Re: [engelang] intensions & extensions (Xorban)

Hmm, I am starting to get the impression that there is no real difference between "s-" and "l-" except how it behaves in scope wrt "r-". 
 

The world of the dreamt need not be, and often isn't, the world of the dreaming.  So "li fi le je xkre
mlte vska'ake snva'aki" would be effectively:

[la'e dscrswrlda'e] li [lo smo] fi le je [ho] xkre [ho] mlte [ho] vska'ake [ha'e] snva'aki

Roughly, "I dream [of some possible world in which] I see a black cat [from that world]."  That's the effective result.  If the syntax allowed it we could more accurately write:

[la'e dscrswrlda'e ha'e] li fi le je xkre mlte vsk[h^]a'ak[h^]e snv[h^]a'ak[lo smo ho]i

...where the h-syntax over the variables are part of the formal definition of "snv-" and "vsk-", and the exact h-quantification over the whole sentence is pragmatically determined; "[la'e dscrswrlda'e ha'e]" = "in the world in which this discourse takes place" is probably the default and most natural interpretation.  I would say that ultimately only primitives, not variables or formulas in general, can interact with [hW] so there have to be some transformations to make sense of this.  For reasons not unlike the reasons keeping "ju" from changing restrictions, I think applying "hW" to a binding is the same as applying it to its predication complement alone, so we can rewrite the original as follows:

=> [la'e dscrswrlda'e] li fi le je xkre mlte vsk[h^]a'ak[h^]e [ha'e] snv[h^]a'ak[lo smo ho]i

The ad-hoc notation "[h^]" is intended to indicate that whatever hW applies to "snv-" also applies to that variable; in other words, the dreamer and the dreaming are in the same world by definition, so let's indicate that:

=> [la'e dscrswrlda'e] li fi le je xkre mlte vsk[h^]a'ak[h^]e [ha'e] snv[ha'e]a'ak[lo smo ho]i

Here's a big step.  I think that applying either "hW" or "lW smW hW" to a variable V is equivalent to applying that to the restriction of its binding, because from a predicate's point of view, that's what a variable is actually bound to.  Please note that "o" is intended to be a unique anonymous variable, not really "o":

=> [la'e dscrswrlda'e] li [lo smo ho] fi le je xkre mlte vsk[h^]a'ak[h^]e [la'a ha'e mslfa'a] [ha'e] snva'aki

Applying "hW" to a unary is the same as applying it to its complement:

=> [la'e dscrswrlda'e] li [lo smo] fi [ho] le je xkre mlte vsk[h^]a'ak[h^]e [la'a ha'e mslfa'a] [ha'e] snva'aki

We've already seen that applying "hW" to a binding is the same as applying it to its predication complement:

=> [la'e dscrswrlda'e] li [lo smo] fi le je xkre mlte [ho] vsk[h^]a'ak[h^]e [la'a ha'e mslfa'a] [ha'e] snva'aki

For the purposes of this illustration alone, I've defined "vsk-" extensionally, and now we have a formal definition of what that means.  It means that the seer, seeing, and the seen are all in the same world, as indicated formally by the double "[h^]".  Let's rewrite that so that [ho] over "vsk" gets applied to the restrictions of the variables of "vsk".

=> [la'e dscrswrlda'e] li [lo smo] fi le je xkre mlte [ho] vsk[ho]a'ak[ho]e [la'a ha'e mslfa'a] [ha'e] snva'aki

=> [la'e dscrswrlda'e] li [lo smo] fi le [ho] je xkre mlte [la'a ho mslfa'a] [ho] vska'ake [la'a ha'e mslfa'a] [ha'e] snva'aki

We're nearly done.  It is hopefully obvious by now that "hW je R1 R2" is shorthand for "je hW R1 hW R2":

=> [la'e dscrswrlda'e] li [lo smo] fi le je [ho] xkre [ho] mlte [la'a ho mslfa'a] [ho] vska'ake [la'a ha'e mslfa'a] [ha'e] snva'aki

"In this world i.e. the world in which this discourse takes place, I in this world do some dreaming in this world of another world in which I in that world do some seeing in that world of a black in that world cat in that world."

And yes, that's precisely what I'd prefer "li fi le je xkre mlte vska'ake snva'aki" to mean and nothing else, except that the sentence-level world is pragmatically determined as mentioned earlier.  I think the rules in summary are:

hW B R P => B R hW P
hW N F => N hW F
hW J F1 F2 => J hW F1 hW F2
BV RV P[hW]V => BV hW RV PV (definition of P)

One other note, regarding the default world of sentences:  If the discourse shifts to topics outside of actual states of affairs wrt the discourse, then IMO that probably should be marked at least once, or at the very least, a speaker should be availed the option of marking such a shift in discourse, maybe something like "I hereby declare we are now talking about Lord of the Rings".  After a speaker signifies that the discourse has shifted into a discussion about the Tolkien universe, one could say "Frodo dreamt about the ring" where the dreaming would occur in a Tolkienian world, and not in this one, and default [ha'e] would become default "lo {Tolkien's universe}o ho" or something.  Incidentally, the worlds of Frodo's dreams would not necessarily be those of Tolkien's universe as he could dream about things that didn't occur in Tolkien canon, but they would be worlds closely related.

But the main point after all of this writing, even if the above formal semantics is not accepted: "je xkre mlte" means "E is a black cat in W" i.e. within any single world, it doesn't mean "E is black in W1 and E is a cat in W2", because that's semantically nonsensical.

I would say it's a question of the definition of "vsk", which is an open lexical design choice.  I think there are good reasons for both lumping and splitting approaches.  However, just to plug one reason to split rather than lump in this instance, if you touch a picture or a statue of a cat, it doesn't seem that you touch a cat, and a speaker who said he touched a cat when he touched a statue would seem rather uncooperative if not outright mendacious.  Another point is that if I see a black cat balled up in someone's home, I might see that cat without immediately recognizing what it is, but I still see that cat.  If see a cat in a movie or a child's drawing but don't recognize what it is, then it seems in that case that I do not see that cat.  It seems that the two meanings are similar with respect to perception, but distinct with respect to cognition and identity within or across worlds. For the record I don't care if "vsk" covers both meanings as long as there is a way to disambiguate if the speaker wishes to do so.

 

Well regardless of whether my sloppiness inadvertently permits or entails that, you can't do that simply because it makes no sense.  Hopefully I successfully cleaned things up a little with this email.

 

Well I guess that would be just "fctl[h^]a" then.  The fact and its being a fact are in the same world, i.e. "A is factual in the world in which it is factual".