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 Wittgenstein's “The limits of my language mean the limits of my world” relate ontology with language?

Since Badiou equates ontology with Mathematics, if both philosophers are to be taken verbatim, there's a triple equivalence to consider: ontology = Mathematics = language.
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Use-mention distinction

Is it 1+1 or “1+1” that is a formula of addition? To my intuition, it is the former, and the latter seems to be a name of the formula. The reason why I ask this question is that provided my intuition ...
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What to read in-depth on Frege's Julius Ceasar problem?

I am planning to get a good grip on Frege's Julius Caesar Problem. I know that classic papers on the topic are Heck and Wright&Hale, but I would be grateful if someone gave me a little piece of ...
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Did logicists use mathematical entities (in their attempt) to reduce mathematics to logic?

Two concepts F,G are equinumerous if there exists a one-to-one correspondence between the objects that fall under F and G. Equinumerosity is one the most fundamental building blocks of Gottlob ...
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Platonism and causality

The Stanford Encyclopedia of philosophy states that - "Because abstract objects are wholly non-spatiotemporal, it follows that they are also entirely non-physical (they do not exist in the physical ...
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1answer
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Is there a form of set theory involving imperatives and interrogatives?

I finally read the article Is there a Logic of Imperatives? Conifold showed me and it elicited the question, for me, whether imperative programming is a form of imperative logic at all? The essay took ...
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2answers
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Is it a logical fallacy? A question about majority opinion and samples

Say a community of X number of people is notified of a sudden policy change by higher authorities, and Y number of people from the community express their opinions for or against the policy change. ...
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4answers
136 views

Why there is geometry in nature? [closed]

We perceive our surrounding as a 3 dimensional world. Geometry is part of math which are a collection of abstract concepts that arose in our mind. Most of the things around us can be described in ...
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3answers
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In mathematics , can't we say that the intuition of the original author of a true conjecture is the proof of it just indescribable on paper- pen

I think that when a person put on a true conjecture in mathematics (we have verified it to be true) ,proof must came in his mind in the form of what we called intuition. I mean if his saying is ...
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2answers
199 views

Is Mathematical Platonism a meaningful thing? [closed]

How can we be sure that asking If Mathematics is Platonic or If it is Our Own Construction is a meaningful thing to ask, and not just abuse of natural language? Can somebody provide a convincing ...
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Are there any systems of mathematics that permit such a wide range of ways to formulate ideas

... that there is no algorithm for determining whether or not a given sequence of symbols is a wff ("well-formed formula"), but instead non-trivial proofs are required, so that some sequence of ...
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How could I possibly apply rule-utilitarianism in real life?

If I believe in rule-utilitarianism as the best moral system we have to judge what actions are right and wrong, how would I go about applying this system pratically in real life decisions? For ...
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Why should a system of set theory represent the following property of x: ((x = h) or (x = k))) using the set that Frege used?

I have been considering the possibility of an approach to set theory that represents the following property of the free variable x, in the terms of parameters h and k: ((x = h) or (x = k))) by means ...
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What goes wrong if we explain Russell's paradox as resulting from an overly rigid link between property satisfaction and elementhood?

An excerpt from a question at Math SE (Bounty of 100 available for an answer): What goes wrong if we explain Russell's paradox as resulting from an overly rigid link between property satisfaction and ...
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Infinity - Sizes vs Types

Suppose there is a line, infinitely long in both directions. Make arbitrarily "uniform" cuts or "integers". Obviously there are infinitely many of these. And there are arbitrary "lengths" BETWEEN ...
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Was Russell's purpose in Principia Mathematica to formalize all the possible constructions of logic?

In writing Principia Mathematica, was one Russell's purposes to formally describe all the possible variations of logical concepts and reasoning that can be used in mathematics? For example, suppose ...
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217 views

Did early Wittgenstein view mathematics as “sense-less” or “non-sensical”?

G. E. M Anscombe makes the following distinction between Wittgenstein's use of sense-less (sinnlos) and nonsense (unsinnig): (page 163) We must distinguish in the theory of the Tractatus between ...
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Although Russell's paradox has the virtue of simplicity, is it a distraction from other paradoxes of naive set theory?

Given that Russell's paradox exhibits a contradiction in naive set theory, the interpretation of the binary relation "∈" called "membership" (where the expression "x ∈ m" is pronounced as "x is an ...
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2answers
149 views

To connect or to disconnect mathematics and platonism?

How [do philosophers] strongly support or refute the view that: mathematics is a bag of tricks for real-world problem solving; undecidable statements are an irrelevant and harmless side-effect of an ...
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What philosophical axes did 19th century mathematicians have to grind?

Tim Button's presentation of set theory motivates the subject by providing a history of 19th century mathematics where the notion of limit allowed definitions of the derivative and continuity. These ...
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105 views

Justification for applied mathematics

I'm familiar with some philosophy of mathematics and what does mathematical knowledge mean (Plato, Kant, Frege, Brouwer etc.). And as mathematicians, we establish a set of axioms and work up from ...
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How are geometry and space related? [closed]

How are geometry and space related? I am asking in what type of relationship are "space" and "geometry". I can think of the relationship "necessity", but it's a very general relationship. I can't ...
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How much math must tenured full philosophy professors know?

I'm talking math not logic. I'm referring to full tenured Professors of Philosophy at world famous universities like Oxbridge, Ivy League, Stanford, or MIT. Please be specific and type the math course ...
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1answer
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Kant's Notion of Synthetic A Prioiri as Logical Entailment

Is there something wrong about interpreting Kant's notion of synthetic a priori statements to be logical entailments? I understand, I think, that Kant didn't want to say such statements (e.g math ...
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What is model theory?

I have never been able to understand any need or even any benefit of model theory. Both Rudolf Caranp and Richard Montague showed how to encode semantics directly in the syntax. Can you help me ...
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3answers
116 views

Are there natural language examples of n-ary relations greater than 3?

Binary relations are obvious, and I see the need to have 3-ary relations such as "being in between things". Are there natural language examples of relations greater 3? Edit: without combining binary ...
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1answer
284 views

Can all formal systems be generalized as specified relations between finite strings? [closed]

https://en.wikipedia.org/wiki/Formalism_(philosophy_of_mathematics) In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be ...
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5answers
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A comprehensive introduction to relationship between math and experience

I am a mathematician with interest in physics and pure logic and exists one problem: the connection between math and physics. Math concerned on pure universal truths and physics concerned on ...
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1answer
111 views

Why is Math not Logic? [duplicate]

So I've heard, "Math is not logic," because logic has no notion of order. However, consider the following argument: There once was a man on a mountaintop. He came down, murdered a villager's cat, and ...
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Minimalist philosophical assumptions to reason, deductively/inductively

I've been thinking a lot about foundations of science recently and I was wondering. Are there existing books/essays/works, or were there attempts that try to achieve the following: With a ...
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4answers
172 views

Mathematical proof of a philosophical theory

Can I prove a philosophical theory mathematically? If yes? How? For example, can the theory of materialism be proved mathematically?
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7answers
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Is mathematics a mental idea?

Is mathematics a mental idea? According to this answer, a mental idea cannot exist without a mind. If mathematics is a mental idea, what does this imply about the laws of physics which can be ...
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1answer
109 views

How can you determine if a hypothesis (mathematical logic ones) is falsifiable enough to be “good”?

We had a group discussion and the prof gave us the following question and left. The problem is that I hardly understand the question. How can you determine if a hypothesis (in particular, ...
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7answers
279 views

Why does mathematics work in the physical sciences?

Why does mathematics work in the physical sciences? I looked at reddit, and they said that it's not surprising it does, just because that's what it's there for. But there's definitely a question ...
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What are numbers? [closed]

What are numbers? Does the number two exist? If so, how?
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Is mathematics truth?

In mathematics there are imaginary numbers which cannot be represented directly in reality (the physical world). For example, you can't have i apples where i = √-1 (square root of -1) Can we ...
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4answers
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Why do we need geometry for pure math?

Karl Weierstrass had a very interesting critique of Riemann's work. Supporters of Riemann, claim that a pure logician would never have been able to see the things that the "geometric imagination" of ...
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Question on Hypothetico-Deductive Method

I had another quiz related Hypothetico-Deductive (HD) Method. I couldn't answer this because the way it was posed is so baffling to me. I am so sorry to ask all the basic questions (I think all ...
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1answer
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Did physicist Eugene Wigner think that every mathematical structure existed as an isolated universe?

I have read that Eugene Paul Wigner thought that all mathematical structures had physical existence. Does that mean that he believed in a multiverse containing all mathematical structures as separate ...
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1answer
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Mechanics of Perception

How is perception formed? By perception I mean 'thought' or 'idea' of the World. What I see by itself does not contribute anything to thought. Only an acknowledgement can contribute to structuring of ...
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Reasoning for Inductive inference?

Just out of curiosity, if I should replace the deductive inference related questions to inductive inference, then which are true? Inductive inferences rearrange current knowledge in such a way that ...
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4answers
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Russel's paradoxical set from a different view

Suppose naïve set theory, let's do a tought experiment: Informally, let's define a set € such that € contains all the sets that don't contain themselves.(yes, all but not necessarily only those), ...
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2answers
151 views

Max Tegmark's Mathematical Universe

Max Tegmark believes the universe to be a mathematical structure, and he further claims any mathematical structure with self-aware substructure will perceive itself in a physical world. What exactly ...
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3answers
144 views

Why is it argued that an argument has one and only one conclusion?

Why can't an argument have more than just one conclusion? If we assume some premises and we assume them to be true, then by some inference rules we are sometimes able to deduce more than just one true ...
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What are some key differences between an argument in logic and a theory in mathematics?

Both are composed from rules and assumptions which enable us to deduce other inevitable truths that results from these rules and assumptions, right?
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Does infinity imply uncertainty? (Or the other way around?)

This is a follow on question from my question here Consider the hypotenuse of a right angle triangle where the opposite and adjacent sides both have length 1. The hypotenuse has length sqrt(2)... ...
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4answers
756 views

Why is there so little discussion / research on the philosophy of precision?

I was thinking the other day about the difference between rational and irrational numbers, and wondering whether the distinction between them is created by leaving out discussion of precision. So for ...
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Poincare says we are born geometric or arithmetic thinkers. Which was Grothendieck and why?

Poincare proclaims that the mathematical continuum originates from the sensible intuition and that intuition by pure number or logic alone could not have given us this notion. Source for the claim: ...
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Did physicist Max Born think that mathematical structures are platonic entities?

It seems that prominent physicist Max Born (https://en.wikipedia.org/wiki/Max_Born) believed in some kind of Platonism. We can infer this, for example, from the book "The Innermost Kernel" (https://...
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Is this an argument about the world or about human cognition?

This is a question about a thesis I have encountered regarding the relation of abstract mathematics ( Category Theory in particular ) with reality and the nature of human cognition. The argument goes ...