[Phil-logic] Geach Kaplan again (and FOL=) - Oops2

[Dennis E. Hamilton]

Ahh, now we're getting somewhere.

5.4 isn't enough.  In particular, it isn't enough to ensure that the same people appreciate x and y and they are also NUCr.  I can see the repair, but I am going to leave it for now. 
	
The question I now have is whether there is actually a finite expression, based on the second condition in 5.4, that, along with the transitivity of MACr, closes on the cliques and doesn't improperly include any non-clique.  This has to be done without counting or recursive set construction or anything like that to be within FOL (or FOL=).  I can also see the possibility of a recursive form of the constraint that doesn't involve counting but always "covers" an clique.  
	
I am weary with some jet lag after 8 nights in gmt+0100, so I am going to leave this until the morning here in gmt-0900, rather than make more mistakes. 

-- Dennis

-----Original Message-----
From: phil-logic-bounces at philo.at [mailto:phil-logic-bounces at philo.at]On
Behalf Of Dennis E. Hamilton
Sent: Saturday, January 31, 2004 17:16
To: Dean Buckner; Phill
Subject: RE: [Phil-logic] Geach Kaplan again (and FOL=)


[ ... ]

	5.4	And here is what ties it all together:

		(x) [Cr(x) -> ACr(x, x)]

		(x) (y) [ (NUCr(x) & NUCr(y) & ACr(x, y)) -> MACr(x, y)]

[ ... ]