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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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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 ...
Joa's user avatar
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4 votes
1 answer
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Is the conceptual possibility of amorphous infinite sets "evidence against" countabilism?

Countabilism is, roughly, a family of standpoints inclusive of: There is one infinite proper set, of size ℵ0, and one infinite proper class, ℵ0ℵ0. (See about e.g. "pocket-sized" and ...
Kristian Berry's user avatar
4 votes
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102 views

What questions or areas in the foundations of mathematics remain active research fields?

By foundations of mathematics I am referring to the mathematical, logical, and philosophical foundations of the subject. I'm interested in seeing which of these have active research going on within ...
IgnorantCuriosity's user avatar
3 votes
1 answer
68 views

Is category theory as philosophically intuitive as basic logic?

So far as I understand, category theory can be used as foundations of mathematics as in that the rest of logic can be defined through categorical ideas. However is category theory as natural a ...
tryst with freedom's user avatar
3 votes
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Rather than "ought to be true = is true" being impossible, might it not just be a trivial stage of moral representation?

I just finished reading Eugenia Cheng's essay on moral phraseology in mathematics, and so I want to go over something she says on pg. 20: A recent lecturer of Part III Category Theory declared that ...
Kristian Berry's user avatar
3 votes
4 answers
226 views

What are an object's properties?

What can we consider an object's properties, for example, when can we consider an object's properties as 'changing'? For example, if I move an object from my desk to my table, has it changed? If I ...
Confused's user avatar
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107 views

How could second-order logic satisfy (neo) Fregean's epistemic goal?

Recently I've been reading Shapiro's Higher Order Logic in The Oxford Handbook of Philosophy of Mathematics and Logic, Chapter 25. There are some paragraphs confusing me:  One traditional goal of ...
23477272's user avatar
3 votes
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174 views

Have the indispensability arguments been examined for probability theory?

Indispensability arguments are widely known in the philosophy of mathematics, the idea being (roughly) that we should commit to the existence of those mathematical entities that are indispensable for ...
Neil Barton's user avatar
3 votes
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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 ...
MaTHStudent's user avatar
3 votes
1 answer
322 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 ...
Amy's user avatar
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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 "...
enrijaja's user avatar
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Using differential equation to estimate epistemological growth constant

I found some tweets (1,2) describing a philosophy paper as follows: I came across this paper from the academic journal of philosophy that tries to solve a differential equation for an ...
gjoncas's user avatar
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173 views

Relation of Mathematical Propositions to Natural Language

Treating Natural Language as a language game, what role does it play in our understanding of mathematics? Does natural language provide meaning to mathematics? Does a proof of a conjecture, say FLT,...
Ajax's user avatar
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3 votes
1 answer
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Looking for references for some remark of Quine's

I'm looking for a comment I think I remember Quine having made. He's talking about our understanding of proofs. I think he says something along the following lines... If you understand many different ...
user65526's user avatar
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1 answer
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How is synthetic knowledge produced in fictionalism?

With the Greek gods being fictional there is still objective knowledge - how many Greek female gods are there, etc. (Or if that's still too ambiguous, how many Greek gods are named Zeus). But "...
J Kusin's user avatar
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Entry points from philosophy into mathematics at higher levels?

Everytime I look up of the link between philosophy and mathematics, I see the topics only of the most foundational levels discussed. As in logic, and stuff. When I study higher mathematics theories, ...
tryst with freedom's user avatar
2 votes
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Turing's bridging argument of conflating mathematical logic and the philosophy of mind?

So I read this paper and I'll quote the relevant parts: 'Turing's machines are humans who calculate On Computable Numbers' thus took on the aspect of a hybrid paper: an attempt to integrate what ...
More Anonymous's user avatar
2 votes
0 answers
51 views

How does aesthetic relate to structure?

If we are to take a subject say mathematics, then often mathematicians may attribute to the well defined structure and precision in describing its theories. I believe there are also other things like ...
tryst with freedom's user avatar
2 votes
0 answers
166 views

What in mathematics has the property of beauty?

I might or might not be at an impasse in my writing... I have around 200 pages of notes, and I finally sat down and tried to compile some of the material, but I feel like the presentation is off ...
Kristian Berry's user avatar
2 votes
0 answers
99 views

Is Frege and Russell's definition of number reducible to Hilbert's?

This is my first post on this site and I hope that its length/format is not inconsistent with any moderation guidelines. My question relates to the distinction that can be drawn between the logicist ...
Menander I's user avatar
2 votes
0 answers
112 views

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 ...
user107952's user avatar
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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....
Kristian Berry's user avatar
2 votes
0 answers
60 views

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 ...
Kristian Berry's user avatar
2 votes
0 answers
91 views

Deductive methodology in philosophy

Introduction Mathematics uses deductive methodology to produce results called theorems that are indisputable truth by logical necessity, with respect to the axioms of the starting axioms and ...
Lilla's user avatar
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What's the role of logic in logical positivism?

I'm reading up on a bit of the ideas of logical positivism. It seems that the main components were the distinction of synthetic and analytic statements, and the verification principle. Without giving ...
Mark's user avatar
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0 answers
56 views

How would a monistic approach account for these categories of probabilities?

Donald Gillies, in his book "Philosophical Theories of Probability," draws a distinction between monistic views and dualistic views of probability, the latter of which, at least in his ...
user48231's user avatar
2 votes
0 answers
123 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 ...
Anon's user avatar
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Transition of Mathematical Propositions

There are axioms, and then there are well established methods of working with them. It is clear that these methods are nothing but logical operations (rules of manipulation of symbols) on previous ...
Ajax's user avatar
  • 1,139
2 votes
0 answers
78 views

Mathematical Universe

I have a beginner question on the type of claims this book or similar theories make. That book claims that universe is math structure. I just want to clarify if I correctly understood his goal: Does ...
gdan's user avatar
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Does Tegmark's hypothesis include dynamical mathematical structures?

Tegmark's hypothesis is the idea that mathematical structures are physical and thus have physical existence (https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis) Zuse's thesis says that ...
Niein Ofinfo's user avatar
2 votes
0 answers
223 views

Does Reflective Set Theory "RfST" fulfill the requirements of founding Category Theory and Mathematics?

On mathoverflow I've posed the question in the title in connection to Muller's 2001 criteria for a founding theory of mathematics, which largely raised in connection to Category theory [see here]. ...
Zuhair's user avatar
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Mathematical structuralism and Saussure

Is mathematical structuralism related with structuralism that arose from Saussurean linguistics?
user472707's user avatar
2 votes
0 answers
211 views

journal for mathematics of philosophy/mythology

I have been working on research involving the use of mathematical formulas and reasoning in order to philosophical concepts, specifically concepts concerning mythology, the Jungian model of the psyche,...
Alexander's user avatar
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2 votes
0 answers
221 views

why is ontological parsimony important for philosophy of mathematics

It appears that one important motivation for being a (Quinean) nominalist about mathematical objects is ontological parsimony: mathematical objects are ontologically extravagant; so if we can rewrite ...
bluether's user avatar
2 votes
0 answers
339 views

Criticisim of Hilbertian Formalism

The two main criticisms against the philosophical position on mathematics which is called game formalism (see here for details) are, The first is the question of applicability: if mathematics is just ...
user avatar
2 votes
0 answers
121 views

Why didn't Newton pursue philosophy?

Why didn't he pursue philosophy in the same way Leibniz did, many "natural philosophers" during that time often delved into many fields since it wasn't really required to specialize yet, but it seems ...
user4281's user avatar
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2 votes
0 answers
145 views

Philosophy and Reading: Towards Math, and Physics

I was reading a book about learning philosophy for beginners called Introduction to Philosophy Classical and Contemporary Readings Edited by John Perry, Michael Bratman, John Martin Fischer It says ...
EnlightenedFunky's user avatar
2 votes
0 answers
322 views

Some questions on Graham Priest's remarks about Russell's solution of paradoxes

In his book Beyond the Limits of Thought while talking about Russell's solution of paradoxes Graham Priest writes (text made bold, footnotes and references omitted), Russell solved these problems ...
user avatar
2 votes
0 answers
98 views

Nominalist views and contradictions

Given a flavor of nominalism which denies that simple sentences and existential quantifiers referring to mathematical objects are literally true (pretense theory, fictionalism, figuralism, etc.), ...
user20658's user avatar
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2 votes
0 answers
149 views

How can rational choice theory be explanatory?

In his work, John Harsanyi appears to have taken issue with classical social theorists' account of social phenomena. For example, he criticized Max Weber's typological approach on the grounds, "If we ...
WZS's user avatar
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0 answers
168 views

Should I take Math GRE Subject Tests for applying to Philosophy Phd to study Philosophy of Math?

If I was interested in studying philosophy of another field (e.g. philosophy of math or physics), would philosophy phd programs I apply to be interested to see my scores on the gre subject test for ...
Smithey's user avatar
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0 answers
150 views

considering the line and circle as not just a contrary, but as a extremes on a continuum

Question: In Greek philosophy, it is generally taken that the line and the circle form a contrary. For example in Aristoteles Physics generally takes that motion can be formed out of this contrary, ...
Mozibur Ullah's user avatar
2 votes
0 answers
364 views

Are numbers universal in Set Theory and nominalist in Category Theory?

The number 3, when considered as a universal, abstracts the property of 3'ness from all groups of 3 objects. One supposes that this universal, by conceptual neccessity of what is understood by the ...
Mozibur Ullah's user avatar
2 votes
2 answers
389 views

Could the axiom of infinity be in itself inconsistent?

I've seen several threads discussing the axiom of infinity but I wasn't able to find a discussion on this particular aspect. And recent conversations with some people have led me to wonder if it is ...
Modesto Rosado's user avatar
1 vote
1 answer
63 views

Is there a set theory which implies the interval [0, 1] but no more?

A deductive system (as a collection of judgments and rules of inference) can be used to describe something commonly called a “set theory”. We can imagine a priori there are certain properties we would ...
Julius Hamilton's user avatar
1 vote
0 answers
54 views

Can every idea including mathematical ideas be reduced to a series of simpler idea without information loss?

Can every idea including mathematical ideas be reduced to a series of simpler idea without information loss? You would naturally think this is the case since most ideas could be explained using a ...
Sayaman's user avatar
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1 vote
0 answers
62 views

Are "A ∧ A" and "A ∨ A" degenerate expressions?

Although some time ago I had become somewhat familiarized with the notion of degeneracy in mathematics and physics, in my musings on the trivial/nontrivial distinction I found that both Wikipedia and ...
Kristian Berry's user avatar
1 vote
0 answers
68 views

Would "to avoid the class/set distinction" be, or not be, an ad hoc reason to propose a couniversal set?

Once upon a time, von Neumann proposed the axiom of limitation-of-size, which says that any class "too large to be a set" is then a "proper class," meaning that there is a ...
Kristian Berry's user avatar
1 vote
0 answers
63 views

Probabilities and Certainties on the Monkey Axis: Yet more about those monkey typists

I was reading with some interest the answers and comments to this question about that familiar, weird and somewhat inhumane infinite-monkey experiment which, somehow, is still generating fresh and ...
Brandon Burt's user avatar
1 vote
0 answers
86 views

Why not move from proof numbers to theories instead of theories to proof numbers?

In mathematics, they do this thing where they figure out what are called "proof-theoretic ordinals" (see this section of the SEP article on proof theory for background details) of theories, ...
Kristian Berry's user avatar