quick "help!" question
CMicheau at UMASD.ORG
Fri Mar 26 16:19:02 UTC 2004
Why not just say Bob and Joe didn't study!
From: Sean McGrew [mailto:mcgrew at dolphin.upenn.edu]
Sent: Friday, March 26, 2004 9:29 AM
To: edling at ccat.sas.upenn.edu
Subject: Re: quick "help!" question
Ok, here's my contribution--pretty hard to do natural language in
math/logic terms at all, much less SIMPLY!
I also feel that
*3. Both Bob and Joe didn't study
Or at least that it's ambiguous and awkward. I myself would either say:
3a) bob and joe didn't both study. (=2)
3b) bob and joe both didn't study. (=1)
As for the mathish way to write it, maybe this:
Say Both X & Y [predicate] = X [predicate] and Y [predicate]
Then the difference is in the scope of the negation, in 3a the whole
sentence is negated, while in 3b only the predicate is negated.
positive version: Both studied
3a) not (both study) = not [ (Bob studied) AND (Joe studied) ]
3b) both (not study) = (Bob didn't study) AND (Joe didn't study)
your 3, if it's acceptable, is ambiguous because the scope of the
negation is unclear.
back to either and neither:
Neither X nor Y predicate = not (X predicate) AND not (Y predicate)
Either X or Y predicate = (X predicate) *OR (Y predicate)
*where OR = exclusive, i.e. either, but NOT both. Logicians and
computer programmers typically have distinct symbols for inclusive and
Then you just need the rule that
not (X predicate) = X not predicate
Neither Bob nor Joe studied = not (Bob studied) AND not (Joe studied)
=(Bob didn't study) and
(Joe didn't study)
Either Bob or Joe didn't study = (Bob didn't study) OR (Joe didn't
Graduate School of Education
University of Pennsylvania
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