# Questions tagged [mathematical-philosophy]

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.

**3**

**2**answers

### Are ITTM's necessary to compute Turing's “computable numbers” and what does that mean for ordinary recursion theory?

**4**

**0**answers

### generate all possible theories compatible with axioms [migrated]

**1**

**0**answers

### Is this theory using defined notions of classes, sets, and membership interpretable in ZFC?

**31**

**15**answers

### Is pure mathematics useful outside of mathematics itself? [closed]

**8**

**5**answers

### Can you do math without knowing how to count?

**0**

**1**answer

### Is a function needed here?

**8**

**0**answers

### Theories of truth

**2**

**1**answer

### Can we choose an element from a class?

**0**

**2**answers

### Is there an analogue of the Lost Melody Theorem in ordinary recursion theory and if not, why not?

**55**

**9**answers

### Proofs of theorems that proved more or deeper results than what was first supposed or stated as the corresponding theorem

**1**

**2**answers

### Has there been any serious attempt at a “circular” foundation of mathematics?

**19**

**5**answers

### Is there a metamathematical $V$?

**50**

**5**answers

### Metamathematics of buts

**1**

**0**answers

### Is this a good way of conceptualising the current status of Foundation of Maths projects?

**0**

**0**answers

### Tutte polynomial of a complete graph and full symmetric group

**9**

**1**answer

### Gödel on pure mathematics and medieval theology

**19**

**2**answers

### Can we take a supremum over all Hilbert spaces?

**7**

**2**answers

### Books on relationship between the Socratic method and mathematics?

**14**

**1**answer

### A “paradox” about the inner model problem

**9**

**3**answers

### What does T+non-Cons(T) mean?

**63**

**22**answers

### Small ideas that became big

**10**

**2**answers

### Gödel's ontological proof & Benzmüller's work

**6**

**2**answers

### Searching for an early, highly theoretical, even philosophical, math paper on models or small-world networks

**1**

**1**answer

### Reference request on Gentzen's proof of the consistency of PA

**6**

**4**answers

### The name for an assumption made for the sake of contradiction

**54**

**15**answers

### Request for examples: verifying vs understanding proofs

**6**

**1**answer

### How can we know the well-foundedness of $\epsilon_0$?

**7**

**1**answer

### What types are to mathematical proofs as types à la Martin-Löf are to constructive proofs, and what's wrong with them?

**20**

**10**answers

### The meaning and purpose of "canonical''

**1**

**0**answers

### Can “description” of models revive formalism?

**28**

**20**answers

### Modeling in pure math

**12**

**2**answers

### Origin of the noun “mathematician” [closed]

**1**

**0**answers

### Arithmetization of Syntax: Can any semantic be encoded as syntax?

**1**

**3**answers

### Regarding Gentzen's note regarding 'Godel-points' (i.e., “Where is the Godel-point hiding?”)

**2**

**0**answers

### Compatible and incompatible sets [closed]

**0**

**1**answer

### Formalizing ontological optimism

**2**

**1**answer

### Overview of interpretations of classical probability

**3**

**0**answers

### Can third-order arithmetic prove the consistency of second-order arithmetic?

**1**

**1**answer

### Proving independence with large cardinals?

**0**

**0**answers

### Is there a criterion for reducibility of equi-interpretable theories?

**1**

**1**answer

### Generalized Fourier integral and steepest descent path, saddle point near the endpoints

**6**

**3**answers

### The Lucas argument vs the theorem-provers — who wins and why?

**8**

**0**answers

### When is a paper finished? [closed]

**28**

**8**answers

### Why not adopt the constructibility axiom $V=L$?

**116**

**17**answers

### Pressure to defend the relevance of one's area of mathematics

**14**

**2**answers

### Set-theoretical foundations of Mathematics with only bounded quantifiers

**9**

**2**answers

### Constructivist defininition of linear subspaces of $\mathbb{Q}^n$?

**-4**

**2**answers

### Is the notion of measurable cardinal definable from the perspective of set-theoretical potentialism?

**8**

**5**answers

### Is there any physical or computational justification for non-constructive axioms such as AC or excluded middle?

**7**

**1**answer