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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.

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3answers
64 views

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 ...
0
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0answers
41 views

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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1answer
82 views

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 ...
8
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7answers
448 views

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 ...
1
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0answers
54 views

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, ...
3
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2answers
61 views

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 ...
3
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2answers
94 views

Is “everything is true unless the opposite is proven” a fundamental math philosophy principle?

I am not a mathematician, though I am aware that: Any forall-statement about empty set is (vacuously) true because $\neg{(\forall x \in \{\}: P)} \rightarrow \exists x \in \{\}: \neg P$, where $\...
0
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0answers
45 views

About Tegmark's mathematical universe

I'm not sure anyone else than Tegmark himself can answer this, but why not give it a try. Would Tegmark consider a cellular automata a mathematical structure? If nature is mathematical, isn't it also ...
1
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0answers
40 views

What qualifies as a geometry? [duplicate]

My question really is: What qualifies as a geometry? As in a Euclidean geometry; a Riemannian geometry, a hyperbolic geometry, etc. To give a sense of the depth of answer that I am seeking; consider ...
3
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1answer
100 views

A Probability Thought Experiment

Scenario: Lets say you have 100 trillion unique locks and their corresponding 100 trillion unique keys. You scramble them up, and then place all the locks and all the keys in two separate boxes. ...
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3answers
85 views

What is the real being(entity?) the word set or class denotes?

It is somewhat philosophical(at least to me). The question is as above. What is the 'substance' referred to as by the word set or class? Especially how is the thing called class defined? I cannot ...
0
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0answers
31 views

Is it possible to generalize without abstracting?

According to Wikipedia, Abstraction: Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which ...
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4answers
93 views

Should math logic reflect “real” logic

In math we use logic. However, it seems mathematicians were free to define some of its rules. Say the OR. It is true, if either of arguments is true - or both. Now we use math to prove some facts ...
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1answer
52 views

How many solvable and unsolvable problems exist

I am unable to quantify it as there are many problems which are in polynomial time and certain problems can be reduced to polynomial time.How exactly to quantify them?
2
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3answers
283 views

What's the difference between a proof and a derivation?

I did a BSc in Theoretical Physics, meaning that a lot of my time was spent deriving equations, making hand-wavy arguments, and arriving at solutions with a distinct lack of rigour. I'm now doing an ...
9
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1answer
448 views

Infinitely many axioms of ZFC vs. finitely many axioms of NBG

It is known that ZFC needs infinitely many axioms, but NBG (Neuman-Bernays-Gödel set theory) is finitely axiomatizable (as first-order theories of course). But both theories agree completely on the ...
0
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2answers
91 views

Why mathematicians use natural language? [closed]

This might be more on the philosophy of math side, but in the same way that lots of math is formalized, and everybody use the symbols in the same way, why not go further and only use an artificial ...
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1answer
55 views

Equation of Tango dancing [closed]

Good evening! I have been encouraged to ask my question on this forum, even though it might be perceived as a pure subjective and open-ended question, but I am 100% sure there is a perfectly ...
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4answers
49 views

How to prove A → (B ∨ C) given A → B

How to prove A → (B ∨ C) given A → B I know this is a valid argument, I'm just terrible at fitch-style proofs and have no idea how to start, let alone finish.
5
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0answers
91 views

Idempotent monads and dialectical materialism. [closed]

This question is part category theory and part philosophy. Lawvere claims that a Hegelian dialectic is an adjunction between idempotent (co)monads. The dialectical materialism of Marx and Engels is ...
16
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7answers
10k views

How to interpret material conditional and explain it to freshmen?

After studying mathematics for some time, I am still confused. The material conditional “$\rightarrow$” is a logical connective in classical logic. In mathematical texts one often encounters the ...
1
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1answer
76 views

Can we see all mathematical concepts as (possibly uncountable-time) algorithms?

Note: I am interpreting “algorithms” broadly, to include algorithms that require an infinite and even uncountable number of computational steps. It seems to me that any definition can be seen as a ...
0
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5answers
781 views

How does one understand and resolve Zeno's paradox?

Zeno, a follower of Parmenides, reasoned that any unit of space or time is infinitely divisible or not. If they be infinitely divisible, then how does an infinite plurality of parts combine into a ...
24
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5answers
3k views

Why isn't finitism nonsense?

This is a by product of this recent question, where the concept of ultrafinitism came up. I was under the impression that finitism was just "some ancient philosophical movement" in mathematics, only ...
0
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1answer
50 views

What makes a good mathematical theory?

I recently read about Galois connections, and that they show up in a lot of different places in mathematics. Given there apparent ubiquity, I thought they might have a rich theory. However, when ...
180
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25answers
15k views

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 ...
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10answers
2k views

Interviews of famous modern mathematicians

I was wondering, are there any good collections of interviews of famous modern mathematicians? It can be text interviews, or audio or video recordings. I am not sure what exactly I mean by "modern". ...
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2answers
53 views

The “correct” standard deviation

This may end up being a question more about scientific best practice than anything else, but I think this is the right community to ask it in to get the insight I'm looking for. Say I have two little ...
2
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1answer
123 views

Are axioms truly the foundation of mathematics?

It is said that the ZFC axiom system is a foundation of mathematics. In my understanding, for something to truly be a foundation, if you gave this system to an entity without any intuition or ...
0
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1answer
47 views

about two differrent opinions in mathematics

My question is: what is the name of mathematicians who ignore the proofs by contradiction and say all of the proofs should be constructive, and what is the name of opposite opinion?
37
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4answers
3k views

If all sets were finite, how could the real numbers be defined?

An extreme form of constructivism is called finitisim. In this form, unlike the standard axiom system, infinite sets are not allowed. There are important mathematicians, such as Kronecker, who ...
0
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2answers
72 views

Given axioms, how do we know it defines a geometry?

It is known that besides using coordinates and algebra, there are axiomisation of geometry such as Tarski, Hilbert and Euclid. However looking at the axioms of Tarski for example: Betweeness $B(\...
0
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2answers
78 views

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 ...
31
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8answers
4k views

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 ...
3
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1answer
93 views

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 ...
6
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2answers
227 views

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 ...
1
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1answer
405 views

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 ...
0
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0answers
10 views

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 ...
2
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1answer
105 views

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 (...
1
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2answers
328 views

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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3answers
619 views

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 ...
80
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7answers
14k views

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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1answer
79 views

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 ...
6
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2answers
85 views

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 (...
5
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1answer
226 views

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 ...
76
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3answers
6k views

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 ...
3
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1answer
126 views

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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1answer
31 views

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? ...
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1answer
69 views

Why is it possible to use logic? [closed]

First of all: there is a philosophy of mathematics tag in this SE, so this could be the proper site for my question. I do not know how to evaluate this. When we assume an axiom to prove something, ...
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0answers
111 views

What is a fair coin?

The title of this question is almost a retorical question. My point is that there is no way to define probability in a non circular manner. Let's say the probality of getting a tail when tossing a ...