Just as a continuation of last week, I think that Brett makes a
good point. I was having trouble seeing
how the two statements could be different, seeing as how, in both, having A, B,
and C leads to D. However, it does seem
to be significant that the consequent of the first formulation is the
conditional relationship between C and D, whereas the consequent of the second
is simply D. If we declared these
equivalent, then couldn’t we translate the second formulation into several
forms, all of which would have to be equivalent as well? For example if:
[(A&B)&C]èD
can be restated as
(A&B)è(CèD),
then can’t we also turn it into
(A&C)è(BèD)
or
(B&C)è(AèD)?
Looking at it this way, I am less inclined to declare the
statements to be equivalent. However, I
am by no means certain. Any further
thoughts?
Turning implication into conjunction eliminates the linear procession of premises and the relationship between them, reducing it instead into a checklist of prerequisites.
ReplyDeleteI think that this would come across far more clearly in written English - recall that the purpose of symbolization is to accurately preserve the relationships between statements made in written/spoken language.
Thanks for appreciating my previous comment, I think that this has been a really helpful thought exercise.
These are so very helpful. Thanks guys.
ReplyDelete