SUO: RE: Re^n: Collections - Aggregation or Set
Dear Chris,
>
> Chris P wrote:
> > Max Black's essay (referred to in an earlier email) starts with a
> > quote from a working mathematician's book on set theory -
> which claims
> > that packs of wolves etc. are standard examples of sets.
>
> A claim that is pretty obviously false. A pack can change its members
> (if, for example, a pup is born) and remain the same pack. Not so the
> set corresponding to the pack at any given time.
MW: Not so obviously in fact. You have assumed a 3D ontology, Chris and I
would assume a 4D ontology (I don't know about Max Black). In this case the
set of members of the flock is the spatio-temporal extent of all members of
the flock, past, present and future. This doesn't change over time.
>
> > If I had the time, I am sure I could come up with other examples.
>
> There are lots of similar examples that go wrong for similar
> reasons --
> flocks of geese, schools of fish, citizens of a country, sets
> of dishes,
> etc. All of these collective entities can change their membership, at
> least to some extent, and remain the same collective entity.
> Not so the
> corresponding sets at any given time.
MW: These are sets too of course.
>
> That said, there is one (and only one) clear thinking philosopher of
> mathematics that I know of who has respectably defended (not to say
> demonstrated) the view that sets of physical objects are themselves
> physical, viz., Penelope Maddy. The locus classicus here is her 1980
> paper "Perception and Mathematical Intuition," Philosophical Review 89
> (1980), pp. 163-196. Maddy is no crackpot -- she's head of the Logic
> and Philosophy of Science program at UC Irvine, author of two highly
> regarded Oxford Univ Press books on philosophy of mathematics, and she
> is a member of the American Academy of Arts and Sciences.
>
> The most interesting thing Maddy does in defense of the physicality
> thesis is to marshall neuroscientific evidence for the existence of
> "set detectors" that enable us to perceive sets of physical objects.
> Such detectors, she argues, if they exist, provide a sound
> naturalistic
> basis for the possibility of set theoretic knowledge. After all, if
> sets really *are* completely abstract things, then they are causally
> inert and so (for the naturalist) a question remains as to how we can
> know anything about them. Maddy, who is both a mathematical realist
> about set theory and a scientific naturalist argues that her appraoch
> fills this epistemological gap.
>
> Chris Menzel
>
>
>
Regards
Matthew
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