Andrej Bauer
Reputation
1,859
Top tag
Next privilege 2,000 Rep.
 Feb 18 comment Introductory books as preparation to read Voevodsky homotopy-theory (HoTT) book Why do you call it "Voevodsky HoTT book"? If anything, it is the "HoTT book written by the participants of the Special Year on Univalent Foundations at Institute for Advanced Study". Feb 5 comment Which is the most powerful language, set theory or category theory? @Fatimah: the connections go deeper than just "translating the alphabet" at the level of symbolic notation. The connections are of a mathematical nature, i.e., the structures involved are related to each other in interesting ways. I added a link to Steve Awodey's paper From Sets to Types to Categories to Sets which explains this very well. Feb 5 revised Which is the most powerful language, set theory or category theory? added 145 characters in body Feb 5 awarded Good Answer Feb 4 awarded Mortarboard Feb 4 awarded Nice Answer Feb 4 comment Which is the most powerful language, set theory or category theory? Is this better now? Feb 4 revised Which is the most powerful language, set theory or category theory? deleted 91 characters in body Feb 4 comment Which is the most powerful language, set theory or category theory? Yes, I want there to be a negative connotation because it is simply false that the set-theoretic foundation is a necessity for the working mathematician. It is a (tremendous) convenience, but so would be a different foundation, as long as it were universally accepted. It is the uniformity of the language and setup of mathematics that really helps, not the fact that there is a foundation in the philosophical sense of the word. Feb 4 comment Which is the most powerful language, set theory or category theory? There are 10 commandments in the bible. There are 10 axioms of set theory. The many many many laws of Judaism you're referring to are more like the equivalents of the axiom of choice. Feb 4 comment Propositional function and Rule of Inference Well, it depends on how you organize things. You could start with the idea of truth tables and get rules from that (like in my story), or you could start with the rules and then observe that truth tables model the rules. Feb 4 answered Which is the most powerful language, set theory or category theory? Feb 4 revised Propositional function and Rule of Inference added 119 characters in body Feb 4 answered Propositional function and Rule of Inference Feb 4 revised Propositional function and Rule of Inference fix latex formatting Feb 4 comment Propositional function and Rule of Inference I cannot find the relevant passage in the book. Are you referring to books.google.si/… ? There it talks about wff's (well-formed formulas, not about "variable letters"). Please be more specific. Feb 4 suggested approved edit on Propositional function and Rule of Inference Jan 12 comment What's an example of an infinitesimal? Right. I think the intuitionistic stuff comes in once you are in a field and have $x^2 = 0$, and you wonder whether $x = 0$. Intuitionistic fields are messy. Jan 11 revised What's an example of an infinitesimal? deleted 338 characters in body Jan 11 comment What's an example of an infinitesimal? @zyx I did come in late and I am not aware of the history. Anyhow, I am not planning to get dragged into this. I answered the question because I was asked to via email, and I'll leave it at that. Have fun fighting for justice.