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Science Forum Index » Logic Forum » Existential quatifier and implications
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| Yoshi Gev |
 Posted: Sun Jan 04, 2004 6:59 am |
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Guest
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I encountered a question in Copi which I have difficulty accepting an answer
to.
The question is no. 16 on page 70 (on Symbolic Logic 4th Edition) -
Symbolize the sentence:
"Some medicines are dangerous only if taken in excessive amounts.
(Mx: x is a medicine. Dx: x is dangerous. Ex: x is taken in excessive
amounts.)"
The answer I found on the internet
(http://www.earlham.edu/~peters/courses/log/answers2.htm, by Peter Suber),
is:
(Ex)[Mx (Dx->Ex)]
- (sorry, but only the first E should be backwards)
The problem I have with this solution, is emerging in the following cases:
1. If there is at least one not-dangerous medicine - the whole sentnce would
be true.
2. If there is at least one medicine that is taken in exccesive amounts -
the whole sentence would be true.
In my opinion, the sentence is not nessasarily true in those cases.
I believe the problem is having an implication inside an existential
sentence, that is, that the original english sentence itself is meaningless
(if looking at "taken in excessive amount" as a predicate of the medicine).
Can anyone explain to me why it is not so?
Thanks,
Yoshi Gev
yoshigev@hotmail.com |
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