Computing Truth-Values

# Computing Truth-Values - Todays Topics (10/28) I. II....

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3/4/11 Today’s Topics (10/28) I. Abbreviations of Propositions II. Abbreviations vs. Propositional Forms III. Computing the Truth-Values of Compound Propositions IV. Constructing Truth-Tables for Complex Propositional Forms

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3/4/11 I. Abbreviations of Propositions To abbreviate propositions, we use CAPITAL letters, connective symbols and parentheses. Example: Let P = Obama is the president
3/4/11 II. Abbreviations versus Propositional Forms Ø P & Q abbreviates “Obama is the president and Obama is a democrat.” Ø “Obama is the president and Obama is a democrat” is a substitution instance What’s the difference? In this context, since P and Q are not variables but abbreviations of “Obama is the president” and “Obama is a democrat,” P & Q cannot said to abbreviate any other conjunctions such as “John is tall and Sarah is short” or “Palin is not the vice-president but Biden is,” etc. In contrast, since p and q are variables for any propositions, any conjunction can be said to be a substitution instance of p & q. Not only is “Obama is the president and Obama is a democrat” a substitution instance of p & q but so is “John is tall and Sarah is short;” “Palin is not the vice-president but Biden is” etc. Since p & q represents a general pattern that all conjunctions share, it itself is not a proposition and so cannot be true or false. In contrast, since in this context P & Q is an abbreviation of a specific

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## This note was uploaded on 03/03/2011 for the course PHIL 100 taught by Professor Forte during the Spring '08 term at Bridgewater State University.

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Computing Truth-Values - Todays Topics (10/28) I. II....

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