Re: SUO: RE: RE: RE: RE: Collections - Aggregation or Set
Chris Partridge <chris_partridge@csi.com>, replying to Matthew West:
>1) Are sets abstract?
>
>I think there is some talking at cross purposes going on here.
>
>My original question was what makes something abstract - what is the basis
>for the abstract/concrete distinction (as there seem to be a number of
>possibilities). A standard answer (in some communities) with a long
>tradition is that abstract things do not have spatio-temporal location - and
>concrete things do. Pat suggested that sets were abstract (a position you
>hold - from what you say below). Pat, I seem to recall, claimed that sets
>were abstract because they could not have spatio-temporal location (sorry if
>I have remembered incorrectly Pat). In other words, his 'definition ' of
>abstract was 'having spatio-temporal location'.
Yes, that will do. I actually don't like the 'abstract' terminology
since it has all kinds of metaphysical baggage. The key contrast for
me is betwen things in space-time - broadly, 'physical' things - and
things which are not, like sets and numbers.
>My point was that some
>people (me and you included) are comfortable with regarding some sets as
>having a spatio-temporal location.
Well whatever you mean by 'set' isn't what I mean, is all I can say.
>So for you and I the claims that
>'abstract means not having spatio-temporal location' and 'sets are
>abstract' - are inconsistent. This is my original point.
>
>As you do not hold to the first claim ('abstract means not having
>spatio-temporal location') you can make the second claim ('sets are
>abstract') without being inconsistent. But this leaves us without a notion
>of what your idea of abstract is. Perhaps you can elaborate. A common claim
>is that sets are by definition abstract (and sometimes (if one is a
>materialist) that only sets are abstract) - in this case the two terms
>collapse into one another.
>
>One place among many to look for a discussion of these problems is David
>Lewis's on the Plurality of Worlds - pp. 81-86 Concreteness.
David Lewis holds some very unique views on these issues, it should
be said. He is probably the only philosopher in recent history who
apparently believes that alternative possible worlds are real, for
example. I mention this only to emphasise that reading Lewis and
nothing else is a bit like trying to live on a diet of bran.
>
>2) Groups and Collections.
>
>Again I think we are talking at cross purposes.
>
>You say:
>What I think you are doing is asking whether, given the one-to-one
>relationship, is it not possible to merge the two objects?
>
>My point was not that one could merge the notion of set and collection
>(though some mereologists have tried this route).
Yes, but part-of becomes subset on this route, not set membership.
>My point was rather that one could have a third notion - of a group - with
>its own way of working.
Seems to me that there are many notions of collection, with various
conditions on what can be members and what properties are shared or
held in common. Flocks, piles, shoals, teams, etc., all have their
uses. Sets and mereosums are both extreme cases which involve
removing one or another constraint altogether. For example, sets are
collections which make no stipulations whatever on the nature of
their members other than being clearly individuated from each other
and retaining that individuation when collected; the key properties
of set-membership all follow from that. Mereosums are collections
with the opposite stipulation that there can be no criteria for
individuating one part of the collection from another (strictly,
there can be, but it will be external to the business of making the
collection, ie will depend on some external structure which is
orthogonal to whatever makes those things part of the collection). So
a mereosum has no distinguished parts: it can be taken apart any way
you like and re-merged to get exactly the same sum back again, so
parthood is transitive. Other kinds of collection tend to be
somewhere in between these extremes: part of a sheep isnt part of a
flock, but any subflock of a subflock is a subflock.
>To return to my question:
> > As you say, in different circumstances one might want to use
> > the set and the
> > fusion approach. However, what happens if you want to use
> > them both in the
> > same situation - or is this just impossible (as you seem to
> > suggest) and if
> > so why?
>And my example:
> > There are examples where we appear to be using both
> > approaches. One of the
> > useful properties of sets (as Frege noticed) was that one can
> > count their
> > members. So if I say 'those two hundred bolts weigh 2 kilo'.
> > Or, that 'there
> > are around 500 nuts in that 10 kilo'. How do we explain this?
> > That we are
> > talking about two closely related things, the fusion and the
> > set? This is
> > possible but requires more work to explain than the surface
> > structure of the
> > phrases suggest.
>
>I presume you would analyse each of these as two statements about two
>different but intimately related things:
>So 'those two hundred bolts weigh 2 kilo' is really saying - that class of
>bolts has 200 members and the fusion of the members weighs 2 kilo.
The thing that weighs 2 kilo is presumably something that when put
onto a scale would register 2 kilo. That would be something like a
pile of bolts. A pile is an example of an aggregate which is both a
material assembly (in contrast to a set) and has distinguished
members - it imposes individuation criteria on its members, so they
are countable - in contrast to a mereosum. It is neither a set nor a
mereosum. It shares countability with the set of its members, and
total mass with the mereosum of its members, but not vice versa.
All this seem fairly obvious to me. What is your overall point? At
times you seem to be saying that sets are physical, other times you
seem to be saying the opposite.
Pat
---------------------------------------------------------------------
IHMC (850)434 8903 home
40 South Alcaniz St. (850)202 4416 office
Pensacola, FL 32501 (850)202 4440 fax
phayes@ai.uwf.edu
http://www.coginst.uwf.edu/~phayes