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
-1
votes
0answers
41 views

What is a prime, in the philosophy of mathematics? [closed]

I was looking at the number 241 on wikipedia, which lists it as the only known Lucas–Wieferich prime to (U, V) = (3, −1). Though unfortunately I did not understand the article for that. I was ...
1
vote
0answers
78 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 ...
6
votes
0answers
65 views

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 ...
1
vote
1answer
177 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 ...
3
votes
2answers
73 views

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 ...
6
votes
3answers
3k views

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 ...
1
vote
0answers
46 views

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 ...
0
votes
0answers
56 views

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 ...
0
votes
1answer
54 views

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 ...
0
votes
1answer
170 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 ...
2
votes
1answer
150 views

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 ...
3
votes
1answer
121 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 ...
3
votes
0answers
39 views

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 "...
4
votes
1answer
66 views

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 ...
2
votes
0answers
38 views

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 ...
4
votes
2answers
124 views

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 ...
0
votes
1answer
97 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.
0
votes
2answers
39 views

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 ...
2
votes
1answer
126 views

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 ...
1
vote
2answers
120 views

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 ...
3
votes
0answers
52 views

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 ...
2
votes
1answer
151 views

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 ...
2
votes
2answers
67 views

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. ...
2
votes
4answers
145 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 ...
0
votes
3answers
198 views

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 ...
2
votes
2answers
203 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 ...
0
votes
1answer
73 views

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 ...
0
votes
1answer
82 views

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 ...
-1
votes
1answer
142 views

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 ...
0
votes
0answers
67 views

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 ...
1
vote
2answers
108 views

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 ...
0
votes
0answers
43 views

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 ...
1
vote
3answers
230 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 ...
0
votes
3answers
185 views

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 ...
1
vote
2answers
151 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 ...
5
votes
2answers
217 views

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 ...
1
vote
0answers
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 ...
0
votes
2answers
67 views

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 ...
0
votes
2answers
125 views

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 ...
1
vote
1answer
37 views

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 ...
-2
votes
2answers
328 views

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 ...
1
vote
3answers
118 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 ...
-1
votes
1answer
291 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 ...
1
vote
5answers
198 views

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 ...
0
votes
1answer
115 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 ...
1
vote
0answers
30 views

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 ...
1
vote
4answers
175 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?
6
votes
7answers
309 views

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 ...
0
votes
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, ...
1
vote
7answers
280 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 ...