R March 1, 2012
Thursday,March01, 210:55 AM
10.2 Overlapping Quantifiers (p. 229)
Everything is better than everything.(x)(y)Bxy
Something is better than something. (∃x)(∃y)Bxy
Nothingis better than anything. (x)(y)~Bxy
Something is not better thansomething(∃x)(∃y)~Bxy
10.3 Expansions& Overlapping Quantifiers(p. 229)
Remember-- (x)Fx requires that every substitutioninstanceof Fx is true. Some holdsfor more
complex sentences: (x)(Fx · Gx) requires every substitutioninstance of (Fx · Gx) is true.
Works the same way for overlappingquantifiers.
Here we want to remove the (x) quantifier.It appliesto everythingthat followsso we need
every substitutioninstance of (y)Lxy to be true. Whentaking a substitutioninstance, only free
occurrences of the variable get replaced.