Rules of Inference 1 - Natural Deduction 7.1 2006 Kevin J....

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Natural Deduction 7.1 © 2006 Kevin J. Browne
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Rules of Inference I Modus Ponens Modus Tollens Disjunctive Syllogism Hypothetical Syllogism
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Modus Ponens p q p _________ q
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Modus Tollens p q ~q _________ ~p
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Disjunctive Syllogism p v q ~p _________ q
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Hypothetical Syllogism p q q r _________ p r
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Solving proofs in natural deduction is based on pattern recognition. Think of it as using the rules to crack a code!
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Example One 1. F v (D T) 2. ~F 3. D /T
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Example One 1. F v (D T) 2. ~F 3. D /T Using one of the rules find a pattern in these premises. The pattern here is DS.
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Example One 1. F v (D T) 2. ~F 1. D /T 2. T 1,2 DS So we draw the conclusion from DS on line 4.
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Example One 1. F v (D T) 2. ~F D /T T 1,2 DS Now use the rules to find another pattern with what we’ve just derived.
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Example One 1. F v (D T) 2. ~F 1. D /T 2. T 1,2 DS 3. 3,4 MP Once we reach the final conclusion we’ve solved the proof!
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A more involved example 1. ~M v (B v ~T) 2. B W 3. M 4. ~W /~T Here there are several patterns to identify. We need all of them to crack this code! Here’s one: MT Here’s another: DS
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A more involved example
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This note was uploaded on 05/05/2008 for the course PHIL 311 taught by Professor D.c. during the Spring '07 term at University of Louisville.

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Rules of Inference 1 - Natural Deduction 7.1 2006 Kevin J....

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