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Negation Rules Reductio Ad Adsurdum Indirect Proof Dash In and Dash Out.

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Presentation on theme: "Negation Rules Reductio Ad Adsurdum Indirect Proof Dash In and Dash Out."— Presentation transcript:

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2 Negation Rules Reductio Ad Adsurdum Indirect Proof Dash In and Dash Out

3 Negation Rules Reductio Ad Adsurdum Indirect Proof Dash In and Dash Out The basic idea: To prove A, Assume -A and derive a contradiction. Since -A leads to a contradiction, -A must be wrong, and so A must be right.

4 Negation Rules Dash In and Dash Out An illustration: Eat your SPINACH. Why? Because if you don’t you won’t get DESERT.

5 Negation Rules Dash In and Dash Out An illustration: Eat your SPINACH. Why? Because if you don’t you won’t get DESERT. -S>-D The parent hopes the child will conclude: S

6 Negation Rules Dash In and Dash Out Eat your SPINACH. Why? Because if you don’t you won’t get DESERT. DA -S>-DA S

7 Negation Rules Dash In and Dash Out Eat your SPINACH. Why? Because if you don’t you won’t get DESERT. Child’s Fantasy DA -S>-DA -SPA S

8 Negation Rules Dash In and Dash Out Eat your SPINACH. Why? Because if you don’t you won’t get DESERT. Child’s Fantasy DA -S>-DA -SPA -D>O D&-D&I S

9 Negation Rules Dash In and Dash Out Eat your SPINACH. Why? Because if you don’t you won’t get DESERT. DA -S>-DA -SPA -D>O D&-D&I S Contradiction! So S is the only choice.

10 Negation Rules Eat your SPINACH. Why? Because if you don’t you won’t get DESERT DA S>-DA SPA 2,34. -D2,3 >O 1,2,35. D&-D1,4 &I 1,26. S3-5 -O An Official Proof

11 Negation Rules Eat your SPINACH. Why? Because if you don’t you won’t get DESERT DA S>-DA SPA 2,34. -D2,3 >O 1,2,35. D&-D1,4 &I 1,26. S3-5 -O An Official Proof

12 Negation Rules -In and -Out a.k.a. Reductio Ad Adsurdum or Indirect Proof A PA : ?&-? -A -In -A PA : ?&-? A -Out To prove a statement, assume the opposite and derive a standard contradiction: a statement of the form ?&-?

13 Avoiding a Confusion -In and -Out a.k.a. Reductio Ad Adsurdum or Indirect Proof A PA : ?&-? -A -In -A PA : ?&-? A -Out Indirect Proof reasoning often confuses people.

14 Avoiding a Confusion G PA P > O P&-P &I -G -In G = My client is guilty P = My client was in Paris. G > P The crime was in Paris -P A witness saw him in Houston

15 Avoiding a Confusion G PA P > O P&-P &I -G -In G = My client is guilty P = My client was in Paris. G > P The crime was in Paris -P A witness saw him in Houston Sleepy Juror: The defense said: ‘Suppose my client is guilty’. So even his own lawyer thinks he is guilty.

16 Avoiding a Confusion G PA P > O P&-P &I -G -In G = My client is guilty P = My client was in Paris. G > P The crime was in Paris -P A witness saw him in Houston How to present an Indirect Proof in Court.

17 Avoiding a Confusion G PA P > O P&-P &I -G -In G = My client is guilty P = My client was in Paris. G > P The crime was in Paris -P A witness saw him in Houston How to present an Indirect Proof in Court: Give the PA to your opponent.

18 Avoiding a Confusion -In and -Out a.k.a. Reductio Ad Adsurdum or Indirect Proof A PA : ?&-? -A -In -A PA : ?&-? A -Out To prove a statement, assume the opposite and derive a standard contradiction: ?&-?. For more click here


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