Questions tagged [philosophy-of-mathematics]

Philosophy of mathematics asks questions about mathematical theories and practices. It can include questions about the nature or reality of numbers, the ground and limits of formal systems and the nature of the different mathematical disciplines.

Filter by
Sorted by
Tagged with
2
votes
0answers
103 views

Nature of mathematics within philosophy

Short version: Considering that science is inevitably dependent on mathematics and metaphysics (Kant tried to raise metaphysics to the status of a science, which I find mandatory to improve the ...
0
votes
5answers
162 views

Is there any conflict with Holism and equals and plus signs of mathematics?

Edit - better phrasing/summary: Maybe this phrasing helps "the same object expressed in different ways". That's one meaning behind 'equals'. 10 = 1+...4 --> 10 really is 1+...4. So if ...
1
vote
3answers
201 views

Why does mathematics manage to represent a function of reality?

Why does mathematics manage to represent a function of reality? My question concerns how your logic and its structure (like topology, or the very fields of advanced logic in mathematics) manage to ...
1
vote
2answers
113 views

What are the mathematical concepts a computer implements?

I am well aware of theoretical work on the topic of algorithms, pioneered by Turing and Churchill as far as I know. Computers implement a large, but finite, set of algorithms. My question goes into a ...
0
votes
1answer
67 views

Can Mathematics be a tool to analyse immaterial existences

Doubt: Can we say that Mathematical thoughts (arguments) can be independent of physical (Time-space continuum or material) world since it is an abstract science. In other words can Mathematics be a ...
1
vote
2answers
104 views

criticisms of mathematical structuralism

A popular, pretty modern trend in the philosophy of mathematics has been to treat mathematical objects as only possessing properties within the context of a mathematical structure. Does anyone know of ...
1
vote
1answer
49 views

How to prove consistency of theory with metalanguage?

I am familiar with first-order model theory. I also know that Tarski's definition of truth was made precisely in order to avoid paradoxes related to metalanguage such as the Liar. My question is: how ...
1
vote
4answers
166 views

Can you cross a space from which a two dimensional plane is missing?

If I travel through 3d space, will my travel be stopped abruptly if I encounter a 2d plane without space? That is if a 2d plane of space is missing? You can consider every type of motion, continuous, ...
0
votes
1answer
180 views

In what sense is mathematics thought to exist in the real world?

It has been said that it is remarkable that the world (at least, parts of it) can be described by mathematics, especially in physics. After reading another question I know that it was Wigner who spoke ...
0
votes
2answers
118 views

What are the areas of mathematics philosophers deal with primarily?

Is it just discrete mathematics? I keep seeing symbols used in discrete mathematics on this stackexchange site. Is there any other area or is it just discrete mathematics, also what are the subfields ...
2
votes
2answers
94 views

Space and time in Kant and space and time in physics

From the Kantian perspective, what would be the relationship between our intuitions of space and time (which form the structure of subjective experience and are not things that exist outside of human ...
1
vote
1answer
56 views

Does deflationary truth collapse into a correspondence theory?

If you ask what justifies a deflationary account of truth, doesn’t that reveal an implicit isomorphism within the justification thus collapsing the account into a traditional correspondence theory?
-1
votes
2answers
139 views

Is mathematics the collection of all tautologies?

What exactly is the definition of mathematics? Some people say it is the study of this or that, but that is simply the study of math, not math itself. I think the definition of math is that it is the ...
3
votes
1answer
103 views

How may the terms “a priori” and “a posteriori” be used in(side) of mathematics?

This question seems either trivial or somewhat vague; let me explain further. I apologize if I am misunderstanding the concepts or missing the point entirely; I am a mathematics student and I ...
7
votes
4answers
323 views

If most numbers are uncomputable, in what sense do they exist?

Since the set of computer programs is countable and the set of real numbers is uncountable, then it means most real numbers are incomputable. i.e. there does not exist an algorithm to compute their ...
-1
votes
3answers
177 views

Must mathematical entities necessarily exist? [duplicate]

Are mathematical entities necessarily existing objects? That is to say, it is impossible for e.g. the real numbers not to exist. Have any philosophers talked about this topic?
1
vote
2answers
106 views

What makes a statement mathematical?

What is the formal definition of a mathematical statement? We can all agree that the statement "Humans are apes" is not a mathematical statement, and the statement "4 is a prime number&...
0
votes
0answers
55 views

Axiom of Choice: correspondence or derivability?

I'd like to ask about a specific impression that I have about issues concerning the Axiom of Choice. It seems to me that either one claims that the axiom is an obvious fact about the modelled concept (...
2
votes
0answers
37 views

Summary of philosophical positions on how belief revision proceeds in mathematics?

Since mathematicians have embraced classical logic, as e.g. MacFarlane points out in his 2021 intro book to philosophical logic (§ 7.4), one needs to distinguish between [meta-]reasoning and argument/...
0
votes
2answers
147 views

Can truths about the natural numbers vary across possible worlds?

The truths of logic are the same in all possible worlds. However, what about truths about natural numbers? Like, for instance, is there a world where there are only finitely many primes, or a world ...
0
votes
0answers
46 views

Technique that “de-trivialising” contradiction (systems)?

Gödel proved that some systems cannot prove their own consistency. As I see, what Gödel proved is no other than that mathematics is freedom, the adventure of a free mind (I.e. not afraid of being ...
0
votes
2answers
103 views

Can the Dirac belt trick (among others!) prove that mathematics is real?

First, I link the following video: https://www.youtube.com/watch?v=Vfh21o-JW9Q It demonstrates the 'Dirac belt trick', which was created by (I believe, Dirac) to demonstrate the calculus of spinors. ...
2
votes
0answers
77 views

Do constructivists (or intuitionists) reject real numbers, except the computable ones?

SEP has a bunch of pages on what (various flavors) of intuitionists or constructivists seem to accept as a model theory or as a set theory (they actually seem to diverge on the latter, in the sense of ...
4
votes
4answers
322 views

Philosophy of Math that talks about group theory, (or other stuff that's math but not numbers or geometry)?

I have just realized today that anytime I've read something about the philosophy of mathematics, the focus is on numbers, figuring out what numbers are, whether they're real, the relationship of ...
0
votes
3answers
147 views

Are theorems of math theorems even before they are proven?

I considered asking this in the math SE, but I decided this was a better option. I got into an argument with a math professor who claimed that Fermat's Last Theorem was a theorem only after it was ...
1
vote
1answer
39 views

How can you make sense of “equinumerosity” in Hume's Principle in a logicist approach to math, without first having functions defined?

I'm pretty sure that I am misunderstanding something here, but I'm not sure what. How can you make sense of "equinumerosity" in Hume's Principle in a logicist approach to math, without first ...
3
votes
5answers
1k views

Why can anything be discovered in mathematics at all?

Imagine a Perfect Mathematician that has superhuman abilities -- if you give him or her a formal foundational system for mathematics like ZFC with all the underlying logical machinery, he or she is ...
1
vote
0answers
92 views

Can we ignore intent if we recognize the extent? [closed]

I am not sure whether the formulation of my question is adequate, but I hope I'll make it clear enough. As a mathematics student, I have come to notice that some mathematical concepts are not defined ...
-1
votes
1answer
69 views

What is implications of well ordering theorem regarding order in nature?

I have recently come across well-ordering theorem. And I found that well-ordering theorem is equivalent to axiom of choice. And as far I know, axiom of choice is what we understand as free will, that ...
2
votes
1answer
284 views

What is a counter argument for the proposition that reaching the truth involves abandoning language and other intellectual instruments?

I have a linguist friend of mine who proposes that one should abandon all labels and paradigms to reach the ultimate truth, as they are deceptive. He proposes that you should strip all intellectual ...
1
vote
4answers
255 views

Is a complete mathematical description of reality possible?

There are definitely states of systems(like mind) which are not quantifiable. For mathematics to work in principle, we need states which are quantifiable or measurable. So, does this go to show that ...
4
votes
3answers
218 views

What should a person interested in the philosophy of mathematics know?

What philosophy should a person interested in the philosophy of mathematics know, at a minimum? Having delved into the subject, it looks like there are things you need to know.
5
votes
1answer
116 views

Did Zeno of Sidon really write that any geometrical system must have some unstated assumptions?

According to this site Zeno of Sidon argued that even if we admit the fundamental principles of geometry, the deductions from them cannot be proved without the admission of something else as well ...
0
votes
4answers
117 views

Probability vs Possiblity vs gambling knowledge gap for a beginner

Probability is a difficult subject for me to grasp. I watch many religious vs atheist vs philosopher debates on YouTube where probability is often brought up, and because of my poor understanding I ...
0
votes
3answers
217 views

Is it possible for there to exist a geometrically perfect square?

The corners of a geometrically perfect square should have no width. But if they have no width they don't exist. Therefore the corners must have a width. If they have a width they can be looked at as ...
1
vote
2answers
102 views

Is Fourier transform a human made tool or an act of nature? [duplicate]

I am a PhD students in physics, and my father is a Math researcher. One time, I asked him "Doesn't the fact that we can use math to explain things that happen in front of us, tell us that math is ...
-2
votes
4answers
376 views

Why is the definition of the real numbers not contradictory? [closed]

I understand that a set whose members can, in principle, be enumerated (by having a formula) can be considered as a well-defined set. Therefore, set of all even numbers, multiples of 3, and so on ...
2
votes
2answers
112 views

Inductive argument for Con(ZFC)

If you ask a mathematician, particularly a set theorist, about whether ZFC is consistent, they will answer that we can't know for sure because of Gödel's theorems. If you ask what evidence at all is ...
1
vote
0answers
106 views

Is paraconsistent logic used in other areas of mathematics other than discrete mathematics and in other areas such as physics and philosophy?

Is paraconsistent logic used in other areas of mathematics other than discrete mathematics and in other areas such as physics and philosophy? I heard that paraconsistent logic is an area of discrete ...
0
votes
1answer
70 views

Is Constructivism (philosophy of mathematics) against classical logic?

Is Constructivism (philosophy of mathematics) against classical logic? I might be wrong, but mathematics' main branch of logic is based on classical logic, and I was wondering if Constructivism was ...
2
votes
2answers
115 views

Do mathematical entities look like anything?

My view is that mathematical entities are not physical or visual objects, so they do not look like anything. Is this view correct? I would love to know whether there are philosophers who claim ...
2
votes
3answers
159 views

Does panpsychism imply mathematical entities are conscious?

Does panpsychism claim that even mathematical entities, like numbers and functions and sets, are conscious entities? Or is it restricted to physical objects?
1
vote
3answers
228 views

Are some mathematical truths contingent on the laws of physics?

Are there at least some mathematical truths that would have been different had the laws of physics been different? Probably most mathematical truths would not change, but are there some that would? Or ...
1
vote
2answers
274 views

Philosophy of mathematics that is not logic

Is there any readings on philosophy of mathematics that does not fall into studies of logical foundations of mathematics such as "definition of 1", "incompleteness theorems", "...
0
votes
0answers
56 views

Is there more than one form of logic in mathematics?

Is there more than one form of logic in mathematics? I would be inclined that mathematics only cover one type of formal logic, but I would be interested to know if there are variants thereof or ...
0
votes
0answers
26 views

True Thinkables - with regards to the Identity Theory of Truth

What exactly is a 'true thinkable'? According to John McDowell, 'true thinkables' are identical with facts(1996:27-8,179-80). This seems, if i may, a bit truistic and am left with no concrete ...
1
vote
0answers
91 views

What is the current status of Foundation-of-Mathematics programmes?

I have been reading 'A Very Short Introduction to Mathematics' by Timothy Gowers and at one point he mentions that most of the mathematical proofs can be finally resolved to a set of logical ...
0
votes
0answers
45 views

Why did Voevodsky feel “objects of a category can never be equal”?

In a lecture that Voevodsky gave at the IAS on the different notions of equality. He specified how this came from people who worked with categories and their higher analogues. The main problem he ...
4
votes
4answers
190 views

Are truth values of all mathematical statements immutable?

Are there some mathematical statements whose truth values are not fixed, but can change? Probably something like 1+2=3 will always be true, but are there at least some mathematical statements whose ...
1
vote
0answers
50 views

Is there some non-classical logic where the van der Waerden theorem does not apply?

The van der Waerden theorem is a theorem in the branch of mathematics called Ramsey theory which states that for any given positive integers r and k, there is some number N such that if the integers {...

1
2 3 4 5
20