At Most - At Most The book gives two different translations...

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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
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This document was uploaded on 11/03/2009.

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At Most - At Most The book gives two different translations...

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