The document discusses different types of reasoning and logical fallacies. It begins by defining deductive reasoning, which uses facts and rules to arrive at a conclusion, and inductive reasoning, which uses patterns to arrive at a conjecture. Examples of each are provided. Common fallacies are also explained, including fallacies of relevance where the argument is irrelevant, causal fallacies where the cause does not make logical sense, false generalizations from insufficient evidence, and fallacies of ambiguity from equivocal language. Overall, the document provides an overview of deductive and inductive reasoning as well as common logical fallacies that can undermine arguments.

1. Deductive and Inductive
Reasoning and fallacies
Darnell Kemp
Adapted from westmwires website

2. An Argument
 Claim – the writer’s main idea or point
(not just opinion, arguable)
 Evidence – to support the claim
 Refutation –discussion of opposing
viewpoint
 Conclusion – a restatement of claim
or call to action

3. Deductive vs. Inductive
Reasoning
The difference:
 Inductive reasoning uses patterns to
arrive at a conclusion (conjecture)
 Deductive reasoning uses facts,
rules, definitions or properties to arrive
at a conclusion.

4. Examples of Inductive Reasoning
 Every quiz has been easy. Therefore,
the test will be easy.
 The teacher used PowerPoint in the
last few classes. Therefore, the
teacher will use PowerPoint
tomorrow.
 Every fall there have been hurricanes
in the tropics. Therefore, there will be
hurricanes in the tropics this coming
fall.

5. Example of Deductive Reasoning
An Example:
The catalog states that all entering
freshmen must take a mathematics
placement test.
You are an entering freshman.
Conclusion: You will have to take a
mathematics placement test.

6. 1. 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°

7. 2. Inductive or Deductive Reasoning?
Geometry example…

10. 3.

11. Deductive Reasoning
 Deductive Reasoning – A type of
logic in which one goes from a general
statement to a specific instance.
 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.

12. Deductive Reasoning
 Syllogism: An argument composed of
two statements or premises (the major
and minor premises), followed by a
conclusion.
Premise A:Governments that fail to ensure
people the God given rights of life, liberty,
and the pursuit of happiness should be
abolished.
Premise B: The King has been destructive of
the colonists’ rights.
Conclusion: “We, therefore” are absolved
from the British Crown, have no political
connections, and are now “free and
independent states.”
The
Declaration of
Independence.
The most
famous
syllogistic
argument

13. Deductive Reasoning
Examples:
All students eat pizza.
Emily is a student at Fullerton College.
Therefore, Emily eats pizza.
All athletes work out in the gym.
Colin Kapernik is an athlete.
Therefore, Colin Kapernik works out in the
gym.

14. Valid and Sound
 A deductive argument is valid if the
premises logically lead to the
conclusion
 A deductive argument is sound if the
premises are actually true
 So it is possible for an argument to be
valid but not true

15. Example of valid but not
sound
All math teachers are over 7 feet tall.
Mr. P is a math teacher.
Therefore, Mr. P is over 7 feet tall.
 This 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)

16. Examples
 No one who can afford health
insurance is unemployed.
All politicians can afford health
insurance.
Therefore, no politician is
unemployed.
4. VALID OR INVALID?????
Valid = the premises logically lead to the conclusion
Sound = the premises are actually true

17. Example
 Some professors wear glasses.
Mr. Einstein wears glasses.
Therefore, Mr. Einstein is a professor.
5. VALID OR
INVALID?????

18. 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.
6. What is the next number in the
sequence 6, 13, 20, 27,…?
There is more than one correct answer.

19. 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. 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.)

20. All bats are mammals.
All mammals are warm-blooded.
So, all bats are warm-blooded.
All arguments are deductive or inductive.
Deductive arguments are arguments in which the conclusion is
claimed or intended to follow necessarily from the premises.
Inductive arguments are arguments in which the conclusion
is claimed or intended to follow probably from the premises.
7. Is the argument above deductive or
inductive?

21. All bats are mammals.
All mammals are warm-blooded.
So, all bats are warm-blooded.
Deductive.
If the premises are true, the conclusion, logically, must also be true.

22. Kristin is a law student.
Most law students own laptops.
So, probably Kristin owns a laptop.
In the example above, the word probably shows that
the argument is inductive.
Arguments by elimination are arguments
that seek to logically rule out various
possibilities until only a single possibility
remains. Arguments of this type are always
deductive.
Either Kurt voted in the last election, or he didn't.
Only citizens can vote.
Kurt is not, and has never been, a citizen.
So, Kurt didn't vote in the last election.

23. Tess: Are there any good Italian restaurants in town?
Don: Yeah, Luigi's is pretty good. I've had their
Neapolitan rigatoni, their lasagna col pesto, and their
mushroom ravioli. I don't think you can go wrong with
any of their pasta dishes.
8. Based on what you've learned, is this argument deductive or
inductive? How can you tell?

24. Don: Yeah, Luigi's is pretty good. I've had their Neapolitan
rigatoni, their lasagna col pesto, and their mushroom ravioli.
I don't think you can go wrong with any of their pasta
dishes.
Inductive.

25. I wonder if I have enough cash to buy my psychology
textbook as well as my biology and history textbooks. Let's
see, I have $200. My biology textbook costs $65 and my
history textbook costs $52. My psychology textbook costs
$60. With taxes, that should come to about $190. Yep, I have
enough.
9. Is this argument deductive or inductive? How can you tell?

26. Mother: Don't give Billy that brownie. It contains walnuts, and I think
Billy is allergic to walnuts. Last week he ate some oatmeal cookies with
walnuts and he broke out in a severe rash.
Father: Billy isn't allergic to walnuts. Don't you remember he ate some
walnut fudge ice cream at Melissa's birthday party last spring? He didn't
have any allergic reaction then.
10. Is the father's argument deductive or inductive? How can you tell?

27. What is a fallacy?
 A FALLACY is an argument in which the
premises do not justify the conclusion
as a matter of logic. An argument can
be fallacious for many reasons. The
argument might mis-apply a legitimate
rule of logic. Or it might omit a crucial
premise or misconstrue a premise. Or
it might misconstrue the conclusion.

28. Fallacies in action
 Watch the video below titled:
 “She’s a witch”
 11. Write down any parts of an
argument you hear.
 Now, on the next slide, look how it
breaks down.

29. The argument
 First, inductive – the mob attempts to
arrive at conclusion by using evidence
◦ Witch’s nose, clothing, hat, and wart
◦ All false premises except wart
◦ Non-witches have warts
1. The failed inductive argument:
The woman has a witch's nose, (false premise)
2. and [she is wearing] witch's clothing, (false premise)
3. and [she is wearing] a witch's hat. (false premise)
4. She has a wart (insufficient for the conclusion)
5. Only witches have witches' noses, clothing, hats, and warts.
6. Therefore, she's a witch!

30. Sir Bedevere's Deductive
Argument
1. If she weighs the same as a duck, she'll float. (false, confuses
weight with density)
2. she does weigh the same as a duck; (true in this case, if the scales
are to be trusted)
3. [conclusion #1] Therefore, she'll float. (valid but unsound)
4. If she floats, she is made of wood. (false, many other things float)
5. She does float; (false/based on conclusion #1)
6. [conclusion #2] Therefore, she's made of wood. (valid but unsound)
7. If she's made of wood, she's a witch. (assumed by all in the scene to
be true)
8. She is made of wood; (false/based on conclusion #2)
9. [conclusion #3] Therefore, she's a witch! (valid but unsound)
Valid = the premises logically lead to the conclusion
Sound = the premises are actually true
Slides 35 and 36 from Mooney’s Theology Blog

31. 11. Argument can fail for two
reasons:
 Factual Error
 Error in logic
◦ Deductive argument premises fail to
provide conclusive support for the
conclusion.
◦ Inductive argument premises fail to
provide even probable support for the
conclusion.

32. Fallacies of Relevance – reason
or conclusion is irrelevant to the
argument
 Straw man – a misrepresentation of opponents
argument
 Ad Hominem
 Red Herring – the example is this one
 Two wrong
 False authority
 Appeal to popular opinion
 Begging the question
 Non sequitur (claims cause & effect but there really
is none)
 Evasion
See Fallacies of Relevance Example below and write
on chart (just the name of the commercial)

33. Causal reasoning fallacies –
cause doesn’t make sense
 Post hoc, ergo propter hoc – example
for this one
 Slippery slope
 Rationalization
 False cause
 See Example below and add to chart

34. False generalization – not
enough info for conclusion
 Hasty generalization – This is a conclusion
based on insufficient or biased evidence (example page 360
textbook)
 False analogy
 Either or
 Over simplification
 See example below and add as
example for hasty generalization “You
Hate Children”

35. Fallacies of Ambiguity
 Equivocation - It is the misleading use of a
term with more than one meaning or sense (by
glossing over which meaning is intended at a
particular time).
◦ Example - Noisy children are a real headache. Two aspirin
will make a headache go away. Therefore, two aspirin will
make noisy children go away.
 Example of numerous fallacies
 Take some notes on what you hear?

36. Some quotes from ad (add to
fallacy chart)
 “Americans are under attack from Islamic
extremists in every corner of the world”
 “…lesbians and feminists are attacking everything
sacred”
 What does every or everything tell you? Which fallacy?
 “…Jackson and Sharpton claim the answer is racial
quotas”
 Does this sound like an extreme representation of their
position?
 “The aliens are here but they didn't come in a
spaceship they came across our unguarded
Mexican border.”
 How is aliens doubly used? Which fallacy?

37. Some quotes from ad (add to
fallacy chart)
 “Americans are under attack from Islamic
extremists in every corner of the world”
 “…lesbians and feminists are attacking everything
sacred”
 Hasty Generalization (write these examples on chart)
 “…Jackson and Sharpton claim the answer is racial
quotas”
 Strawman (write this example on your chart)
 “The aliens are here but they didn't come in a
spaceship they came across our unguarded
Mexican border.”
 Equivocation (write this example on your chart)

38. An explanation of my personal
pet peeve and just a really cute
one
 Begs the Question (see below)
 Fallacies in Mean Girls (see below)