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.

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49 views

Is ∞ the mathematical limit to any quantity?

For example, assuming someone figured out how to bypass all physical limitations, they would never be able to have more than infinity for any physical quantity. Even if you multiplied infinity by any ...
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102 views

What is the philosophical basis of the relation among reasoning, formal logic, and Turing machines?

Turing's machine is a generalisation of the concept of 'computation'. 'Formal logic' seems to be some sort of form of 'computation'. How are reasoning, computation, and formal logic related? Are forms ...
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What is epistemic probability?

I have read that there are three types of probability: epistemic, credence and physical. It is not clear at all to me what are epistemic probabilities and how they differ with credence. Moreover, I am ...
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Is there any philosophical difference between "I have no horns" and "I have horns, but they have zero volume"?

The common idea is that, on one hand we have "I don't have X", on the other hand we have "I have X, but X has some its quality equal to zero, making it to behave the same way as if it ...
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Are there mathematical concepts which we are unable to think of as meaningful representations of real-world things?

In my limited experience, I cannot think of any mathematical concept which is not obviously linked to the intuitions we have about the real world (irrespective of whether these are actually true or ...
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What is the status of mathematical fictionalism or nominalism, are they losing popularity?

There is only 1 paper out for each out in 2021 according to PhilPapers https://philpapers.org/browse/mathematical-fictionalism and https://philpapers.org/browse/mathematical-nominalism. This seems odd ...
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125 views

Is mathematics universal and can therefore be used as a generic form of communication?

Let me preface this question with the following: I have a background in physics and thereby some knowledge on mathematics, but little knowledge about philosophy itself. The question in the title arose ...
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117 views

What is the difference between infinity and endlessness?

Rudy Rucker, author of the book Infinity and the Mind, writes this: To understand how something can be endless but not infinite, think of a circle. A fly can walk around and around the rim of a glass ...
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Hyper real Number Theory [closed]

Is there a rich theory of numbers concerning infinite hypernatural numbers? Do we have prime number theorems that work?
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90 views

Is there a conflict between self-reference and ontology? (In relation to mathematics)

I am a total layman when it comes to math, but I promise at least to clearly spell out my thought process. Some like Elaine Landry say "mathematics is not metaphysics" https://youtu.be/...
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Do Godel's incompleteness theorems create a contradiction/paradox?

I have seen Godel's theorems presented as a paradox. However, I was only able to infer it's supposed to be one because it proves mathematics to be incapable to be consistent AND complete at the same ...
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Why don't we say the "unreasonable effectiveness of language"?

What's so special or unique about mathematics that we keep coming back to this phrasing? It isn't universal concision - there are many concepts more concisely put in English than math. Like to show ...
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What is left of physics if the mathematics is removed?

My question is in the title. It seems to me that (theoretical) physics studies mathematical models of the physical world, and constantly revises them. But isn't studying mathematical models ...
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Is it possible for everything that exists to have a definition?

Is it possible for everything that exists to have a definition? I actually started out asking this in the linguistics - semantics stack and was directed here. By definition I mean at least in the ...
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1answer
28 views

Questions about Reichenbach's Principle and causes

Is "statistical dependences need to be explained causally" an accurate depiction of Reichenbach's Principle? (Rob Spekkens https://youtu.be/n8NRSPCekmI?t=1575) Does one need to accept this ...
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What are the philosophic positions regarding the ontology of mathematical facts?

1+1=2 and, discarding any mildly clever counter-examples that don't really matter (eg 1.4 + 1.4 = 2.8, which rounds to 3), I have a hard time imagining how the discrete quantity 1 could ever be added ...
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176 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 ...
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176 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 ...
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213 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 ...
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2answers
124 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 ...
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73 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 ...
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2answers
111 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 ...
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57 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 ...
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4answers
172 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, ...
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186 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 ...
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126 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 ...
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107 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 ...
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61 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?
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151 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 ...
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115 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 ...
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351 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 ...
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196 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?
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164 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&...
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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 (...
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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/...
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151 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 ...
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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 ...
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118 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. ...
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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 ...
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349 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 ...
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152 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 ...
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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 ...
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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 ...
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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 ...
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71 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 ...
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290 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 ...
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4answers
270 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 ...
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233 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.
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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 ...
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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 ...

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