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 what happened with the emergence of non-Euclidean geometries deny the existence of axioms in the innate sense?

I read this text a while ago (in Arabic): Supporters of contemporary mathematics believe that mathematics results are relative in certainty and not fixed, because the emergence of the axiom system ...
زكريا حسناوي's user avatar
1 vote
3 answers
144 views

What is meant by the expression ∃xHx, if H stands here for “is a human being”?

How academics would go about explaining in everyday English, so without any philosophical or mathematical jargon, what is meant by the expression ∃xHx, if H would stand here for “is a human being”. On ...
Speakpigeon's user avatar
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2 votes
3 answers
172 views

Does paradoxes in a theory mean that the theory is incorrect and should be discarded?

I have two questions which relate to two different subjects, Science and Mathematics have different meanings of "theory", first is based on ever-growing scientific evidence while other is ...
Dheeraj Gujrathi's user avatar
6 votes
10 answers
4k views

What is a philosophical interpretation of Bayes’s theorem when one of the probabilities is zero?

Bayes' Theorem P(H) = probability of a hypothesis P(E) = probability of evidence P(E|H) = probability of evidence given the hypothesis P(H|E) = probability of hypothesis given the evidence P(H|E) = P(...
Agent Smith's user avatar
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2 votes
4 answers
138 views

Can mathematical models be indistinguishable from the phenomena they model?

Mathematical models of the phenomena of the world, such as the weather, are used to make predictions about the outcome of the phenomena from an initial state. These models are applied as computer ...
8Mad0Manc8's user avatar
1 vote
1 answer
65 views

Questions about mathematical models of the real world

I'm just starting to learn about mathematical modelling but i'm getting stuck understanding how real world processes and objects are modelled by maths. The way i'm thinking about at the moment it is ...
Richard Bamford's user avatar
0 votes
0 answers
71 views

Why do variables in mathematics always represent properties of objects?

When I read about mathematical modelling, a variable is always used to represent a property of an object, for example the mass of an object. "let m be a real number that represents the mass of an ...
Richard Bamford's user avatar
2 votes
5 answers
703 views

Interpretations of quote - "Mathematics attracts because..." [closed]

I am reading "Probability and Stochastics" by Cinlar. Here is the following quote in the preface of the book. As Martin Barlow put it once, mathematics attracts us because the need to ...
Kartik Pandey's user avatar
4 votes
4 answers
284 views

What is intuitionistic mathematics?

What is intuitionistic mathematics? What are its claims, and what are their justifications? 1a. Intuitionism as a philosophy. L. E. J. Brouwer is credited as the originator of intuitionistic ...
Julius H.'s user avatar
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3 votes
3 answers
442 views

Is it a problem for arithmetic or our representation (or both) that there is incompleteness?

Is this a settled (as much as it can be) philosophical area? I feel like I understand that there will always be incompleteness for a finite set of axioms trying to capture all of arithmetic. But I ...
J Kusin's user avatar
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4 votes
1 answer
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Demonstrate that a term cannot be well-typed?

This problem is coming from Exercise 3.3 in Bacon's A Philosophical Introduction to Higher-order Logics. I am trying to do my due-diligence here and not skip problems, but this one stuck out to me. ...
C D's user avatar
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11 votes
11 answers
3k views

Can axioms be false?

I have often wondered, can axioms be false? For example, I could take as an axiom that "Dogs don't exist", but that is false. To give a more mathematical example, I could take as an axiom ...
user107952's user avatar
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2 votes
2 answers
192 views

What philosophy of mathematics denies the existence of uncountable sets?

Finitism denies the existence of infinite mathematical objects (e.g. quantification over infinite domains is not considered meaningful). Is the position that denies the existence of uncountable sets (...
user avatar
3 votes
6 answers
170 views

Do contingent propositions about the world rely on the consistency of mathematics?

Assume that a contradiction in mathematics is discovered, say '0=1'. Then, by the principle of explosion from classical logic (by the rules of which, arguably, the world adheres as well) we can derive ...
Александр's user avatar
-1 votes
1 answer
82 views

If mathematics is invented for a deterministic reason, then do we discover that prior reason through our inventiveness? [closed]

Consider that mathematics is invented in some predetermined way. Would it then still be possible to claim that it is really invented and not discovered? Is there a point, modulo determinism, where the ...
Timotej Šujan's user avatar
17 votes
21 answers
3k views

What is a natural number?

It’s been on my mind lately. I do maths and work with them daily, but I’m not entirely sure of what they really are. I understand they are symbols at a surface level, but there is obviously more to it....
Fraser Pye's user avatar
4 votes
2 answers
337 views

Why do constructive mathematicians claim that mathematical truth is temporal?

(crossposted here, wasn't sure where it belongs...) It seems to me (and correct me if this is a misconception) that the traditional divide in the interpretation and practice of mathematics is between ...
user9812063's user avatar
0 votes
0 answers
126 views

What are the First Principles of Euclidean Geometry (Besides the Axioms)?

On first principles, Wikipedia says: A first principle is an axiom that cannot be deduced from any other within that system. The classic example is that of Euclid's Elements; its hundreds of ...
DDS's user avatar
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3 votes
3 answers
277 views

How to apply the classical theory of concepts on the mathematical concept of a limit?

I am studying the limit concept from mathematics using the classical theory of concepts. According to this theory a concept is; "A structured mental representation which is characterised by a ...
user21312's user avatar
  • 139
8 votes
4 answers
2k views

If Large Language Models can do Maths, is Formalism true?

A slightly flippant question, but curious to see what my platonist rivals might have to say! One of the proported reasons that Open-AI was having business politics trouble was the suggestion that ...
Paul Ross's user avatar
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5 votes
4 answers
568 views

What is it that is done when we DO mathematics?

I want to understand more deeply and philosophically what exactly mathematicians do. Wikipedia lists some major subareas like analysis, geometry but ends its lead paragraph with There is no general ...
user107952's user avatar
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1 vote
2 answers
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What does philosophy have to do with category theory? [closed]

Category theory seems very abstract and unrelated to philosophy. Why does it seem to be a part of philosophy? Is category theory used in philosophy and in the development of logical arguments? Isn't ...
ale_7's user avatar
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7 votes
5 answers
2k views

Is mathematics analytic or synthetic?

This question is related to another question I posted but I think it requires its own treatment since of the already wide scope of the other question i.e. Is the classical theory of concepts ...
user21312's user avatar
  • 139
3 votes
1 answer
153 views

Is the classical theory of concepts compatible with logical positivism's view on analyticity of mathematics?

Doing some work on theory of mathematical concepts and need a good framework that suits my own views. Is the classical theory of concepts, which seems to no to suffer very much when considered in ...
user21312's user avatar
  • 139
5 votes
6 answers
618 views

Are laws separate “objects” or are they inextricably part of the universe?

This question came forth from a discussion I was having. Suppose that the universe is deterministic because of some laws. But those laws themselves exist for no reason. Does this mean that the laws, ...
thinkingman's user avatar
2 votes
4 answers
933 views

Is Fermat's last theorem a logical necessity or a different kind of necessary truth?

Fermat's Last Theorem states that no three positive integers a, b, and c satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2. The question was, is this a logically necessary ...
Vihan 's user avatar
  • 105
3 votes
2 answers
110 views

Are Bourbaki and Deligne Mathematical Realists?

The following are two closely related questions. What was Bourbaki's position on the ontological status of mathematical objects? Were they some kind of Realist/Platonist or were they Formalist? ...
Luqman Waheeduddin's user avatar
0 votes
1 answer
78 views

Omniscience leads to necessitarianism

You have probably seen these types of arguments before on incompatibility of omniscience and free will. The question is are these arguments valid and what can be a good refutation? Let G= x is known ...
Vihan 's user avatar
  • 105
1 vote
0 answers
59 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
1 answer
193 views

Gödel's Asymmetry

First of all, The Liar sentence, off of which Gödel constructed his argument. L = This sentence is false. As the story goes, L implies contradiction AND ~L implies contradiction. So far so bad. Then ...
Agent Smith's user avatar
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1 vote
2 answers
149 views

Applicability of Mathematics

Suppose that an alien civilization exists, in a planet somehow similar to our own (oxygen-based, plants, animals), in an evolutionary stage similar to ours (large cities, advanced communications, near-...
Ioannis Paizis's user avatar
-3 votes
1 answer
216 views

Which mathematical operations leave the ontology invariant? [closed]

So usually one maps a math equation to an ontology in physics. Imagine me modelling a ball rolling up an inclined plane at an arbitrary angle. Now, the moment I make the inclined angle 90 degrees to ...
More Anonymous's user avatar
3 votes
0 answers
70 views

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
4 votes
4 answers
593 views

How to understand the notion of majority when comparing infinite sets?

Suppose I make the argument: It is very unlikely that in a naturalistic universe, the constants have life sustaining values, since the majority of metaphysically possible universes do not have such ...
Mani's user avatar
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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
3 answers
688 views

Can location be assigned to an entity, given a lack of length, depth, or width?

If one is to postulate an entity that has a complete or absolute lack of height, depth, and width, can such an entity be located anywhere? Or does attribution of location to an entity entail length, ...
Max Maxman's user avatar
11 votes
15 answers
7k views

Can Mathematics Fully Describe the Universe?

To what extent mathematics can capture all physical phenomena? Drawing an analogy from computer science: finite automata can handle regular expressions (does "(([a-z]))" match "((h))&...
PHV's user avatar
  • 113
1 vote
0 answers
61 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
18 votes
13 answers
9k views

Why would infinite monkeys not produce the works of Shakespeare?

Apologies if this is a very basic/obvious question. I have no training in philosophy, but have been making my way through Peter Adamson's History of Philosophy podcast. Recently I listened to his ...
Uzai's user avatar
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1 vote
4 answers
527 views

How can zero exist if zero is nothing [closed]

I understant why it has to exist, but how can zero exist, if zero is nothing, then nothing is something wich means that zero cant exist, ive seen similar questions but i still dont get it, help
axel's user avatar
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1 vote
0 answers
85 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
3 votes
3 answers
843 views

Axioms, meaning, and notation

According to at least one philosophy of mathematics, the axioms determine the meaning of the primitive symbols that are used in the axioms. The phrase "used in" is somewhat imprecise, so ...
Ren Eh Daycart's user avatar
3 votes
6 answers
1k views

Why do numbers apply to such disparate concepts?

I understand numbers to be defined as objects defined to have certain convenient properties in relation to certain operations. It is very surprising that the exact same group objects should be ...
tom894's user avatar
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0 votes
3 answers
506 views

Can this be an example of sophism?

Foreword: 0 is considered an even number, but if 0 would be an even number, then 0 apples would count an even number of apples. Example: 3 apples [🍏🍏🍏] 2 apples [🍏🍏 ] 1 apple [🍏 ] ...
user avatar
4 votes
1 answer
88 views

Do some philosophers-of-mathematics give priorities to different epistemologies of math, rather than (over)committing to one epistemology?

Take Kant and Gödel, for example. Kant was neither just an intuitionist nor just a formalist, nor even absolutely a non-realist (the forms of space and time are, after all, empirically real and ...
Kristian Berry's user avatar
8 votes
2 answers
714 views

Does the incomputability of kolmogorov complexity imply that we will never have a final theory of everything?

The Kolmogorov Complexity is the size of the simplest program that produces a specific output. By the Curry-Howard Correspondence, "programs" are isomorphic to "axiomatic systems" ...
charmoniumQ's user avatar
-2 votes
1 answer
141 views

Gödel's Incompleteness Theorem

I'll keep this short and sweet. Construct Axiomatic System A in which we can do math. Gödel Sentence G = G is unprovable in A. Gödel's Argument (I) If G is provable then there's proof that G has no ...
Agent Smith's user avatar
  • 3,484
2 votes
2 answers
204 views

A problem I noticed with if-then-ism in the philosophy of mathematics

In the philosophy of mathematics, if-then-ism is the view that mathematical assertions of existence, like the statement that there exist numbers which are their own squares, should, strictly speaking, ...
user107952's user avatar
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2 votes
4 answers
208 views

Is mathematics based on formal logic, or vice versa?

Math is obviously based on logic in a heirarchical sense, but what about the historical sense? Is there any historical evidence of a "transition" from first order logic to mathematics? All ...
Steven Harder's user avatar
6 votes
7 answers
3k views

Difference between how a physicist and mathematician approach science?

I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce. Freeman Dyson Is there a ...
More Anonymous's user avatar

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