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Unit 5 part 1 2011

# Unit 5 part 1 2011 - UNIT 5 Part 1 SYMBOLIZATION PREDICATES...

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Logic Unit 5 Part 1: Symbolization for Predicate Logic © Niko Scharer 1 UNIT 5 Part 1 SYMBOLIZATION: PREDICATES AND QUANTIFIERS 5.1: THE LOGIC OF SUB-SENTENTIAL RELATIONS Consider this argument: All humans are mortal. Socrates is human. __________________________ Socrates is mortal. It is clearly a valid argument, but if we try to symbolize it using an abbreviation scheme for sentential logic we will not be able to derive the conclusion from the premises: P: All humans are mortal. Q: Socrates is human. R: Socrates is mortal. P Q _________ R Despite the failure of this symbolization scheme to capture the validity of the argument, it is obviously valid. The symbolization techniques that we’ve learned won’t show it because the logical relations in this example concern the properties and terms that occur within a sentence (“all”, “Socrates”, being mortal, being human.) In our sentential logic we were concerned with the logical relations between atomic sentences (those symbolized with a single letter) but we never considered the logical relations that stem from structures within an atomic sentence. There must be another way to symbolize arguments! We want to extend our symbolization techniques so we can capture these types of subsentential logical structures. We want to be able to express the logical form: Every thing that is ‘ S ’ has property ‘ P ’. a ’ is ‘ S ’. ___________________________________ a ’ has property ‘ P ’. The logical form has to do with the internal structure of the sentence the relations between the subjects and the predicates . (These are ‘subsentential’ relationships, relationships between parts of a sentence.) Any properly constructed assertion has: a subject: the object(s), person(s) or place(s) that the sentence is about. a predicate: what is being said about (or predicated of) the subject often a property or an action. We want to be able to consider the logical relations between subjects and predicates of different sentences.

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