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A first reply to Nick:
> The following will be very very very confusing. & and X, bear with it:
> it is intended as an SL-compatible accommodation of the excellent
> solution. Which has taken five hours out of my life. The rest of you:
> it may be hard for you to believe that this is more compatible with
> Standard Lojban than the Excellent Solutions --- but it is
>
> Incompatibly with SL, this solution introduces weird quantifications:
> PA lo piPA, ci'ipa lo PA, ci'ipa loi PA, PA loi. These are to be
> understood as shorthands of quantifications converting between the
> countability types of collective, substance and individual. I mark the
> weird quantifications as (Weird 1), (Weird 2) and (Weird 3) below
>
> This is a response to Excellent Solution 3, and an attempt to be
> equally powerful
>
> Mad Propz to And and all, but I simply could not understand XS4
That is unfortunate, because it is probably substantially different
in SL-compatibility. The main differences in expressive power
between 3XS and 4XS is that 4XS allows you to quantify over pairs
(and other n-somes) of broda and over halves (and other fractions)
of broda. I will post another message giving the gist of 4XS.
> Point by point
>
> 1. No drastic redefinitions of cmavo or default quantification should
> be required
>
> 2. The Nicolaic properties aren't my idea, they're Johannine.
You pinned them down to prototype & made a ruling that solved the
problem of uninheritable properties. ("The zoologist studies the lion"
!= lo'e cinfo)
> If you're
> prepared to make lo Kind, you've already tossed the Fundament out, so
> you might as well use lo'e for something else. So you can do as you
> please with them in XS. I will keep them mental constructs
>
> 3. lo remains a gadrow for Individual, and loi a gadrow for LojbanMass,
> defined as a union of substance and collective. Kind is handled by
> non-quantification on the outer quantifier (tu'o)
>
> 4. I'm not clear on the difference between extensional and intensional
> sets, but the solutions And proposes are compatible with a more
> fundamentalist Lojban
Two extensional sets are identical if they have the same membership.
Two intensional sets are identical if they have the same defining
feature (the same membership criterion).
> 5. The implicit outer PA on any gadri is NOT mo'ezi'o, but mo'ezo'e,
> and indeed mo'ezu'i. However, this default *is defeasible*. In
> particular, context may dictate a value of mo'ezi'o instead of
> mo'ezo'e. All extensional contexts force mo'ezo'e, however. I assume
> the Standard Lojban default outer quantifiers
>
> 6. The default inner PA is mo'ezo'e, which is glorked from context. For
> an atomic property, it is ro, understood as rosu'eci'ino (at most
> aleph-0). For a substance property, it is necessarily rosu'oci'ipa (at
> least aleph-1). This captures the fact that substances are
> indefinitely subdividable, and atoms and groups-of-atoms are not
>
> 7. Inner quantification does not properly include tu'o, since the set
> of all possible portions of substance does have a (transfinite)
> cardinality --- which is assuredly not mo'ezi'o.
Okay, but I can't promise that we won't find differences between
"is water" and "is a portion of water".
> In the following,
> however, feel free to substitute tu'o for ci'ipa
>
> Uncountability is encoded by inner (and outer, as we will see) ci'ipa.
> In cases where the property quantified over is atomic, this coerces a
> conversion to atom-goo. For atoms, this is also done by fractional
> quantification
>
> lo ci'ipa remna = loi ci'ipa su'osi'e be lo su'eci'ino remna
> pisu'o lo su'eci'ino remna = pisu'o loi ci'ipa su'osi'e be lo
> su'eci'ino remna
>
> Where su'osi'e is a possible bit of the substance (what I have been
> doing in my ontologies as memzilfendi.)
>
> Countability is encoded by inner su'eci'ino: countables have a
> cardinality either finite or aleph-0
>
> These are prolix inner quantifiers, and I will not shed a tear if we
> revert to ro and tu'o. But ro clearly applies to transinfinites as
> well, so I believe this is kind of cheating
It is cheating under the 'bit of substance' analysis.
> As an abbreviation ONLY, I will use ro and tu'o below as inner
> quantifiers for cisinfinite and transinfinite quantification. Because
> they are prolix
>
> 8. In the following, I give in brackets acceptably defaulted-out
> quantifiers and gadri
>
> * pa lo broda [pa broda]: a single broda, whether an atom (pa lo ro
> broda) or an indvidual of substance (pa lo tu'o broda= pa lo ci'ipa
> broda) (INDIVIDUAL)
>
> Individual of substance is also a coercion:
>
> * pa lo ci'ipa broda = pa lo piro loi broda = pa lo su'eci'ino spisa be
> piro loi ci'ipa broda (INDIVIDUAL OF SUBSTANCE)
>
> Where spisa refers to a physically discrete portion of the substance
>
> (Weird1)
>
> This introduces the non-canonical quantification PA lo piPA, which I
> define as equivalent to PA lo su'eci'ino spisa be piPA:
>
> pisu'o loi djacu = some water
> re lo pisu'o loi djacu = two pieces of some water
> = re lo djacu
Why not abbreviate thus:
pa lo su'eci'ino [spisa be piro loi ci'ipa] broda
instead of thus:
pa lo [su'eci'ino spisa be piro loi] ci'ipa broda
? That seems more SL-conformant.
[massive snip, which I will have to properly digest later]
> Individuals:
>
> {tu'o lo broda remei} is a couple of mermaids, not two mermaids. When
> you speak to {lo remna remei}, you speak to a collective, it is when
> you speak to {lo remna se remei} that you speak to the individuals {ro
> lo remna se remei = re lo remna}. So to force an individual,
> distributive rather than collective notion of quantified Kind:
>
> {tu'o lo broda se pamei} = {tu'o lu'i loi pa lo broda} = Mr One Broda
> {tu'o lo broda se remei} = {tu'o lu'i loi re lo broda} = Mr Two Broda
> (the members of Mr Pair of Broda)
> {tu'o lo broda se romei} = {tu'o lu'i loi ro lo broda} = Mr All Broda
> (the members of Mr Collective of All Broda)
We need to quantify over members of Mr Broda Pair. How do we do that?
{PA lu'i tu'o lo(i)}?
I haven't worked out how to quantify over subkinds of Mr Broda, either.
Ah: here it is:
> PA Kinds of the Kind expressed by {tu'o lo broda}... would need to be
> expressed by {PA lo tu'o lo broda}. But since this introduces ambiguity
> (I've been using non outermost tu'o to mean ci'ipa = ci'ipa loi
> su'osi'e be), and it is messy anyway, I would prefer it to be expressed
> by bridi
"by brivla", you mean? If you set aside your abbreviations, and use
tu'o only where it isn't an abbreviation, then {PA lo tu'o lo broda}
makes perfect sense.
> I haven't written this cleanly, I fully admit. But I think this is more
> SL-compatible than the Excellent Solution. In particular,
>
> lo broda remains an individual rather than a kind. Or rather, lo broda
> expresses both an individual and a kind, but the latter is marked as
> tu'o lo broda
4XS is compatible with lo broda remaining an individual, if loi broda
becomes a kind. Of course, then {loi} would not mean a jbomass.
> I clean up a logical confusion between tu'o = uncountably many and tu'o
> = uncounted
That's not a logical confusion. It's a confusion about the meaning
of substance selbri ('substance' vs 'bit of substance').
> I have a mechanism for secondary and tertiary combinations of
> collective, substance, and individual
>
> I retain the default quantifications as much as possible
>
> & and X, over to you. It's butt-ugly, sure. But does it work? If not,
> how not? I suspect X had already proposed tu'o once for Kind and
> abandoned it; why? Because if we define outer quantifier as "what goes
> in the outer prenex", and the Kind never goes in the outer prenex,
> isn't zi'o exactly what is going on here?
I don't see a problem with {tu'o} for kind, though {PA lo tu'o}
should give us subkinds.
I have fought my way through only 2/3 of your two megapostings.
I think what I'll probably do next is see if I can apply your
proposal myself to 4XS.
I'm not sure how kludgesome yours really is. A lot of the verbosity
is due to conversions between types that in practise would be
left to glorking. I don't think we often want to convert between
su'omei and substance.
--And.