Unanswered Questions
140 questions with no upvoted or accepted answers
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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 ...
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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 ...
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What is the 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 ...
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how to Hellman's structuralism preserve original mathematical practice for proof
I am reading Hellman’s Mathematics Without Numbers. I’ve read exactly up to page 26, and my understanding is roughly this: Hellman does not understand mathematical sentences as sentences about certain ...
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Is there a counterpart semantics available for the multiverse standpoint in set theory?
I've been working on something that might be usefully denoted "the Dual Continuum Hypothesis," which is based on the following from Asaf Karagila on the Math Stack Exchange:
We know that ...
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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 ...
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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 ...
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Did Gauss criticize cardinals?
In a well-known passage, Gauss criticized the use of infinity in mathematics in the following terms:
I protest first of all against the use of an infinite quantity as a completed one, which is never ...
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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 ...
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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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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 ...
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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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Does Gödel’s findings boil down to part of classical mathematics (as opposed to computation) is flawed?
According to artificial intelligence researcher Joscha Bach, only classical mathematics is affected by Gödel’s incompleteness theorem however not computation where calculations are performed in a step-...
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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 ...
