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* Monday, 2012-09-24 at 02:28 -0400 - John Cowan <cowan@hidden.email>:
> Martin Bays scripsit:
>
> > So we're forced to introduce a new operation - myopic singularisation.
> > You seem to have this applying to individuated sets, although it's not
> > clear to me that the individuatedness is important.
>
> It does matter. The MS of John Cowan is just John Cowan, because of
> the identity of indiscernibles.
I'm not sure what you mean here.
I meant to ask whether it is key that the individuals over which you MS
have no overlaps (pairwise common parts). For example, if you picked
three points equally spaced around the equator, and talked of three
consecutive sun-lives observed from those points, but acknowledged that
they overlap, could you nonetheless form the MS? I don't see why not.
> Notation: A temporal English word followed by * means its spatio-temporal
> equivalent. Thus "always*" means "always and everywhere", "when*" means
> "when or where", etc.
>
> > In any case, the result is a new kind of thing. In particular, it is
> > illegal to take the sum of a cat and a myopic singularisation of cats.
>
> Not so much illegal as uninteresting. That sum usually* has 2 heads,
> 8 legs, etc.
This behaviour isn't important, so I'll ignore it.
> > (i) how are their properties and relations related to those of the
> > individuals they originated with?
>
> I don't know how to specify it formally, but informally it works
> like this. Consider the MS of the set {Barack Obama, John Cowan}.
> This entity always* has a head, never* has a tail, and is sometimes*
> brown-skinned and sometimes* pink-skinned. The MS of the set {x |
> x is a cat} almost always* has four legs and a tail, is never* green,
> but otherwise has different colors at different times*.
>
> Define a "Sun-life" as the brightest object in the sky between a sunrise
> and the following sunset at a fixed observation point. The MS of the set
> of Sun-lives between a summer solstice and the following winter solstice
> is always* yellow-white, always* the brightest object in the sky, and
> always rises at a different place (declination) at sunrise.
Interesting.
But couldn't, as John Clifford was I think suggesting, these things also
be true of the corresponding masses/bunches? If I ask how many legs the
mass of cats has, the answer might be large, but if ask how many legs it
has *at the location of a particular cat*, wouldn't it make just as much
sense to say that the answer to this is 4 as it would to say this for
the MS?
If this is so, then what is gained by having both masses and MSs in the
ontology?
> > (ii) Can MSs be summed with each other? Can I take an MS of dogs and
> > an MS of cats, and bunch the two together?
>
> Certainly. That object always* has claws and teeth except when* they
> have been removed. It almost always* has a tail. It sometimes* barks
> and sometimes* meows.
I take it you would say the same of the MS of the union of all cats and
all dogs?
> > (iii) Relatedly: can we myopically singularise myopic
> > singularisations? Do you want to leave open the possibility that any
> > thing might be considered to be an MS of some other things?
>
> It makes no difference whether you MS two MSes or the union of the
> underlying sets. The MS of all the half-yearly Sun-life MSes is the
> MS of all the Sun-lives, which may be considered the single object
> "the apparent Sun".
Martin
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