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DISJUNCTIVE AND HYPOTHETICAL SYLLOGISMS

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). 1. DISJUNCTIVE SYLLOGISMS. THE MEANING OF THE DISJUNCTIVE PROPOSITION:

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DISJUNCTIVE AND HYPOTHETICAL SYLLOGISMS

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  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) 1

  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. 2

  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. 3

  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. 4

  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. 5

  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. 6

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

  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. 8

  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. 9

  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 10

  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.” 11

  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. 12

  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.) 13

  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. 14

  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 15

  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. 16

  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!!! 17

  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. 18

  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 19

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