Re: a union is always a join!
Date: Sun, 1 Mar 2009 14:43:53 -0500
Message-ID: <_zBql.17414$YU2.17201_at_nlpi066.nbdc.sbc.com>
This is the way I see it: That which states what is the case is the disjunction of all and only true propositions. Divide that into two parts: one that states what has been the case (not necessarily what had been the case--just that which obtained since the last change), and one that states what is happening. Whenever nothing is happening, what has been the case /is/ the case. For example, if Joe has been second in line at the bank and nothing is happening, then Joe is still second in line. On the other hand, if the person who has been first in line is now being served, then Joe is no longer second in line but is instead first in line. The disjunction of the two statements: "Joe has been second in line" and "Joe is no longer second in line but is instead first in line" yields "Joe is first in line." In symbols,
from p \/ (~p \/ q), derive (p \/ ~p) \/ q since (p \/ ~p) is vacuously true, eliminate it and what is left is just q