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

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Presentation transcript:

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

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 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 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 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 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 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 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 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 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 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 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 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