Lecture05

Lecture05 - PHIL V3411 PHIL G4415 Introduction to Symbolic...

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PHIL V3411 / PHIL G4415 • Introduction to Symbolic Logic Lecture 5 Sentential Logic: The Disjunction Connective; Tautologies and Contradictions

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The Disjunction Connective (Section 2.2.2) ! For every pair of sentences A and B there is another sentence called the disjunction of A and B . ! English: Either A or B (or both) ! ! left disjunct right disjunct ! Symbolization: A " B ! Semantics: A " B is T if at least one of A and B is T ; otherwise A " B is F Truth table : A B A " B T T T T F T F T T F F F ! Note: as with conjunction, the following general principles hold Principle of Commutativity : A " B # B " A Principle of Associativity : ( A " B ) " C # A " ( B " C )
Disjunction in Natural Languege (Section 3.1.3) ! Disjunction as a joiner of nouns Like conjunction, disjunction can be used as a joiner of nouns. But there is no room for a collective reading, so no problems here. Jack or Jill took driving lessons \$ Jack took driving lessons " Jill took driving lessons Jack or Jill painted this picture \$ Jack painted this picture " Jill painted this picture ! Disjunction acts as a joiner of other sorts of expressions: Again, no room for a collective reading, so no problems: John was crying or laughing \$ John was crying " John was laughing John ran fast or silently \$ John ran fast " John ran silently John was skinny or rich \$ John was skinny " John was rich

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Inclusive vs. Exclusive uses of “or” ! In English we can distinguish two uses of “either . .. or”: Inclusive reading: At least one of the two disjuncts (possibly both) must be T in order for the disjunction to be
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Lecture05 - PHIL V3411 PHIL G4415 Introduction to Symbolic...

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