# 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.

**25**

**8**answers

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

**105**

**16**answers

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

**13**

**2**answers

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

**8**

**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?

**16**

**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?

**23**

**2**answers

### Complex analytic vs algebraic geometry

**-1**

**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]

**8**

**0**answers

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

**0**

**1**answer

### Criterion of completeness

**50**

**5**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

**33**

**3**answers

### On Critical Reviews of Hawking's “Gödel and the End of the Universe” Lecture

**1**

**2**answers

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

**2**

**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 $ZFC^2$

**11**

**1**answer

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

**50**

**7**answers

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

**0**

**1**answer

### Forcing the existence of a weakly inaccessible cardinal in some strong set theory

**14**

**3**answers

### History of the abstract method in mathematics

**70**

**4**answers

### The enigmatic complexity of number theory

**13**

**2**answers

### (Fictive) story of a time where people reasoned only up to isomorphism

**5**

**0**answers

### Why are real-valued measurable cardinals never explicitly mentioned in Gödel's “What is Cantor's Continuum Problem”?

**37**

**5**answers

### How to improve writing mathematics?

**26**

**5**answers

### Why aren't functions used predominantly as a model for mathematics instead of set theory etc.? [closed]

**-4**

**2**answers

### Can only the constructible sets be proven to exist in $ZF$ without benefit of extra assumptions? [closed]

**41**

**1**answer

### Hilbert's alleged proof of the Continuum Hypothesis in “On the Infinite”

**4**

**0**answers

### Have chromatic techniques actually been used to compute more stable homotopy groups of spheres?

**1**

**0**answers

### Can $GPK^{+}_{\infty}$ + $AC_{WF}$ prove "$ZFC$ proves that the class of ordinals is not weakly compact for definable classes?

**1**

**0**answers

### Second-order characterizability and forcing

**9**

**1**answer

### How are material set theory and structural set theory related from the point of view of category theory?

**33**

**1**answer

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

**49**

**10**answers

### Axiom of choice, Banach-Tarski and reality

**3**

**1**answer

### Extensions of the Ackermann interpretation to nonstandard theories of arithmetic

**5**

**1**answer

### Is $PRA$ + $TI({\epsilon_0})$ mutually interpretable with some theory in the language of set theory?

**2**

**1**answer

### Is the statement “All numbers are counting numbers” independent of $PA$?

**19**

**3**answers

### Why would the category of sets be intuitionistic?

**10**

**2**answers