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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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INTRODUCTION TO SYMBOLIC LOGIC, LECTURE 5 P. 1 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 )
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INTRODUCTION TO SYMBOLIC LOGIC, LECTURE 5 P. 2 Disjunction in Natural Language (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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INTRODUCTION TO SYMBOLIC LOGIC, LECTURE 5 P. 3 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 T
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