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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Mathematics vs Time

Suppose we have a person that one day states "x+3=5". The next day he again states "x+3=5". As events, we can say they are different but does the meaning of the expression has changed? It seems ...
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What is Number again

I came here having asked on the math stack exchange site about number. There are several responses to that question or one similar that suggest that here is the best place to ask the question. On ...
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Is Quantum Bayesianism a viable solution to interpretational problems of quantum mechanics? [closed]

I noticed that Quantum Bayesianism (Qbism) seems to solve a number of issues in QM like non-locality, decoherence and the measurement problem. But I am not sure if physicists and philosophers would ...
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295 views

Which problems do you consider as most important open problems in philosophy of mathematics?

At the "intersection" of mathematics and philosophy, or, rather, within their "union", surely some problems are still open and no general consensus is attained when those problems are discussed. ...
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Axiomatic system and symbolic, formal, mathematical language

Is there any need for axiomatic systems to be in a symbolic, formal, mathematical language? Equivalently is there any prohibition of axioms in axiomatic systems being in natural language? In other ...
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Is the attempt to separate between Philosophy and Mathematics may be considered as some kind of Philosophy?

When deal with fundamental notions, many mathematicians and some philosophers agree that Philosophy is not an appropriate framework for mathematical frameworks' developments. Is the attempt to ...
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409 views

The notion of a point vs space as the most primitive notion?

I hear the notion of a point being the most primitive notion in geometry. But to talk about a point, one needs to think of a space of some sort. Only then, the point can be understood as a position ...
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Kant, combinatorics and the supreme principle of synthetic judments : on a possible analogy

One striking thing in combinatorics is that , in order to count the number of objets having a given property, we make a " detour " and count instead the total number of possible ways to produce or ...
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309 views

Are there universes where rules of mathematics do not follow?

According to Max Tegmark the ultimate reality is the Mathematical world. Mathematically possibility also refers to physical possibility. Can there be such a type of universe where mathematical ...
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Is there anything beyond mathematical universe

If Mathematics is empirical , physical events which defies the rules of mathematics may also generate new mathematics?
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On reading Kripke

I've recently read that Saul Kripke has had a huge impact in philosophy over the last century, especially philosophy of language and "truth". My question is wether reading his works (or studying it ...
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Do Mathematics “exist” in some sort of “Reality” that is different from our Physical Reality

I will explain why I am asking this question. Let's say, there are mathematical truths and truths about our physical reality. But, there is no way we can establish the truth of any statement about our ...
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Two positions at once is logically impossible

Assume that the position of an object is x1 and x2 at once, where x1 does not equal x2. Let's define the statements A and B as: A: The position of the object is x1. B: The position of the object ...
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When does “zero” exist? [closed]

When does zero exist? ex: if i say, "I dont have a hat" it seems more fair to say -1(hat) rather than 0(hat) ,because 0(hat)=0 would mean (hat)=0 and -1(hat)=(-hat) implying there is a hat in ...
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Why was the zero not discovered long ago or in the beginning? [closed]

The rules governing the use of zero appeared for the first time in Brahmagupta's Brahmasputha Siddhanta (7th century). This work considers not only zero, but also negative numbers and the algebraic ...
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Human Mind vs Computer

We start from axioms, use rules of logic, and derive theorems. These theorems establish what is the case in relation to the context. In all disciplines employing mathematics, we reason by saying '...
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Another critique of the unreasonable effectiveness of mathematics in natural sciences

It seems the majority of scientists hold for a the hyper-effectiveness of mathematics in natural sciences as a sign that nature is deeply mathematical. Although I believe that some mathematisism is ...
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What are the possible philosophical inspirations for the philosophical concept of “antifragility” that was defined by Taleb?

It seems to me that this is just a generalization of "hormesis" by trivially abstracting some of it's aspects but I am not very well versed in philosophy.
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Can we imagine a perfect circle?

Applied mathematicians often work with circles, but I'm guessing it's an abstraction that cannot save all the empirical data. Can we conceive of a perfect circle in our visual field -- as apparently ...
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When is it meaningful to say that an undecided conjecture is true or false?

I see that other questions have already been asked about mathematical truth but here I want to ask clarifications on a particular perspective. One can think the answer to the question could be "when ...
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126 views

Are mathematical axioms arbitrary?

I've been thinking recently about whether or not mathematical axioms are arbitrary. I'm trying to figure out what axioms in systems are derived from and just how arbitrary they really are. My main ...
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214 views

(Non-)Mathematical examples - towards a philosophy of mathematics-

I need your help: I'm looking for a list of interesting examples (see below) that are of high interest to philosophy of mathematics. To specify this, I need you to consider the following: ''...
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1answer
201 views

Why does Gödel's incompleteness theorem apply to multiple formal systems?

Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor ...
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Does Weyl's tile argument defeat the discrete spacetime?

Weyl shows that in a discrete spacetime Pythagoras's theorem fails to arise. Of course it may be that although Pythagoras's theorem arises naturally but actually does not model the real world. So Does ...
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Isn't the notion that everything will occur in an infinite timeline an example of the gambler's fallacy?

I've seen a few different formulations of this, but the most famous is "monkeys on a typewriter" - that if you put a team of monkeys on a typewriter, given infinite time, they will eventually produce ...
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263 views

Mathematical models of dynamic algorithmic processes

This question primarily concerns dynamical or time-dependent phenomena in philosophy and to what extent such heuristic discourse features in more precise mathematical settings. In order to model ...
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Hume on infinity

I know Hume argued against dividing finite space into infinitely many regions, but I can't seem to find anything regarding his thoughts on infinity itself. From his Enquiry you sort of get that he ...
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202 views

Comparisons between two notions of existence

I have the following, rather naive question: To what extent can the a priori existence of mathematical objects be reasonably compared with the seemingly a posteriori existence of objects established ...
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In non-platonism, can undecidable statements have truth value?

Most sources I can find about Gödel's incompleteness theorems summarize the result as "there exist true arithmetical statements that have no proof." It seems coherent to say that there exist ...
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Why does Wittgenstein have a problem with writing “f(a, b). a = b"?

Why does Wittgenstein have a problem with logical statements saying nothing ? (5.5303) . How would Wittgenstein want us to interpret f(a,a) ? He also mentions axiom of infinity from which Russell ...
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If intuitionism were true, could a mathematical system exist that is incompatible to our system?

If mathematical intuitionism were true, could there be a System that Describes reality accurately and consistently like current maths do Consists of equations that cannot be described by current ...
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About Wigner's view on the relation between mathematics and physics?

Physicist Eugene Wigner argued that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it ...
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What is the meaning of Principle C'' in Hartry Field's 'Science Without Numbers'?

For Field, the following is 'perfectly obvious', but I would like confirmation that I understand it completely. Let A be a nominalistically statable assertion. Let A* be the assertion that results by ...
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200 views

How do philosophers formally characterise mathematical objects?

In the Stanford Encyclopedia of Philosophy article 'Platonism in the Philosophy of Mathematics' the following formalisation is given for the existence of a mathematical object: "Existence can be ...
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A Kantian Platonist view of mathematics

So my question, essentially, is this: is there any reasonable way in which one can say that mathematical Platonism is compatible with Kantian constructivism? For the sake of context, I was asked to ...
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131 views

What evidence is there that Gödel believed the mind to be non-physical?

On the Stanford Encyclopedia of Philosophy's article on Platonism in Metaphysics, the author writes that "Gödel's version of this view — and he seems to be alone in this — involves the idea that the ...
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Has Alexandre Grothendieck ever expounded a particular stance on metaphysics or ontology?

It seems that in Recoltes et Semailles, he does go into quite a bit of philosophizing. the only thing of relevance I've found is that he notes how Riemann "in passing" said how he thought perhaps the "...
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Did Descartes believe arguments for Euclid's parallel postulate were cogent?

If Descartes wanted to found philosophy on the certainty of mathematics, it seems he must have considered arguments for Euclid's parallel postulate cogent, or at least not doubted them. Gerolamo ...
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Is 'in re' structuralism a non-eliminative theory in mathematical structuralism?

As far as I understand it the definitions are: Non-eliminative structuralists believe that talk of structures is ontologically committed to the existence of abstract structures. In re structuralism ...
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Question about conditionalization and probability

I am working on a problem set and I am not sure if I am heading in the right direction. The scenario: "Suppose three identical boxes are presented to you, and you are told that one box contains two ...
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134 views

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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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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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
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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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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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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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