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

On Fri, Sep 7, 2012 at 1:17 PM, And Rosta <and.rosta@hidden.email> wrote:
 

Jorge Llambías, On 07/09/2012 03:21:


> 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

The "everything true of some X is true of every X" is a conventional implicature, which in logical terms means it's outside the scope of any illocutionary.

E.g. "ca li bcdi fghi" = "je jo si bcdi fghi ri bcdi fghica sibcdi fghi"

Unfortunately, I don't believe that "jo si bcdi fghi ri bcdi fghi" stops encoding the useless meaning that I demonstrated that it encodes merely by shuffling it outside of some scope, that of an illocutionary or anything else.

 
>> 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.

But Mike was saying you can't go from lV to rV/sV, and I think that lV does entail both sV and rV. "la ma xrxe rgntna, ra ma xrxe rgntna, sa ma xrxe rgntna" (is Argentinian) are each true of the same construal of the same world.

It's pretty clear that "la mlta xkra" doesn't entail "ra mlta xkra", unless the universe of discourse is ham-handedly purged of non-black cats, and even in that case that entailment seems purely circumstantial.  I really dislike this pretense that the universe can vacillate so drastically with every new sentence added to the discourse, not only because that does violence to the very concept of a universe, but also because the underlying formalized meaning of "cat" itself depends on positing countless possible worlds full of cats, not just the handful of cats that might happen to comprise the current discourse topic.  So constraining the model in this way not only feels rather arbitrary, but it wreaks enormous havoc on the underlying semantics as well.

I should note that ' Semantics of "l-" ' was less than ideal a choice for a thread title;  I am mainly interested in how "l-" might be understood to work within FOL, at least for right now.  Thanks to your ideas and Jorge's, I am fairly confident that "lV RV" can be defined as "sV [[R]]V" and equivalently "rV [[R]]V" and get that job done with relative ease.  I think we have a good impression of what's inside the black box [[R]]; if not, a fully satisfying explanation can wait until another day.