FOM: Re: Arbitrary Objects

[charles silver]

> 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?

Torkel Franzen:
>   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.

    This makes sense (and is in accord with Harvey saying 'arbitrary' isn't
an adjective here), but I want to think it over a bit.

Charlie