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. 1 1. DA 2 2. -S>-DA 3 3. -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. 1 1. DA 2 2. -S>-DA 3 3. -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