DEDUCTIVE REASONING

1. DEDUCTIVE REASONING INDUCTIVE REASONING SYLLOGISM FALSE PREMISE

2. DEFINITIONS • DEDUCTIVE REASONING—begins with a general/ universal statement and moves to a specific, more limited statement. • I remember it by using this acronym: D. O. G. S. = deductive OR general to specific • SYLLOGISM—a form of deductive reasoning which is made up of three parts: a major premise, a minor premise, and a conclusion.

3. MORE DEFINITIONS • PREMISE—A general or universal statement which is said to be true. • MAJOR PREMISE—must make a universal statement. This means that it must be true of all, every, no, or none of the objects, people, or events. It can never contain such limiting words as some, most, or many. • MINOR PREMISE -- Fact or truth stated must be related to the major premise.

4. EXAMPLES • Deductive Reasoning: All men are mortal. (Major Premise) Joe is a man. (Minor Premise) Therefore, Joe is mortal. (Conclusion) John is in the 7th grade. (Minor P.) All 7th graders must take math. (Major Premise) John must take math. (Conclusion)

5. DETERMINE MAJOR PREMISE/ MINOR PREMISE/ CONCLUSION HOLES IS A BOOK. ALL BOOKS HAVE PAGES. HOLES HAS PAGES. ALL PENS ARE FOR WRITING. THIS IS A PILOT PEN. THIS IS FOR WRITING. (Answers will appear on the next slide)

6. DETERMINE MAJOR PREMISE/ MINOR PREMISE/ CONCLUSION HOLES IS A BOOK. -Minor Premise ALL BOOKS HAVE PAGES.-Major P. HOLES HAS PAGES.-Conclusion (ANSWERS ARE ON THE NEXT SLIDE.) ALL PENS ARE FOR WRITING.-Major THIS IS A PILOT PEN.-Minor THIS IS FOR WRITING.-Conclusion

7. VALID DEDUCTIVE ARGUMENT THREE CONDITIONS MUST BE TRUE *The major premise must make a universal statement. *Both of the premises must be true. *The argument must be valid (follow rules of reasoning).

8. VALID DEDUCTIVE ARGUMENT? • NO REPTILES HAVE FUR. (universal?/true?) ALL SNAKES ARE REPTILES. (true?) NO SNAKES HAVE FUR. (reasonable?) NO HEALTHY FOOD IS FATTENING. ALL CAKES ARE FATTENING. NO CAKES ARE HEALTHY. (Answers will appear on the next slide.)

9. VALID DEDUCTIVE ARGUMENT? • NO REPTILES HAVE FUR. -Universal ALL SNAKES ARE REPTILES.-True NO SNAKES HAVE FUR.-Reasonable NO HEALTHY FOOD IS FATTENING.-No (depends how much you eat.) ALL CAKES ARE FATTENING.-No (Angel Food Cake Is only fattening if you eat too much.) NO CAKES ARE HEALTHY.--Not valid Since premises not true)

10. SYLLOGISMSVALID ARGUMENT? NO LAZY PEOPLE PASS EXAMS. SOME STUDENTS PASS EXAMS. SOME STUDENTS ARE NOT LAZY. ALL HORSES HAVE HOOVES. SAMBO IS A HORSE. SAMBO HAS HOOVES. (Answers will appear on next slide.)

11. SYLLOGISMSVALID ARGUMENT? NO LAZY PEOPLE PASS EXAMS.-False Major Premise-Universal though SOME STUDENTS PASS EXAMS.—True minor premise SOME STUDENTS ARE NOT LAZY.-Not valid since based on false premise ALL HORSES HAVE HOOVES.-True Major Premise, Universal SAMBO IS A HORSE.-True, minor premise SAMBO HAS HOOVES.-Valid argument

12. DEFINITION • INDUCTIVE REASONING—BEGINS WITH SPECIFIC AND GOES TO GENERAL.(IF NOT D.O.G.S., THEN INDUCTIVE) EXAMPLE: THE WORD, HOT HAS LETTERS. THE WORD, A HAS A LETTER IN IT. ALL WORDS HAVE ONE OR MORE LETTERS.

13. SUPPLY INDUCTIVE CONCLUSIONS • Phaethon, A GREEK MYTH, HAS THE GOD APOLLO IN IT. Narcissus and Echo, A GREEK MYTH, HAS THE GODDESS APHRODITE IN IT. THEREFORE, ___________________________. *THIS RED MARBLE IS ROUND. THAT BLUE MARBLE IS ROUND. THEREFORE, _____________________ (Answers will appear on next slide.)

14. SUPPLY INDUCTIVE CONCLUSIONS • Phaethon, A GREEK MYTH, HAS THE GOD APOLLO IN IT. Narcissus and Echo, A GREEK MYTH, HAS THE GODDESS APHRODITE IN IT. THEREFORE, GREEK MYTHS HAVE GODS OR GODDESSES. *THIS RED MARBLE IS ROUND. THAT BLUE MARBLE IS ROUND. THEREFORE, ALL MARBLES ARE ROUND.

15. VALID INDUCTIVE ARGUMENTS? • 1ST PERIOD IS 50 MINUTES LONG. 2ND PERIOD IS 50 MINUTES LONG. ALL CLASSES ARE 50 MINUTES LONG. *THERE ARE 5 PENNIES IN A NICKEL. THERE ARE 5 NICKELS IN A QUARTER. THEREFORE, ALL DOLLARS HAVE 5 QUARTERS. (Answers will appear on next slide.)

16. VALID INDUCTIVE ARGUMENTS? • 1ST PERIOD IS 50 MINUTES LONG.-True 2ND PERIOD IS 50 MINUTES LONG.-True ALL CLASSES ARE 50 MINUTES LONG.--Valid *THERE ARE 5 PENNIES IN A NICKEL.--True THERE ARE 5 NICKELS IN A QUARTER.-True THEREFORE, ALL DOLLARS HAVE 5 QUARTERS. ----Invalid—4 quarters in a dollar

17. MORE VALID INDUCTIVE ARGUMENTS? • THE NUMBER 10 HAS ONE ZERO. THE NUMBER 200 HAS TWO ZEROES. ALL MULTIPLES OF 10 HAVE ONE OR MORE ZEROES. *SEPTEMBER HAS 30 DAYS. OCTOBER HAS 30 DAYS. ALL MONTHS HAVE 30 DAYS. (Answers will appear on next slide.)

18. MORE VALID INDUCTIVE ARGUMENTS? • THE NUMBER 10 HAS ONE ZERO.-True THE NUMBER 200 HAS TWO ZEROES.-True ALL MULTIPLES OF 10 HAVE ONE OR MORE ZEROES.—Valid Inductive Argument *SEPTEMBER HAS 30 DAYS.--True OCTOBER HAS 30 DAYS.—False Premise ALL MONTHS HAVE 30 DAYS.-Invalid Inductive Argument ---

19. INDUCTIVE OR DEDUCTIVE? • NO HOMEWORK IS FUN. HUNTER HAS HOMEWORK HIS HOMEWORK IS NOT FUN. *THIS CAT HAS NO TAIL. THAT CAT HAS A TAIL. CATS CAN BE WITH/WITHOUT TAILS. (Answers will appear on next slide.)

20. INDUCTIVE OR DEDUCTIVE? • NO HOMEWORK IS FUN. HUNTER HAS HOMEWORK HIS HOMEWORK IS NOT FUN.-Deductive ( Hint: D.O.G.S.) *THIS CAT HAS NO TAIL. THAT CAT HAS A TAIL. CATS CAN BE WITH/WITHOUT TAILS. -Inductive

21. MORE INDUCTIVE OR DEDUCTIVE? • THE PECAN TREE IS NOT EDIBLE. THE ELM TREE IS NOT EDIBLE. NO TREES ARE EDIBLE. *NO CUPS IN THE CUPBOARD ARE NEW. THIS PURPLE CUP IS IN MY CUPBOARD. THIS CUP IS NOT NEW. (Answers will appear on next slide.)

22. MORE INDUCTIVE OR DEDUCTIVE? • THE PECAN TREE IS NOT EDIBLE. THE ELM TREE IS NOT EDIBLE. NO TREES ARE EDIBLE.-Inductive *NO CUPS IN THE CUPBOARD ARE NEW. THIS PURPLE CUP IS IN MY CUPBOARD. THIS CUP IS NOT NEW.-Deductive (Hint: D.O.G.S.)

23. THE END