesnt mean learing those symbols and ...
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Coarsenings In Deutsch Et Al's Constructor Theory

Disclaimer: I posted a questions on constructor theory here a few days ago but received two closing votes, I guess because it consisted of several subquestions, so I deleted it and now try to focus on ...
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Philosophy of Math- Does Maths exist and what branches of maths support this [closed]

Clarifying Question What proof does mathematics offer that it is a universal rather than general/specific language? For context, please see the original message below. Original Message I want to ...
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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 ...
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What is this process/action called in English?

it is a fairly generate question regarding a terminology. People without science or engineering discipline makes an unfounded claim X, but people with such discipline start with proven facts A, B, C, ...
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Negative introspection axiom and Euclidean property of accessibility relation

Revising the modal logic principles, I have encountered an negative introspection axiom: $$\vDash \neg \square \alpha \longrightarrow \square \neg \square \alpha$$ with additional information, that ...
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Variables and Language

I've been thinking lately about the kind of language we use when doing math involving variables. Consider a typical variable defining statement: "Let x = 2." If we try to parse this statement ...
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Why do we call complex numbers “numbers” but we don’t consider 2-vectors numbers?

We refer to complex numbers as numbers. However we refer to vectors as arrays of numbers. There doesn’t seem to be anything that makes one more numeric than the other. Is this just a quirk of history ...
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How Brouwer think about mathematics as a non linguistic phenomenon?

I have a course in mathematical logic and i heard some argument about intuitionism math. I'am curious about it and i look at some book and i am just confused about phenomenon. But i realized brouwer ...
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The importance of prime numbers in physical theories

Imagine that a friend asks me about what is the importance of prime numbers in physics. What should I tell him/her? I know that natural numbers should be important in quantum mechanics because there ...
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Is category theory “conceptual”? [closed]

Warning: This question is in part philosophical in nature. Several prominent authors in category theory (CT) have claimed that CT is 'conceptual'. It is my impression that this sentiment is widely ...
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Does Mereological Logicism fit the Logicism program of philosophy of mathematics?

It appears that Ackermann's set theory can find a nice interpretation of its primitives in a theory that has logicistic genre. This is a personal work of mine of this issue, its present here. I ...
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What's the difference between predicate logic and model theory?

I studied model theory a little bit, and now that I'm reading the Wikipedia aricle on predicate logic, it seems to me that this is precisely model theory in that there is also the notion of signature (...
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What are the other foundations of math?

I know there are at least three foundations of math: Zermelo-Frankel set theory. (Sp?) ECTS Category theory Are there any others? Experimental foundations are welcome.
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Are there examples of mathematical problems proven by abduction?

Proof by deduction is simple. For example: All humans are mortal, and Bill is a human; Therefore, Bill is mortal. However, proof by abduction differs. A famous example: The lawn is wet. But ...
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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 "...
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Different math in physical multiverses or black holes?

Are there thoughts that different physical multiverses or black holes have different math, I.d. physical events follow the mathematics that is not discovered yet, whose logic may be different from ...
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Can a mathematical proof always be objectively determined as correct or incorrect?

Fields medalist Michael Atiyah claimed a simple proof of the Riemann hypothesis, but many mathematicians rejected his proof. Am I right in saying that Atiyah's proof is either objectively correct (...
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Formalist understanding of metalogical proofs

How can a formalist understand a metalogical proof such as the completeness theorem? These proofs exist exclusively outside of a logical system where the "rules of the game" are undefined. These sorts ...
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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 ...
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Is there criticism in literature of Euclid's fifth common notion (“The whole is greater than the part”)?

In Book I of Euclid's Elements, the fifth common notion says "The whole is greater than the part". For Euclid, magnitudes are objects that can be compared, added, and subtracted, provided they are of ...
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What is the minimum number of things needed to declare you have a variety? [closed]

When people say things like "we have a wide variety of products" or "product x can run in a variety of modes", what is the lowest number of modes or products which one can comfortably call a variety? ...