Jiri Lebl wrote: > Karl Malbrain wrote: > > Patricia Shanahan wrote: > > > Ultimately, I don't think the subject of this thread even asks the right > > > question. It should be "Set theory: Should you use?". I don't even know > > > what it means to believe set theory. > > > > > > > Believing means to agree with the axioms of set theory. > > > > intransitive verb > > 1 a : to have a firm religious faith b : to accept as true, genuine, or > > real <ideals we believe in> <believes in ghosts> > > To say that is about as stupid as to say something like "Do you believe > in a screwdriver." It is a tool that you use, just like set theory.
Far from stupid, I believe in a screwdriver when I meet up with a loose screw -- I suppose others might believe in a hammer.
> Mathematics is saying A=>B, there is nothing that forces anyone to > "believe" A is true. If people just say "B", then they are implicitly > assuming that everyone knows there is some axiom system in the > background and most people would assume something in terms of ZFC
I thought that we're talking about an axiomatic system as foundation (or not).
> or > some such and that B is really just a result "ZFC => B." However, to > state that for just about every result in the literature would become > cumbersome.
encumber: 1. To impede the motion or action of, as with a burden; to retard with something superfluous; to weigh down; to obstruct or embarrass; as, his movements were encumbered by his mantle; his mind is encumbered with useless learning.
> Most mathematicians would, in my opinion, "agree" that ZFC are most > probably consistent, and most probably the best basis (currently) for > modeling the real world. Pragmatic acceptance is all that is required > to work with ZFC. Belief is not neccessary (but of course not > disallowed).
By the definition I gave above, it is. When you work within the ZFC system you have to agree to the axioms of ZFC. What is the difference between "pragmatic acceptance" and belief?