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 answers only
not deleted
user 3106
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.
5
votes
Why should I believe Martin's Maximum++?
Although it's not really a scholarly publication, the Quanta Magazine article, To Settle Infinity Dispute, a New Law of Logic, gives a good introduction to the topic. That article mentions a conferenc …
- 82.7k
10
votes
In what sense does the sentence $\operatorname{con}(\mathsf{PA})$ "say" that $\mathsf{PA}$ i...
There is really nothing peculiar about Con(PA) in this regard. Let's take a simpler statement, such as
$$(\exists x \exists y \exists z : xxx + yyy - zzz = 114) \vee (\exists x \exists y \exists z : …
- 82.7k
2
votes
How much should the average mathematician know about foundations?
François G. Dorais's answer is excellent, but there are two things I would like to add in connection with the original question of what every mathematician should know about foundations.
The first ha …
32
votes
Are there any fields of academic mathematics whose epistemic status as math is controversial...
There are several possible dimensions to the question, "Is it math?"
Does it belong in the mathematics department? I think you mostly want to exclude this dimension, because of your comment about pur …
12
votes
Causality, if any, in mathematics itself
The short answer, as you surely suspected, is that there is no rigorous notion of the type you're asking for, that would allow us to say that (in a particular case) that $X$ definitely causes $Y$, or …
- 82.7k
16
votes
Comparative analysis of history of mathematics
I'm not aware of anything exactly like what you have in mind, but here are a few things which might be close. They all take aim at the widespread belief that the intellectual development of mathemati …
- 82.7k
58
votes
Accepted
Why is integer factoring hard while determining whether an integer is prime easy?
What I think you're asking for are examples of search problems that seem to be hard, while a corresponding decision problem is solvable in polynomial time (but not totally trivial). It is true that s …
- 82.7k
4
votes
Accepted
Formalisation of intuitive concepts in the language leading to mathematical progress
An example that is closely related to computation is proof. Mathematicians have been proving theorems ever since Euclid (and presumably even earlier). But it was not until the 20th century that the …
- 82.7k
14
votes
Is rigour just a ritual that most mathematicians wish to get rid of if they could?
Another MO question about rigor got me thinking about this old question again. One valuable feature of rigor, which I don't think has been said explicitly in the other answers, is that rigor allows m …
13
votes
Accepted
Has there been any mathematical study of causality?
I am converting my comments into an answer.
Setting aside the alleged parallel between causation and inference for a moment, there has indeed been some mathematical investigation of cause and effect. …
- 82.7k
14
votes
Swimming against the tide in the past century: remarkable achievements that arose in contras...
There are various examples of certain areas of mathematics being regarded as sterile and disconnected from the rest of mathematics, but nevertheless being pursued doggedly by some researchers, and eve …
20
votes
Why is game theory formulated in terms of equilibrium instead of winning strategies?
Let me address the criticism that the Nash equilibrium is of questionable real-life significance.
I'll begin by openly admitting something that theorists often are reluctant to admit: One big reason f …
- 82.7k
29
votes
Accepted
Mathematical fictionalism
As I suggested in response to a related MO question, one difficulty with answering this type of question is that most mathematicians outside of logic and set theory lack well-developed "positions" on …
3
votes
Mathematicians with aphantasia (inability to visualize things in one's mind)
I do not think I have aphantasia, but I want to point out that "mental imagery" is very different from an image that you are directly looking at. Consider a map of the world. If you ask me to mental …
3
votes
Analytic/synthetic distinction in mathematics besides geometry?
Based on others' responses and some followup reading I have done, I would like to summarize the situation as I understand it.
One can infer from the nLab entry on synthetic mathematics that the use of …