DEDUCTIVE REASONING
INDUCTIVE REASONING
SYLLOGISM
FALSE PREMISE
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.
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.
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)
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)
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
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).
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.)
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)
SYLLOGISMS
VALID 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.)
SYLLOGISMS
VALID 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
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.
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.)
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.
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.)
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
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.)
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
---
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.)
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
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.)
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.)
THE
END