# 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.

**5**

**3**answers

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

**53**

**15**answers

### Request for examples: verifying vs understanding proofs

**6**

**1**answer

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

**6**

**1**answer

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

**21**

**10**answers

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

**1**

**0**answers

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

**27**

**18**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]

**25**

**8**answers

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

**114**

**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?

**7**

**5**answers

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

**7**

**1**answer

### Explaining the consistency of PRA and ZF from predicative foundations

**14**

**0**answers

### Does inner model theory seek canonical models for large cardinals?

**17**

**1**answer

### Axiom of Choice versus V=L in opposition to large cardinals

**2**

**0**answers

### Does this axiomatic system satisfy requirements for founding mathematics?

**30**

**3**answers

### Complex analytic vs algebraic geometry

**0**

**1**answer

### “Mathematics is the science of the infinite” [closed]

**5**

**0**answers

### Theorems conditional on false conjectures

**22**

**4**answers

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

**10**

**1**answer

### Quantum functional analysis

**5**

**3**answers

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

**16**

**0**answers

### What's the point of cubical type theory?

**0**

**1**answer

### Criterion of completeness

**58**

**6**answers

### The logic of Buddha: a formal approach

**-3**

**1**answer

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

**15**

**1**answer

### Does every model of ZF-foundation have an extension, with no new well-founded sets, where every set is bijective with a well-founded set?

**36**

**11**answers

### Contemporary philosophy of mathematics

**34**

**4**answers

### On critical reviews of Hawking's lecture “Gödel and the end of the universe”

**1**

**2**answers

### What is against having distinct membership relations on sets in the Platonic realm?

**1**

**1**answer

### Where do models of false theories exist?

**-2**

**1**answer

### Is it natural to hold that Ur-elements, small & big sets and proper classes exists? [closed]

**6**

**2**answers

### Reasoning Using Countable Subsets of Real Numbers

**1**

**0**answers

### The universe and multiverse views of set theory from the perspective of $ZFC^2$

**12**

**1**answer

### When we count the same set, must the number always be the same?

**53**

**7**answers

### In what respect are univalent foundations “better” than set theory?

**0**

**1**answer