WikiDiscuss

---

wrote:

>
> pc:
> > Ix: x group & xF Iz: z group & xCz z
> > d-G & z is Q of x
> >
> > Remember that we aare here in inspecificity
> (if
> > that is the right distinction)
>
> Where does that show in the above formula?

I suppose (though I am not sure I understand just
whatspecificity is all about --even after
Cowan's explanation, which I have lost anyhow) in
the fact that there is no further identification
(or whatever you want to call it) than as a
grouup that Fs and as aa group subordinate to
that.

> > so that
> > IDENTIFICATION, if that means putting a name
> to
> > or pointing out or the like — outside the
> > context --is not what is required.
>
> I don't think identification is ever involved
> when it
> comes to standard quantifiers. You talked of
> identifying
> first and then denumerating. My point was that
> the
> denumeration, in that formula, is done at the
> same time
> as anything we may recognize as identification.

Are we talking linguistically or physically here?
Linguistically the "identification" is most of
the sentence away from the enumeration;
physically it might be hard to pick out a group
without noticing at least a rough enumeration
(assuming the group is not too big of course --
and even "too big" counts as an acceptable sort
of enumeration).
>
> > This is A
> > broda, not out of context this broda or
> Charlie
> > Brod or whatever.
>
> That sounds good for {lo broda}.
>
> But not what I would want for {su'o da poi
> broda cu brode},
> which is merely Ex: x broda x brode, and
> where the
> quantifier operates on a sentence, it does not
> refer.

Sorry, I thought we were talking about {lo broda}
(well actually {Q lo broda}). The case of what
are bare quantifiers in Lojban remain as bare
quantifiers in the translation, except that the
whole is put in terms of groups: [Ix: x group &
xF & Ay: yF xCy] Iz: xCz zG & z Q of x. I
think that this amounts to the ordinary — though
not here supported for the moment — Qx:xFxG,
but — the reasoning behind this analysis holds
-- brings some useful but often hidden factors to
light: the Fs, for example, and the sepparation
of enumeration from identification (both for lack
of better words at the moment).

> > Particular quantifiers (and at
> > the logic level we seem to need only them and
> > universals)
>
> Given negation, either one of them will do. We
> can get
> the other in terms of it and negation.

True, but not necessarily very useful. A in
terms of I is messy (a conjunction of quantified
sentences) I in terms of A is worse because it is
hard to get the importing back in after a
negation: ~A+ = O-, so ~A~ is I- rather than I+.

> > amount to saying whaat kind of thing
> > we have selected but not what it does.
> Standard
> > logical notation is not very good on this;
> > restricted quantification is better but still
> > leaves something to be desire. The "Y"
> notation
> > is a bit better yet but may still fall short,
> > though I don't see just exactly how at the
> > moment.
>
> What would be good keywords to Google for this?
> I tried "most likely" and "Y notation" but it's
> too general
> and nothing related comes up. I had never heard
> about this
> before.

I don't remember the standard terminology (this
is mine, from an unfinished from long ago).
Maybe "indefinite description" (though there are
some large number of things that go by that name.
The only thing I can remember the name of which
at all related (and it is a different language
altogether, though to the same point
eventually)is Hans Hermes "Term Logic with Choice
Operator," Lecture Notes in Mathematics 6,
Springer Verlag, 1965. It is not the whole story
but probably enough to get you over the rough
bits. (The "most likely Fs" is, as hinted, not
strictly correct but has proven pedagogically
useful in the past.)

> > But, in any case, it is useful to notice
> > that these three (standard — not group --
> plural
> > quantification, restricted quantfication, and
> the
> > Y language) are all equivalent to one
> another
> > though they make different things "obvious."
> The
> > Y notation makes the relation to Lojban at
> least
> > more obvious than the other two, which shows
> a
> > good intuition on JCB's part half a century
> ago
> > (when most of the logic here was as yet
> > unexplored and some not even hinted at).
>
> I haven't noticed the equivalence yet, but then
> I still
> don't very well understand this Y notation.
>
The crude equivalence is something like the
following: translate among these notations
Ix(xF & xG), Ix: xF xG, Yx: xFG. They
ought to be true in exactly the same situations
(there are tricky cases for each of them, but
manageable and the general pattern holds). The
English analogs are "There are somethings which
are both F and G", "Some Fs are Gs" ("some" in
phonmnetically reduced form "sm") and "Some Fs
are Gs" ("some" in full form). (Or maybe the
phonology goes the other way, I forget.)