From Pycyn@xxx.xxx Tue Dec 21 08:26:11 1999
X-Digest-Num: 317
Message-ID: <44114.317.1743.959273825@eGroups.com>
Date: Tue, 21 Dec 1999 11:26:11 EST
From: Pycyn@xxx.xxx
Subject: Re: Re & on ?

My turn not to understand. 
The question is, why is it better to use the inference
"for all x, if x = Paul, then ..x..; for some x, x = Paul; therefore, for 
some x, ..x.." rather than "..Paul.., therefore, for some x, ..x.."? The 
answer seems to be that the former, but not the latter, tells us that Paul 
exists. The point of xu'a was precisely to mark those contexts in which 
non-referential names were used in true sentences, so, the assumption goes, 
in the absence of xu'a, "Paul" would be denoting name (Paul would exist) and 
no problem would ensue in generalization. 

As for the argument that "Paul" has an intension, it seems at best to make 
the case that "= Paul," an admitted predicate, has an intension. But even 
that is not clear, since all that is required directly is that "= Paul" have 
a non-empty extension. Depending upon one's view of intensions, this may or 
may not require one ("= Paul" might be defined only ostensively, for one 
contrary example). 

The point about restricted quantifiers is just that ASP entail ISP in 
Aristotelian logic, and A(B&C)P entails (in a couple of steps) IBP. So, 
"Every thing x which is Paul is ..x.." entails "Some thing x is ..x.." The 
latter moves require some help from propositional logic, for which he have to 
finally thank the Stoic, Chrysippus.

The final point is just that some pairs of utterance have the same logical 
form but very different information content because of pragmatic factors. We 
can manage to fake up a bit of logical form to cover some of those pragmatic 
factors, but the process will never end -- there will always be a residuum 
that goes unmarked until the next round of fakery. "All" seems to generate 
this sort of problem more often than many related words (well, "the" is a 
contender) and, in this case, it calls for a fine grained discrimination that 
the situation does not. There seems no logical way to satisfy both demands 
except to note that pragmatically, the answer "a bottle of milk" is a 
satisfactory answer, even when it is not possible to say WHICH bottle it is 
by some system of identifying bottles of milk (easier than atoms, harder than 
puppies to identify). We could fadge up a logic to do it, but it would be 
hideously complex, of limited usefulness, and would just raise a whole new 
set of even more gruesome problems. Best to just stop at a reasonable place 
with logic and get by on conventions (more or less -- usually less -- 
explicit) from there on.
pc