>Pat Hayes schrieb:
>>
>> If you can represent it as a set, then it is a set.
>>
>
>>> That doesn't mean the universe "is" a set. To say that something can
>>> be represented as a set for purposes of defining truth-values of
>>> sentences is a very different thing from saying it IS a set.
>>>
>>
>> I disagree. I think these are exactly the same
>> thing to say. To say that a collection is a set
>> is to say nothing about it at all.
>>
>
>In many philosophical contexts it is important to keep *sets* (abstract
>non-temporal entities) whose members are spatiotemporal entities
>distinct from the *aggregate* (Mario Bunge) or the *collection* (Peter
>Simons) of the same spatiotemporal entities. However, in many contexts
>it doesn't matter whether one talks of sets or of
>aggregates/collections. (01)
Perhaps I used "collection" differently from
Simon's usage; if so, I apologize for creating
confusion. But I certainly wouldnt want to say
that an 'aggregate' is a set, no. But then I
wouldn't count it as a 'collection' in my
informal sense, either. (02)
>I guess Pat Hayes is working within the latter
>kind of contexts; it is a pity that it misleads him into thinking that
>"what you can represent as a set, is a set". (03)
All I mean by this is that its "being" a set is
simply saying that it can be described using set
theory; and if it can be so described, then it is
a set, pretty much by definition. There is no
independent, metaphysical notion of "being a
set", any more than there is of being a group (in
the mathematical sense); if something satisfies
the axioms, then it is indeed one of the things
described by those axioms. That is all I meant.
Bungean aggregates do not satisfy those axioms;
mereological sums do not; ergo, these are not
sets. (04)
>
>Recommended reading: Peter Simons, ³Against Set Theory². In Experience
>and Analysis . Proceedings of the 2004 Wittgenstein Symposium, ed. J. C.
>Marek and M. E. Reicher. Vienna: öbv&hpt, 2005, 143152.
>
>Best wishes from,
>Ingvar J (the real one, not the corresponding singleton set) (05)
Of course. One of the great merits of set theory
is that (unlike mereology) it does not confuse a
thing with the 'collection' (forgive me, Im using
this here to mean only set OR mereological sum)
containing that thing alone. (06)
Pat (07)
>
>
>--
>Ingvar Johansson
>IFOMIS, Saarland University
> home site: http://ifomis.org/
> personal home site:
> http://hem.passagen.se/ijohansson/index.html
>
>
>
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