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Re: Substance vs Bit of Substance



cu'u la xorxes
la nitcion cusku di'e

The bits of substance that I've been talking about (anything from "the
top quarter of" to {pi ro}) are, I would claim, extensionally defined
notions of substances.

I agree. You're not really talking about Substance as such but
a quantifiable derivation ("bits of substance"). That bits
can physically contain or overlap other bits is not really
relevant to their quantifiability. Quantifiablility is not
the same as countability.

(I think this means you're agreeing with me. Which I guess is why you say "I agree" :-) )

I think right now numbers are atomic (qua platonic ideals), and
division is not a legitimate instantiation of ve memzilfendi. But even
if I'm wrong, we can think of a number as being the substance of all
smaller numbers that add up to it. That is one way to think about a
number; it's just a nightmarishly spaced out one. :-)

Be careful with zero there. Is it the only atom among the reals?

It would be possible. However:

If I'd set constraints on possible memzilfendi, this problem would not arise. memzilfendi is a division of x, such that if the memzilfendi pieces y1 and y2 are themselves divided, no piece z1 of y1 is also contained in y2. (So, the pieces of memzilfendi are mutually exclusive.)

If I divide number a into real numbers y1 and y2: a = y1 + y2 , there is always a number y3 such that y1 = y3 + j, y2 = y3 + k. Therefore the memzilfendi necesarily overlap. Therefore, division into smaller numbers is not a legitimate memzilfendi. Therefore numbers are atomic.

Real numbers are quantifiable: you can talk of "each real number",
"no real number", "at least one real number", "not all real
numbers". That the cardinality of the set is aleph-one does not
make them into Substance. If you can single out the members of
the set then you can quantify over that set, whatever the
cardinality.

Eh, but what do you mean by single out? Atomic, or something else?

--
Dr Nick Nicholas. Unimelb, Aus.  nickn@hidden.email;  www.opoudjis.net
 Many among their proselytes had sold their lands and houses to increase
  the public riches of the sect --- at the expense, indeed, of their
  unfortunate children, who found themselves beggars because their
  parents had been saints. (Edward Gibbon, _Decline and Fall_.)