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* Sunday, 2012-09-16 at 16:12 +0100 - And Rosta <and.rosta@hidden.email>:
> Martin Bays, On 16/09/2012 01:28:
> > * Sunday, 2012-09-16 at 00:44 +0100 - And Rosta<and.rosta@hidden.email>:
> >> I meant "li gi [windowsill]i [fireplace]i"
> >
> > OK! But I'm afraid I haven't been following development closely enough
> > to know how g_ works, beyond having the vague impression that it's a bit
> > like joi. Is "li gi Pi Qi" different from "li ja Pi Qi"?
>
> li gi Pi Qi is the union of Pi and Qi.
Of li Pi and li Qi, you mean? I still don't know how that differs from
li ja Pi Qi, but that's just a symptom of the larger problem that I don't
really have a clue how l_ works. See below!
> >>> So at this point, I'm reading "la Ra Pa" as actually meaning: Pa
> >>> where a is the mereological sum of all e which satisfy Re in the
> >>> situation a = (+) { e | Re } , with the presupposition made that the
> >>> situation does contain this sum and that this sum itself satisfies R
> >>> (in other words: a is the unique maximal element of { e | Re }).
> >>>
> >>> Or in notation: "la Ra Pa" --> P(\iota x. (R(x) /\ Ay. (R(y) ->
> >>> y<=x)))
> >>>
> >>> Does this miss anything?
> >>
> >> "Mereological sum" sounds to me like a massification rather than
> >> a myopic singularization, but maybe mereology has a broader sense than
> >> I realize. If not, then something broader than "merological sum" is
> >> required.
> >
> > Hmm. I was hoping these were the same thing.
> >
> > Can you give me an example of a predicate which would hold of the
> > massification of all cats (say) but not of the myopic singularisation?
>
> What John said. Also "has millions of heads" versus "has one head".
But you do have them both satisfying mlt_, yes?
Assuming so, it seems I'm still far from understanding your meaning of
la Ra Pa.
Let me try again!
* Saturday, 2012-09-15 at 14:17 +0100 - And Rosta <and.rosta@hidden.email>:
> Martin Bays, On 15/09/2012 03:59:
> > So with "la mlta Pa", we're forced by the presupposition to interpret it
> > in a (quantifier-domain restricting) situation containing just one of
> > the various cat-types. Depending on the context (including the hints
> > given by P), this could naturally be "cats in general", or "black cats
> > in general", or "this cat here", or "the noon-yesterday-stage of this
> > cat here", or various other things. Is this right?
>
> Yes, but it's not the main part of the story, for me. The UoD may be
> one which the only cat is Tiddles, e.g. a story world, but (now that
> I've given the matter more thought) I don't see the UoD as shrinking
> as appropriate to ensure that there is only one. That is, if Tiddles
> is sitting on the windowsill, and I say "la mlta li [windowsill]i
> [sitting on]aki", I don't think I am temporarily shrinking the UoD to
> contain only Tiddles; rather, I think I'm performing some sort of
> singularization -- myopic singularization, massification, whatever
> suits the context -- on all catdom in the UoD.
So in light of the above, and in the hope of inducing clarity, I guess
the first question I want to ask is: what happens to these various
singularisations when you apply one of the singularisations? For
example, if both the massification and the myopic singularisation
satisfy mlt_, and you myopically singularise everything which satisfies
mlt_, then the massification is going to be part of what you're
singularising. So will all the intermediate massifications. So e.g. the
weights of the things you're singularising varies from a hundred grams
or so for a kitten to billions of kg if you take the entirety of current
catdom. So why would you have it weighing on the order of a kilogram?
(Of course I don't expect you to be able to give precise rules for
answering questions like "[what is the weight of] la mlta"! I'm looking
only for general ideas.)
I suppose the answer must be along the following lines: the myopic
singularisation is itself performed with respect to a choice of
individuating criterion. In this case, you happened to pick the one
which looks at individual cats. But you reserve the right to instead
e.g. singularise species (in which case you would presumably decline to
answer a silly question like "what's its weight?").
So now I'm imagining something along the lines of taking the
mereological sum, but then dividing up that sum into "individuals"
according to some criterion, and assigning the m.s. those properties
which hold "generically" of those pieces... but perhaps this is wildly
inaccurate?
Then there's the complementary question: if these myopic
singularisations satisfy mlt_, then (one would naively expect) they'll
end up in massifications. How does that work, or is it just disallowed?
Martin
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