FOM: Re: Arbitrary Objects

[Torkel Franzen]

Charlie Silver says:

  >It's difficult for me to
  >believe that an answer to what arbitrary objects are is just to say that
  >'arbitrary' is not an adjective.   If not an adjective, what is it?

  A part of the phrase "an arbitrary object". "Let x be an arbitrary
real number..." has the same meaning as "Let x be any number...". When
asked to "press any key", Homer Simpson asked "Where is any key?", and
the present conundrum is rather similar!

  >Since
  >mathematicians *use* arbitrary objects constantly, it seems to me there
  >should be some well-developed and clearly understood account of them.

  Mathematicians use arbitrary objects the way we press any key.