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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Does psychology/cognition come prior to mathematics?

I am not a hundred percent sure this belongs in Philosophy SE, but I couldn't think of a better SE to ask it, so I am asking it here. I got into an argument with a friend who claimed that the science ...
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Why was Russell discontent with Wittgenstein's view on "logic as tautologies"?

While reading Logicomix, I came across a scene that I don't quite understand. Russell: ...Logicians are creating elaborate ways to "say the same things in different words"...this "...
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What is the idea behind "p or not p" being a tautology?

Most (all?) logic books consider "p or not p" to be a tautology, hence always true, and this is usually stated without any further discussion. (I never gave it a second thought.) In common ...
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Is there an alternative to infinity?

We can say that a discrete set with 1 and 2 allows us to count just from 1 to 2 but a sequential set with 1 and 2 allows us to count from 1 to 2 in an infinite way (1.1, 1.2, 1.3 ...) but no man can ...
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Are there any resources that discuss the relevance of mathematical fields/problems to philosophy?

I've been enjoying reading Scott Aaronson's paper Why Philosophers Should Care About Computational Complexity. The paper discusses how the field of computational complexity is of major relevance to ...
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{Stipulativism vs. ostensivism} vs. {Formalism/if-then-ism vs. ante rem realism}

The SEP article on definitions includes the following two passages: See Frege 1914 for a defense of the austere view that, in mathematics at least, only stipulative definitions should be countenanced....
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Why do mathematical platonists believe in the abstract when math clearly comes from FOL, a non-abstract?

To assure ourselves first order logic is as free of paradox, errors, and impermanence, mathematicians and logicians "grounded" math in a language/system everyone can agree upon. Here is a ...
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132 views

Why should universal generalization work for abstract objects?

I am reading a logic book in my free time and usually the inference rule of universal generalization is motivated by real-life examples: Imagine having the statement that all people with brown hair ...
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Is the Quine-Duhem thesis valid also for mathematics?

I have been studying the lack of consensus regarding e.g. the first Hilbert problem (whether a problem is solved or unsolved). It is clear for several of the problems that a fair amount of ...
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Forcing in other axiomatic systems [closed]

What axioms do you need before you can use forcing? Does forcing use the axiom of infinity? Is there forcing in geometry as opposed to set theory?
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Why mathematicians\logicians try to establish totally mechanical frameworks, in the first place?

As much as I know, at least for the past 200 years mathematicians\logicians are doing their best in order to reduce their works into syntax (into some totally mechanical frameworks) accoding to some ...
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How can one believe in truth-value realism while denying the existence of mathematical objects?

I had started reading a book called "A Historical Introduction to The Philosophy of Mathematics" where it began by outlying some common beliefs within the philosophy of Mathematics. One such ...
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How did Descartes made a logical skeptic argument against logic, without falling into a paradox, in his Metaphysical Meditations? Is it actually valid

René Descartes seems to have made some arguments against logic and mathematics in his Metaphysical Meditations, however it seems that these arguments are still logical, and the problem is whether that ...
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Definition of 'Identity' [duplicate]

This may seem like a very specific or stupid question, but I'm new to this, I'm interested in the idea of 'identity' and 'identical. I've heard some description of the idea different 'copies' or ...
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148 views

Mathematical objects existing as different instances

I have a slightly complex conceptual question about the idea of 'multiple' instances of mathematical objects. In particular Real Numbers, and generally the idea of having multiple instances of ...
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1answer
176 views

What does Alain Connes think of Tegmark's hypothesis?

The mathematician and mathematical physicist Alain Connes has expressed in many occasions that he is a Platonist and he thinks that mathematics itself does exist in the same level (or even in a "...
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Is the axiomatic method an inherently well-founded method?

It occurred to me a little while ago, that there is a trichotomy in set theory that maps to the positive solutions to the problem of the regress of inferential reasons. Namely, well-founded sets map ...
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What is the difference between truth and fact in mathematics and science?

I am particularly curious on how one can closely talk about truths and facts with the areas of knowledge mathematics and science. I cannot seem to distinguish between these two terms with respect to ...
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4answers
262 views

To what extent is mathematics a tool to grasp the world beyond human intuition?

To what extent are mathematical formalisms an extension of intuitive reasoning to grasp the world such as in the fields of Quantum Physics and Relativity? My first thought is that when intuitive ...
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186 views

Set theory vs. type theory vs. category theory

IIRC, in the univalent-foundations program (per Voevodsky), category theory is represented as a possible sort of evolution or new wave of type theory. Maybe my memory is off, but anyway, in nlab they ...
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A Take on Application of Mathematics

The passage: "To introduce rigorous mathematics, I believe it's essential to discuss the whys and establish a core relation between mathematics and application. Mathematics begins with ...
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Mathematical style and ethical fictionalism

The SEP article on mathematical style got me thinking: what is the relationship between mathematical style, mathematical fictionalism, and ethical style/fictionalism? There seem to be at least three ...
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1answer
256 views

What is mathematics? What are some of the most predominant philosophical definitions of mathematics?

Philosophers have given the nature of mathematics a lot of thought. As a beginner exploring philosophy, one of the questions which presents itself is 'what is X', and in this case, X is mathematics. ...
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Infinite Trolley Problems

Recently, I was thinking about some rather interesting generalizations of the trolley problem to tracks containing an infinite number of people, and I was wondering how to formulate a moral argument ...
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Math, semantic meaning, and human senses as ungrounded

(1) Let's say I understand how one section of math behaves, maybe the natural numbers, and all of math is connected such that any one section of math can be interchanged for any other (my naive, ...
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133 views

What is the relationship between Logicism and Platonism?

I am not exactly sure about these two ideas. For me, it seems that logicists believe that axioms means something more than a string of symbols, and mathematics reduces to logical facts, so they ...
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603 views

Large cardinals and in intellectu existence?

I have had some success in the philosophy of mathematics. Briefly I compare Cantor's sets to the clear and distinct ideas of Descartes which is regarded as philosophically rigorous work; on the other ...
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1answer
116 views

How do finite processes and endless mathematical objects relate to reality?

There seem to be several philosophers who believe science (plus human norms for Sellars) can in principle leave no unanswered questions about reality. I would call this finite or exhaustible. Sellars: ...
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What type of subjective probability is adopted by Quine?

I am wondering what type of subjective probability is adopted by Quine. Is Quine sympathetic towards de Finetti's probability or Bayes'ones?
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How does geometry fit into Plato's ideas of forms? "Be specific"

I am really stuck trying to figure out exactly how geometry fits into Plato's idea of forms. The question directs that I "be specific" but I'm struggling even to be vague. Perhaps I am ...
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1answer
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Is ∞ the mathematical limit to any quantity? [closed]

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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1answer
505 views

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

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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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? [closed]

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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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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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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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
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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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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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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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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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129 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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79 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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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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