A presentation on inductive and deductive reasoning with a sample from The Princess Bride.

1. Deductive
&
Inductive
Reasoning
(or how to argue good
so you can win and stuff)

2. Terms and Definitions
 Logic – The science of correct reasoning.
 Reasoning – The drawing of inferences or
conclusions from known or assumed facts.
When solving a problem, one must understand the
question, gather all pertinent facts, analyze the
problem i.e. compare with previous problems (note
similarities and differences), perhaps use pictures or
formulas to solve the problem.

3. Terms and Definitions
 Argument: A series of statements called the
premises intended to determine the degree of truth
of another statement, the conclusion.
 Premise: A proposition supporting or helping to
support a conclusion
 Conclusion: A statement or proposition for which
the premises are intended to provide support. (In
short, it is the point the argument is trying to make.)

4. Deductive Reasoning
 Deductive Reasoning – A type of logic in which
one goes from a general statement to a specific
instance. It uses facts, rules, definitions or properties
to arrive at a conclusion.
 The classic example
All men are mortal. (major premise)
Socrates is a man. (minor premise)
Therefore, Socrates is mortal. (conclusion)
The above is an example of a syllogism.

5. Law of Syllogism:
You can use this law to state a
conclusion from two true conditional
statement.

6. Deductive Reasoning
 Deductive reasoning is when you start from things
you assume to be true, and draw conclusions that
must be true if your assumptions are true.
For Example:
All dogs have a tail.
Ziggy is a dog.
Therefore Ziggy has a tail.

7. Deductive Reasoning
 Syllogism: An argument composed of two
statements or premises (the major and minor
premises), followed by a conclusion.
 For any given set of premises, if the conclusion is
guaranteed, the arguments is said to be valid.
 If the conclusion is not guaranteed (at least one
instance in which the conclusion does not follow),
the argument is said to be invalid.
 BE CARFEUL. DO NOT CONFUSE TRUTH
WITH VALIDITY!

8. In Science:
The law of gravity means everything that goes up must
come down.
I threw a baseball in the air.
That means the baseball must come down.
In Social Studies:
To be elected president you must obtain at least 270
electoral votes
Donald Trump won 304 electoral votes.
Therefore Donald Trump is the president.
When do you use it?

9. Deductive Reasoning
Examples:
1.
 All students eat pizza.
 Rainer is a student at Trinity.
 Therefore, Rainer eats pizza.
2.
 All athletes work out in the gym.
 Barry Bonds is an athlete.
 Therefore, Barry Bonds works out in the gym.

10. Deductive Reasoning
3.
All science teachers are over 7 feet tall. (major premise)
Mr. T. is a science teacher. (minor premise)
Therefore, Mr. T is over 7 feet tall. (conclusion)
 The argument is valid, but is certainly not true.
 The above examples are of the form
If p, then q. (major premise)
x is p. (minor premise)
Therefore, x is q. (conclusion)

11. Venn Diagrams
 Venn Diagram: A diagram consisting of various
overlapping figures contained in a rectangle called the
universe.
U
This is an example of all A are B. (If A, then B.)
B
A

12. Venn Diagrams
This is an example of No A are B.
U
A
B

13. Venn Diagrams
This is an example of some A are B. (At least one A
is B.)
The yellow oval is A, the blue oval is B.

14. Example
 Construct a Venn Diagram to determine the validity
of the given argument.
#14 All smiling cats talk.
The Cheshire Cat smiles.
Therefore, the Cheshire Cat talks.
VALID OR INVALID?

15. Example
Valid argument; x is Cheshire Cat
things
that talk
smiling cats
x

16. Examples
#6
 No one who can afford health insurance is
unemployed.
 All politicians can afford health insurance.
 Therefore, no politician is unemployed.
VALID OR INVALID?

17. Examples
X=politician. The argument is valid.
people who can afford
health care
politicians
X
unemployed

18. Example
 #16
 Some professors wear glasses.
 Mr. Einstein wears glasses.
 Therefore, Mr. Einstein is a professor.
Let the yellow oval be professors, and the blue oval
be glass wearers. Then x (Mr. Einstein) is in the
blue oval, but not in the overlapping region. The
argument is invalid.

19. Inductive Reasoning
Inductive Reasoning, involves going from a series
of specific cases to a general statement. The
conclusion in an inductive argument is never
guaranteed.
Example: What is the next number in the sequence 6,
13, 20, 27,…
There is more than one correct answer.

20. Inductive Reasoning
Here’s the sequence again 6, 13, 20, 27,…
 Look at the difference of each term.
 13 – 6 = 7, 20 – 13 = 7, 27 – 20 = 7
 Thus the next term is 34, because 34 – 27 = 7.
 However… what if the sequence represents the
dates?

21. Inductive Reasoning
 Then the next number could be 3 (31 days in a month).
 The next number could be 4 (30 day month)
 Or it could be 5 (29 day month – Feb. Leap year)
 Or even 6 (28 day month – Feb.)

22. Examples of Inductive Reasoning
1) Every quiz has been easy. Therefore,
the test will be easy.
2) The teacher used PowerPoint in the
last few classes. Therefore, the
teacher will use PowerPoint
tomorrow.
3) Every fall there have been hurricanes
in the tropics. Therefore, there will
be hurricanes in the tropics this
coming fall.
2.4 Deductive Reasoning

23. Deductive and Inductive Reasoning
Now for a fun bit of mostly deductive
reasoning with a tad of inductive
thrown in as well.

24. Deductive Reasoning in A Princess Bride

25. 1) Step 1
• P1: A great fool would place it in his own glass.
• P2: A great fool would reach for his own glass.
• P3: I am not a great fool.
• C1: I can clearly not choose the wine in front of you.
2) Step 2
• P4: But you knew I was not a great fool.
• P5: You would know I would never fall for [it].
• C2: I can clearly not choose the wine in front of me.
3) Step 3
• P6: Poison is powder made from iocane.
• P7: Iocane comes only from Australia.
• P8: Australia is peopled with criminals.
• P9: Criminals are not trusted.
• P10: I don't trust you.
• C3: I can clearly not chose the wine in front of you.
Vizzini’s Argument (part 1)

26. 4) Step 4
P11: You know I knew the origin.
P12: You know I know about criminals.
C4: I can clearly not choose the wine in front of me.
5) Step 5
P13: You have beaten my Turk.
P14: You are incredibly strong.
P15: Count on strength to save you.
C5: I can clearly not choose the wine in front of you.
6) Step 6
P16: You have bested my Spaniard.
p17: He studied for his excellence.
P18: You have studied.
P19: You are aware how mortal we are.
P20: You don't want to die.
C6: I can clearly not choose the wine
in front of me.
Vizzini’s Argument (part 2)

27. 7) Step 7
P21: I have learned everything from you.
P22: Only a genius could have deduced it.
C7: I am a genius.
Vizzini’s Argument (part 3)

28. I N D U C T I V E O R D E D U C T I V E ?
Your Turn
A. B.
A. Deductive B. Inductive

29. Inductive or Deductive Reasoning?
Geometry example…
60◦
x Triangle sum property –
the sum of the angles of any
triangle is always 180 degrees.
Therefore, angle x = 30°
Deductive Reasoning – conclusion is based on a property

30. Inductive or Deductive Reasoning?
Geometry example…
What comes next?
Colored triangle rotating 90° CW
in the corners of the square
Is there a rule?
Inductive Reasoning