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Results tagged with metamathematics
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user 1176
the mathematical discipline that applies mathematical methods to the study of mathematical theories themselves.
20
votes
Top-down mathematics, or "Where it all begins"
Here is a possible viewpoint to contemplate:
Foundations of mathematics do not begin anywhere.
This happens to be my (current) personal belief. I agree with Monroe that the answer to the question as …
- 48.8k
25
votes
"Let $x \in A$", beginning a proof of "$\forall x \in A$ ...", if A were empty
Please print this and hang it on your office door for your colleagues to see.
The inference rule for $\forall x \in A . \phi(x)$ is as follows (in natural deduction style):
$$\frac{\begin{matrix}[x\i …
- 48.8k
20
votes
Can you have a type theory where there is type of all types?
Of course you can have $\mathsf{Type} : \mathsf{Type}$, the consequence of that is that all types are inhabited (by Girard's paradox). Some people call this an inconsistency, but that only makes sense …
- 48.8k