Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with mathematical-philosophy
Search options not deleted
user 20597
Philosophical aspects of logic and set theory; truth status of mathematical axioms; Philosophy of Mathematics; philosophical aspects of mathematics in general; relation of mathematics to philosophy; etc. Consider also posting at http://philosophy.stackexchange.com/, where philosophy-of-mathematics is one of the most popular tags.
69
votes
5
answers
9k
views
What was Hilbert's view of Gödel's Incompleteness Theorems?
According to Solomon Feferman, in his slide presentation "Three Problems for Mathematics", Hilbert wrote (in regards to Gödel's second incompleteness theorem):
...the end goal [is] to establish as …
- 6,132
45
votes
1
answer
3k
views
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 analy …
- 6,132
10
votes
1
answer
831
views
Are there 'finitistic' nonrecursive functions (assuming Church's Thesis is false)?
[Note: In what follows, I will be using the same type of argument Laszlo Kalmar did in his paper "An Argument Against the Plausibility of Church's Thesis" found in Constructivity in Mathematics, (Amst …
- 6,132
9
votes
1
answer
999
views
How are material set theory and structural set theory related from the point of view of cate...
In his comments to both cody and Nik Weaver regarding his answer to user7280899's mathoverflow question "What kind of foundation are mathematicians using when proving metatheorems?", Mike Shulman writ …
- 6,132
7
votes
Belief in consistency of extremely large cardinals
There is another path that can be used to justify the existence of very large cardinals. Consider, for example, the abstract to Magidor's paper, "On the Role of Supercompact and Extendible Cardinals …
- 6,132
7
votes
Why hasn't mereology succeeded as an alternative to set theory?
Considering the nature of your question, you might be interested in the following paper by Geoffrey Hellman and Stewart Shapiro:
"The Classical Continuum without Points", The Review of Symbolic Logic …
- 6,132
6
votes
1
answer
206
views
Is $PRA$ + $TI({\epsilon_0})$ mutually interpretable with some theory in the language of set...
As is well known, the following theory is equiconsistent with $PA$:
$ZFC$ with the axiom of infinity replaced by its negation.
Since this theory is equiconsistent with $PA$, it would seem reason …
- 6,132
6
votes
3
answers
3k
views
The Lucas argument vs the theorem-provers -- who wins and why?
In his paper, "Minds, Machines and Gödel", J.R. Lucas writes the following:
Gödel's theorem [First Incompleteness Theorem, that is—my comment] must apply to cybernetic machines, because it is of t …
- 6,132
5
votes
0
answers
320
views
Can the Kunen inconsistency (or the existence of Reinhardt cardinals) be 'properly formulate...
In their paper "Generalizations of the Kunen Inconsistency" (arXiv:1106.1951v1 [math.LO]10 Jun. 2011), Hamkins, Kirmayer, and Perlmutter write the following:
The first [metamathematical issue--my …
- 6,132
5
votes
0
answers
940
views
Why are real-valued measurable cardinals never explicitly mentioned in Gödel's "What is Cant...
It is a matter of mathematical folklore that Gödel "entertained the idea of so called stronger axioms of infinity deciding $CH$...." (this quote from Radek Honzik's paper, "Large cardinals and the Co …
- 6,132
5
votes
1
answer
475
views
Extensions of the Ackermann interpretation to nonstandard theories of arithmetic
In their paper, " On Interpretations of Arithmetic and Set Theory" (Notre Dame Journal of Formal Logic, Vol. 8, No. 4 (2007), pp. 497-510) in section 7, "Fragments of Arithmetic and Set Theory", Kaye …
- 6,132
4
votes
Why should we believe in the axiom of regularity?
Consider first the Unrestricted Axiom of Comprehension
($\exists$y)($\forall$x)(x$\in$y $\leftrightarrow$ $\phi$(x))
and the resulting Russell paradox
y$\in$y $\leftrightarrow$ y$\notin$y
One can cert …
- 6,132
3
votes
Has Dedekind's proof of existence of infinite sets been analyzed by historians?
You might want to take a look at Greg Oman's preprint
"Unifying Some Notions Of Infinity In $ZC$ and $ZF$",
It was to appear in Reports on Mathematical Logic, but you can find the preprint in …
- 6,132
3
votes
0
answers
342
views
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 …
- 6,132
3
votes
1
answer
618
views
Are the paradoxes of material or strict implication used anywhere to prove theorems in mathe...
In the Stanford Encyclopedia of Philosophy entry "Relevance Logic", the following inference is listed as classically valid:
The moon is made of green cheese. Therefore, it is raining in Ecuador n …
- 6,132