TITLE: Is Logic/Set Theory necessary for studying Topos Theory?
QUESTION [6 upvotes]: I have just completed a postgraduate course, in which I studied Category Theory, without having a background in Set Theory and Logic - this probably already sounds absurd to many. This did not seem to be a problem - at least until now. 
As a (reasonable, I thought) progression to my studies, I am trying to teach myself Topos Theory. Until the notion of geometric morphisms, I thought it might be ok to just omit the Logic examples from my studying. And it worked fine, I could keep up with learning. But I have now arrived to the concept of a classifying topos. It feels that now my lack of knowledge in Logic is going to be a very big obstacle. It seems almost impossible to continue. I am worried that this was a big mistake from the beginning. So I am asking the Topos theorists that read this, for their opinion on how stupid they think I have been by thinking in this way, and maybe what is the best way/source to learn what is needed. Thanks for any help.

REPLY [12 votes]: My first advice is to stop worrying about what progression you should be learning stuff. Just read things you find interesting, and if you find yourself reading something that makes no sense to you then you can start backtracking and looking at prerequisites. You don't need to plan ahead so much. Anyway, I second the recommendation of the book of Mac Lane and Moerdijk.
Also, I don't think it sounds absurd to study category theory without having a background in set theory/logic. Most people who know a lot of category theory do not, either; I would say most applications of category theory are in topology/algebraic geometry and related areas. But there are also logicians (as you mention), computer scientists, mathematical physicists, and many others that apply category theory in their work.
Finally, there's a big risk your question is going to closed. Don't take it personally, it's just a bit too discussion-y to be a great fit for the MO "format".