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

Well, thanks for teaching your mother to suck eggs. Sure intensions are fundamental and extensions derived -- in the formal system (although even that is suspect, since you can't have a function from worlds to things without worlds and things, both extensional). But this is about language for people to speak in their world and epistemically (pace Plato) things come before concepts. In addition, this is to be speakable FOPL (with a lot of frills) and that is painfully extensional.

{tu'a} is not particularly strange; it is just a bit vague: iirc it stands for lo [abstractor] ce'a X (where I may have {ce'a} wrong but it is somewhere around there an x is a term). What abstractor is involved depends upon the predicate to which this is an argument and what bridi bit goes in for the dummy depends upon what the case is: with {djica} it's usually something about having (often left undefined). The cute (though dubious) thing about Lojban is that all these abstracts are in the domain, though not necessarily realized. So the whole {tu'a X} is an extensional _expression_. But it get unpacked in the semantics into an appropriately intensional way -- as a realized state in some alternate world. It is a tad messy, but it does the important things within FOPL, preventing quantifying out and interchange identicals. A better system might do more and do this more simply, but getting JCB and the LLG up to this point has been about half my life and I don't see much likelihood in getting much further. By the way, I don't see Xorban as making steps in that direction and earlier attempts to persuade the instigators on this always bogged down in a morass of level confusions.

Sent from my iPad

On Sep 10, 2012, at 4:23 PM, "Mike S." <maikxlx@gmail.com> wrote:

On Mon, Sep 10, 2012 at 10:05 AM, John E Clifford <kali9putra@hidden.email> wrote:

In well used Lojban, every argument (sumti) is either intensional or extensional, never both. The problem (aside from bad usage) is then twofold. Intensional sumti contain thing that look like extensional sumti (and, indeed, are -- in the alternate worlds to which the intensions lead us). Further, while (probably) most predicates take only extensional arguments and a few take only intensional ones, quite a few can take either. The result is mistakes like {mi djicu lo xorma} rather than {mi djicu tu'a lo xorma} when there is no particular horse I want, any will do. 'fV' looks like a plausible way to go here, although I don't quite understand exactly how it functions, theoretically.

For the very reason you cite, I don't know why you regard intensions as such bugaboos. Intensions are foundational to predicate semantics and extensions are subsidiary. In Montague's system, given an intension you can always get to the extension if you know the world. In fact, intensions are formally simply functions from worlds to extensions, plain and simple. The opposite is not true; given an arbitrary extension, you cannot get back to the intension, because several intensions might have contain the exact same extension for a given world. That is why one of the rules in Montague's framework if you read the fineprint is that you are not allowed to apply the up- and down-operators in any order. In particular, you can't apply "up" after you've already applied "down".

This is also why Old Lojban's "tu'a" particle seems so strange to me. You supposedly start with an extension, which is just a set of individuals with no "meaning" holding them together, and somehow get back to an intension. Obviously this intension has to be glorked, and obviously it's going to be glorked based on the complement of "tu'a", and no human is going to resist reading that complement intensionally, so the idea that you actually started with an extension is a charade. It would have made more sense to start with "lo mlatu" or maybe "lo'e mlatu" involving an intension and interpret "su'o" and "ro" as invoking Montague's down operator to yield a quantification over the extension in the appropriate world, and allow "lo mlatu" or maybe "lo'e mlatu" to stand for themselves when intensional arguments are needed.

None of that is to suggest that "lo" or "l-" necessarily bind intensional objects in the languages under consideration. It's just that if you need to choose, it makes more sense to start with intensions and get extensions as you need them than vice versa.