Chris and everyone

Apologies, fried brain sydrome, my implications are back to front, although,

having corrected them, the orignal arguement should still follow.

Sean Barker, Bristol

Chris Menzel wrote:

On Feb 25, 2010, at 3:57 PM, sean barker wrote:
>* ...*
>* If we define a concept C, which is defined using an axiom Q, and replace Q *
>* with an axiom P such that Q implies P but not vice versa (P is "stronger *
>* than" Q), then any process that had Q as a post-condition may produce invalid *
>* answers. (01)*
Niggling point: You are turning around the usual understandings of "stronger"
and "weaker". If Q implies P (Q=>P) but not vice versa, then Q is stronger
than P and P weaker than Q. Thought of model theoretically, Q has fewer models
and hence "says more" than P. (02)
Less niggling point: Perhaps I am misunderstanding what you have in mind by an
"answer", but if post-condition Q of a process A is replaced by an axiom P such
that Q=>P but not vice versa, then every "answer" generated through the use of
P rather than Q could have been generated by the use of Q. So if the use of P
produces invalid answers, so does the use of Q. Seems to me the danger in
question arises only if you replace Q with an axiom R such that R=>Q but not
vice versa. For then the possibility arises of new answers that could not be
generated through the use of Q -- answers that are perhaps "invalid" in some
relevant sense. (03)
> If we replace Q with a weaker axiom R, such that R implies Q but not vice
>* versa, then any process which uses Q as a precondition can no be used, as *
>* the preconditions may be violated. (04)*
Parallel comments here. (05)
Chris Menzel