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150 - handout 12 - 2 march 2010 - sentential logic

# 150 - handout 12 - 2 march 2010 - sentential logic -...

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P HILOSOPHY 150: I NTRODUCTION TO L OGIC H ANDOUT 12: 2 M ARCH 2010 Alison Duncan Kerr S ENTENTIAL L OGIC Sentential Logic (also known as Propositional Logic) is a branch of Deductive Logic. Sentential Logic is the study of the ways to join or modify sentences, statements, or propositions to form more complicated sentences, statements, or propositions; it studies the logical relationships that are derived from these methods of combining or modifying the sentences, statements, or propositions. A major difference between inductive arguments and deductive arguments is that only in deductive arguments can one determine whether the argument is valid based on form alone (not on content or background). In order to evaluate a deductive argument for validity, we can translate it into a symbolic language and use truth tables to decide whether its logical form is valid. T HE SYMBOLIC LANGUAGE contains FIVE CONNECTIVE SYMBOLS : (“dot” for conjunction) (“wedge” for disjunction) (“arrow” for conditional) (“double-arrow” for biconditional) ~ (“tilde” for negation) It also contains capital letters (e.g., A, B, C) that stand for sentences and lower-case letters (e.g., p, q, r) that are variables. T YPES OF SENTENCES : Conditionals: If p, then q p q arrow; p: antecedent; q: consequent Conjunctions: (both) p and q p • q dot; p: first conjunct; q: second conjunct Disjunctions: (either) p or q p q wedge; p: first disjunct; q: second disjunct Biconditionals: p if and only if q p q double arrow; p: left side of ; q: right side of Negations: It is not the case that p ~ p tilde Atomic: p S YMBOLIC L ANGUAGE : Sentential connectives: , •, , , ~ 2-place connectives: , •, , Variables: p, q, r, … Sentences: A, B, C, …

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P HILOSOPHY 150: I NTRODUCTION TO L OGIC H ANDOUT 12: 2 M ARCH 2010 Alison Duncan Kerr 2 The key to translating a sentence of English into our symbolic language is discovering the logical form of the English sentence. In order to discover the logical form, we need to find the connectives in the English sentence.
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