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* 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.
> >>>> A user could be of any of these three sorts:
> >>>>
> >>>> A. The user construes things as types that have subtypes, using l
> >>>> to point to the type, and s& r to quantify over subtypes. Every
> >>>> subtype has its own subtypes so there are uncountably infinitely
> >>>> many types. B. [...]
> >> In Type-A ontology, there aren't levels, only types, and types satisfy
> >> mlt_.
> >
> > Let's stick with A.
> >
> > 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. 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?
> 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? 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.
> > 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?
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?
> > 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 }? 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?
> > Do you mean something like using "re mneka Pe" in the scope of a
> > binding of 'a' to a cat-type (which would have to have been done with
> > something other than "la mlta"!)?
>
> It wasn't what I'd meant, but "la mlta re mneka bcde" works.
This fits with my new understanding.
> 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.
Martin
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