At Most
The book gives two different translations of “at most” on page 352: a longer
version and a shortened version.
After consulting numerous logic books and
discussing the matter with other people, it’s apparent that the longer version is
correct, but the shortened isn’t.
Here’s an example of a correct translation of “There are at most two P’s”:
[1]
(
2200
x)(
2200
y)(
2200
z)[((Px & Py) & Pz)
⊃
((x = y v x= z) v y = z)]
This translation has all the semantic features we want: it’s false in any case
where there are three distinct objects in the extension of P, but true if there are
two or less.
The book claims that the following is an acceptable shortened version of the
above statement:
1
[2]
(
2200
x)(
2200
y)(
2200
z)[((Px & Py) & Pz)
⊃
(z = y v z = x)]
Now, this translation does capture one of the semantic features we want: it’s
false in any case where there are three distinct objects in the extension of P.
Unfortunately, as some of you have pointed out, it can be made false in cases
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 Logic, Semantics, distinct objects

Click to edit the document details