From: Chris Barker Date: Sun, 31 Oct 2010 14:34:55 +0000 (-0400) Subject: edits X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=7b960aed1552ab5ee4b17428ae4e293decaee2b7 edits --- diff --git a/week7.mdwn b/week7.mdwn index ba845b29..bc8dc8ef 100644 --- a/week7.mdwn +++ b/week7.mdwn @@ -199,7 +199,7 @@ Note the extra `#` attached to the directive `use`. Here's the idea: since people can have different attitudes towards different propositions that happen to have the same truth value, we -can't have sentences denoting simple truth values. Then if John +can't have sentences denoting simple truth values. If we did, then if John believed that the earth was round, it would force him to believe Fermat's last theorem holds, since both propositions are equally true. The traditional solution is to allow sentences to denote a function @@ -220,16 +220,16 @@ Vs s->t->e->t s->(s->t)->(s->e)->t thought This system is modeled on the way Montague arranged his grammar. -(There are significant simplifications: for instance, determiner +There are significant simplifications: for instance, determiner phrases are thought of as corresponding to individuals rather than to -generalized quantifiers.) If you're curious about the initial `s`'s +generalized quantifiers. If you're curious about the initial `s`'s in the extensional types, they're there because the behavior of these expressions depends on which world they're evaluated at. If you are in a situation in which you can hold the evaluation world constant, -you can further simplify the extensional types. (Usually, the +you can further simplify the extensional types. Usually, the dependence of the extension of an expression on the evaluation world is hidden in a superscript, or built into the lexical interpretation -function.) +function. The main difference between the intensional types and the extensional types is that in the intensional types, the arguments are functions @@ -243,8 +243,9 @@ types. Wouldn't it be nice to keep the complicated types to just those attitude verbs that need to worry about intensions, and keep the rest of the grammar as extensional as possible? This desire is parallel to our earlier desire to limit the concern about division by -zero to the division function, and let the other functions ignore -division-by-zero problems as much as possible. +zero to the division function, and let the other functions, like +addition or multiplication, ignore division-by-zero problems as much +as possible. So here's what we do: