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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>: OK, I think I see what you mean. You want to consider defining the language as a two-step process - first, some syntactic translation into a "logical form", and then giving a semantics (formal or informal) for that. Since you doubt the plausibility/desirability of giving a *formal* semantics for the logical form, you consider only the first syntactic operation to be part of the formal specification of the language. Is that right? It does seem reasonable. (Although I think the clearest way to give an informal semantics might be to try to give a formal semantics!)That's right. The reason I doubt the desirability of the formal semantics is that there is a risk of that leading to closing down the range of meanings that the language can express.I can see that. Although one advantage of an engelang (particularly an as yet unossified one) is that you can add/modify constructs to deal with any lack of expressivity you might discover.
Indeed -- I said before I was open to having a range of devices for incompatible requirements, each catering to a different expressive requirement.
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.Hmm. This is quite different from what I'd understood previously.
Yes, I did a load of new introspecting, whereas the fluctuating UoD idea was Jorge's way of describing things.
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.
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.
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.
In particular, there's no way to get at other cat-types in P, not even at the proper subtypes of a, because we have to interpret Pa in a situation in which a is the only cat-type. Correct?Ah, I see an inadvertent ambiguity in "only one". I meant "exactly one", as in "the cardinality of the set of cats (individuated by a given body of criteria) is One", rather than "by any body of individuating criteria, the cardinality of the set of cats is nothing but One". So -- with different individuating criteria -- you can get at the subtypes of a.If I understand correctly, you don't really mean to calculate cardinalities of sets here. In the above situation, no two of Felix, Tiddles and Felix+Tiddles would actually be *equal*, so the cardinality |{ Felix, Tiddles, Felix+Tiddles }| = 3, but your individuating criterion is such that when you count the number of cats involved you get 1. Much like if I put a length of string on a table, the cardinality of the set of string-segments on the table is uncountably infinite, but when you count the number of lengths of string you get 1. Right?
Yes to the bit about lengths of string, which is at my level of understanding.
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.
I don't understand the notation "a = (+) { e | Re }" or "<=", tho I guess "<=" means "is a 'part' of or is equal to", 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'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. It's over twenty years since I looked at much logical notation, and even then I only skimmed with scant understanding.)
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?
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.
Only certain ontologies recognize a distinction between types and individuals. So the loglang, IMO, needs either to be ontologically "secular", recognizing no specific ontology, or else to be ontologically "ecumentical", with means of catering to many diffeent incompatible ontologies.I don't think this is a good idea, and would rather that the language broadly specified an ontology in the sense we're talking about... but I'm not sure how to argue this, so I won't try.
I'm happy to see what you come up with (tho will I be able to understand it?). Worst case, we just agree to differ on that one bit of the design. --And.