# mathematical-philosophy's questions - English 1answer

256 mathematical-philosophy questions.

### 55 Why hasn't mereology succeeded as an alternative to set theory?

I have recently run into this wikipedia article on mereology. I was surprised I had never heard of it before and indeed it seems to be seldom mentioned in the mathematical literature. Unlike set ...

### 34 Contemporary Philosophy of Mathematics

11 answers, 7.719 views reference-request mathematical-philosophy
Starting to write an introduction to the philosophy of mathematics I find tons of positions that are of historical interest. My question to the research community in mathematics is which positions are ...

### Criterion of completeness

Wittgenstein (PR 181) talks about a criterion of completeness for the irrationals. I am trying to understand what this might mean. Completeness of the reals, in the decimal number system, is the ...

### 22 Does Zorn's Lemma imply a physical prediction? [duplicate]

4 answers, 1.383 views set-theory mathematical-philosophy
A friend of mine joked that Zorn's lemma must be true because it's used in functional analysis, which gives results about PDEs that are then used to make planes, and the planes fly. I'm not super ...

### 7 Alternative axiom to induction

Is anyone aware of alternative axioms to induction? To be precise, consider peano axioms without induction PA-. Is there any axiom/axiom schema that is equiconsistent to induction, assuming PA-? If so,...

### 33 Silver's approach to the inconsistency of $ZFC$

As all probably know, Jack Silver passed away about one month ago. The announcement released, with delay, by European Set Theory Society includes a quote by Solovay about his belief on inconsistency ...

### 10 Quantum functional analysis

Can one explain some philosophy behind "quantum functional analysis" (or "quantized functional analysis") which was initiated and developed by such researchers as: Ruan Z.-J., Pisier J., Effros E.G., ...

### 36 Were Bourbaki committed to set-theoretical reductionism?

A set-theoretical reductionist holds that sets are the only abstract objects, and that (e.g.) numbers are identical to sets. (Which sets? A reductionist is a relativist if she is (e.g.) indifferent ...

### 5 Counting without one-to-one correspondence? [closed]

Ash and Gross in their wonderful book Fearless Symmetry found it worth mentioning (and thus suggesting) another way of counting for which "we do not even need to know how to count" (in the sense of ...

### 14 Variable-centric logical foundation of calculus

Since calculus originated long before our modern function concept, much of our language of calculus still focuses on variables and their interrelationships rather than explicitly on functions. For ...

### 7 what's the point of cubical type theory?

I have been following through the development of homotopy type theory since 2013 because I was really interested in the foundation of mathematics. The novel idea of combining programming with homotopy ...

### 15 Is PA consistent? do we know it?

1) (By Goedel's) One can not prove, in PA, a formula that can be interpreted to express the consistency of PA. (Hopefully I said it right. Specialists correct me, please). 2) There are proofs (...

### 5 Ultrainfinitism, or a step beyond the transfinite

Cantor has, in the immortal words of D. Hilbert, given all of us a paradise (or perhaps, I would rather say, a great vacation spot), the TRANSFINITE. $\aleph_0, \aleph_1,\aleph_2\dots$ the lists ...

### 49 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 ...

### -3 What is the intuitive notion that ZF-Extensionality-Foundation+Collection can be said to capture? [closed]

This question has been moved to philosophy.stackexchange.com I'll try to abbreviate it here: the question asks about the "informal notion" that the fragment of $\text{ZFC}$ that is axiomatized by ...

### 28 Excellent mathematical explanations

8 answers, 4.713 views mathematical-philosophy big-list
In the Stanford Encyclopedia of Philosophy there is an entry on mathematical explanation. The basic philosophical question is: What makes a proof explanatory? Two main "models" of mathematical ...

### 37 Can a problem be simultaneously polynomial time and undecidable?

The Robertson-Seymour theorem on graph minors leads to some interesting conundrums. The theorem states that any minor-closed class of graphs can be described by a finite number of excluded minors. As ...