Unanswered Questions
150 questions with no upvoted or accepted answers
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Can Balaguer’s argument we don’t, and couldn’t, have any good argument for Platonism or ficitonalism in math extend to realism/antirealism in general?
Mark Balaguer is a philosopher who advances the position there is one form of mathematical Platonism, that every consistent mathematical object exists, and one form of anti Platonism, ficitonalism. ...
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Has anyone ever studied which proof types are feasible for which theorems in mathematics? If not, why not?
For instance, when asked to prove that sqrt(2) is irrational, we go straight for the proof by contradiction where we assume it’s equal to a/b in lowest terms and end up with a and b not being in ...
- 29.2k
4
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What does it mean to say that two theorems (provable statements) are 'equivalent'?
sometimes one sees/reads assertions such as "[the bounded inverse theorem] is equivalent to both the open mapping theorem and the closed graph theorem", but taken formally and literally this ...
- 1,761
4
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1
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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 ...
CommunityBot
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5
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273
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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 ...
CommunityBot
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4
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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 ...
3
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2
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Objection to indirect proof in Intuitionism
From my understanding, Brouwer's conception of intuitionism is that mathematical objects only exist in the mind once they have been constructed. And we can create constructions using computable ...
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3
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Knowing-that-we-know in plenitudinous Platonism
SEP background:
If every consistent mathematical theory is true of some universe of mathematical objects, then mathematical knowledge will, in some sense, be easy to obtain: provided that our ...
- 16.7k
3
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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 ...
CommunityBot
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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 ...
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3
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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 ...
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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 ...
- 131
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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 "...
- 81
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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 ...
- 59
3
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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,...
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