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* Sunday, 2012-09-16 at 00:44 +0100 - And Rosta <and.rosta@hidden.email>:
> Martin Bays, On 15/09/2012 17:33:
> > * Saturday, 2012-09-15 at 14:17 +0100 - And
> > Rosta<and.rosta@hidden.email>:
> >> Martin Bays, On 15/09/2012 03:59:
> >>> * Thursday, 2012-09-13 at 14:30 +0100 - And
> >>> Rosta<and.rosta@hidden.email>:
> > So am I right in thinking that we could interpret this without
> > mention of individuating criteria by changing the presupposition
> > from "exists unique a s.t. mlta" to "exists unique maximal a s.t.
> > mlta", maximality being with respect to the parthood relation, and a
> > now being bound to the unique maximal cat in the situation?
>
> For me, I think the answer is Yes, so long as "parthood" is understood
> loosely and with the proviso that I don't know what "s.t." means.
Cool, I think this is actually a definition of l_ which I can imagine
understanding!
"s.t." means "such that". Sorry for the mathematical jargon, it's a hard
habit to kick.
> >> The evidence is that if Tiddles is on the windowsill and Felix is
> >> by the fire, this can be described as "la mlta li je [windowsill]i
> >> [fireplace]i [sat at]aki".
> >
> > Uhoh. Did you really mean that?
>
> No I didn't, I meant "li gi [windowsill]i [fireplace]i", but didn't
> think about it enough to realize that.
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"?
> > If so, how am I to understand "li je [windowsill]i [fireplace]"? Not
> > a singularisation of all the things which are both windows and
> > fireplaces, because there are no such things. Nor a singularisation
> > of all pluralities which contain windows and fireplaces, because that
> > would be the totality of the universe.
>
> It's generous of you to suppose that I actually meant "je"...
>
> Even tho I didn't mean "je", I think it would be a singularization of
> all the things which are both windows and fireplaces. A group
> containing windows and fireplaces is, if properties of parts inherit
> to the whole, both fenestral and focal.
Oh, but they can't do that. You don't want a group which comprises
a fireplace, a window and a cat to be part of "la mlta", surely?
> > 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?
> I don't understand the notation "a = (+) { e | Re }"
a is the mereological sum of all the e which satisfy R.
"(+)" is ascii for a plus sign in a circle, which I think is the
favoured symbol of those wacky mereologists.
> or "<=", tho I guess "<=" means "is a 'part' of or is equal to",
Yes (though I think it's just "is a part of", with equality being
a special case).
> in which case I think that's okay, so long as scarlet is part of red,
> seven is part of oddnumberdom, B is part of consonantdom, terror is
> part of fear, and so forth.
I think that's okay, as long as seven isn't a part of the set of odd
numbers, and so forth.
> >>> I'm still not sure I understand what you mean by "using [...] s&
> >>> r to quantify over subtypes", though.
> >>
> >> I meant that "sa/ra mlta" is interpreted as quantifying over
> >> subtypes of the type Mlt.
> >
> > Where by "the type Mlt" you again mean a maximal element of the { a
> > | mlta }?
>
> (Oh, "{ a | mlta }" is the set of all cats.
Yep!
> It's over twenty years since I looked at much logical notation, and
> even then I only skimmed with scant understanding.)
Sorry, I'll aim to use words or define my symbols.
> Yes, I think so. But it wouldn't surprise me if crucial issues were
> going unnoticed over my head. For example, what does "maximal element"
> mean?
A maximal element of a set S is an element x of S which is part of no
element of S other than x itself. For example, if the sum of everything
in S is itself in S, then that would be a maximal element - in fact it
would be the only maximal element.
> > For the purposes of s/r, is there any need to mention or
> > even assume the existence of such a thing, as opposed to mere saying
> > that it quantifies over things satisfying mlt according to some
> > individuating criterion?
>
> The latter formulation suffices.
Excellent.
Of course this raises the question of how to signal the individuating
criterion you have in mind. But I'm happy to ignore that for now.
Martin
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