1. 1 DISJUNCTIVE AND HYPOTHETICAL SYLLOGISMS DISJUNCTIVE PROPOSITIONS: E.G EITHER WHALES ARE MAMMALS OR THEY ARE VERY LARGE FISH. DISJUNCTS: WHALES ARE MAMMALS.(P) 2. WHALES ARE VERY LARGE FISH.(Q)

2. 2 DISJUNCTIVE SYLLOGISMS  THE MEANING OF THE DISJUNCTIVE PROPOSITION:  TWO POSSIBILITIES, ONE OR THE OTHER. BUT ALSO A THIRD POSSIBILITY. BOTH!!!  DISJUNCTIVE SYLLOGISM: A SYLLOGISM WITH ONE DISJUNCTIVE PROPOSITION.

3. 3 DISJUNCTIVE SYLLOGISMS  STANDARD FORM.  FIRST PROPOSITION (FIRST LINE): DISJUNCTIVE PROPOSITION  SECOND LINE: AFFIRMATION OR NEGATION OF ONE OF THE DISJUNCTS.  CONCLUSION: AFFIRMATION OR NEGATION OF ONE OF THE DISJUNCTS.

4. 4 DISJUNCTIVE SYLLOGISMS  E.G., 1) EITHER THE MEETING IS IN ROOM 305 OR IT IS IN ROOM 306.  2) IT IS NOT IN ROOM 305.  3) IT IS IN ROOM 306.  NON-STANDARD FORM:  E.G. “YOU CAN’T HAVE YOUR CAKE AND EAT IT TOO.”  TRANSLATE: -[ P + Q] NOT BOTH, ONLY ONE.

5. 5 DISJUNCTIVE SYLLOGISMS  CONJUNCTIVE PROPOSITION  ALSO, “EITHER YOU DON’T EAT THE CAKE OR YOU DON’T HAVE THE CAKE.”  TRANSLATE: EITHER –P OR –Q.  VALIDITY:  A DISJUNCTIVE SYLLOGISM IS INVALID IF IT AFFIRMS ONE OF THE DISJUNCTS IN THE SECOND PREMISE AND AFFIRMS THE OTHER IN THE CONCLUSION.

6. 6 DISJUNCTIVE SYLLOGISMS  THE EXCLUSIVE AND INCLUSIVE SENSE OF “OR.”  EXCLUSIVE: IN TEXT EXAMPLE: EITHER THE BABY WILL BE A BOY OR IT WILL BE A GIRL. ETC.  INCLUSIVE: EITHER P OR Q OR BOTH.

7. 7 DISJUNCTIVE SYLLOGISMS  WHAT IT MEANS: WE HAVE THREE POSSIBILITIES OR PROBABLE OUTCOMES.  1. P  2. Q  3. P AND Q (P +Q)

8. 8 DISJUNCTIVE SYLLOGISMS  PRINCIPLE TO DETERMINE WHICH TO USE:  ONLY IN CONTEXT WHERE IT IS CLEARLY KNOWN THAT THE THIRD OUTCOME IS NOT POSSIBLE SHOULD THE EXCLUSIVE SENSE OF “OR” BE USED. OTHERWISE, THE INCLUSIVE SENSE SHOULD BE USED.

9. 9 DISJUNCTIVE SYLLOGISMS  IMPLICATION FOR VALIDITY:  WITH EXCLUSIVE SENSE OF “OR” IT IS ALLOWABLE FOR THE SECOND PREMISE TO AFFIRM ONE DISJUNCT AND THEN FOR THE CONCLUSION TO NEGATE THE OTHER.  EG. 1. EITHER P OR Q  2. P  3.- Q  P. QUIZ, 10.1, P. 285.

10. 10 HYPOTHETICAL SYLLOGISMS  SYLLOGISMS WITH HYPOTHETICAL PROPOSITIONS.  HYPOTHETICAL PROPOSITIONS.  IF I GET THE MIDTERM BACK TODAY, THEN I WILL BE HAPPY.  IF P, THEN Q.  P= ANTECEDENT  Q=CONSEQUENT BOTH ARE EXPRESSED

11. 11 HYPOTHETICAL PROPOSITIONS  MEANING: HAVING Q IS CONDITIONAL UPON HAVING P.  ASSERTS A LOGICAL RELATIONSHIP OF CONDITIONALITY, BUT P IS NOT THE ONLY THING THAT CAN BRING ABOUT Q.  “THE TRUTH OF P WOULD BE SUFFICIENT TO GUARANTEE THE TRUTH OF Q.”

12. 12 HYPOTHETICAL PROPOSITIONS  NON-STANDARD FORMS OF HYPOTHETICAL PROPOSITIONS:  1. “I’LL STAY HOME TOMORROW IF I FEEL SICK.”  ANTECEDENT AND CONSEQUENT ARE SWITCHED.  STANDARD FORM: IF I FEEL SICK, THEN I WILL STAY HOME TOMORROW.

13. 13 HYPOTHETICAL PROPOSITIONS  2. “I’LL STAY HOME ONLY IF I’M SICK.”  P ONLY IF Q.  BEING SICK IS THE ONLY THING THAT WILL KEEP ME HOME.  TWO WAYS TO TRANSLATE:  IF NOT Q, THEN NOT P.  (IF I’M NO SICK, THEN I WILL NOT STAY HOME.)  IF Q, THEN P.  (IF I STAY HOME, THEN I AM SICK.)

14. 14 HYPOTHETICAL PROPOSITIONS  3. P IF AND ONLY IF Q.  MEANING: EACH IS DEPENDENT ON THE OTHER.  YIELDS TWO PROPOSITIONS:  IF P, THEN Q  IF Q, THEN P.  BOTH SERVE AS ANTECEDENT AND CONSEQUENT FOR THE OTHER.

15. 15 HYPOTHETICAL PROPOSITIONS  4. P UNLESS Q. “THE PLANT WILL DIE UNLESS YOU WATER IT.”  TRANSLATE: P IF NOT Q  BETTER: IF NOT Q, THEN P : “IF YOU DO NOT WATER THE PLANT, THEN THE PLANT WILL DIE.”  5. “WHENEVER I GET ANXIOUS, I START EATING MORE.”  TRANSLATE: IF P, THEN Q

16. 16 HYPOTHETICAL PROPOSITIONS  6. “WITHOUT DISTRIBUTION REQUIREMENTS, MOST STUDENTS WOULD TAKE TOO NARROW A RANGE OF COURSES.”  “IF X DOES NOT OCCUR, THEN Q.” “WITHOUT X, THEN Q.”  P.QUIZ 10.2, P. 290.

17. 17 HYPOTHETICAL SYLLOGISMS  2 TYPES  PURE HYPOTHETICAL SYLLOGISMS:  BOTH PREMISES AND CONCLUSIONS ARE HYPOTHETICAL PROPOSITIONS.  FORM: IF P, THEN Q  IF Q, THEN R  IF P, THEN R  ALWAYS VALID!!!

18. 18 HYPOTHETICAL SYLLOGISMS  2. MIXED HYPOTHETICAL SYLLOGISM  FORMS: IF P, THEN Q  P  Q  MODUS PONENS  E.G., IF YOU PLAY WITH FIRE, THEN YOU WILL GET HURT.  YOU PLAYED WITH FIRE  YOU WILL GET HURT.  THIS FORM IS ALWAYS VALID.

19. 19 HYPOTHETICAL SYLLOGISMS  MODUS TOLLENS: IF P, THEN Q  -Q  -P  ALWAYS VALID.  2 OTHER FORMS, BOTH INVALID:  DENYING THE ANTECEDENT, SO AS TO DENY THE CONSEQUENCE. (SEE P. 292)  AFFIRMING THE CONSEQUENT, SO AS TO AFFIRM THE ANTECEDENT.  P. QUIZ, 10.3, P. 294