Subject: HW #3
From: "William J. Rapaport" <rapaport@buffalo.edu>
Date: Thu, 1 Oct 2009 10:46:17 -0400 (EDT)

A student writes:
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For question #4 (P.48, #32 b)

Why can't the sentence "There is a horse that can add."

be written as, Ex[Horse(x)->CanAdd(x)]

I guess I'm just confused as to when you need to use "->" and "^"
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Reply:

The quick rule of thumb, which I've discussed in lecture, is:
For universally quantified propositions, "->" is more likely to be
correct than "^", but for existentially quantified propositions
(such as this one), "^" is more likely to be correct.

The reason that your translation above is wrong is this:
What you wrote says: "There is something in the domain that has the
following property: If it is a horse, then it can add." Now, I hope you
agree that the original English sentence is only true if there is a
horse that can add. But your translation would be true even if there
are no horses (because the antecedent would be false if there are no
horses; hence, the conditional would be true).

If you are still confused, please re-read the webpage:
On the Translation of "Some Dogs Are Pets"
http://www.cse.buffalo.edu/~rapaport/191/F09/somedogsarepets.html