email@example.com (Leonard Blackburn) wrote in message news:<firstname.lastname@example.org>... > email@example.com (George Dance) wrote in message news:<firstname.lastname@example.org>... > > G. Frege <email@example.com> wrote in message news:<firstname.lastname@example.org>... > > > On 8 Apr 2003 23:24:15 -0700, email@example.com (George Dance) wrote: > > > > > > > > > > > > > And the number 3 is ...in which apple? In all three? Or in only one of them? :-) > > > > > > > > > It's obviously a property of the set. > > > > > > > Great!!! (Congratulations!) > > > > > > Now originally you said: > > > > > > > > > > > > So what's a natural number? Do they exist in space and time? I've > > > > > > argued that they do, as properties of things; they exist in things, > > > > > > not independently. > > > > > > If "numbers exist in space and time, as properties of things" then sets are > > > things in space and time, right? ... Are they? > > > > > > I mean... If there are 3 apples on my desk, where (the heck) is the set??? I > > > CAN'T see it! > > > > Then what do you mean by 'apples'? If you're not referring to the > > apples as a set, why do you mean by the plural? And why are you > > describing it as "3"? > > > > You've got the idea that "there are three apples on my desk"; and you > > claim you did not get that from seeing (or, I presume, from any > > perception at all) of the things on your desk. Whence did it come, > > then? > > > > > Now you also said "they [numbers] exist in things" ... In _which_ things? > > > Obviously not in the apples... Now if the number 3 is not in the 3 apples on my desk in which thing (the heck) is it then??? > > > > If, as you claim, "the number 3 is not in the 3 apples," then why are > > you calling them "the 3 apples"? > [snip] > > What do you mean by "in the 3 apples"?
I mean that, iff the statement "There are three apples on my desk" is true, then it is a physical fact about the apples on my desk that there are three of them.
> Is it physical?
The three apples (or the two lighters in the real example I gave you) are physical.
> Is it made up of atoms?
I believe the lighters are made up of atoms; if so, the fact that there are three lighters would depend on the particular arrangement of particular atoms.
> If so, which atoms?
Whatever atoms there are that make these three objects lighters, I suppose.
> If the number 3 is "in the 3 apples" then is it wholly intact in each > one of them, or is it split up, a third of itself in each? I'm not > getting this. What do you mean by a "property" of a physical object > and by a "property" of a collection of physical objects? > Leonard
I really don't understand what you're not getting. Maybe a further example would make it clearer.
"I have some blue lighters on my desk." Would you agree that that statement is either true or false? Would you further agree that whether the statement is true or false depends on physical facts about the lighters? If so, we can move on to see why '2' is similar.
If not, is the problem that you have trouble also getting what the statement "There are some blue lighters on my desk," means? After all, I haven't told you how 'blue' is in the lighters; or whether 'blue' is made of atoms; or whether the 'blue' is intact in each lighter, or split up so that only 1/3 of blue is in each?
There are many different possible answers to this 'problem of universals' (as it's known), and if that is your barrier here, we can spend some time on talking about them. I'd really rather not get into universals unless you honestly cannot see how the lighters can be blue in fact, or that there can actually be two of them.