Inductive/Deductive Reasoning. Mendocino College Critical Thinking class, Spring 2012

2. Constructing Arguments:
Inductive &
Deductive
Reasoning

3. What is an Argument?

4. An argument is a
form of thinking
in which certain
statements
(reasons) are
offered in
support of
another
statement
(conclusion).

5. Reasoning
Thinking that uses statements of reason
in support of conclusions.

6. Reason
 The faculty of reason (rationality) is a mental ability found in
human beings and normally considered to be a definitive
characteristic of human nature. It is closely associated with such
human activities as language, science, art, mathematics, and
philosophy.
 Reason is the way rational beings propose and consider
explanations concerning cause and effect, true and false, and what
is good or bad. The ways in which human beings reason through an
argument are the subject of inquiries in the field of logic.

7.  Reasons—Statements that support another
statement (known as the conclusion). Reasons
justify a conclusion, or make it more probable.
 Conclusion—A statement that explains,
asserts or predicts on the basis of statements
known as reasons that are offered as evidence
for it.

8. Inductive Reasoning

9. Inductive Reasoning:
An argument form in which one reasons from premises that
are known or assumed to be true to a conclusion that is
supported by the premises but does not necessarily follow
from them.
The kind of thinking that is done to form general ideas based
on experience and observation.
Inductive reasoning allows us to create generalizations about
things, such as people, places, events, the environment, etc.

10. Inductive Reasoning:
 The process of recognizing patterns or
observing patterns and drawing a conclusion
based on that pattern.
 Reasoning from a specific case or cases and
deriving a general rule.

11. Inductive Reasoning:
 by example
 by cause
 by authority
 by sign
 by analogy

12. By Example
Owls turning head
http://www.youtube.com/watch?v=8TL8pSFd-hQ&NR=1&feature=fvwp
http://www.youtube.com/watch?v=hoc42xegVt8&NR=1
http://www.youtube.com/watch?v=h-jtQZwPPGQ
We can induce from these examples that owls (or most or many owls)
have the ability to turn their heads in a unique way.

13. By Cause
Argument by cause
attempts to establish
a cause and effect
relationship between
two events. The link
below gives us a
causal explanation
for the owl’s ability to
turn its head.
Owl head-turning explained—also an authority speaking on her area of expertise
http://www.youtube.com/watch?v=pBe4Kz0RsKE

14. By Authority
A person who is a
legitimate expert is more
likely to be right than
wrong when making
considered claims within
her area of expertise. The
claim is being accepted
because it is reasonable
to believe that the expert
has tested the claim and
found it to be reliable.
here’s an authority on wild cheetahs
http://izismile.com/2011/04/20/woman_confronts_wild_cheetahs_then_pets_one.html

15. By Sign
This is in some ways a
type of tightly linked
cause and effect
reasoning that has more
certainty. Footprints are
an indication that
someone has walked by
recently. The sun rising
is a sign of the morning.
Here’s Sherlock Holmes inferring many truths from a hat
http://www.youtube.com/watch?v=1bCS4icTrH0

16. By Analogy/Comparison
if it quacks like a duck…

17. Inductive conclusions are
established in four stages:
• Observation: collect facts, without bias.
• Analysis: classify the facts, identifying patterns of regularity.
• Inference: From the patterns, infer generalizations about the
relations between the facts.
• Confirmation: Testing the inference through further
observation.

18. Opinion Polls
A recent Gallop Poll reported that 74% of the American
Public believes abortion should be legal.
A poll is a form of empirical generalization, a general
statement about an entire group made on the basis of
observing some members of the group.

19. Questions to Ask About Polls
 Is the sample known?
 Is the sample sufficient?
 Is the sample representative?
 Do the conclusion seem reliable?
 Why or why not?

20. Inductive arguments can include:
• Part-to-whole: where the whole is assumed to be like
individual parts (only bigger).
• Extrapolations: where areas beyond the area of study
are assumed to be like the studied area.
• Predictions: where the future is assumed to be like the
past.

22. Deductive Reasoning

23.  Deductive reasoning starts with a general case
in order to draw conclusions about specific
instances.
 Deductive reasoning starts with an assumed
hypothesis, theory or truth. This assumption
may be well-accepted or rather shaky—but if it’s
true, the conclusion can not be questioned.
 Deductive reasoning is used by scientists to
take a general scientific law and apply it to a
certain case when they assume that the law is
true.

24. All planets revolve around stars.
The earth is a planet.
Therefore the earth revolves around a star.
The earth revolves around the sun.
Therefore the sun is a star.

25.  Deductive reasoning assumes that the basic law
from which you argue is applicable in all cases.
 Scientists will prove a general law for a
particular case and then do many deductive
experiments to demonstrate that the law holds
true in many different circumstances.
 Using deductive reasoning usually is a credible
and safe form of reasoning, but it is based on
the assumed truth of the rule or law on which it
is founded.

26. Deductive arguments are
generally based on the
following:
 laws
 rules
 widely accepted principles
 theories
 hypotheses

27. Deductive Reasoning
Premise
Premise
Conclusion

28. Deduction begins with the general and
ends with the specific.
All men are mortal
Socrates is a man
Therefore Socrates is mortal.
syllogism

29. A syllogism
The
syllogism is
at the core of
traditional
deductive
reasoning.
cartoon

30. Valid Argument: An argument in
which the reasons support the
conclusions so that the conclusion
follows the reasons offered.
Invalid Argument: An argument in
which the reasons do not support the
conclusion so that the conclusion does
not follow from the reasons offered.

32. What’s Wrong with this?
 Penguins are black and white.
 Some old TV shows are black and
white.
 Therefore some penguins are old
TV shows.

33. All men are mortal.
Socrates is mortal.
Therefore Socrates is man.
not a valid argument, why?

34. THE general Rule:

35. Syllogism: THE general Rule

36. Premise: Birds fly

37. Deductive Reasoning
 If the premises are true, the
conclusion is also true.

38. A DEDUCTIVE ARGUMENT
 Premise 1: Birds fly.
 Premise 2: An owl is a
bird.
 Conclusion: Owls fly.
owl flying

39. But Is the premise
correct?
Do birds fly?

40. Test Your Premise
Remember: The general rule tells us
that the basic law from which you
are arguing must be applicable in all
cases.

41. AN UNSOUND ARGUMENT:

42. AN UNSOUND ARGUMENT:
Valid structure, but invalid premise(s).

43. Checking our premises:
Is a penguin is a bird?
BBC: Do Penguins Fly?
From the BBC
http://www.youtube.com/watch?v=9dfWzp7rYR4
BBC Explanation
http://www.youtube.com/watch?
v=lzhDsojoqk8&feature=watch_response

44. Premises
Birds. Class *Aves. Birds are feathered,
winged, bipedal, warm-blooded, egg-laying
vertebrates.
Aves is Latin for birds and is universally used as
the scientific term for the class of organisms to
which birds belong.
Either our premise that all birds fly is wrong, or our premise
that penguins are birds is wrong.

45. If, by definition penguins are feathered, winged, bipedal,
warm-blooded, egg-laying vertebrates, then they are
birds. The next question has to be, do all birds fly or
just some?
If the answer is “some,” then your premise, “birds fly”
is wrong, and therefore your conclusion is wrong.
From Wikipedia:
“All living species of birds have wings—the now extinct flightless
moa of New Zealand were the only exception. Wings are evolved
forelimbs, and most bird species can fly. Flightless birds include
ratites, penguins, and a number of diverse endemic island species.”

46. In deductive reasoning you must
expain and defend the premises
There is no way to admit the truth of a premise and
deny the truth of the conclusion.
premise: birds fly
premise: a penguin is a bird
conclusion: penguins fly

47. Penguins (order
Sphenisciformes,
family Spheniscidae)
are a group of
aquatic, flightless
birds living almost
exclusively in the
southern hemisphere,
especially in
Antarctica.

48. True reasons, valid structure = Sound Argument
False reasons, valid structure = Unsound Argument
True reasons, invalid structure = Unsound Argument
False reasons, invalid structure = Unsound Argument

49. modus tollens
denying the consequence
• If Michael is a good friend, he will loan
me his car for the weekend.
• Michael won’t loan me his car.
• Therefore Michael is not a good friend.

50. Silver Blaze

51. modus tollens
denying the consequence
From Sherlock Holmes, Silver Blaze
 Dogs bark at strangers.
 The dog didn’t bark when the horse disappeared.
 Therefore whoever took the horse away was not a
stranger.