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Common Valid Deductive Forms: Dilemma

Common Valid Deductive Forms: Dilemma. p or q If p the r If q then s Therefore, r or s Either Bill Frist will win the 2008 election or Hillary Clinton will win the 2008 election. If Bill Frist wins the election, Republicans will be happy. If Hillary Clinton wins

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Common Valid Deductive Forms: Dilemma

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  1. Common Valid Deductive Forms: Dilemma p or q If p the r If q then s Therefore, r or s Either Bill Frist will win the 2008 election or Hillary Clinton will win the 2008 election. If Bill Frist wins the election, Republicans will be happy. If Hillary Clinton wins the election, Democrats will be happy. Therefore, either Republicans will be happy or Democrats will be happy. (use F,C, R, D) P1. Either F or C P2. If F then R P3. If C then D Therefore, Either R or D

  2. Common Valid Deductive Forms: Reductio ad absurdum Also known as indirect proof. Conclusions are established by showing that assuming the opposite of the conclusion leads to absurdity. Example: If NAFTA is ratified, then wages will go down in the US. If NAFTA is not ratified, then manufacturers will not increase their profits. If manufacturers do not increase their profits, US wages will go down. Either NAFTA will be ratified or it will not. Thus, US wages will go down.

  3. Common Valid Deductive Forms: Reduction ad absurdum If NAFTA is ratified, then wages will go down in the US. If NAFTA is not ratified, then manufacturers will not increase their profits. If manufacturers do not increase their profits, US wages will go down. Either NAFTA will be ratified or it will not. Thus, US wages will go down. Step 1: Make a dictionary N=NAFTA is ratified; D=wages will go down; I= increase their profits Step 2: Put the argument into logical form: P1. If N Then D P2. If not-N then not-I P3. If not-I then D P4. Either N or not-N Therefore, D

  4. Common Valid Deductive Forms: Reductio ad absurdum (continued) Step 3: Use Reductio strategy Assume opposite of conclusion: P1. If N Then D P2. If not-N then not-I P3. If not-I then D P4. Either N or not-N Therefore, D P5. Not-D Now, make inferences from the remaining premises:

  5. Common Valid Deductive Forms: Reductio ad absurdum (continued) P1. If N Then D P2. If not-N then not-I P3. If not-I then D P4. Either N or not-N Therefore, D P5. Not-D 6. Not-N (from P5 and P1 using modus tollens) 7. Not-I (from 6 and P2 using modus ponens) 8. D (from P3 and 7 using modus ponens) Reductio: P5 and 8.

  6. More exercises • Either Pat Buchanan or John Hagelin will be the Reform Party candidate. If Pat Buchanan is the Reform Party candidate, the Reform party will not win the election. If John Hagelin is the Reform Party candidate, the Reform party will not win the election. Thus, the Reform party candidate will not win theelection. • Use P, J, and W • P1. Either P or J • P2. If P then not W • P3. If J then not W • Therefore, not W • Valid

  7. More Exercises • If I do well on this exam, I’m on my way to an ‘A’ for the semester. I did not do well on this exam. Therefore, I’m not on my way to an ‘A’ for the semester. • Use W and A • P1. If W then A • P2. Not W • Therefore, Not A • Invalid

  8. More Exercises We should reject the belief in G-d only if it is unnecessary to explain our experience. The belief that there is a G-d is unnecessary to explain our experience. Therefore, we should reject the belief in G-d (use R, U) P1. If R then U P2. U Therefore, R Invalid Why? U is a necessary condition—we can only reject the belief in G-d if belief in G-d is unnecessary… Premise 1 does not tell us that if the belief in G-d is unnecessary we must reject it.

  9. More Exercises Either you will serve jury duty or you will avoid your civic duty. If you avoid your civic duty, you may suffer the consequences. If you serve jury duty you have to sacrifice your salary for one week. So, you will either suffer the consequences or lose most of your salary for one week. (use J, A, S, and L) P1. Either J or A P2. If A then S P3. If J then L Therefore, S or L Valid

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