Re: [engelang] Xorban: Semantics of "l-" (and "s-" and "r-") - engelang messages

On Thu, Sep 6, 2012 at 10:21 PM, Jorge Llambías <jjllambias@hidden.email> wrote:

On Thu, Sep 6, 2012 at 10:48 PM, Mike S. <maikxlx@gmail.com> wrote:
> On Thu, Sep 6, 2012 at 7:40 PM, And Rosta <and.rosta@hidden.email> wrote:
>>
>> Hence it behaves like a constant. There are (rightly, IMO) no constants
>> in Xorban, but their crucial logical property is that when there is only one
>> X, some X is Y iff every X is Y; everything true of some X is true of every
>> X.
>
> I tried something like that yesterday and it doesn't work formally:
>
> Assume def: li Ri Pi <=> jo si Ri Pi ri Ri Pi <=> jo ri Ri Pi si Ri Pi

I think you need: li Ri Pi <=> je jo si Ri Pi ri Ri Pi jo si Pi Ri ri Pi Ri

i.e. there's only one thing that Ri, and it's the only thing that Pi.

That's a bit puzzling. Semantically, I don't see how "la mlta xkra" has anything to do with a claim that the only thing black is a cat. Formally, I don't see how that expansion can help demonstrate the curious "l-" identity "na li Ri Pi <=> li Ri na Pi", an identity which appears to be a complete nose-thumbing at FOL. (By the way, if *any* FOL expansion exists such that that identity holds, I'd like to see it, whether it matches the semantics of "l-" or not.)

> I don't think "la bcda fgha" implies "sa bcda fgha" much less "ra bcda
> fgha", though either of the latter does imply "la bcda fgha".

Not in the same context. You can only move from "sa bcda fgha" or "ra
bcda fgha" to "la bcda fgha" by changing the universe of discourse to
one where bcda (and to some extent fgha as well) is no longer
dividuated, which is typically not the case in universes where it
makes sense to use s- or r-. So it's not a logical implication that
can take us from s-/r- to l- unless we are already in l-'s territory,
in which case you wouldn't be using s-/r- in the first place.

Well, even the awkwardly phrased "either no cat is black, or cats are black" seems to logically hold, and "either not every cat is black, or cats are black" also seems to hold (the converses clearly don't, however). Smoother would be "If one-or-more cat is black, then cats are black; if every cat is black, then cats are black". I suppose you have some counterexample in mind. If you are right and my guess is wrong, then it only adds to the idea that "l-" is an ill-fitting overlay on top of FOL without some more elaborate but up-until-now unelaborated formal interface between them.

>In the future,
> it's probably worthwhile to consider the possibility that the intension of a
> set of individuals is behind the scenes of "l-"; in the meantime, I think
> it is useful to note identities and implications as they become apparent.

I think so, as long as nobody is tempted to say that l- directly
refers to the intension, which seems to say that intensions can do
things like talk or walk.