# Tagged Questions

**2**

votes

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### Meta$^{n{-}th}$ mathematics [duplicate]

Metamathematics has a reasonably clear connotation,
enough to have a Wikipedia page,
with GĂ¶del, Tarski, and Turing playing leading roles;
Kleene's book (Introduction to Metamathematics (Amazon ...

**2**

votes

**2**answers

1k views

### In What Sense is Set Theory a 'Foundation' for Mathematics? [closed]

In what sense is set theory a foundation for mathematics? To my mind (for what that is worth), there are at least three (somewhat) distinct senses in which set 'theory' (I put "theory" in scare ...

**1**

vote

**0**answers

448 views

### Arguments against Reductio ad Absurdum [closed]

Could Reductio ad Absurdum not be consireded a valid proof method? Are there any compelling arguments against it, or at it's favor?
I feel like I am assuming some metamathematical hypothesis about my ...

**6**

votes

**5**answers

2k views

### A meta-mathematical question related to Hilbert tenth problem

I am reading Bjorn Poonen's very nice survey on Hilbert's Tenth problem
(http://www-math.mit.edu/~poonen/papers/uniform.pdf), and while I believe I understand the mathematics well, I have widespread ...

**13**

votes

**3**answers

878 views

### Are there examples of nonconstructive metaproofs?

This came up in a question on the xkcd forums. Is it possible to have a nonconstructive metaproof, i.e. a proof that there exists a proof in some formal system which does not construct said proof? Are ...

**12**

votes

**5**answers

1k views

### Consistency strength needed for applied mathematics

Given that we can never proof the consistency of a theory for the foundations of mathematics in a weaker system, one could seriously doubt whether any of the commonly used foundational frameworks (ZFC ...

**11**

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**3**answers

1k views

### Are there natural examples of mathematical statements which follow from consistency statements?

Motivation
One of the methods for strictly extending a theory $T$ (which is axiomatizable and consistent, and includes enough arithmetic) is adding the sentence expressing the consistency of $T$ ( ...

**6**

votes

**1**answer

832 views

### Using the multiverse approach to decide the law of the exluded middle?

Recently, in response to deciding the Continuum Hypothesis $CH$, Hamkins and Gitman have proposed consider a multiverse of set-theoretic universes, some in which $CH$ is true, some in which $\neg CH$ ...

**0**

votes

**1**answer

523 views

### Formal definition of 'useful' ?

Has anyone worked out a formal, general-enough definition of what is 'useful', so that it could reflectively be used in mathematics? I am aware of the work in utility theory from economics (but ...