[YG Conlang Archives] > [jboske group] > messages [Date Index] [Thread Index] >
hasty reply to Nick:
> And, thank you for hanging in there. My immodest prediction (and Bob
> actually adumbrated this on the board) is that if we (as fundie vs.
> progressive formalists) get our story straight, this will be accepted
> at large. So let's see
The signs are encouraging. I have little idea about what is and isn't
consistent with current SL, because that seems so hard to decide.
> > A first reply to Nick:
> > > 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
>
> I'll wait for that before posting Kludgesome Solution #2 (and I'll be
> putting in more and more illustrative examples.)
I'm not sure if I'll have time, and anyway xorxes wants changes to
4XS such that I have to rethink it. But I'll try to explain the issues
in my reply to him.
In the meantime, I would like to see +specific counterparts to all
your examples.
> > > 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)
>
> Sure, but both of these were ultimately at John's behest
>
> > > 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)
>
> Oh. Got it. As in, the former is the denotation of lx.P(x); the latter
> is, more or less, the expression lx.P(x). OK, I'll try and incorporate
> this
One possibility for intensional sets is {tu'o (lo) du be lV'i},
but this only works if tu'o IS treated as having scope over
lV'i. Otherwise, there is no difference between:
tu'o du be lo'i jboskepre
and
lo'i jboskepre ku goi ko'a zo'u tu'o du be ko'a
whereas the intention is that only the latter should be equivalent
to:
tu'o du be la xorxes ce la nik ce la xod ce la djan ce la and...
> > > 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"
>
> Well, there are three things one can speak of:
>
> 1. substance(x): x contains at least one bit that is P, but x contains
> no atom of P
>
> 2. bit of substance(x): the transinfinitely many bits of x.
> Transinfinitely means uncountable because, if you think you have
> counted all the possible portions of the substance (top 16/th cube,
> middle 16/th cube, central 19/th sphere), you can always come up with a
> portion you haven't accounted for. Just as with Real numbers and the
> diagonalisation proof
(I still wouldn't know what the difference between 'transinfinite'
and 'transfinite' is, but at least I understand the two sorts of
infinity found in the natural and real numbers.)
> In fact, since bits of substance are delimited by 3D space, which are
> delimited by 3D points, which are specified by real numbers, that
> cardinality is necessarily the same as real numbers
I hope this talk of '3D space' is prototypical rather than strictly
definitional.
> You objected that real numbers are surely countable, and substances
> have no individual bits. But you see, they do. Take the 1m * 1m * 1m
> cube. You can divide that into 1/2 cubes (there are 2**3 = 8), 1/3
> cubes (27), 1/4 cubes (81), and so on. You can also combine any two
> adjacent bits and get a bit (2/3, 3/4, 2/5...) And the cardinality of
> such fractional subcubes is Q, the number of rational numbers, which is
> aleph-0: fractions are countably many. But you can chop it into
> non-cubes, too, and for any fraction, you can always find a real number
> not covered
>
> So no, there are countable bits of the substance. It's just that they
> are not all the possible bits of the substance. Just as natural and
> rational numbers are countable subsets of the uncountable set of real
> numbers. So I believe the analogy holds. A substance is something with
> aleph-1 bits, a non-system has at most aleph-0 bits
The difference is that any bit of substance will still contain
aleph-1 bits. Similarlay a *portion* of the number line, say
the stretch between 2 and 4, will contain aleph-1 bits. BUT
we can say that {2, 3, 4} has cardinality 3 -- it contains 2 numbers,
whereas if you take some bits of substance and try to say how many
you have, then the cardinality is always aleph-1.
This was my objection, which amounts to saying that numbers aren't
substance. {ci fi'u ro ci'i pa} can quantify over numbers, but
in quantifying over substance the numerator and denominator
if treated as cardinalities would always be {ci'i pa fi'u ro ci'i pa},
so instead we have to use {pa ci'i re} ("1 in every 2 bits") or
{me'i fi'u ro} or {su'o fi'u ro}, or whatever.
> 3. physically distinct bit of substance. I defined this at the end of
> Ontology #3 as spisa. This is a portion of substance of P, wholly
> surrounded in 3D space by non-P. The glassful of water, physically
> separated by the glass from the pitcherful of water. These spisa are
> countably many
Fine, so long as the 3-D space is the prototype rather than strictly
definitional.
> By portion of water, you probably mean (3),
No, I meant "bit of water".
> which is countable. But we
> also need to be able to reason about (2) (bits of water), which is
> uncountable
My concern is that you don't give us a way to do (1). For example,
take "my fondness for Nick". I certainly can't count my fondnesses
for Nick, but nor do know how to quantify over bits of fondness
-- I don't even know how to distinguish ro bits from me'i bits.
> > > 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
>
> I believe it is. When the founders said a substance was pisu'o loi ro
> (and they did), the substance was ro of something. This can't just be
> ro of spisa (because you can say half the glass is irradiated, and so
> the spisa is not atomic.) So I contend it is quantificaation over bits
> of substance
The Founders said that jbomass was pisu'o loi ro. So what that means,
there is no definite way of telling.
It's true that djacu and similar gismu are defined not as "is water"
but "is an amount of water". But the fact remains that we might want
to define predicates whose argument is a substance, not a bit of
substance.
> > > {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)}?
>
> Hm. Hm. I have only introduced lu'i as a last minute thing, and so I
> didn't really think this through, but I suspect the answer is yes. I'll
> need to revisit the INDIVIDUALS IN COLLECTION definition
>
> > 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
>
> Perhaps more pedantically, PA lo ro lo tu'o lo broda. I would rather
> use ci'ipa than tu'o, but we do at any rate have tu'o doing two
> different things (uncountably many vs. kind), and that's not quite
> right anyway
Furthermore, zero quantification is not always the same as kind.
Take the collective of {nitcion, xorxes, xod}, or the collective
of all jboskepre. Since there is only one of them, quantification
over collectives of all jboskepre or of n,x,x is redundant and
unnecessary. Yet there is still a distinction between kind and
nonkind versions of these things.
(Note that the same doesn't hold of sets, because sets are inherently
kinds.)
> > > 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')
>
> Well, it's a confusion, anyway
I think a KS solution would be to take the gimste at close to face
value and read "is an amount of" as "is a bit of". But that doesn't
mean that "is stuff" is not a possible predicate, and your scheme
needs to accommodate this.
--And.