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Re: [ontolog-forum] Ontological Assumptions of FOL

To: Ingvar Johansson <ingvar.johansson@xxxxxxxxxxxxxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Sun, 18 Mar 2007 15:15:06 -0500
Message-id: <p0623090bc2234c737491@[]>
>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, ≥Against Set Theory≤. In Experience
>and Analysis . Proceedings of the 2004 Wittgenstein Symposium, ed. J. C.
>Marek and M. E. Reicher. Vienna: Ųbv&hpt, 2005, 143≠152.
>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
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