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Lecture

# R March 1, 2012.pdf

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School
Department
Modes Of Reasoning
Course
MODR 2640
Professor
All Professors
Semester
Winter

Description
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. (x)(y)Lxy 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.
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