# Tagged Questions

3answers
86 views

### Can a statement in FOL be equivalent to two separate independent statements?

This may seem like a dumb question, and it certainly seems dumb to me asking it, but I'm running into a contradiction. I'm looking at the problem of finding a statement $\phi$ such that $\psi$ and ...
1answer
85 views

### Arrows-only implication & disjunction in $\mathbf{Set}.$

Just before the truth-arrows in a topos subsection of Goldblatt's "Topoi: A Categorial Analysis of logic," descriptions of the truth functions $\Rightarrow$ and $\smallsmile$ are given in ...
4answers
352 views

### The standard role of intuitive numbers in the foundations of mathematics

In my career I've been formed mostly in the formal side of mathematics, that is, standard set theory and every classical branch of mathematics that uses set theory. However, I am not quite sure about ...
2answers
96 views

### Abstract Objects in Logic

I am confused on the concept of extensionality versus intensionality. When we say 2<3 is True, we say that 2<3 can be demonstrated by a mathematical proof. So, according to mathematical logic, ...
3answers
247 views

### P entails Q implies P

I have been looking at the following: P entails Q implies P And developed the proof as follows: ...
4answers
97 views

4answers
752 views

### How did the ancients view *infinitesimals*?

With some category/topos theory we can now put infinitesimals on a rigorous ground, as in Bell's A Primer of Infinitesimal Analysis, where the author introduces $\epsilon$ satisfying ...
2answers
217 views

### why does soundness seem to be less important than consistency for the structuralist?

If I am not wrong, many mathematicians (I believe this is not only restricted to structuralists) agree that an inconsistent formal system does not have any model. By model I mean some kind of set ...
1answer
235 views