conservative definitions

John McCarthy <>
Date: Mon, 6 Jan 92 11:36:52 -0800
From: John McCarthy <>
Message-id: <9201061936.AA20084@SAIL.Stanford.EDU>
Subject: conservative definitions
1. Keeping definitions conservative has the advantage that during
an argument or in connection with a communication, a definition
may be introduced at any time by a human or a computer program.
All that needs to be verified is that an object exists satisfying
the defining sentence exists.  As discussed previously, for the
most common forms of definition, e.g. <new symbol> = <rhs>, this
is immediate.

2. Someone introduced and I discussed the idea of a partial definition
that is successively refined.  I proposed something, found a
bug in my proposal, and opined that it could be worked out.
My present opinion is that the bug is rather fundamental,
because it jeopardizes the conservative character of definitions.

Suppose someone introduces a partial definition of some set.  Then
suppose he (or some program) shows that an object exists satisfying
this partial definition and with some <other property> as well.  Now
suppose he (or it) refines the original partial definition.  Of
course he still must show that an object satisfying the extended
definition exists.  However, his use of the unextended definition
is now jeopardized, because there may not exist an object satisfying
the extended definition and the <other property>.