Questions tagged [philosophy-of-mathematics]
Philosophy of mathematics asks questions about mathematical theories and practices. It can include questions about the nature or reality of numbers, the ground and limits of formal systems and the nature of the different mathematical disciplines.
1,498 questions
5
votes
1
answer
110
views
Question about Dummett's interpretation of Frege's Context Principle
I am reading Dummett’s The Context Principle: Centre of Frege’s Philosophy. In Chapter 5, Dummett presents the main objections that are raised concerning whether Frege really abandoned the context ...
- 645
9
votes
5
answers
421
views
Does the plurality of type-theoretic foundations disprove logical monism?
There is apparently controversy around accepting logical pluralism - the view that there is more than one "correct" logic, which is surprising to me as a mathematicians.
Logical pluralism ...
- 101
-4
votes
1
answer
85
views
Can mathematics be done, in some form, in complete and decidable foundations? Is foundational incompleteness a consequence of our epistemic standards? [closed]
My question in a single line: could we help to "automate the formal sciences" in guaranteeing desirable (for computing) properties of foundations (completeness, computability, decidability, ...
- 398
3
votes
2
answers
155
views
Does the need to use mathematics to describe physical theories undermine physicalism? [duplicate]
Reprinted from Communications in Pure and Applied Mathematics, Vol. 13, No. I (February 1960). New York:
John Wiley & Sons, Inc. Copyright © 1960 by John Wiley & Sons, Inc.
THE UNREASONABLE ...
- 4,292
0
votes
3
answers
178
views
Why is the Hamiltonian of the system (me) not a self sufficient description?
Alfred Tarski’s work on truth and semantics—particularly his Undefinability Theorem—provides a deep reason why, as “language beings,” we cannot have an adequate (i.e., fully self-contained and ...
- 3,074
6
votes
5
answers
2k
views
How many axioms is too many?
I was reading The Joy of Cats, and on pg. 383 it goes:
Also Top is definable by topological axioms in Spa(F). However, a proper class of such axioms is needed.
Some random factoid, in context (pg. ...
- 6,595
7
votes
12
answers
2k
views
Why is mathematics able to produce such persuasive, rigorous proofs?
It seems that of all the types of "proof" available, mathematical proofs are both the most rigorous and the least contestable. Generally, when mathematical proofs are published and vetted, ...
- 95
3
votes
6
answers
306
views
What are the historical reasons for the "unreasonable popularity" of formalism in mathematics?
We have all heard the story: late 19th– to early 20th-century mathematics was being shaken by paradoxes (Cantor’s set-theoretic puzzles, Russell’s paradox, etc.). That crisis created a demand for a ...
- 522
1
vote
1
answer
128
views
What correspondence it there between non-confluence of classical logic and the Kochen-Specker theorem in physics?
What correspondence it there between non-confluence of classical logic and the Kochen-Specker theorem in physics?
They look quite similar, because they both hint at reality which is unstructured and ...
- 131
-3
votes
1
answer
104
views
What does X=not X mean in Laws of Form by G. Spencer Brown?
I read a comment saying he writes equations like that which lead to as this comment puts it:
The first part of it is simple Boolean logic. There's no paradigm shift. It's unremarkable. It is simple, ...
- 894
4
votes
3
answers
241
views
Is mathematical finitism actually an argument based on physics?
At present, we have no way of knowing whether the universe is finite or infinite. But suppose physicists somehow were able to establish that the universe is in fact infinite, and thus we knew that (...
- 1,179
7
votes
7
answers
2k
views
How certain do mathematicians consider their axioms today?
Kant believed that mathematical axioms are immediately certain. I think this is only true for some, not all. But what interests me more is how many mathematicians still hold this view for some axioms? ...
- 708
7
votes
1
answer
405
views
Did NSA lead to new ideas/new questions in the philosophy of mathematics?
Nonstandard analysis (NSA) has reintroduced infinitesimals and has shown that they can be used in a rigorous way, simplifying the presentation of analysis/calculus by basing it on a theory of ...
- 17.1k
4
votes
2
answers
633
views
A couple of questions on Wheeler's "it from bit" and "pregeometry" ideas
Physicist John A Wheeler proposed an interesting idea which he summarized in a phrase "it from bit" which basically proposes that the universe and its laws of physics (including the most ...
- 911
2
votes
6
answers
402
views
Is the definition of infinity that it is something that is larger than any natural number?
If there are an infinite number of natural numbers, and an infinite number of fractions in between any two natural numbers, and an infinite number of fractions in between any two of those fractions, ...
- 77