All Questions
11 questions
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Is there any correspondence between Gödel and Kreisel that supports Kreisel's observation that Gödel changed his mind about his 1938 set theory note?
At a conference in 1965 there were some interesting comments made by Kreisel and Mostowski asserting that Gödel later changed his mind regarding his1938 note on his set theory results (see Problems in ...
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70
votes
6
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The logic of Buddha: a formal approach
Buddhist logic is a branch of Indian logic (see also Nyaya), one of the three original traditions of logic, alongside the Greek and the Chinese logic. It seems Buddha himself used some of the features ...
45
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1
answer
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Hilbert's alleged proof of the Continuum Hypothesis in "On the Infinite"
As is known, Hilbert attempted a proof sketch of the Continuum Hypothesis in the latter part of his paper, "On the Infinite". It is also known that it is false.
Has there ever been a published ...
- 6,132
12
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3
answers
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Has Dedekind's proof of existence of infinite sets been analyzed by historians?
This pdf by David Joyce notes that in paragraph 66 of his famous essay, Dedekind claims to prove the existence of an infinite set.
The proof exploits the assumption that there exists a set $S$ of all ...
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13
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Arguments against Freiling's argument against Continuum Hypothesis
Freiling's axiom of symmetry ($\sf AS$) is known as a justification for falsity of Continuum Hypothesis. Freiling in his 1986 paper, Axioms of symmetry: throwing darts at the real number line, ...
21
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2
answers
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Philosophical arguments in defense (or against) large cardinals
The question is essentially what is asked in the title. I split it into two parts
(A) (Arguments supporting the existence of large cardinals) What are the main philosophical arguments in defense of ...
9
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2
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The impact of large cardinals in mathematics [closed]
What are the main applications of large cardinals in ordinary mathematics, and what is the philosophy behind using them. In particular:
Question 1. What is the philosophy behind accepting large ...
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11
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Last Status of Feferman's Conjecture on Indefinite Value of Continuum
The "true" value of $2^{\aleph_0}$ is one of the most fundamental open questions of mathematics and its philosophy. Hundreds of set theoretic results during the last century don't say anything more ...
user45939
26
votes
7
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What "forces" us to accept large cardinal axioms?
Large cardinal axioms are not provable using usual mathematical tools (developed in $\text{ZFC}$).
Their non-existence is consistent with axioms of usual mathematics.
It is provable that some of ...
user47697
3
votes
0
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A Question Regarding Boolean-valued Models
What were the intuitions motivating the creation (or discovery, if you will) of Boolean-valued models? I have searched for the Scott-Solovay paper on the subject, but to no avail. There also seems to ...
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43
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Essential reads in the philosophy of mathematics and set theory
I am graduate student and have a decent understanding of logic and set theory.
Recently I have got interested in the philosophy of mathematics and set theory. I have read a number of papers by ...