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Business Logic Agnes Sunga

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Table of Contents
Course Description ..................................................................................................................................... 2
Managerial Judgment and Critical Thinking .............................................................................................. 3
Introduction to Logic
Definition and Importance of Logic............................................................................................................ 13
Truth and Validity .................................................................................................................................. 14
Arguments and Explanation ...................................................................................................................... 22
What is an argument?............................................................................................................................... 23
Identifying arguments ............................................................................................................................... 24
Uses and Function of Language ............................................................................................................... 29
Disputes and Definition ............................................................................................................................. 36
Disputes and Disagreements .................................................................................................................... 37
Definition ................................................................................................................................................. 39
Fallacy......................................................................................................................................................... 47
Formal ..................................................................................................................................................... 48
Informal ................................................................................................................................................... 48
Deductive Reasoning ................................................................................................................................ 57
Deductive and Inductive Argument ........................................................................................................... 58
Deductive Argument ................................................................................................................................ 59
Inductive Reasoning .................................................................................................................................. 67
Inductive Argument and Statistical Generalization .................................................................................... 68
Explanation ............................................................................................................................................... 73
Analogical Argument ............................................................................................................................... 77
Causal Reasoning .................................................................................................................................... 79
Critical Thinking as a Qualified Decision-Making Tool ............................................................................ 85
Business Logic
Course Description:
This course is designed to develop the analytical and critical thinking skills of business students. It will cover
the following key subject areas in deductive and inductive logic: recognizing arguments, formal and informal
fallacies, categorical logic, inductive reasoning, decision making methods and moral reasoning. This course
aims to enable students to bring their critical perspective to various fields in business, and make them
explicit through problem solving, uncovering assumptions, evaluation of ideas and independent judgment.
Each part of this learning material contains the following: (i) Expository text that focuses on a specific topic;
(ii) Worked examples of the critical and logical thinking process; (iii) Exercises that encourage students to
practice what they learn. A List of references and educational videos is also provided for further reading and
to supplement the content of this instructional material.
Below is a table that will serve as a guide in the completion of this course.
Target Date
Week 1
1 hour
Title of Topics
Course Orientation
Week 2
Week 3
3 hours
3 hours
Critical Thinking in Business
Introduction to Logic
• Definition and Importance of Logic
• Truth and Validity
Week 4
Week 5
3 hours
3 hours
Recognizing Arguments
Uses and Function of Language
Week 6
5 hours
Week 7 -8
Week 9
Week 10-11
Week 12-14
Week 15
Week 16
6 hours
3 hours
6 hours
6 hours
3 hours
Disputes and
Answer exercises that you might have missed
Deductive Reasoning
Inductive Reasoning
Critical Thinking and Decision Making
Preparation for submission (All exercises
Critical Thinking In Business
4 Hours
a) Define critical thinking
b) Relate the study of critical thinking to business management.
c) Examine the different critical thinking skills that are relevant to business practices.
d) Evaluate the importance of soft skills like critical thinking in today’s global economy.
READINGS AND VIDEOS (Please see the digital copies of the materials.)
Reading 1.1 Exton W. (1991). Managerial Judgment and Critical Thinking in A Review of General
Semantics 48 (1) pp. 16-21. Retrieved from http://www.jstor.com/stable/42582311
Reading 1.2
Noel, L. Pierre, S. & Watson, J. (2017) Critical Thinking, Decision Making and Mindfullness in
Fischler College of Education: Student Articles. 16. Retrieved from
Video 1.1
Do Companies Actually Want Critical Thinkers? in
LECTURES (Please refer to the Powerpoint presentations)
Write a 100 – 200 words reflection paper on Why critical thinking matters?
Author(s): William Exton, Jr.
Source: ETC: A Review of General Semantics , Spring 1991, Vol. 48, No. 1, SPECIAL
ISSUE: General Semantics: Current Research and Applications (Spring 1991), pp. 16-21
Published by: Institute of General Semantics
Stable URL: http://www.jstor.com/stable/42582311
JSTOR is a not-for-profit service that helps scholars, researchers, and students
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ETC: A Review of General Semantics
N THE BUSINESS WORLD, the most conspicuous material
go to those who demonstrate a capacity to exercise
judgment effectively in matters involving economic gain or loss.
The market economy offers ample opportunity to apply one’s
judgment for profit and advancement.
How to foster development of superior judgment in
business matters has been the subject of extensive and
amply financed research and experimentation. The results
are manifest in a wide range of training, education, and
developmental activity has great relevance to “critical
thinking”—and vice versa.
Surely “critical thinking” and “sound judgment” not only are
parallel in function, but overlap greatly. The competencies
implied by the term critical thinking have much in common with
those we attribute to an effective manager. And, just as surely,
the enormous methodological resources available for teaching such
management skills as problem-solving and decision-making can be
appropriately adapted for teaching critical thinking in the schools.
It is, then, not
* William Exton, Jr., was a management consultant and designer
of teaching aids. He was president of the Institute of General
Semantics at the time of his death in December 1988.
† Adapted from the article of the same title included in Thinking
Creoticalf y: A S ys- tematic, Interdisciplinary Approach to
Creative-Critical Thinking, edited by Kenneth G. Johnson
(Englewood, N.J.: Institute of General Semantics, 1991).
necessary for those who would teach critical thinking to
reinvent the wheel. For many aspects of critical thinking,
educators need only adapt practices found useful in
management training.
As a management consultant, I searched for a consistent,
integrated methodology—one that was so general in its
applica- bility that it could be taught per se, or in relation to
virtually any body of content. I wanted an intellectual
discipline—at least poten- tially rigorous—that provided
synergistic formulations with a his- tory of successful
applications. Fortunately, such a discipline already existed,
known internationally as general semantics. Its applications
in business are well illustrated in CommuniCation and
Organizational Behavior, by William Haney.(1)
General semantics has been taught at many universities in
reg- ular or special courses. Its potentials have been
explored in more than 120 doctoral dissertations, including
several that suggest gen- eral semantics can be taught at
elementary and high-school levels with positive effects on
critical and creative thinking.(2)
Many of us grew up with textbook problems that provided
all of the necessary information—and the assumption that
all pro- vided information was valid. In the business world (or
the world generally) we never have all of the information—
and we cannot assume that the information we have is valid.
Critical thinking requires (among other things):
1. Validity of the information (observations or data) that
under- lies the assumptions to which values and logical
processes are applied.
2. Validity of the assumptions, both initial and sequential,
based upon the available information.
3. Validity of the values applied in the exercise of evaluative
4. Validity of the logic of processes involved in inference, generalization, deduction, extrapolation, etc.
5. Recognition of hidden assumptions, unfounded implications,
dubious inferences, subjective orientations, prejudice, bias,
slanting, questionable perspectives, etc., both in one’s own
evaluative process and in the communications of others.
We base our thinking largely on our assumptions. But we are
often not conscious of the assumptions entering into our evaluations and decisions. General semantics training aims at develop-
Et cetera • S RING
ing optimum consciousness of assumptions—as well as
conscious- ness of abstracting.
Critical thinking should help us to identify those values
most likely to foster valid understanding and to guide our
decisions along lines that are best suited to our own longterm—rather than short-term—interests.
As we experience the world around us, it is the inevitable
ten- dency of our perceptual function to evaluate our
perceptions by association with past experience, and thus,
inevitably, in terms of the more-or-less familiar. This process
often leads us to notice similarities of a new perception to an
old perception—and to dis- regard significant differences.
Once we label the new perception on the basis of similarities
alone, we have taken a first step toward uncritical thinking.
The more the situation looks familiar, the more likely we are to
overlook elements that appear unfamiliar—and that might
involve unfamiliar consequences. So we must learn to be
critical of our own perceptions, to silently question,
reinterpret, relabel, and reevaluate what our senses tell us.
But the kind of critical thinking that we apply to direct experience will not serve us adequately when we evaluate the
commu- nicated experience we derive from the words we hear
or read. We inust take into account the unique nervous system
(map-maker) that produced those words, the map-makers'
values and perspec- tives, and the nature of language as a
symbolic process.
We must learn to understand the limitations of language and
the ways in which the very structure of language distorts
communi- cahon from the intent of its originator, as well as the
ways that com- munication is subject to distortion through
individual poverty of expression, unfamiliar terminology,
equivocal vocabulary, misap- prehension, etc. But we must
also be aware of the ways in which each item of linguistic
communication is inevitably shaped by, and reflects, the
evaluative and purposive orientations and both con- scious and
unconscious assumptions of its uniquely individual human
origins. Only through such understanding can we begin to
detect—and to discount, allow for, and protect ourselves from—
bias, slanting, propaganda, planned deceit, and deliberate
false- hoods. Only then can we be sensitive to inconsistencies,
false assumptions, self-deceptions, deluded beliefs, distorted
reportage, and purposeful omissions that characterize so
much of what is broadcast, printed, and echoed in the
conversations of those we know.
We also require a workable notion of epistemology—how we
“know” what we claim to “know.” And we need an adequate
appreciation of the extraordinary neuro-linguistic processes that
enable us to translate our perceptions into words—and to translate the words of others into something meaningful and, we hope,
having some correspondence to the intended message. We must
learn to “perceive ourselves in the process of perceiving.”
There is one unique methodological discipline that, in a creatively integrated way, addresses both epistemology and neurolinguistics. This dynamic synthesis distinguishes general semantics and renders it outstandingly relevant to the development and
exercise of critical thinking.
To me, the most useful and effective pedagogical device for illustrating how language relates to what it is intended to represent is
found in the map-territory analogy.
Visualize, if you will, the United States as you know it: a
continent-wide expanse of territory, with extremely varied terrain;
with all its states, counties, cities, towns, and villages; with rivers,
mountains, roads, streets, bridges, railways, power lines, etc., etc.
Now consider a map of the United States, as complete and
detailed as any map can be.
The relationship between that “map” and that “territory” can best be
summarized in these statements:
1. The map is not the territory. By analogy, words are not the
things they represent. This may seem obvious. But we
do, far more often than we realize, act as i{the word we
have used (or heard) is the thing itself, the words on
paper are the situation.
2. The map is not all the territory. Even the most detailed map
cannot represent oil aspects of the territory. Words, no matter
how many, can never tell us all about anything.
3. The map is self-reflexive. Every map reflects the mapmaker. Words reflect—and tell us something about—the
person who speaks or writes them.
Those who learn to apply the three-fold principles of mapterritory relationships to what they hear or read (or speak or think)
will have made significant progress in the direction of critical thinking, because they will be aware of the perceptions behind the
com- munications.
In this age of the “Information Explosion,” we are often overwhelmed by the flood of information available to us. We face an
Et cetera • SPRING
overkill of information—sought and unsought, relevant and
irrele- vant, reliable and misleading, useful and distracting—all
of which makes demands on our time and attention.
To cope with situations of any degree of complexity, we not
only must sort out that part of the available information that is
useful, but also must sense what information is needed for an
adequately formed evaluation.
The kind of critical thinking required here is clearly linked to
the consonance of words with perceptions, of map with
territory, of our perceptions of the problem-situation with the
situation “outside our skins.”
Consciousness of abstracting, a key principle in general
seman- tics, reminds us that any process from which we may
derive a per- ception has an infinite number of
characteristics, which is why we can never know all about
anything. It also reminds us that each person abstracts
differently. People do not necessarily abstract the same
characteristics, and they evaluate characteristics differently.
This bit of epistemological insight should help us to realize
that the process of abstracting is fallible and the results of that
should be tested—evaluated and reevaluated.
Abstracting should be recognized as a multiordinal process.
We can go from the label “apple” to higher-order abstractions
(“fruit,” “produce,” “agricultural product,” “item in the market
economy,” etc.). However, once we enter upon the process of
more inclusive labeling, it will no longer be clear to others that
we are still refer- ring to an “apple.”
Critical thinking demands that we seek out the lower-order
abstractions underlying the higher-order abstractions we
use or accept from others. In business as in politics (and in
many other forms of human activity as well), we often give or
receive higher- order abstractions cut loose from their
moorings. The words may sound profound, but we are left to
wonder what they refer to in the world “out there.” The
extensional orientation recommended by Korzybski includes
checking maps against territories, higher- order abstractions
against lower-order abstractions. It requires that we move
through levels of abstraction rapidly, using certain levels to
validate or test other levels.
It is noteworthy that many managers in business and
industry have found in general semantics a coherent
methodology for relat- ing their perceptions to an
increasingly complex world.
1. William V. Haney, Communication and Organizational Behavior, Text and Cases
(Homewood, 111. : Richard D. Irwin, 1960; rev. ed. 1967).
2. Kenneth G. Johnson, comp., Graduate Research in General Semantics (Englewood,
N.J.: Institute of General Semantics, 1985).
The more the situation looks familiar, the more likely we are to
overlook elements that appear unfamiliar—and that might involve unfamiliar
Introduction to Logic
3 Hours
Define logic, truth and validity.
Understand the relationship between truth and validity.
Differentiate premise and conclusion.
Analyze the different kinds of arguments which true/false and conclusion.
Apply the concepts of truth and validity by writing their own argument.
READINGS AND VIDEOS (Please see the digital copies of the materials.)
Reading 2.1 Gensler, H. (2010).Introduction to Logic Second Edition. New York: Routledge
Reading 2.2
Copi, I., Cohen, C & McMahon, K. (2014). Introduction to Logic Fourteenth
Edition. London: Pearson Education Limited
Video 2.1
Critical Thinking –Fundamentals: Truth and Validity in
Critical Thinking –Fundamentals: Truth and Validity in
Video 2.2
LECTURES (Please refer to the Powerpoint presentations)
Answer Exercise 2.1 (Write your answer in a separate sheet of paper)
2.1 Topic: Introduction to Logic
Definition and Importance of Logic
Truth and Validity
Source: Introduction To Logic
Harry Gensler
2nd Editon
Logic is about reasoning – about going from premises to a conclusion. As we
begin our study of logic, we need to be clearer on what logic is and why it’s
important. We also need to learn some concepts (like “valid” and “argument”)
that are central to the study of logic.
1.1 Logic
Logic is the analysis and appraisal of arguments. When you do logic, you try to clarify reasoning
and separate good from bad reasoning. As you work through this book, you’ll examine
reasoning on various topics, both philosophical (like free will and determinism, the existence of
God, and the nature of
morality) and non-philosophical (like backpacking, water pollution, football, Supreme Court
decisions, and the Bible). You’ll come to see logic not as an irrelevant game with funny symbols,
but as a useful tool to clarify and evaluate our reasoning – whether on life’s deeper questions or
on everyday topics.
Why study logic? I can think of three main reasons. First, logic is important because reasoning
is important. While you’ve been reasoning about things all your life, this may be the first time
that you try to understand reasoning and become better at it. Reasoning and general analytical
skills are important in
law, politics, journalism, education, medicine, business, science, mathematics, computer
science, and most other areas.
Second, logic can deepen your understanding of philosophy. Philosophy can be defined as
reasoning about the ultimate questions of life. Philosophers ask questions like “Why accept or
reject free will?” or “Can one prove or disprove God’s existence?” or “How can one justify a
moral belief?” If you don’t know any logic, you’ll have only a vague grasp of such issues; and
you’ll lack the tools needed to understand and evaluate philosophical reasoning. If you’ve
studied philosophy, you’ll likely recognize many of the pieces of philosophical reasoning in this
book. If you haven’t studied philosophy, you’ll find this book a good introduction to the subject.
In either case, you should get better at recognizing, understanding, and appraising philosophical
reasoning. Finally, logic can be fun. Doing logic is like playing a game or doing puzzles; logic
will challenge your thinking processes in new ways. The rigor of logical systems will likely
fascinate you. Most people find logic enjoyable.
1.2 Valid arguments
I begin my basic logic course with a multiple-choice test. The test has ten problems; each
problem gives information and asks what conclusion necessarily follows. The problems are
easy, but most students get about half wrong.1 Here are two of the problems – with the right
answers boxed:
If you overslept, you’ll be late.
You aren’t late.
(a) You did oversleep.
(b) You didn’t oversleep.
(c) You’re late.
(d) None of these follows.
If you overslept, you’ll be late.
You didn’t oversleep.
(a) You’re late.
(b) You aren’t late.
(c) You did oversleep.
(d) None of these follows.
While almost everyone gets the first problem right, many students wrongly pick “(b)” for the
second problem. Here “You aren’t late” doesn’t necessaryfollow, since you might be late for
some other reason; maybe your car didn’t start. Most students, once they grasp this point, will
see that (b) is wrong. Untrained logical intuitions are often unreliable. But logical intuitions can
be developed; yours will likely improve as you work through this book. You’ll also learn special
techniques for testing arguments.3An argument, in the sense used in logic, is a set of
statements consisting of premises and a conclusion. The premises are statements that give
supporting evidence; the conclusion is what is allegedly supported by these statements.
Arguments put into words a possible act of reasoning. Here’s an example:
If you overslept, you’ll be late.
You aren’t late.
Á You didn’t oversleep. (“Á” = therefore)
An argument is valid if it would be contradictory (impossible) to have the premises all true and
conclusion false. In calling an argument valid, we aren’t saying whether the premises are true.
We’re just saying that the conclusion follows from the premises – that if the premises were all
true, then the conclusion also would have to be true. In saying this, we implicitly assume that
there’s no shift in the meaning or reference of the terms; hence we must use “overslept,” “late,”
and “you” the same way throughout the argument.
Our argument is valid because of its logical form – its arrangement of logical notions (like “ifthen” and “not”) and content phrases (like “You overslept”and “You’re late”). We can display an
argument’s form by using words orsymbols for logical notions and letters for content phrases:
If you overslept, you’ll be late.
You aren’t late.
Á You didn’t oversleep.
If A then B Valid
Á Not-A
Our argument is valid because its form is correct. If we take another argument
of the same form, but substitute other ideas for “A” and “B,” then this second
argument also will be valid. Here’s an example:
If you’re in France, you’re in Europe.
You aren’t in Europe.
Á You aren’t in France.
If A then B Valid
Á Not-A
Logic studies forms of reasoning. The content can deal with anything – backpacking,
mathematics, cooking, physics, ethics, or whatever. When you learn logic, you’re learning tools
of reasoning that can be applied to any subject. Consider our invalid example:
If you overslept, you’ll be late.
You didn’t oversleep.
Á You aren’t late.
If A then B Invalid
Á Not-B
Here the second premise denies the first part of the if-then; this makes itinvalid. Intuitively, you
might be late for some other reason – just as, in this similar argument, you might be in Europe
because you’re in Italy:
If you’re in France, you’re in Europe.
You aren’t in France.
Á You aren’t in Europe.
If A then B Invalid
Á Not-B
1.3 Sound arguments
Logicians distinguish valid arguments from sound arguments: An argument is valid if it would be
contradictory to have the premises all true and conclusion false.
An argument is sound if it’s valid and has every premise true. Calling an argument “valid” says
nothing about whether its premises are true. But calling it “sound” says that it’s valid (the
conclusion follows from the premises) and has true premises. Here’s an example of a sound
and true
If you’re reading this, you aren’t illiterate.
You’re reading this.
Á You aren’t illiterate.
When we try to prove a conclusion, we try to give a sound argument. We must make sure that
our premises are true and that our conclusion follows from our premises. If we have these two
things, then our conclusion has to be true. The conclusion of a sound argument is always true.
An argument could be unsound in either of two ways: (1) it might have a false premise or (2) its
conclusion might not follow from the premises:
First premise false:
All logicians are millionaires.
Gensler is a logician.
Á Gensler is a millionaire.
Conclusion doesn’t follow:
All millionaires eat well.
Gensler eats well.
Á Gensler is a millionaire.
When we criticize an opponent’s argument, we try to show that it’s unsound. We try to show
either that one of the premises is false or that the conclusion doesn’t follow. If the argument has
a false premise or is invalid, then our opponent hasn’t proved the conclusion. But the conclusion
still might be true – and our opponent might later discover a better argument for it. To show a
view to be false, we must do more than just refute an argument for it; we must invent an
argument of our own that shows the view to be false.
Besides asking whether premises are true, we could ask how certain they are, to ourselves or to
others. We’d like our premises to be certain and obvious to everyone. We usually have to settle
for less than this; our premises are often educated guesses or personal convictions. Our
arguments are only as strong as their premises. This suggests a third strategy for criticizing an
argument; we could try to show that one or more of the premises are very uncertain. Here’s
another example of an argument. In fall 2008, before Barack Obama was elected US president,
he was far ahead in the polls. But some thought he’d be defeated by the “Bradley effect,”
whereby many whites say they’ll vote for a black candidate but in fact don’t. Barack’s wife
Michelle, in a CNN interview with Larry King (October 8), argued that there wouldn’t be a
Bradley effect:
Barack Obama is the Democratic nominee.
If there was going to be a Bradley effect, Barack wouldn’t be the nominee
[because the effect would have shown up in the primary elections].
Á There isn’t going to be a Bradley effect.
Once she gives this argument, we can’t just say “Well, my opinion is that there will be a Bradley
effect.” Instead, we have to respond to her reasoning. It’s clearly valid – the conclusion follows
from the premises. Are the premises true? The first premise was undeniable. To dispute the
second premise, we’d have toargue that the Bradley effect would appear in the final election but
not in the primaries; but it’s unclear how one might defend this. So an argument like this
changes the nature of the discussion. (By the way, there was no Bradley effect when the
general election took place a month later.) Logic, while not itself resolving substantive issues,
gives us intellectual tools to reason better about such issues. It can help us to be more aware of
reasoning, to express reasoning clearly, to determine whether a conclusion follows from the
premises, and to focus on key premises to defend or criticize. I have two points on terminology.
We’ll call statements true or false (notvalid or invalid). And we’ll call arguments valid or invalid
(not true or false). While this is conventional usage, it pains a logician’s ears to hear “invalid
statement” or “false argument.”So far we’ve seen deductive arguments, where the conclusion is
claimed to follow with necessity. There also are inductive arguments, where the conclusion is
claimed to follow only with probability; this claim is either implicit orelse expressed by terms like
“probably.” Consider these examples:
Deductively valid Inductively strong
All who live in France live in Europe.
Pierre lives in France.
Á Pierre lives in Europe.
Most who live in France speak French.
Pierre lives in France.
This is all we know about the matter.
Á Pierre speaks French (probably).
The first argument has a tight connection between premises and conclusion; it would be
impossible for the premises to all be true but the conclusion false. The second has a looser
premise–conclusion connection. Relative to the premises, the conclusion is only a good guess;
it’s likely true but could be false (perhaps Pierre is the son of the Polish ambassador and speaks
no French).
2.2 Truth and Validity
Source: Introduction to Logic
Irving Copi
Carl Cohen
Kenneth McMahon
14th edition
There are many possible combinations of true and false premises and conclusions in both valid
and invalid arguments. Here follow seven illustrative arguments, each prefaced by the
statement of the combination (of truth and validity) that it represents. With these illustrations
(whose content is deliberately trivial) before us, we will be in a position to formulate some
important principles concerning the relations between truth and validity.
I. Some valid arguments contain only true propositions—true premises and a
true conclusion:
All mammals have lungs.
All whales are mammals.
Therefore all whales have lungs.
II. Some valid arguments contain only false propositions—false premises and
a false conclusion:
All four-legged creatures have wings.
All spiders have exactly four legs.
Therefore all spiders have wings.
This argument is valid because, if its premises were true, its conclusion
would have to be true also—even though we know that in fact both
the premises and the conclusion of this argument are false.
III. Some invalid arguments contain only true propositions—all their premises
are true, and their conclusions are true as well:
If I owned all the gold in Fort Knox, then I would be wealthy.
I do not own all the gold in Fort Knox.
Therefore I am not wealthy.
The true conclusion of this argument does not follow from its true
premises. This will be seen more clearly when the immediately following
illustration is considered.
IV. Some invalid arguments contain only true premises and have a false conclusion.
This is illustrated by an argument exactly like the previous one
(III) in form, changed only enough to make the conclusion false.
If Bill Gates owned all the gold in Fort Knox, then Bill Gates would be wealthy.
Bill Gates does not own all the gold in Fort Knox.
Therefore Bill Gates is not wealthy.
The premises of this argument are true, but its conclusion is false.
Such an argument cannot be valid because it is impossible for the premises
of a valid argument to be true and its conclusion to be false.
V. Some valid arguments have false premises and a true conclusion:
All fishes are mammals.
All whales are fishes.
Therefore all whales are mammals.
The conclusion of this argument is true, as we know; moreover, it
may be validly inferred from these two premises, both of which are
wildly false.
VI. Some invalid arguments also have false premises and a true conclusion:
All mammals have wings.
All whales have wings.
Therefore all whales are mammals.
From Examples V and VI taken together, it is clear that we cannot
tell from the fact that an argument has false premises and a true conclusion
whether it is valid or invalid.
VII. Some invalid arguments, of course, contain all false propositions—false
premises and a false conclusion:
All mammals have wings.
All whales have wings.
Therefore all mammals are whales.
These seven examples make it clear that there are valid arguments with false conclusions
(Example II), as well as invalid arguments with true conclusions (ExamplesIII and VI). Hence it
is clear that the truth or falsity of an argument’s conclusion does not by itself determine the
validity or invalidity of that argument. Moreover, the fact that an argument is valid does not
guarantee the truth of its conclusion (ExampleII). Invalid arguments can have every possible
combination of true and false premises and conclusions.
Invalid Arguments
True Conclusion False Conclusion
If an argument is valid and its premises are true, we may be certain that its conclusion is true
also. To put it another way: If an argument is valid and its conclusion is false, not all of its
premises can be true. Some perfectly valid arguments do have false conclusions, but any such
argument must have at least one false premise. When an argument is valid and all of its
premises are true, we call it sound. The conclusion of a sound argument obviously must be
true—and only a sound argument can establish the truth of its conclusion. If a deductive
argument is not sound—that is, if the argument is not valid or if not all of its premises are true—
it fails to establish the truth of its conclusion even if in fact the conclusion is true. To test the
truth or falsehood of premises is the task of science in general, because premises may deal with
any subject matter at all. The logician is not (professionally)interested in the truth or falsehood of
propositions so much as in the logical relations between them. By logical relations between
propositions we mean those relations that determine the correctness or incorrectness of the
arguments in which they occur.
The task of determining the correctness or incorrectness of arguments falls squarely within the
province of logic. The logician is interested in the correctness even of arguments whose
premises may be false. Why do we not confine ourselves to arguments with true premises,
ignoring all others? Because the correctness of arguments whose premises are not known to be
true may be of great importance. In science, for example, we verify theoriesby deducing testable
consequences from uncertain theoretical premises—but we cannot know beforehand which
theories are true. In everyday life also, we must often choose between alternative courses of
action, first seeking to deduce the consequences of each. To avoid deceiving ourselves, we
must reason correctly about the consequences of the alternatives, taking each as a premise. If
we were interested only in arguments with true premises, we would not know which set of
consequences to trace out until we knew which of the alternative premises was true. But if we
knew which of the alternative premises was true, we would not need to reason about it at all,
because our purpose was to help us decide which alternative premise to make true. To confine
our attention to arguments with premises known to be true would therefore be self-defeating.
Source: Introduction to Logic
Irving Copi
Carl Cohen
Kenneth McMahon
14th edition
Exercise 2.1
For each of the argument descriptions provided below, construct a deductive argument
(on any subject of your choosing) having only two premises.
1. A valid argument with one true premise, one false premise, and a false conclusion
2. A valid argument with one true premise, one false premise, and a true conclusion
3. An invalid argument with two true premises and a false conclusion
4. An invalid argument with two true premises and a true conclusion
5. A valid argument with two false premises and a true conclusion
6. An invalid argument with two false premises and a true conclusion
7. An invalid argument with one true premise, one false premise, and a true conclusion
8. A valid argument with two true premises and a true conclusion
Arguments and Explanation
3 Hours
a) Define and identify arguments.
b) Differentiate arguments from explanation..
c) Apply the different techniques in recognizing arguments.
READINGS AND VIDEOS (Please see the digital copies of the materials.)
Reading 3.1 Van Cleave, M. (2016). Introduction to Logic and Critical Thinking. Retrieved from
Reading 3.2
Copi, I., Cohen, C & McMahon, K. (2014). Introduction to Logic Fourteenth
Edition. London: Pearson Education Limited
Video 3.1
Arguments vs Explanation in https://www.youtube.com/watch?v=lEWTwbSRsaw
LECTURES (Please refer to the Powerpoint presentations)
Answer Exercise 3.1 and 3.2 (Write your answer in a separate sheet of paper)
Introduction to Logic and Critical Thinking
Matthew J. Van Cleave
3. Arguments and Explanation
3.1 What is an argument?
Both logic and critical thinking centrally involve the analysis and assessment of arguments.
“Argument” is a word that has multiple distinct meanings, so it is important to be clear from the
start about the sense of the word that is relevant to the study of logic. In one sense of the word,
an argument is a heated exchange of differing views as in the following:
Sally: Abortion is morally wrong and those who think otherwise are seeking to justify murder!
Bob: Abortion is not morally wrong and those who think so are right-wing bigots who are
seeking to impose their narrow-minded views on all the rest of us!
Sally and Bob are having an argument in this exchange. That is, they are each expressing
conflicting views in a heated manner. However, that is not the sense of “argument” with which
logic is concerned. Logic concerns a different sense of the word “argument.” An argument, in
this sense, is a reason for thinking that a statement, claim or idea is true. For example:
Sally: Abortion is morally wrong because it is wrong to take the life of an innocent human being,
and a fetus is an innocent human being. In this example Sally has given an argument against
the moral permissibility of abortion. That is, she has given us a reason for thinking that abortion
is morally wrong. The conclusion of the argument is the first four words, “abortion is morally
wrong.” But whereas in the first example Sally was simply asserting that abortion is wrong (and
then trying to put down those who support it), in this example she is offering a reason for why
abortion is wrong.
We can (and should) be more precise about our definition of an argument. But before we can do
that, we need to introduce some further terminology that we will use in our definition. As I’ve
already noted, the conclusion of Sally’s argument is that abortion is morally wrong. But the
reason for thinking the conclusion is true is what we call the premise. So we have two parts of
an argument: the premise and the conclusion. Typically, a conclusion will be supported by two
or more premises. Both premises and conclusions are statements. A statement is a type of
sentence that can be true or false and corresponds to the grammatical category of a
“declarative sentence.” For example, the sentence,The Nile is a river in northeastern Africa is a
statement. Why? Because it makes sense to inquire whether it is true or false. (In this case, it
happens to be true.) But a sentence is still a statement even if it is false. For example, the
sentence, The Yangtze is a river in Japan is still a statement; it is just a false statement (the
Yangtze River is in China). In contrast, none of the following sentences are statements:
Please help yourself to more casserole
Don’t tell your mother about the surprise
Do you like Vietnamese pho?
The reason that none of these sentences are statements is that it doesn’t make sense to ask
whether those sentences are true or false (rather, they are requestsor commands, and
questions, respectively).
So, to reiterate: all arguments are composed of premises and conclusions, which are both types
of statements. The premises of the argument provide a reason for thinking that the conclusion is
true. And arguments typically involve more than one premise. A standard way of capturing the
structure of an argument is by numbering the premises and conclusion. For example, recall
Sally’s argument against abortion:
Abortion is morally wrong because it is wrong to take the life of an
innocent human being, and a fetus is an innocent human being.
We could capture the structure of that argument like this:
1. It is morally wrong to take the life of an innocent human being
2. A fetus is an innocent human being
3. Therefore, abortion is morally wrong
By convention, the last numbered statement (also denoted by the “therefore”) is the conclusion
and the earlier numbered statements are the premises. This is what we call putting an argument
into standard argument form. We can now give a more precise definition of an argument. An
argument is a set of statements, some of which (the premises) attempt to provide a reason for
thinking that some other statement (the conclusion) is true. Although arguments are typically
given in order to convince or persuade someone of the conclusion, the argument itself is
independent of one’s attempt to use it to convince or persuade. For example, I have just given
you this argument not in an attempt to convince you that abortion is morally wrong, but as an
illustration of what an argument is.
3.2 Identifying arguments
The best way to identify whether an argument is present is to ask whether there is a statement
that someone is trying to establish as true by basing it on some other statement. If so, then
there is an argument present. If not, then there isn’t. Another thing that can help in identifying
arguments is knowing certain key words or phrases that are premise indicators or conclusion
indicators. Forexample, recall Sally’s abortion argument:
Abortion is morally wrong because it is wrong to take the life of an innocent human
being, and a fetus is an innocent human being.
The word “because” here is a premise indicator. That is, “because” indicates that what follows is
a reason for thinking that abortion is morally wrong. Here is another example:
I know that the student plagiarized since I found the exact same sentences on a website
and the website was published more than a year before the student wrote the paper.
In this example, the word “since” is a premise indicator because what follows it is a statement
that is clearly intended to be a reason for thinking that thestudent plagiarized (i.e., a premise).
Notice that in these two cases, the premise indicators “because” and “since” are
interchangeable: I could have used “because” in place of “since” or “since” in the place of
“because” and the meaning of the sentences would have been the same. In addition to premise
indicators, there are also conclusion indicators. Conclusion indicators mark that what follows is
the conclusion of an argument. For example,
Bob-the-arsonist has been dead for a year, so Bob-the-arsonist didn’t set the fire at the
East Lansing Starbucks last week.
In this example, the word “so” is a conclusion indicator because what follows it is a statement
that someone is trying to establish as true (i.e., a conclusion).
Here is another example of a conclusion indicator:
A poll administered by Gallup (a respected polling company) showed candidate x to be
substantially behind candidate y with only a week left before the vote, therefore
candidate y will probably not win the election.
In this example, the word “therefore” is a conclusion indicator because what follows it is a
statement that someone is trying to establish as true (i.e., a conclusion). As before, in both of
these cases the conclusion indicators “so” and “therefore” are interchangeable: I could have
used “so” in place of “therefore” or “therefore” in the place of “so” and the meaning of the
sentences would have been the same.
a list of some common premise and conclusion indicators:
Premise indicators
given that
seeing that
for the reason that
is shown by the fact that
Conclusion indicators
implies that
it follows that
we may conclude that
Although these words and phrases can be used to identify the premises and conclusions of
arguments, they are not failsafe methods of doing so. Just because a sentence contains them
does not mean that you are dealing with an argument. This can easily be shown by examples
like these:
I have been running competitively since 1999.
I am so happy to have finally finished that class.
Although “since” can function as a premise indicator and although “so” can function as a
conclusion indicator, neither one is doing so here. This shows that you can’t simply mindlessly
use occurrences of these words in sentences to show that there is an argument being made.
Rather, we have to rely on our understanding of the English sentence in order to determine
whether an argument is being made or not. Thus, the best way to determine whether an
argument is present is by asking the question: Is there a statement that someone is trying to
establish as true or explain why it is true by basing it on some other statement? If so, then there
is an argument present. If not, then there isn’t. Notice that if we apply this method to the above
examples, we will see that there is no argument present because there is no statement that
someone is trying to establish as true by basing it on some other statement. For example, the
sentence “I have been running competitively since 1999” just contains one statement, not two.
But arguments always require at least two separate statements—one premise and one
conclusion, so it cannot possibly be an argument.
Another way of explaining why these occurrences of “so” and “since” do not indicate that an
argument is present is by noting that both premise indicators and conclusion indicators are,
grammatically, conjunctions. A grammatical conjunction is a word that connects two separate
statements. So, if a word or term is truly being used as a premise or conclusion indicator, it must
connect two separate statements. Thus, if “since” were really functioning as a premise indicator
in the above example then what followed it would be a statement. But “1999” is not a statement
at all. Likewise, in the second example “so” is not being used as a conclusion indicator because
it is not conjoining two separate statements. Rather, it is being used to modify the extent of
“happy.” In contrast, if I were to say “Tom was sleeping, so he couldn’t have answered the
phone,” then “so” is being used as a conclusion indicator. In this case, there are clearly two
separate statements (“Tom was sleeping” and “Tom couldn’t have answered the phone”) and
one is being used as the basis for thinking that the other is true.
If there is any doubt about whether a word is truly a premise/conclusion indicator or not, you can
use the substitution test. Simply substitute another word or phrase from the list of premise
indicators or conclusion indicators and see if the resulting sentence still makes sense. If it does,
then you are probably dealing with an argument. If it doesn’t, then you probably aren’t. For
example, we can substitute “it follows that” for “so” in the Bob-the-arsonist example:
Bob-the-arsonist has been dead for a year, it follows that Bob-the-arsonist didn’t set the
fire at the East Lansing Starbucks last week.
However, we cannot substitute “because” for “so” in the so-happy-I-finished that-class example:
I am because happy to have finally finished that class. Obviously, in the latter case the
substitution of one conclusion indicator for another makes the sentence meaningless, which
means that the “so” that occurred originally wasn’t functioning as a conclusion indicator.
3.3 Arguments vs. explanations
So far I have defined arguments in terms of premises and conclusions, where the premises are
supposed to provide a reason (support, evidence) for accepting the conclusion. Many times the
goal of giving an argument is simply to establish that the conclusion is true. For example, when I
am trying to convince someone that obesity rates are rising in the U.S. I may cite evidence such
as studies from the Center for Disease Control (CDC) and the National Institute of Health (NIH).
The studies I cite would function as premises for the conclusion that obesity rates are rising. For
We know that obesity is on the rise in the U.S. because multiple studies carried out by
the CDC and NIH have consistently shown a rise in obesity over the last four decades.
We could put this simple argument into standard form like this:
1. Multiple studies by the CDC and NIH have consistently shown a rise in
obesity over the last four decades.
2. Therefore, obesity is on the rise in the U.S.
The standard form argument clearly distinguishes the premise from the conclusion and shows
how the conclusion is supposed to be supported by the evidence offered in the premise. Again,
the goal of this simple argument would be to convince someone that the conclusion is true.
However, sometimes we already know that a statement or claim is true and we are trying to
establish why it is true rather than that it is true. An argument that attempts to show why its
conclusion is true is an explanation. Contrast the previous example with the following:
The reason that the rate of obesity is on the rise in the U.S. is that the foods we most
often consume over the past four decades have increasingly contained high levels of
sugar and low levels of dietary fiber. Since eating foods high in sugar and low in fiber
triggers the insulin system to start storing those calories as fat, it follows that people who
consume foods high in sugar and low in fiber will tend to store more of the calories
consumed as fat.
This passage gives an explanation for why obesity is on the rise in the U.S. Unlike the earlier
example, here it is taken for granted that obesity is on the rise in the U.S. That is the claim
whose truth we are trying to explain. We can put the obesity explanation into standard form just
like any other argument. In order to do this, I will make some paraphrases of the premises and
conclusion of the argument.
1. Over the past four decades, Americans have increasingly consumed
foods high in sugar and low in fiber.
2. Consuming foods high in sugar and low in fat triggers the insulin
system to start storing those calories as fat.
3. When people store more calories as fat, they tend to become obese.
4. Therefore, the rate of obesity is on the rise in the U.S.
Notice that in this explanation the premises (1-3) attempt to give a reason for why the
conclusion is true, rather than a reason for thinking that the conclusion is true. That is, in an
explanation we assume that what we are trying to explain (i.e., the conclusion) is true. In this
case, the premises are supposed to show why we should expect or predict that the conclusion
is true. Explanations often give us an understanding of why the conclusion is true. We can think
of explanations as a type of argument, we just have to distinguish two different types of
argument: those that attempt to establish that their conclusion is true (arguments), and those
that attempt to establish why their conclusion is true (explanations).
Introduction to Logic and Critical Thinking
Matthew J. Van Cleave
Exercise 3.1 : Which of the following are arguments? If it is an argument, identify the conclusion
of the argument.
1. The woman in the hat is not a witch since witches have long noses and she doesn’t have
a long nose.
Argument, Conclusion - The woman in the hat is not a witch the other two are the premises
that supports the conclusion.
2. I have been wrangling cattle since before you were old enough to tie your own shoes.
3. Albert is angry with me so he probably won’t be willing to help me wash the dishes.
4. First I washed the dishes and then I dried them.
5. If the road wasn’t icy, the car wouldn’t have slid off the turn.
6. Albert isn’t a fireman and he isn’t a fisherman either.
7. Are you seeing that rhinoceros over there? It is huge!
8. The fact that obesity has become a problem in the U.S. is shown by the fact that obesity
rates have risen significantly over the past four decades.
9. Bob showed me a graph with the rising obesity rates and I was very surprised to see
how much they’ve risen.
10. Albert isn’t a fireman because Albert is a Greyhound, which is a kind of dog, and dogs
can’t be firemen.
11. Charlie and Violet are dogs and since dogs don’t sweat, it is obvious that Charlie and
Violet don’t sweat.
12. The reason I forgot to lock the door is that I was distracted by the clown riding a unicycle
down our street while singing Lynyrd Skynyrd’s “Simple Man.”
13. What Bob told you is not the real reason that he missed his plane to Denver.
14. Samsung stole some of Apple’s patents for their smartphones, so Apple stole some of
Samsung’s patents back in retaliation.
15. No one who has ever gotten frostbite while climbing K2 has survived to tell about it,
therefore no one ever will.
Exercise 3.2: Which of the following is an explanation and which is an argument? Identify the
main conclusion of each argument or explanation. (Remember if the premise(s) seems to be
establishing that the conclusion is true, it is an argument, but if the premise(s) seems to be
establishing why the conclusion is true, it is an explanation.)
1. Wanda rode the bus today because her car was in the shop.
2. Since Wanda doesn’t have enough money in her bank account, she has not yet picked
up her car from the shop.
3. Either Bob or Henry rode the bus to work today. But it wasn’t Henry because I saw him
riding his bike to work. Therefore, it was Bob.
4. It can’t be snowing right now since it only snows when it is 32 degrees or below and
right now it is 40 degrees.
5. The reason some people with schizophrenia hear voices in their head is that the
cognitive mechanism that monitors their own self-talk is malfunctioning and they
attribute their own self-talk to some external source.
6. Fracking should be allowed because, although it does involve some environmental risk,
it reduces our dependence on foreign oil and there is much greater harm to the
environment due to foreign oil drilling than there is due to fracking.
7. Wanda could not have ridden the bus today because today is a citywide holiday and the
bus service is not operating.
8. The Tigers lost their star pitcher due to injury over the weekend, therefore the Tigers will
not win their game against the Pirates.
9. No one living in Pompeii could have escaped before the lava from Mt. Vesuvius hit. The
reason is simple: the lava was flowing too fast and there was nowhere to go to escape it
in time.
10. The reason people’s allergies worsen when they move to Cincinnati is that the pollen
count in Cincinnati is higher than almost anywhere else in the surrounding area.
Uses and Function of Language
3 Hours
d) Distinguish the different functions of language.
e) Explore ways in which sentences/passage serve multiple functions.
f) Differentiate linguistic form from language functions
g) Explore the many uses and forms of language.
READINGS AND VIDEOS (Please see the digital copies of the materials.)
Reading 4.1 Hall, R. Logic: A Brief Introduction. Retrieved from
Reading 4.2
Copi, I., Cohen, C & McMahon, K. (2014). Introduction to Logic Fourteenth
Edition. London: Pearson Education Limited
Video 4.1
Functions of Language in https://www.youtube.com/watch?v=XsWjk020ag0
LECTURES (Please refer to the Powerpoint presentations)
Answer Exercise 4.1 (Write your answer in a separate sheet of paper)
4.0 Uses and Functions of Language
Source: Introduction to Logic
Irving Copi
Carl Cohen
Kenneth McMahon
14th edition
A mixture of functions is a natural feature of almost all our uses of language.We can see this in
our own speech and writing. Emotive language may be used toadvance our purposes in
directing others: “That conduct is utterly disgusting!”says parent to child, expressing an attitude,
seeking to direct behavior, and (with those same words) probably reporting a fact. We may say
that language has three major functions:
1. Informative
2. Expressive
3. Directive
To these we may add less common types of use:
4. Ceremonial language (as when we say, “How do you do?” upon being introduced to a
stranger), in which words may combine expressive and other functions; and
5. Performative language (as when we say, “I apologize for my foolishremark”), in which words
themselves serve, when spoken or written, to perform the function they announce. Other
examples are “I congratulateyou, . . .” “I accept your offer, . . .” and “I promise you that. . .
”Logicians are chiefly concerned with language used informatively–affirming or denying
propositions, formulating or evaluating arguments, and so on. In reasoning it is this
informative function of language that is the principal concern.
The uses of language must be distinguished from the forms of language. The several uses
of language (informative, expressive, etc.) are implemented using different forms. Sentences
(the units of our language that express complete thoughts) may be declarative in form, or
exclamatory, or imperative, or interrogative.
In summary, the principal uses of language are three: informative, expressive, and directive.
The grammatical forms of language are essentially four: declarative, interrogative, imperative,
and exclamatory. There is no sure connection between the grammatical form of a passage and
the use or uses its author intends.
Language that serves any one of the three principal functions may take any one of the four
grammatical forms.
Source: Logic : A Brief Introduction
Ronald Hall, Stetson University
These broad categories of non-informative uses language will include the following:
Ritual (in Copi’s book – Ceremonial)
Identifying these different uses is often not an easy matter. Skill in doing so will come only with
attentive practice. We must develop an ear, as it were, for picking out which use is most
prominently involved in the passages we are interpreting. Recognizing the primary use that a
particular sentence is intended to have requires close attention to context and content. And
again, developing this skill in recognizing differences in languages uses will take practice.
• The Expressive Use
I have tried to make it clear that not every sentence has an informative use. Indeed, we
quite often use sentences for purposes other than providing information. A very common
example of such a use of language is what we will call its expressive function. Expressive
Directive Performative Ritual .3 Consider this example: Someone says, “I am so sorry your cat
is ill. Please accept my sympathy." It should be clear to you that the primary function of these
sentences is not to inform someone of something. There is little, if any, intention to inform,
despite the fact that some information is conveyed (information about the health of the cat, the
psychological state of the speaker, and so forth). Rather, in this case, the speaker’s primary
interest is not to inform, but to express his or her emotions or feelings. Because such sentences
are not used primarily to inform and as such have no content that can be evaluated as true or
false, such sentences would not ordinarily figure in the construction of arguments.
One caution: Don’t be misled by the use of “express” here, for while all uses of language
may be considered “expressions”, we are using the term “expressive” in this context as roughly
equivalent to the ideas of venting, revealing, manifesting, evoking, or provoking feelings. We
use language in this expressive function when we are trying to vent our own emotions or when
we are trying to evoke emotions in our audience, or both.
As an example of the use of language both to vent and to evoke feelings, consider this:
“OMG!” “How vicious can a person be?
• The Directive Use
Here we have yet another task that sentences are used to accomplish. In this case, the
task is to get someone to do, or not to do some action. Suppose someone says: “Take your cat
to the veterinarian!” It would be a mistake to think that this person was trying merely to convey
information or to express his or her feelings. Rather, in this case the speaker’s primary intention
is to provoke action in his or her audience; as we might put it, the speaker here is issuing a
command or an imperative. We call this the directive language use. The speaker is not
providing information but has issued a directive that is neither true nor false.
Accordingly, directives do not ordinarily form a part of arguments. However, even though
such directives are neither true nor false, it does make sense to appraise them as, for example,
appropriate or inappropriate, warranted or unwarranted, loving or hateful.
Another caution: There is a difference between the sentence “Take your cat to the
veterinarian!” and “You ought to take your cat to the veterinarian.” The latter sentence may
express some claim that is either true or false. Consider this example: Someone notices that
your cat has a runny nose and watery eyes. He says to you, “These are symptoms of feline
upper respiratory infection. This is a serious feline illness. A veterinarian may be able to help
your cat recover. You ought to take the cat to the veterinarian.” Now we have an argument. The
conclusion of this argument is intended to cause some action, but also to inform the cat owner
of some course of action that the facts call for. Such arguments have often been called practical
syllogisms or practical arguments, since their conclusions do serve the practical function of
informing us of what course of action we ought to take.
What this example also makes clear is that one and the same sentence can involve
more than one language use. Indeed, more than two functions can be present. With a certain
urgency of voice, I may well add the expressive function to my claim and directive: “Take your
cat to the veterinarian right now!” Because language uses can be combined in this way, I have
made a point to refer to the “the primary intention” of a speaker or writer in determining the
primary language use at play in the particular passage under investigation. Accordingly, we will
identify the language use of a sentence as informative, expressive, or directive if that function is
the primary one. Making this identification does not preclude acknowledging that other functions
may also be at play in the passage that is being interpreted.
• The Performative Use
It was J. L. Austin who helped to bring our attention to the performative language use.
As he pointed out, in successful performative utterances we accomplish an action in and
through the saying of certain words. Here we must not be confused by the fact that all language
uses involve doing things with words, for example, informing, directing, venting. The
performative language use is a special case of doing things with words. In the case of the
performative language use, some particular action is accomplished in and by saying certain
things in certain circumstances.
Consider the act of making a bet or a promise. The way that we engage in these actions
is by saying certain things in certain circumstances with the appropriate sincerity, etc. The way
that I engage in the act of betting you something is by saying to you, “I bet you…” If you agree,
and you are competent, sincere, and so forth, the bet is on. Similarly, the way that I promise you
something is by saying certain words to you with the appropriate earnestness and with your
willingness to trust me. Usually, I say, “I promise…”
While such performative utterances are neither true nor false, and accordingly cannot be
used to construct arguments, they certainly can be assessed as being successful or not. For
example, just saying the words, “I bet you,” is not sufficient for engaging in the act of betting, for
among other things, you must agree to enter the wager. Lots of things can go wrong. If you do
not agree, my attempt to bet you something fails: I said the words, “I bet” but I did not bet you.
• The Ritual Use
The ritual language use is very closely related to the performative function. As in the
case of the performative, the ritual function may involve the accomplishment of some deed by
the use of words. For example, in saying the words of the pledge of allegiance to the flag, we
may well be doing something, namely, pledging our allegiance to our country. But we need not
be doing this. Indeed we might just be going through the motions of a ritual. This use of
language marks it off from the performative in an important way. We put this difference as
follows: unlike its performative cousin, in its ritual function, words are not used to bring
something about.
There are countless such ritual uses of language, for example, saying a prayer, saying
"Good-bye," saying "Happy Birthday," toasting newlyweds, and so forth. Normally, when we say
to someone “How ya doing?” this is not an inquiry into his or her well-being, but a ritual greeting.
We engage in the act of greeting someone by saying these words. The words, we might say,
constitute a kind of handy formula for greetings. Of course we can greet each other differently,
with different words, but when we adopt commonly accepted formulas, we are using language in
its ritual function. Perhaps you can think of some further examples of this ritual use of language.
Source: Introduction to Logic
Irving Copi
Carl Cohen
Kenneth McMahon
14th edition
Exercise 4.1
A. Which of the various functions of language are exemplified by each of the following
1. Check the box on line 6a unless your parent (or someone else) can claim
you as a dependent on his or her tax return.
—U.S. Internal Revenue Service, “Instructions,”Form 1040, 2006
Answer: Directive
2. ‘Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.
—Lewis Carroll, Through the Looking-Glass, 1871
3. What traveler among the ruins of Carthage, of Palmyra, Persepolis, or Rome, has not been
stimulated to reflections on the transiency of kingdoms and men, and to sadness at the thought
of a vigorous and rich life now departed . . . ?
—G. W. F. Hegel, Lectures on the Philosophy of History, 1823
4. Moving due south from the center of Detroit, the first foreign country one encounters is not
Cuba, nor is it Honduras or Nicaragua or any other Latin American nation; it is Canada.
5. I was a child and she was a child,
In this kingdom by the sea,
But we loved with a love that was more than love—
I and my Annabel Lee—
—Edgar Allan Poe, “Annabel Lee,” 1849
6. Reject the weakness of missionaries who teach neither love nor brotherhood, but chiefly the
virtues of private profit from capital, stolen from your land and labor. Africa awake, put on the
beautiful robes of Pan-African Socialism!
—W. E. B. Dubois, “Pan-Africa,” 1958.
7. If I speak in the tongues of men and of angels, but have not love, I am a noisy gong or a
clanging cymbal.
—I Cor. 13:1
8. I herewith notify you that at this date and through this document I resign the office of
President of the Republic to which I was elected.
—President Fernando Collor De Mello, in a letter to the Senate of Brazil, 29 December 1992
9. American life is a powerful solvent. It seems to neutralize every intellectual element, however
tough and alien it may be, and to fuse it in the native good will, complacency, thoughtlessness,
and optimism.
—George Santayana, Character and Opinion in the United States, 1934
10. The easternmost point of land in the United States—as well as the northernmost point and
the westernmost point—is in Alaska.
B. What language functions are most probably intended to be served by each of the following
1. There is no caste here. Our Constitution is color-blind, and neither knows nor tolerates
among citizens. In respect of civil rights, allcitizens are equal before the law. The
humblest is the peer of the most powerful.
—Justice John Harlan, dissenting in Plessy v. Ferguson, 163 U.S. 537, 1896
Answer: Informative. The purpose of the passage is to inform that the United States permits no
system of caste or preference.
2. Judges do not know how to rehabilitate criminals—because no one knows.
—Andrew Von Hirsch, Doing Justice—The Choice of Punishment
(New York: Hill & Wang, 1976)
3. When tillage begins, other arts follow. The farmers therefore are the founders of human
—Daniel Webster, “On Agriculture,” 1840
4. The only thing necessary for the triumph of evil is for good men to do
—Edmund Burke, letter to William Smith, 1795
5. They have no lawyers among them, for they consider them as a sort of
people whose profession it is to disguise matters.
—Sir Thomas More, Utopia, 1516Answer: The primary function of this passage is expressive,
evoking the reader’s antipathy toward lawyers
6. White society is deeply implicated in the ghetto. White institutions created it, white institutions
maintain it, and white society condones it.
—The National Commission on Civil Disorders (Kerner Commission), 1968
7. The bad workmen who form the majority of the operatives in many branches of industry are
decidedly of the opinion that bad workmen ought to receive the same wages as good.
—John Stuart Mill, On Liberty, 1859
Disputes and Definition
6 Hours
a) Distinguish the different kinds of definition and their uses.
b) Analyze statements that contain different kinds of disputes.
c) Differentiate the kinds of disputes
d) Apply the rules of definition.
READINGS AND VIDEOS (Please see the digital copies of the materials.)
Reading 5.1 Hall, R. Logic: A Brief Introduction. Retrieved from
Reading 5.2
Copi, I., Cohen, C & McMahon, K. (2014). Introduction to Logic Fourteenth
Edition. London: Pearson Education Limited
Video 5.1
Video 5.2
Types of disputes in https://www.youtube.com/watch?v=VIMpIOMZcDQ
Definition in https://www.youtube.com/watch?v=gbbetx-kkpw
LECTURES (Please refer to the Powerpoint presentations)
Answer Exercise 5.1 and 5.2 (Write your answer in a separate sheet of paper)
Source: Introduction to Logic
Irving Copi
Carl Cohen
Kenneth McMahon
14th edition
5.1 Disputes and Disagreements
Many disputes, whether about beliefs or about attitudes, are genuine. However, some disputes
are merely verbal, arising only as a result of linguistic misunderstanding. The terms used by the
disputing parties may have more than one meaning—they may be ambiguous—but such
ambiguity may be unrecognized by the disputing parties. To uncover and to resolve verbal
disagreements, ambiguities must be identified, and the alternative meanings of the critical terms
in the dispute must be distinguished and clarified. Disputes fall into three categories. The first is
the obviously genuine dispute. If Aroots for the Yankees, and B for the Red Sox, they are in
genuine disagreement, though they disagree mainly in attitude. If C believes that Miami is south
of Honolulu, and D denies this, they too are in genuine disagreement, but in thisdispute about
geographic facts a good map can settle the matter.
A second category is disputes in which the apparent conflict is not genuine and can be resolved
by coming to agreement about how some word or phrase is to be understood. These may be
called merely verbal disputes. F may hold that a tree falling in the wilderness with no person to
hear it creates no sound, while G insists that a sound really is produced by the falling tree. If a
“sound” is the outcome of a human auditory sensation, then F and G may agree that there was
none; or if a “sound” is simply what is produced by vibrations in the air, then they may agree that
a sound was indeed produced. Getting clear about what is meant by “sound” will resolve the
disagreement, which was no more than verbal.
A third category, more slippery, is disputes that are apparently verbal but really genuine. A
misunderstanding about the use of terms may be involved in such cases, but when that
misunderstanding has been cleared up there remains a disagreement that goes beyond the
meanings of the words. For example, should a film in which explicit sexual activity is depicted be
considered “pornography”? J holds that its explicitness makes it pornographic and offensive; K
holds that its beauty and sensitivity make it art and not pornography. Plainly they disagree about
what “pornography” means—but after that ambiguity has been exposed, it is likely that the
parties will still disagree in their judgment of that film. Whether the film is “pornographic” may be
settled by a definition of that term, but a deeper disagreement is then likely to be exposed. The
word “pornographic” plainly carries pejorative associations. J, who finds the film objectionable,
understands the word “pornographic” in one way, while K, who approves of the film, uses the
word “pornographic” differently. Does the sexually explicit content of the film make it
objectionable and thus “pornographic”? J and K differ in their uses of the word, but for both of
them the emotional meaning of the word is very negative; and they also differ about the criteria
for the application of that negative word, “pornography.”
In summary, when confronting a dispute that arises in discourse, we must first ask whether
there is some ambiguity that can be eliminated by clarifying the alternative meanings in play. If
there is, then we must ask whether clearing up that linguistic issue will resolve the matter. If it
does, the dispute was indeed merely verbal. If it does not, the dispute was genuine, although it
may have appeared to be merely verbal.
Source: Introduction to Logic
Irving Copi
Carl Cohen
Kenneth McMahon
14th edition
Exercise 5.1
Discuss each of the following disputes. If the dispute is obviously genuine, indicate each of the
disputers’ positions with respect to the proposition at issue. If it is merely verbal, resolve it by
explaining the different senses attached by the disputers to the key word or phrase that is used
ambiguously. If it is an apparently verbal dispute that is really genuine, locate the ambiguity and
explain the real disagreement involved.
1. Daye: Pete Rose was the greatest hitter in the history of baseball. He got more hits than
any other major-league player.
Knight: No, Barry Bonds deserves that title. He hit more home runs than any other
major-league player.
Answer: This is a genuine disagreement on belief regarding the greatest hitter in the
history of baseball and this can easily be resolved by making an appeal to facts.
2. Daye: Despite their great age, the plays of Sophocles are enormously relevant today.
They deal with eternally recurring problems and values such as love and sacrifice, the
conflict of generations, life and death—as central today as they were over two thousand
years ago.
Knight: I don’t agree with you at all. Sophocles has nothing to say about the pressing
and immediate issues of our time: inflation, unemployment, the population explosion,
the energy crisis. His plays have no relevance to today.
3. Daye: Bob Jones is certainly a wonderful father to his children. He provides a beautiful
home in a fine neighborhood, buys them everything they need or want, and has made
ample provision for their education.
Knight: I don’t think Bob Jones is a good father at all. He is so busy getting and
spending that he has no time to be with his children. They hardly know him except as
somebody who pays the bills.
4. Daye: Amalgamated General Corporation’s earnings were higher than ever last year, I
see by reading their annual report.
Knight: No, their earnings were really much lower than in the preceding year, and they
have been cited by the Securities and Exchange Commission for issuing a false and
misleading report.
5. Daye: Business continues to be good for National Conglomerate, Inc. Their sales so far
this year are 25 percent higher than they were at this time last year.
Knight: No, their business is not so good now. Their profits so far this year are 30
percent lower than they were last year at this time.
6. Daye: Ann is an excellent student. She takes a lively interest in everything and asks very
intelligent questions in class.
Knight: Ann is one of the worst students I’ve ever seen. She never gets her
assignments in on time.
Logic: A Brief Introduction
Ronald L. Hall, Stetson University
5.2 Definitions
The best way to avoid verbal disagreements in belief is to define one’s terms very clearly. To
do this, we need to talk about what makes for a good and clear definition, that is, a definition
that could find its way into a dictionary and be accepted into common usage. Those terms that
find their way into standard dictionaries are called lexical definitions. However, before can
provide a clear definition of a lexical definition and discuss how they are formulated, evolve, and
gain acceptance, we need to take a moment to point out that there are some definitions that are
not usually included in dictionaries. There are four such non-lexical kinds of definition: (1.
Stipulative; (2) Precising; (3) Theoretical; (4) Emotive.
1. Stipulative Definitions: In many cases, a discussion can be advanced when all of the
parties in it agree to use a particular term in the same way throughout the discussion. Suppose,
for example that we agree to use “murder” in only its legal sense, or even more particularly in
the legal sense of the term that is found in the legal definition of “first degree murder.” That is,
we may, for the sake of a particular discussion agree to use “murder” to mean only those cases
in which there is a premeditated intention to murder. In this case, killing in self-defense, or
manslaughter would not count as "murder." Since defining terms in this way depends on
agreement, there is no way for such definitions to be mistaken or incorrect. In fact, there is
nothing that keeps us from agreeing to use the word “cold” to mean “hot” if we agree to do so.
The advantage of stipulating definitions is that it reduces ambiguity. This is especially useful
when terms with many and varied meanings are at play in the discussion. Just keep in mind that
stipulative definitions are neither true nor false and you will not find them in a dictionary.
2. Precising Definitions: In some cases, we need to use a particular term in a way that is more
precise than what we might find in a dictionary. This need occurs, for example, in the writing of
legislation. Most bills in fact have a section in which some of the important terms in the would-be
law are given precise definitions. Suppose that we are drafting a Scenic Rivers Bill. We want to
protect a green corridor on either side of a certain river. We propose that a corridor of 1000 feet
on either side of the river be protected from development. The problem with this is that some
riverbanks, especially in low country, are constantly shifting. So we give “riverbank” a precising
definition as “the mean high water mark.” In this case this precise definition is also a stipulative
definition since it is introduced with the understanding that all the parties will agree to use the
term “riverbank” in just this precise way. Such a move saves much potential confusion. Again,
such definitions are not to be found in dictionaries.
3. Theoretical Definitions: Sometimes it is helpful to formulate definitions to fit theoretical
discussions. In discussions of this kind we may find it useful to define "water" as H 2 O, or
"energy" as MC2 . Sometimes we will have to stipulate such theoretical definitions. In addition,
often the purpose of such a stipulation is to make a particular term more precise. Sometimes we
find theoretical definitions included in dictionaries but most often not.
4. Emotive Definitions: Finally, we may define terms emotively. We do this when we want to
influence others. If I define abortion as “murder,” I am clearly trying to get my audience to have
a negative attitude toward abortion. Earlier we saw that many define “argument” as a fight. Such
a definition evokes negative feelings toward arguments. Similarly, if we define "logical" as “cold
and calculating” we are again trying to evoke negative feelings. If, on the other hand, we define
"logic" as mankind’s highest achievement, or define "rational thinking" as economic cost-benefit
analysis, we are certainly trying to produce a positive attitude toward logic and economic costbenefit analysis. Recently we have heard environmentalists referred to as “green Nazis.” No
doubt about what this definition is designed to provoke.
5.2.1Lexical Definitions
For the most part when we think of definitions we are thinking of lexical definitions.
Unlike stipulative definitions, these definitions can be correct or incorrect. The fact is, we can,
and we often do, misuse words. Most of us have to consult a dictionary from time to time.
Extension and Intension
Now we must ask, how are lexical definitions formulated? Lexical definitions are
assignments of meanings to terms that are primarily based on etymology and common usage.
But we must note here that there are two kinds of meaning that can be assigned to terms; they
are: extensive and intensive meaning. The extension of a term consists of all of the objects
named, or referred to, or denoted by that term. The intension (with an “s”) of a term
consists of the common attributes of the objects referred to by the term.
The extension of a term is sometimes called its denotative meaning and the intension of a term
is sometimes called its connotative meaning. The extension of the term “human being” consists
of the entire collection of human beings, dead and alive. Being a language using rational and
moral agent is part of the intension of the term “human being.” The extension of a term is related
to its intension. Obviously, the intension of a term determines its extension but not vice versa. If
we add the term “living” to the term “human being” we increase its intension (we add an
attribute) and thereby decrease its extension (we decrease the number of objects it refers to.)
Sometimes there is no variation when we increase the intension of term. For example, by
adding “mortal” to “living human being,” we increase the intension of the term but the extension
remains the same. Accordingly, we adopt a simple rule: When the intension of a term causes a
variation in its extension that variation will be an inverse one.
Lexical definitions can be formulated relative to either the extension or intension of a
term. So let's consider definitions of both types.
• Extensive Definitions
To define a term by reference to an object in its extension is to define it by example. If
we want to define “human being” we can say, "Joe, for example, is what I mean." As well, we
can define a term by example by simply pointing to an object in the extension of a term.
Conveying the meaning of a term by pointing with a gesture or with words, or with both, to an
example of one of the objects in its extension, is to give the term what is called an ostensive
• Intensive Definitions
Even though definitions by example are useful, this technique for defining terms has its
limitations. Suppose we want to define the term “brown” and we point to your brown hair. Now
suppose we want to define “hair,” how do we point just to your hair, or just to its color? And
there are other problems. Suppose that we want to define a term like “unicorn.” We can’t exactly
point to one, since no examples exist. We would not want to conclude from the fact that
“unicorn” has no extension that it has no meaning. This tells us that terms can have a meaning
even if their extension is empty.
These considerations lead us to think that lexical definitions that focus on intension have
advantages that make them more useful than lexical definitions that focus only on extension.
Defining terms intensively, however, is not without its own problems and limitations. First, we
must notice that what a term connotes can vary from individual to individual. For example, some
person may associate the term “river” with danger because of his or her experience of almost
drowning in one. For this person, we might say, "river" means (connotes) "danger." Moreover,
terms can have many attributes that are not commonly recognized, accepted, or used. It is
certainly true that rivers can be classified as geologically new or old. Ordinarily, however, the
geological age of a river does not seem like an essential attribute of the term.
When dictionaries formulate a lexical definition, they usually restrict the attributes of the
terms it defines to the ones that are commonly accepted as central to that term. Attributes that
are central to its ordinary use include things like “body of water” and “flowing.” Again, good
intensive definitions should avoid idiosyncratic (subjective) attributes, that is, attributes that
depend on the particular experience of a person; and they should also avoid some 6 attributes
that may objectively apply to a term (objective attributes) but are not central to its ordinary
meaning as it is commonly used. In contrast to both, dictionaries prefer lexical definitions that
define a term in a way that reflects the central attributes that are recognized in its ordinary
usage both currently and historically. We can call these commonly recognized connotations of a
term as its conventional attributes.
In sum then, dictionaries prefer intensive rather than extensive definitions.
Moreover, we must point out that there are three kinds of intensive definitions.
• Intensive Definitions with Synonyms
Sometimes it is effective to define terms intensively by providing synonyms. We
say, for example, that the term “cryptic” means “hidden.” Often this is an effective way to
clarify the meaning of a term. We call such clarifications synonymous definitions;
dictionaries make copious use of this technique. The fact is however, that synonymous
definitions are limited. In order for such definitions to work a term must have a synonym
whose meaning is known, and this is not always easy to find, if indeed there is one.
• Intensive Operational Definitions
A second kind of intensive definition is called an operational definition. We often
define terms intensively by referring to some observational effect that the term is
supposed to produce. I may, for example, define “good” in the phrase “a good tennis
shot” as "a shot that wins the point." While these definitions are sometimes helpful, they
also suffer from being too restrictive. In normal usage, we think that it is possible to
make a bad tennis shot (one with bad form, or a lucky miss-hit) that nevertheless wins
the point. Operational definitions do not always reflect normal usage. As such, they are
widely used in dictionaries.
• Intensive Genus Species Definitions
Fortunately, there is another technique for intensive definitions that avoids
these limitations. This is the technique of genus species definitions. Indeed, this
is the technique that is preferred by most logicians for it provides the clearest
definition, at least of general terms. It is sometimes difficult, however, to apply this
technique correctly. Lots can go wrong in our attempts to provide a genus species
definition. Before we say what some of these ways of going wrong are, we must say
something about the technique itself.
To define a term intensively by the genus species technique, we must first find a
general category (a genus, or class) of which the referent of the term we are defining is a
member. For example, if we are defining the term “human being” we determine that it is
a member of a genus or class. We want this class to be general enough but not too
general. In this case it is obvious that a good candidate here is the class “animal,” rather
than, say the class “living thing,” since plants would be included in that very broad
category. If the class is too general, it becomes more difficult to proceed to the second
step in this definition technique. What it is this step? Simply this: now we must go on to
say how this member of the class of animals is different from all of its other members.
That is, we must look for specific differences, differences that mark the way this term has
a use that is narrower than the genus term under which it fall. Such specific differences
are what make this kind of animal the particular species of the class of animal that it is.
For example, we might say, as Aristotle once did, that the human being is a “rational
It is easy to see how this technique can be expanded. We may define “triangle”
as a member of the class of plane geometrical figures that has an attribute that is its
specific difference from all other such figures, namely the attribute of having only three
connected sides and three angles. As well, we may define “raincoat” as a member of the
class “outer garments” and as being different from all other outer garments in being
“designed to provide protection from rain.”.
5.2.2 Recognizing Defective Definitions
Even though the genus species technique of formulating intensive definitions
gives us the most precise definitions of terms, it also has many ways of going wrong.
This fact, makes the effort to formulate such definitions very difficult. However, if we are
aware of the various ways that such definitions can go wrong, we will advance our goal
of avoiding ambiguities that can mislead us.
I might point out that even though the search for definitions that are as clear as
possible is required for the purposes of evaluating formal arguments in logic, we can
also appreciate a positive side of this difficulty. The fact is, our language is profoundly
complex and rich in its inherent ambiguity. When we are not doing logic, but simply
having conversations, or writing poetry or prose, the ambiguity of our words reveals a
depth of thought that may be eclipsed by logic’s search for definitions that are as
univocal as possible.
But our business in this course is logic. So we must try to eliminate
ambiguity as much as we can when it comes to formulating arguments and
evaluating them. The following are helpful guides in this process. They are defects in
genus species definitions that need to be avoided.
Genus Species definitions are defective if they are:
1. Too broad
2. Too narrow
3. Too broad and too narrow
4. Circular
5. Figurative Emotive
6. Accidental
7. Negative
8. Obscure
1. Too Broad: “Human beings are featherless bipeds.” The genus here is the class of
bipeds (things that walk on two feet.) The specific difference that is claimed to make
human beings different from other bipeds is that they are featherless. This definition fails
because it is TOO BROAD; it is too broad because it includes too much, for example, it
includes plucked chickens as human beings, which they obviously are not.
2. Too Narrow: "Human beings are the only animals that are accountable before the
law.” The genus here is animals. The specific difference that is claimed to make human
beings different from other animals is that they are accountable before the law. This
definition fails because it is TOO NARROW; it is too narrow because it excludes too
much, for example, it excludes children from being human beings, for clearly, if young
enough, they are not accountable before the law and yet they are surely human beings.
3. Too Broad and Too Narrow: “Human beings are the only animals that can
communicate.” The genus here is animals. The specific difference that is claimed to
make human beings different from other animals is that they communicate. This
definition fails because it is both TOO BROAD AND TOO NARROW; it is too broad
because it includes too much, for example, it includes dogs and cats; it is too narrow
because it excludes too much, for example human beings who are in deep comas.
4. Circular: “Human beings are the only animals that are essentially human.” The genus
here is the class of animals. The specific difference that is claimed to make human
beings different from other animals is that they are essentially human. This definition
fails because it is CIRCULAR; it is circular because there is no specific difference that is
cited to mark the difference between other animals in the genus, and the word being
defined is used in the definition itself. While it is sometimes useful to give synonymous
definitions, when one is attempting to give a genus species definition, it gets us nowhere
to define a term with other terms that are essentially equivalent to the term being
5. Figurative: “Human beings are thinking reeds.” The genus here is the class of
“reeds” (no doubt this is a figure for things that are fragile). The specific difference that is
claimed to make human beings different from other “reeds” is that they think. This
definition fails because it uses figures of speech, images, or metaphors, instead of the
essential attributes associated with a term. This definition fails because it is
FIGURATIVE; it is figurative because it does not aim to provide a literal definition.
6. Emotive: “Human beings are the only animals that are blights on the environment.”
The genus here is the class of animals. The specific difference that is claimed to make
human beings different from other animals is that they are 8 blights on the environment.
This definition fails because it is EMOTIVE; it is emotive since it attempts to arouse
emotions and feelings rather than provide a literal definition. In this example the intention
is to express a negative attitude toward human beings.
7. Accidental: “Human beings are the only animals that are inclined to appreciate
beautiful sunsets.” The genus here is the class of animals. The specific difference that is
claimed to make human beings different from other animals is that they are inclined to
appreciate beautiful sunsets. This definition fails because it is ACCIDENTAL; it is
accidental because it makes no attempt to define "human beings" in terms of its
conventional attributes. There are many attributes that qualify human beings, but a
definition of them should aim to specify the attributes that are commonly accepted as
essential to the term.
8. Negative: “Human beings are not gods.” The genus here is the class of beings. The
specific difference that is claimed to make human beings different from other beings is
that they are not gods. This definition fails because it is NEGATIVE; it is negative
because it defines a term by saying what it is not, rather than what it is. Knowing that
human beings are not gods does not get us very far in defining what they are.
9. Obscure: “Human beings are enigmas wrapped up in a conundrum.” The genus here
is the class of, well, what? It is not clear. It could be the class of things; but this would be
much too general. The specific difference claimed here is that human beings are
different from other things or animals insofar as they are enigmas wrapped up ina
conundrum. This definition fails because it is OBSCURE; it is obscure because it uses
language even less well known than that which is being defined. Indeed, we are left
more mystified than enlightened after being given this definition. We need to be as clear
as possible.
Source: Introduction to Logic
Irving Copi
Carl Cohen
Kenneth McMahon
14th edition
Exercise 5.2
A. Arrange each of the following groups of terms in order of increasing intension:
1. Animal, feline, lynx, mammal, vertebrate, wildcat.
Answer: Animal,vertebrae, mammal, feline, wildcat, lynx
2. Alcoholic beverage, beverage, champagne, fine white wine, white wine,
3. Athlete, ball player, baseball player, fielder, infielder, shortstop.
4. Cheese, dairy product, Limburger, milk derivative, soft cheese, strong
soft cheese.
5. Integer, number, positive integer, prime number, rational number, real
B. Divide the following list of terms into five groups of five terms each,
arranged in order of increasing intension:
Aquatic animal, beast of burden, beverage, brandy, cognac, domestic animal, filly, fish,
foal, game fish, horse, instrument, liquid, liquor, musical instrument, muskellunge,
parallelogram, pike, polygon, quadrilateral, rectangle, square, Stradivarius, string
instrument, violin.
C. Define the following terms by example, enumerating three examples for
each term:
1. actor
2. boxer
3. composer
4. vlogger
5. element
6. flower
7. general (officer)
8. president
9. inventor
10. poet
D. Identify and discuss the defects in definition in the following statements
1. A flower is a testimony that the world is designed for our enjoyment.
-Source: https://www.familyfriendpoems.com/poems/nature/flower/
This definition fails because it is EMOTIVE; it is emotive since it attempts to arouse emotions
and feelings rather than provide a literal definition.
2. Knowledge is true opinion.
—Plato, Theaetetus
3. Life is the art of drawing sufficient conclusions from insufficient
—Samuel Butler, Notebooks
4. “Base” means that which serves as a base.
—Ch’eng Wei-Shih Lun, quoted in Fung Yu-Lan, A History of Chinese Philosophy, 1959
5. Honesty is the habitual absence of the intent to deceive.
6. Hypocrisy is the homage that vice pays to virtue.
—François La Rochefoucauld, Reflections, 166
7. The word body, in the most general acceptation, signifieth that which filleth, or occupieth
some certain room, or imagined place; and dependeth not on the imagination, but is a
real part of that we call the universe.
—Thomas Hobbes, Leviathan, 1651
8. Torture is “any act by which severe pain or suffering, whether physical
or mental, is intentionally inflicted on a person for such purposes as obtaining
from him or a third person information or a confession.”
—United Nations Convention Against Torture, 1984
9. A hazard is anything that is dangerous.
—Safety with Beef Cattle, U.S. Occupational Safety and Health Administration, 1976
10. To sneeze [is] to emit wind audibly by the nose.
—Samuel Johnson, Dictionary, 1814
11. A bore is a person who talks when you want him to listen.
—Ambrose Bierce, 1906
8 Hours
a) Distinguish the different categories of fallacy
b) Analyze statements that contain different kinds of fallacy.
c) Differentiate the types of fallacy.
d) Explain and illustrate the most common type of fallacy in ordinary language.
READINGS AND VIDEOS (Please see the digital copies of the materials.)
Reading 6.1
Reading 6.2
Copi, I., Cohen, C & McMahon, K. (2014). Introduction to Logic Fourteenth
Edition. London: Pearson Education Limited
Van Cleave, M. (2016). Introduction to Logic and Critical Thinking. Retrieved
from https://open.umn.edu/opentextbooks/textbooks/introduction-to-logic-andcritical-thinking
Reading 6.3
Gensler, H. (2010).Introduction to Logic Second Edition. New York: Routledge
Video 6.1
Video 6.2
Video 6.3
Video 6.4
Introduction to Fallacies in https://www.youtube.com/watch?v=M39XcakMDqw
Fallacy Detective in https://www.youtube.com/watch?v=Od2cpE7YMSQ
Top 10 Fallacies in https://www.youtube.com/watch?v=IawIjqOJBU8
31 Logical in 8 Minutes in https://www.youtube.com/watch?v=Qf03U04rqGQ
LECTURES (Please refer to the Powerpoint presentations)
Answer Exercise 6.1 & 6.2 (Write your answer in a separate sheet of paper)
Source: Introduction to Logic
Irving Copi
Carl Cohen
Kenneth McMahon
14th edition
6.0 Fallacy
6.1. Informal Fallacy
One reasons incorrectly when the premises of an argument fail to support its conclusion, and
arguments of that sort may be called fallacious. So ina very general sense, any error in
reasoning is a fallacy. Similarly, any mistakenidea or false belief may sometimes be labeled
A formal fallacy is a pattern of mistake that appears in deductive arguments of a certain
specifiable form. There are other formal fallacies. Most fallacies, however, are not formal
butinformal: They are patterns of mistake that are made in the everyday uses of language.
Informal fallacies, arise from confusions concerning the content of the language used. There is
no limit to the variety of forms in which that content may appear, and thus informalfallacies are
often more difficult to detect than formal ones. It is language that deceives us here; we may be
tricked by inferences that seem plausible on the surface but that are in reality not warranted.
6.2 Informal fallacies are numerous and can therefore be best understood if they are grouped
into categories, each with clearly identifiable features. This classification of fallacies is a
controversial matter in logic. There is no one correct taxonomy of fallacies. Logicians have
proposed lists of fallacies that vary greatly in length; different sets have been specified, and
different names have been given toboth the sets and the individual fallacies. Any classification
of the kind that willfollow here is bound to be arbitrary in some degree. Our aim is to provide a
comprehensive scheme within which the most common informal fallacies can be
helpfully identified—and avoided.
II.The outline of this classification and description of each fallacy appears immediately
Fallacies of relevance are the most numerous and the most frequently encountered. In these
fallacies, the premises of the argument are simply not relevant to the conclusion. However,
because they are made to appear to be relevant, they may deceive. We will distinguish and
• R1: The appeal to the populace
This fallacy is sometimes defined as the fallacy committed in making an emotional appeal; but
this definition is so broad as to include most of the fallacies of relevance. It is defined more
narrowly as the attempt to win popular assent to aconclusion by arousing the feelings of the
multitude. The argument ad populum (“to the populace”) is the baldest of all fallacies, and yet
it is one of the mostcommon. It is the instrument on which every demagogue and propagandist
relieswhen faced with the task of mobilizing public sentiment. It is a fallacy because, instead of
evidence and rational argument, the speaker (or writer) relieson expressive language and other
devices calculated to excite enthusiasm for or against some cause.
Example: Sixteen Million people voted for this president, that makes him the best president.
• R2: The appeal to emotion
One variety of the appeal to emotion that appears with great frequency is the argument
ad misericordiam. The Latin word misericordiam literally means “merciful heart”; this fallacy is
the emotional appeal to pity.
Example: “Please give me a passing grade, my old poor parents are expecting me to graduate
this year!”
Logicians give special names to other clusters of fallacious emotional appeals.Thus one might
also distinguish the appeal to envy (ad invidiam), the appeal to fear (ad metum), the appeal to
hatred (ad odium), and the appeal to pride (ad superbium). In all of these, the underlying
mistake is the argument’s reliance on feelings as premises.
• R3: The red herring
The red herring is a fallacious argument whose effectiveness lies in distraction. Attention is
deflected; readers or listeners are drawn to some aspect of the topic under discussion by which
they are led away from the issue that had been the focus of the discussion. They are urged to
attend to some observation or some claim that may be associated with the topic, but that is not
relevant to the truth of what had originally been in dispute. A red herring has been drawn
across the track.
In the world of finance, a prospectus issued to attract investors in a company about to go public,
which tells much about the company but not the price of its shares, is also called a red herring.
• R4: The straw man
It is very much easier to win a fight against a person made of straw than against one made of
flesh and blood. If one argues against some view by presenting an opponent’s position as one
that is easily torn apart, the argument is fallacious, of course. Such an argument commits the
fallacy of the straw man.
One may view this fallacy as a variety of the red herring, because it also introduces a distraction
from the real dispute. In this case, however, the distractionis of a particular kind: It is an effort to
shift the conflict from its original complexity into a different conflict, between parties other than
those originally in dispute. So common is this variety of distraction that the pattern of argument
that relies on it has long carried its own name: the straw man argument.
Example: You are you against death penalty? So, you think that the lives of murderers and
criminals are more important than the lives of their innocent victims?
• R5: The attack on the person
The phrase ad hominem translates as “against the person.” An ad hominem argument is one in
which the thrust is directed, not at a conclusion, but at some person who defends the conclusion
in dispute. An important qualification is called for at this point. Ad hominem arguments are
fallacious (and often unfair to the adversary) because an attack against some person is
generally not relevant to the objective merits of the argument that person has put forward.
This personalized attack might be conducted in either of two different ways, for which reason we
distinguish two major forms of the argument ad hominem: the abusive and the circumstantial
• Abusive
One is tempted, in heated argument, to disparage the character of one’s opponents,
to deny their intelligence or reasonableness, to question their understanding, or
their seriousness, or even their integrity. However, the character of an adversary
is logically irrelevant to the truth or falsity of what that person asserts, or to the
correctness of the reasoning employed.
Example: Of course it will be hard for you to understand why college education
matters? You always got the lowest score in our class!
• Circumstantial
The circumstances of one who makes (or rejects) some claim have no more bearing
on the truth of what is claimed than does his character. The mistake made in the
circumstantial form of the ad hominem fallacy is to treat those personal
circumstances as the premise of an opposing argument.
Example: Oh for sure she is in favor of the anti-terror bill! She cannot be a good
senator; she’s her father’s daughter!
• R6: The appeal to force
It seems odd to suppose that one could hope to establish some proposition as true, or persuade
some other person of its truth, by resorting to force. Threats or strong-arm methods to coerce
one’s opponents can hardly be considered arguments at all. Traditionally, a category of fallacies
of this kind has been identified as the appeal to force or the argument ad baculum (appeal ad
baculum means literally “appeal to the stick”!), and it surely is clear that however expedient
force may prove to be, it cannot replace rational methods of argument. “Might makes right” is
not a subtle principle, and we all reject it.
Example: You are not force to follow this rule, but one must be prepared to face the
consequence though.
• R7: Missing the point (irrelevant conclusion)
Aristotle, the first to give a systematic classification of the informal fallacies, explains the fallacy
we call missing the point, or ignoratio elenchi, as a mistake that is made in seeking to refute
another’s argument. The Latin word elenchi is derived from a Greek word that means a
“disproof,” or a “refutation.” An ignoratio elenchi is a mistaken refutation, one that goes haywire
because the person presenting it does not fully understand the proposition in dispute. He
refutes, or tries to refute, a claim other than that which was originally at issue. He misses the
Example: Somebody asked about the missing funds in an agency and you reply by pointing out
how employees enjoyed the perks and bonuses that they receive
In fallacies of defective induction, which are also common, the mistake arises from the fact that
the premises of the argument, although relevant to the conclusion, are so weak and ineffective
that relying on them is a blunder. We will distinguish and discuss:
• D1: The argument from ignorance
Someone commits the fallacy argumentum ad ignorantiam if he or she argues that something is
true because it has not been proved false, or false because it has not been proved true. Just
because some proposition has not yet been proved false,we are not entitled to conclude that it
is true. The same point can be made in reverse: If some proposition has not yet been proved
true, we are not entitled to conclude that it is false. Many true propositions have not yet been
proved true, of course, just as many false propositions have not yet been proved false. The fact
that we cannot now be confident rarely serves as a good reason to assert knowledge of falsity,
or of truth. Such an inference is defective; the fallacy is called the argument from ignorance,
or the argument ad ignorantiam. Ignorance sometimes obliges us to suspend judgment,
assigning neither truth nor falsity to the proposition
in doubt.
Example: There is no need for digitization; our generation has survived on logbooks and
• D2: The appeal to inappropriate authority
The fallacy of the appeal to inappropriate authority arises when the appeal is made to parties
who have no legitimate claim to authority in the matter at hand. Thus, in an argument about
morality, an appeal to the opinions of Darwin, a towering authority in biology, would be
fallacious, as would be an appeal to the opinions of a great artist such as Picasso to settle an
economic dispute. Care must be taken in determining whose authority it is reasonable to rely
on, and whose to reject. Although Picasso was not an economist, his judgment might plausibly
be given some weight in a dispute pertaining to the economic value of an artistic masterpiece;
and if the role of biology in moral questions were in dispute, Darwin might indeed be an
appropriate authority. This is not to say that an authority in one field might not be correct when
speaking outside his or her area of expertise—to allege that would constitute a species of
argumentum ad hominem circumstantial. In every instance, an argument must be judged upon
its own merits.
Example: According to the governor suob is the best cure for Covid-19, so, it must be true.
• D3: False cause
It is obvious that any reasoning that relies on treating as the cause of something or event what
is not really its cause must be seriously mistaken. Often we are tempted to suppose, or led to
suppose, that we understand some specific cause and effect relation when in fact we do not.
The nature of the connection between cause and effect, and how we determine whether such a
connection is present, are central problems of inductive logic and scientific method. Presuming
the reality of a causal connection that does not really exist is a common mistake; inLatin the
mistake is called the fallacy of non causa pro causa; we call it simply the fallacy of false cause.
Example: My business prospers, thanks to the money tree necklace that you gave me!
• D4: Hasty generalization
Throughout our lives, we rely on statements about how things generally are and how people
generally behave. Nonetheless, general claims, although critical in reasoning, must be carefully
scrutinized: The universality of their application ought never be accepted or assumed without
justification. Hasty generalization is the fallacy we commit when we draw conclusions about all
the persons or things in a given class on the basis of our knowledge about only one (or only a
very few) of the members of that class.
Example: I was in the supermarket yesterday and I saw some shoppers, who are not wearing
facemasks, ahh! Filipinos are hardheaded! We have to blame them for rising Covid -19 cases.
In fallacies of presumption, too much is assumed in the premises. The inference to the
conclusion depends mistakenly on theseunwarranted assumptions. We will distinguish and
• P1: Accident
Circumstances alter cases. A generalization that is largely true may not apply in a given case
(or to some subcategory of cases) for good reasons. The reasons the generalization does not
apply in those cases have to do with the special circumstances, also called the “accidental”
circumstances, of that case or those cases. If these accidental circumstances are ignored, and
we assume that the generalization applies universally, we commit the fallacy of accident.
Example: One may believe that silence speak volumes, but if you are a lawmaker you cannot
claim that you do not speak that much because of that belief.
• P2: Complex question
One of the most common fallacies of presumption is to ask a question in such a way as to
presuppose the truth of some conclusion that is buried in the question. The question itself is
likely to be rhetorical, with no answer actually being sought. But putting the question seriously,
thereby introducing its presupposition surreptitiously, often achieves the questioner’s purpose
Example: Why is student X better than student Y?
• P3: Begging the question
The fallacy called begging the question is widely misunderstood, partly because its name is
misleading. It is the mistake of assuming the truth of what one seeks to prove. The “question” in
a formal debate is the issue that is in dispute; to “beg” the question is to ask, or to suppose, that
the very matter in controversy be conceded. This is an argument with no merit at all, of course,
and one who makes such an assumption commits a gross fallacy.
Example: To be well known one must be famous, to be famous one must be well known.
The incorrect reasoning in fallacies of ambiguity arises from the equivocal use of words or
phrases. Some word or phrase in one part of the argument has a meaning different from that of
the same word or phrase in another part of the argument. We will distinguish and discuss:
• A1: Equivocation
Most words have more than one literal meaning, and most of the time we have no difficulty
keeping those meanings separate by noting the context and using our good sense when
reading and listening. Yet when we confuse the several meanings of a word or phrase—
accidentally or deliberately—we are using the word equivocally. If we do that in the context of an
argument, we commit the fallacy of equivocation.
Example: Ana went window shopping yesterday, when she came home not a window in sight.
• A2: Amphiboly
The fallacy of amphiboly occurs when one is arguing from premises whose formulations are
ambiguous because of their grammatical construction. The word “amphiboly” is derived from the
Greek, its meaning in essence being “two in a lump,” or the “doubleness” of a lump. A statement
is amphibolous when its meaning is indeterminate because of the loose or awkward way in
which its words are combined. An amphibolous statement may be true in one interpreon and
false in another. When it is stated as premise with the interpretation that makes it true, and a
conclusion is drawn from it on the interpretation that makes it false, then the fallacy of amphiboly
has been committed.
Ladies, don’t forget the rummage sale. It’s a chance to get rid of those things not worth keeping
around the house. Bring your husbands.
- Grammarbook.com
• A3: Accent
We have seen that shifting the meaning of some term in an argument may result in a fallacy of
ambiguity. Most commonly that shift is an equivocation, as noted earlier. Sometimes, however,
the shift is the result of a change in emphasis on a single word or phrase, whose meaning does
not change. When the premise of an argument relies on one possible emphasis, but a
conclusion drawn from it relies on the meaning of the same words emphasized differently, the
fallacy of accent has been committed.
Example: Some advertisements that give emphasis on some words in order to entice
SALE ALERT! Up to 50% 0ff on selected items.
• A4: Composition
The term fallacy of composition is applied to both of two closely related types of mistaken
argument. The first may be described as reasoning fallaciously from the attributes of the parts of
a whole to the attributes of the whole itself. A flagrant example is to argue that, because every
part of a certain machine is light in weight, the machine “as a whole” is light in weight. The error
here is manifest when we recognize that a very heavy machine may consist of a very large
number of lightweight parts. Not all examples of fallacious composition are so obvious, however.
Some are misleading. One may hear it seriously argued that, because each scene of a certain
play is a model of artistic perfection, the play as a whole is artistically perfect. This is as much a
fallacy of composition as to argue that, because every ship is ready for battle, the whole fleet
must be ready for battle.
• A5: Division
The fallacy of division is simply the reverse of the fallacy of composition. In it the same
confusion is present, but the inference proceeds in the opposite direction. As in the case of
composition, two varieties of the fallacy of division may be distinguished. The first kind of
division consists of arguing fallaciously that what is true of a whole must also be true of its parts.
To argue that, because a certain corporation is very important and Mr. Doe is an official of that
corporation, therefore Mr. Doe is very important, is to commit the fallacy of division. This first
variety of the division fallacy is committed in any such argument, as in moving from the premise
that a certain machine is heavy, or complicated, or valuable, to the conclusion that this or any
other part of the machine must be heavy, or complicated, or valuable. To argue that a student
must have a large room because the room is located in a large dormitory would be still another
instance of the first kind of fallacy of division.
The second type of division fallacy is committed when one argues from the attributes of a
collection of elements to the attributes of the elements themselves. To argue that, because
university students study medicine, law, engineering, dentistry, and architecture, therefore each,
or even any, university student studies medicine, law, engineering, dentistry, and architecture is
to commit the second kind of division fallacy. It is true that university students, collectively, study
all these various subjects, but it is false that university students, distributively, do so. Instances
of this fallacy of division often look like valid arguments, for what is true of a class distributively
is certainly true of each and every member. Thus the argument,
Dogs are carnivorous.
Afghan hounds are dogs.
Therefore Afghan hounds are carnivorous.
is perfectly valid.
Closely resembling this argument is another,
Dogs are frequently encountered in the streets.
Afghan hounds are dogs.
Therefore Afghan hounds are frequently encountered in the streets.
Exercise 6.1 Fallacy
Identify and explain any fallacy in the following statements.
1. The problem of broken family started when girls were allowed to have college degrees,
during my time couples seldom separate because men work and woman stay at home.
Answer: False cause, there are many reasons for having a broken family, it is wrong to
blame it on women having education, there is no proof that having more education
means having broken relationships.
2. To the doctors who are complaining of lack of government support, the pandemic is not
a time to be worried of an unknown enemy; this is the time to show our patriotism and
loyalty to the state.
3. You hate corruption? Oh c’mon looks who’s talking!
4. A computer is a machine use for computing.
5. This must be best book of 2020 everybody is reading it.
6. I just saw a policeman who beat a minor. I must say all me in uniform are violent and
7. Someone ask a politician why he barely speaks in the senate floor, his reply was, “less
talk less mistake.”
8. Andrew is an activist he came from a family of activists.
9. We should give the promotion to Pedro I heard he is the breadwinner in the family.
10. You have to convert to our religion, judgment day is coming!
11. This guy does not understand what poverty is; he came from a rich family.
12. Filipinos are spiritual, thus, the entire universe is spiritual.
13. This commissioner should not be fired; he is an honest man since no one can prove that
he is corrupt.
14. Ever since I bought this lucky charm, my business grew beyond compare.
15. If you want to live a happy and blissful life don’t get married according to an article
published in a magazine.
Introduction to Logic Second Edition
Harry Gensler
Exercise 6.2: Identify and explain any fallacy in the following statements
1. Are you still wasting time with all that book-learning at the university?
2. The Bible tells the truth because it’s God’s word. We know the Bible is God’s
word because the Bible says so and it tells the truth.
3. You should vote for this candidate because she’s intelligent and has much
experience in politics.
4. The Equal Rights Amendment was foolish because its feminist sponsors were
nothing but bra-less bubbleheads.
5. No one accepts this theory anymore, so it must be wrong.
6. Either you favor a massive arms buildup, or you aren’t a patriotic American.
7. The president’s veto was the right move. In these troubled times we need decisive
leadership, even in the face of opposition. We should all thank the president for
his courageous move.
8. Each member of this team is unbeatable, so this team must be unbeatable.
9. My doctor told me to lose weight and give up smoking. But she’s an overweight
smoker herself, so I can safely ignore her advice.
10. Belief in God is explained in terms of one’s need for a father figure; so it’s false.
11. There are scientific laws. Where there are laws there must be a lawgiver. Hence
someone must have set up the scientific laws to govern our universe, and this
someone could only be God.
12. The lawyer for the defense claims that there’s doubt that Smith committed the
crime. But, I ask, are you going to let this horrible crime go unpunished because
of this? Look at the crime; see how horrible it was! So you see clearly that the
crime was horrible and that Smith should be convicted.
13. Free speech is for the common good, since unrestrained expression of opinion is
in people’s interest.
14. This is a shocking and stupid proposal. Its author must be either a dishonest bum
or a complete idiot.
15. Aristotle said that heavy objects fall faster than light ones, so it must be true.
16. Each of these dozen cookies (or drinks) by itself isn’t harmful; one little one won’t
hurt! Hence having these dozen cookies (or drinks) isn’t harmful.
17. Before Barack Obama became the Democratic candidate for US president, he ran
in a series of primary elections. He noted that he played basketball before the
Iowa primary, and then won the vote, while he neglected to play before the New
Hampshire primary, and then lost. He concluded (in jest) “At that point I was
certain that we had to play on every primary.”
18. Only men are rational animals. No woman is a man. Therefore no woman is a
rational animal.
19. I’m right, because you flunk if you disagree with me!
20. The discriminating backpacker prefers South Glacier tents.
Deductive Reasoning
8 Hours
a) Distinguish the different types of categorical propositions.
b) Identify the premise and conclusion of a standard form categorical proposition.
c) Explain the mood and figure of a syllogism
d) Test the validity of the syllogism using Venn Diagram.
READINGS AND VIDEOS (Please see the digital copies of the materials.)
Reading 7.1
Reading 7.2
Copi, I., Cohen, C & McMahon, K. (2014). Introduction to Logic Fourteenth
Edition. London: Pearson Education Limited
Van Cleave, M. (2016). Introduction to Logic and Critical Thinking. Retrieved
from https://open.umn.edu/opentextbooks/textbooks/introduction-to-logic-andcritical-thinking
Reading 7.3
Gensler, H. (2010).Introduction to Logic Second Edition. New York: Routledge
Video 6.1
Video 6.2
Introduction to Formal Logic in https://www.youtube.com/watch?v=KcNESCrkIiQ
Venn Diagrams and Categorical Syllogism in
Answer Exercise 7.1 & 7.2 (Write your answer in a separate sheet of paper)
Source: Critical Thinking
Noel Moore & Richard Parker. — 9th ed.
Logicians recognize two kinds of good arguments: A good “deductive” argument and a good
“inductive” argument. Before we explain these arguments, we should point out that the
distinction between the two is second nature to instructors of critical thinking, and it is easy for
them (and for us) to sometimes forget that it is new to many people. In addition, within the past
few pages we have already brought up several new ideas, including “critical thinking,”“claim,”
“argument,” “premise,” “conclusion,” “issue,” and more. Thisis quite a load, so don’t worry if you
don’t understand the distinction immediately.
Deductive Arguments
The first type of good argument, a good deductive argument , is said to be “valid,” which
means it isn’t possible for the premises to be true and the conclusion false. Take this argument
about one of our former students:
Premise: Josh Fulcher lives in Alaska.
Conclusion: Therefore, Josh Fulcher lives in the United States.
This is a valid argument because it isn’t possible for Josh Fulcher to live in Alaska and not live in
the United States. One more example:
Premise: Josh Fulcher is taller than his wife, and his wife is taller than his son.
Conclusion: Therefore, Josh Fulcher is taller than his son.
This, too, is a valid argument, because it isn’t possible for that premise to be
true and the conclusion to be false.
To put all this differently, the premises of a good deductive argument, assuming they are
true, prove or demonstrate the conclusion.
Inductive Arguments
The premises of the other type of good argument, a good inductive argument , don’t prove or
demonstrate the conclusion. They support it. This means that, assuming they are true, they
raise the probability that the conclusion is true.
Premise: Fulcher lives in Alaska.
Conclusion: Therefore, he uses mosquito repellent.
Fulcher’s living in Alaska makes it more probable that Fulcher uses mosquito repellent.
Premise: People who live in Butte City already spend a lot of time in the sun.
Conclusion: Therefore, a tanning salon won’t do well there.
The premise of this argument (assuming it is true) raises the probability that the conclusion is
true; thus it supports the conclusion.
The more support the premises of an argument provide for a conclusion, the stronger the
argument is said to be.
Source: Critical Thinking
Noel Moore & Richard Parker. — 9th ed.
Deductive Arguments
Categorical logic is logic based on the relations of inclusion and exclusion among classes
(or“categories”) as stated in categorical claims. Its methods date back to the time of Aristotle,
and it was the principal form that logic took among most knowledgeable people for more than
two thousand years. During that time, all kinds of bells and whistles were added to the basic
theory, especially by monks and other scholars during the medieval period. So as not to weigh
you down with unnecessary baggage, we’ll just set forth the basics of the subject in what
Studying categorical and truth-functional logic can teach us to become more careful and precise
in our own thinking. Getting comfortable with this type of thinking can be helpful in general, but
for those who will someday apply to law school, medical school, or graduate school, it has the
added advantage that many admission exams for such programs deal with the kinds of
reasoning discussed in this chapter.
Let’s start by looking at the four basic kinds of claims on which categorical Logic is based.
A categorical claim says something about classes (or “categories”) of things. Our interest lies
in categorical claims of certain standard forms. A standardform categorical claim is a claim
that results from putting names or descriptions of classes into the blanks of the following
(note: these are also known as propositions A – Universal Affirmative, E- Universal Negative, IParticular affirmative, O- Particular Negative)
A: All ________ are _________ .
( Example: All Presbyterians are Christians.)
E: No _________ are _________ .
( Example: No Muslims are Christians.)
I: Some ________ are ________.
( Example: Some Christians are Arabs.)
O: Some ________ are not _________ .
( Example: Some Muslims are not Sunnis.)
The phrases that go in the blanks are terms; the one that goes into the first blank is the subject
term of the claim, and the one that goes into the second blank is the predicate term. Thus,
“Christians” is the predicate term of the first example above and the subject term of the third
example. In many of
the examples and explanations that follow, we’ll use the letters S and P (for “subject” and
“predicate”) to stand for terms in categorical claims. And we’ll talk about the subject and
predicate classes, which are just the classes that the terms refer to.
But first, a caution: Only nouns and noun phrases will work as terms. An adjective alone, such
as “red,” won’t do. “All fire engines are red” does not produce a standard-form categorical claim,
because “red” is not a noun or noun phrase. To see that it is not, try switching the places of the
terms: “All red are fire engines.” This doesn’t make sense, right? But “red vehicles” (or even “red
things”) will do because “All red vehicles are fire engines” makes sense (even though it’s false).
Looking back at the standard-form structures just given, notice that each one has a letter to its
left. These are the traditional names of the four types of standard-form categorical claims. The
claim “All Presbyterians are Christians”is an A-claim, and so are “All idolators are heathens,” “All
people born between 1946 and 1964 are baby boomers,” and any other claim of the form “All S
are P.” The same is true for the other three letters and the other three kinds of claims.
Venn Diagrams
Each of the standard forms has its own graphic illustration in a Venn diagram, as shown in
Figure through 4 . Named after British logician John Venn, these diagrams exactly represent the
four standard-form categorical claim types. In the diagrams, the circles represent the classes
named by the terms, shaded areas represent areas that are empty, and areas containing Xs
represent areas that are not empty—that contain at least one item. An area that is blank is one
that the claim says nothing about; it may be occupied, or it may be empty.
Figures 1-4
Notice that in the diagram for the A-claim, the area that would contain any members of the S
class that were not members of the P class is shaded—that is, it is empty. Thus, that diagram
represents the claim “All S are P,” since there is no S left that isn’t P. Similarly, in the diagram
for the E-claim, the area
where S and P overlap is empty; any S that is also a P has been eliminated. Hence: “No S are
For our purposes in this chapter, the word “some” means “at least one.” So, the third diagram
represents the fact that at least one S is a P, and the X in the area where the two classes
overlap shows that at least one thing inhabits this area.
Finally, the last diagram shows an X in the area of the S circle that is outside the P circle,
representing the existence of at least one S that is not a P. We’ll try to keep technical jargon to a
minimum, but here’s some terminology we’ll need: The two claim types that include one class or
part of one class within another, the A-claims and I-claims, are affirmative claims; the two that
exclude one class or part of one class from another, the E-claims and O-claims, are negative
Although there are only four standard-form claim types, it’s remarkablehow versatile they are. A
large portion of what we want to say can be rewritten,or “translated,” into one or another of
them. Because this task is sometimes easier said than done, we’d best spend a little while
making sure we understand how to do it. And we warn you in advance: A lot of standard-form
translations are not very pretty—but it’s accuracy we seek here, not style.
A syllogism is a two-premise deductive argument. A categorical syllogism (in standard form)
is a syllogism whose every claim is a standard-form categorical claim and in which three terms
each occur exactly twice in exactly two of the claims. Study the following example:
All Americans are consumers.
Some consumers are not Democrats.
Therefore, some Americans are not Democrats.
Notice how each of the three terms “Americans,” “consumers,” and “Democrats”
occurs exactly twice in exactly two different claims. The terms of a syllogism
are sometimes given the following labels:
Major term: the term that occurs as the predicate term of the syllogism’s conclusion
Minor term: the term that occurs as the subject term of the syllogism’s conclusion
Middle term: the term that occurs in both of thepremises but not at all in the conclusion
The most frequently used symbols for these three terms are P for major term, S for minor term,
M for middle term. We use these symbols throughout to simplify the discussion.
In a categorical syllogism, each of the premises states a relationship between the middle term
and one of the other terms . If both premises do their jobs correctly—that is, if the proper
connections between S and P are established via the middle term, M—then the relationship
between S and P stated by the conclusion will have to follow—that is, the argument is valid.
In case you’re not clear about the concept of validity, remember: An argument is valid if, and
only if, it is not possible for its premises to be true while its conclusion is false. This is just
another way of saying that, were the premises of a valid argument true (whether or not they are
in fact true), then the truth of the conclusion would be guaranteed. In a moment, we’ll begin
developing the first of two methods for assessing the validity of syllogisms.
First, though, let’s look at some candidates for syllogisms. In fact, only one of the following
qualifies as a categorical syllogism. Can you identify which one? What is wrong with the other
1. All cats are mammals.
Not all cats are domestic.
Therefore, not all mammals are domestic.
2. All valid arguments are good arguments.
Some valid arguments are boring arguments.
Therefore, some good arguments are boring arguments.
3. Some people on the committee are not students.
All people on the committee are local people.
Therefore, some local people are nonstudents.
We hope it was fairly obvious that the second argument is the only proper syllogism. The first
example has a couple of things wrong with it: Neitherthe second premise nor the conclusion is
in standard form—no standard-form categorical claim begins with the word “not”—and the
predicate term must be a noun or noun phrase. The second premise can be translated into
“Some cats are not domestic creatures” and the conclusion into “Some mammals are
notdomestic creatures,” and the result is a syllogism. The third argument is okay up to the
conclusion, which contains a term that does not occur anywhere in the premises: “nonstudents.”
However, because “nonstudents” is the complement of “students,” this argument can be turned
into a proper syllogism by obverting the conclusion, producing “Some local people are not
Once you’re able to recognize syllogisms, it’s time to learn how to determine their validity. We’ll
turn now to our method, the Venn diagram test.
The Venn Diagram Method of Testing for Validity
Diagramming a syllogism requires three overlapping circles,one representing each class named
by a term in the argument. To be systematic, in our diagrams we put the minor term on the left,
the major term on
the right, and the middle term in the middle but lowered a bit. We will diagram the following
step by step:
No Republicans are collectivists.
All socialists are collectivists.
Therefore, no socialists are Republicans.
In this example, “socialists” is the minor term, “Republicans” is the major term, and “collectivists”
is the middle term. See diagram for the three circles required, labeled appropriately.
We fill in this diagram by diagramming the premises of the argument just as we diagrammed the
A-, E-, I-, and O-claims earlier. The premises in the foregoing example are diagrammed like this:
First: No Republicans are collectivists (Figure 8 ). Notice that in this figure we have shaded the
entire area where the Republican and collectivist circles overlap.
Second: All socialists are collectivists . Because diagramming the premises resulted in the
shading of the entire area where the socialist and Republican circles overlap, and because that
is exactly what we would do to diagram the syllogism’s conclusion, we can conclude that the
syllogism is valid. In general, a syllogism is valid if and only if diagramming the premises
automatically produces a correct diagram of the conclusion. * (The one exceptionis discussed
When one of the premises of a syllogism is an I- or O-premise, there can be a problem about
where to put the required X. The following example presents such a problem (see Figure 10 for
the diagram). Note in the diagram that we have numbered the different areas in order to refer to
them easily.
Some S are not M.
All P are M.
Some S are not P.
(The horizontal line separates the premises from the conclusion.) An X in either area 1 or area 2
of Figure 10 makes the claim “Some S are not M” true, because an inhabitant of either area is
an S but not an M. How do we determine which area should get the X? In some cases, the
decision can be made for us: When one premise is an A- or E-premise and the other is an I- or
O-premise, diagram the A- or E-premise first. (Always shade before putting in Xs.) Refer to
Figure 11 to see what happens with the current example when we follow this rule.
Once the A-claim has been diagrammed, there is no longer a choice about where to put the X—
it has to go in area 1. Hence, the completed diagram for this argument looks like Figure 12 . And
from this diagram, we can read the conclusion “Some S are not P,” which tells us that the
argument is valid.
A syllogism like this one still leaves us in doubt about where to put the X, even after we have
diagrammed the A-premise ( Figure 13 ): Should the X go in area 4 or 5? When such a question
remains unresolved, here is the rule to follow: An X that can go in either of two areas goes on
the line separating the
areas, as in Figure 14 .
In essence, an X on a line indicates that the X belongs in one or the other of the two areas,
maybe both, but we don’t know which. When the time comes to see whether the diagram yields
the conclusion, we look to see whether there is an X entirely within the appropriate area. In the
current example, we would
need an X entirely within the area where S and P overlap; because there is no such X, the
argument is invalid. An X partly within the appropriate area fails to establish the conclusion.
Please notice this about Venn diagrams: When both premises of a syllogism are A- or E-claims
and the conclusion is an I- or O-claim, diagramming the premises cannot possibly yield a
diagram of the conclusion (because A- and E-claims produce only shading, and I- and O-claims
require an X to be read from the diagram). In such a case, remember our assumption that every
class we are dealing with has at least one member. This assumption justifies our looking at the
diagram and determining whether any circle has all but one of its areas shaded out. If any circle
has only one area remaining unshaded, an X should be put in that area. This is the case
because any member of that class has to be in that remaining area. Sometimes placing the X in
this way will enable us to read the conclusion, in which case the argument is valid (onthe
assumption that the relevant class is not empty); sometimes placing the X will not enable us to
read the conclusion, in which case the argument is invalid, with or without any assumptions
about the existence of a member within the class.
Source: Introduction to Logic
Irving Copi
Carl Cohen
Kenneth McMahon
14th edition
Exercise 7.1 : Venn Diagram
Write out each of the following syllogistic forms, using S and P as the subject
and predicate terms of the conclusion, and M as the middle term.
Then test the validity of each syllogistic form using a Venn diagram.
1. AEE -1
We are told that this syllogism is in the first figure, and therefore the middle
term, M, is the subject term of the major premise and the predicate term of the
minor premise. The conclusion of the syllogism is an E proposition and therefore
reads: No S is P. The first (major) premise (which contains the predicate
term of the conclusion) is an A proposition, and therefore reads: All M is P. The
second (minor) premise (which contains the subject term of the conclusion) is
an E proposition and therefore reads: No S is M. This syllogism therefore reads
as follows:
All M is P.
No S is M.
Therefore no S is P.
Tested by means of a Venn diagram, as in Figure 10, this syllogism is shown to be invalid, it is
reflected in the diagram that there is an S which is P that is not shaded and this contradicts the
conclusion that no S is P.
2. EIO–2
3. OAO–3
4. AOO–4
*5. EIO–4
6. OAO–2
7. AOO–1
8. EAE–3
9. EIO–3
*10. IAI–4
11. AOO–3
12. EAE–1
13. IAI–1
14. OAO–4
*15. EIO–1
7.2. Put each of the following syllogisms into standard form, name its mood and
figure, and test its validity using a Venn diagram:
*1. Some reformers are fanatics, so some idealists are fanatics, because all reformers are
Some reformers are fanatics.
because all reformers are idealists
so some idealists are fanatics.
Some M are P
All M are S
So,Some S are P
This argument is valid since Some S is P is reflected on the diagram, and no S which is P is
2. Some philosophers are mathematicians; hence some scientists are philosophers, because all
scientists are mathematicians.
3. Some neurotics are not parasites, but all criminals are parasites; it follows that some
neurotics are not criminals.
4.. All underwater craft are submarines; therefore no submarines are pleasure vessels, because
no pleasure vessels are underwater craft.
5. No criminals were pioneers, for all criminals are unsavory persons, and no pioneers were
unsavory persons.
6.. No musicians are astronauts; all musicians are baseball fans; consequently,no astronauts
are baseball fans.
Inductive Reasoning
8 Hours
a) Distinguish deductive arguments from inductive argument.
b) Appraise analogical arguments.
c) Show that a given argument is mistaken by refuting through logical analogy.
d) Examine the concept of cause and causal connections.
READINGS AND VIDEOS (Please see the digital copies of the materials.)
Reading 8.1 Van Cleave, M. (2016). Introduction to Logic and Critical Thinking. Retrieved from
Reading 8.2 Copi, I., Cohen, C & McMahon, K. (2014). Introduction to Logic Fourteenth
Edition. London: Pearson Education Limited
Video 8.1
Video 8.2
Video 8.3
What is inductive reasoning? in https://www.youtube.com/watch?v=4ZKa1S1wPy4
Deductive and Inductive Reasoning in
Inductive Arguments in https://www.youtube.com/watch?v=kUeqO90agT8
Answer Exercise 8.1 to 8.4 (Write your answer in a separate sheet of paper)
Source: Introduction to Logic and Critical Thinking
Version 1.4
Matthew J. Van Cleave
8.1 Inductive arguments and statistical generalizations
An inductive argument is an argument whose conclusion is supposed to follow from its premises
with a high level of probability, rather than with certainty. This means that although it is possible
that the conclusion doesn’t follow from its premises, it is unlikely that this is the case. We said
that inductive arguments are “defeasible,” meaning that we could turn a strong inductive
argument into a weak inductive argument simply by adding further premises to the argument. In
contrast, deductive arguments that are valid can never be made invalid by adding further
premises. Recall our “Tweets” argument:
1. Tweets is a healthy, normally functioning bird
2. Most healthy, normally functioning birds fly
3. Therefore, Tweets probably flies
Without knowing anything else about Tweets, it is a good bet that Tweets flies. However, if we
were to add that Tweets is 6 ft. tall and can run 30 mph, then it is no longer a good bet that
Tweets can fly (since in this case Tweets is likely an ostrich and therefore can’t fly). The second
premise, “most healthy, normally functioning birds fly,” is a statistical generalization. Statistical
generalizations are generalizations arrived at by empirical observations of certain regularities.
Statistical generalizations can be either universal or partial. Universal generalizations assert that
all members (i.e., 100%) of a certain class have a certain feature, whereas partial
generalizations assert that most or some percentage of members of a class have a certain
feature. For example, the claim that “67.5% of all prisoners released from prison are rearrested
within three years” is a partial generalization that is much more precise than simply saying that
“most prisoners released from prison are rearrested within three years.” In contrast, the claim
that “all prisoners released from prison are rearrested within three years” is a universal
generalization. As we can see from these examples, deductive arguments typically use
universal statistical generalizations whereas inductive arguments typically use partial statistical
generalizations. Since statistical generalizations are often crucial premises in
both deductive and inductive arguments, being able to evaluate when a statistical generalization
is good or bad is crucial for being able to evaluate arguments. What we are doing in evaluating
statistical generalizations is determining whether the premise in our argument is true (or at least
well supported by the evidence). For example, consider the following inductive argument, whose
premise is a (partial) statistical generalization:
1. 70% of voters say they will vote for candidate X
2. Therefore, candidate X will probably win the election.
This is an inductive argument because even if the premise is true, the conclusion
could still be false (for example, an opponent of candidate X could systematically kill or
intimidate those voters who intend to vote for candidate X so that very few of them will actually
vote). Furthermore, it is clear that the argument is intended to be inductive because the
conclusion contains the word “probably,” which clearly indicates that an inductive, rather than
deductive, inference is intended. Remember that in evaluating arguments we want to know
about the strength of the inference from the premises to the conclusion, but we also want to
know whether the premise is true! We can assess whether or not a statistical generalization is
true by considering whether the statistical
generalization meets certain conditions. There are two conditions that any statistical
generalization must meet in order for the generalization to be deemed “good.”
1. Adequate sample size: the sample size must be large enough tosupport the
2. Non-biased sample: the sample must not be biased
A sample is simply a portion of a population. A population is the totality of members of some
specified set of objects or events. For example, if I were determining the relative would be the
total number of cars and trucks that drive down my street on a given day. If I were to sit on my
front porch from 12- 2 pm and count all the cars and trucks that drove down my street, that
would be a sample. A good statistical generalization is one in which the sample is
representative of the population. When a sample is representative, the characteristics of the
sample match the characteristics of the population at large. For example, my method of
sampling cars and trucks that drive down my street would be a good method as long as the
proportion of trucks to cars that drove down my street between 12-2 pm matched the proportion
of trucks to cars that
drove down my street during the whole day. If for some reason the number of trucks that drove
down my street from 12-2 pm was much higher than the average for the whole day, my sample
would not be representative of the population I was trying to generalize about (i.e., the total
number of cars and trucks that drove down my street in a day). The “adequate sample size”
condition and the “non-biased sample” condition are ways of making sure that a sample is
representative. In the rest of this section, we will explain each of these conditions in turn.
It is perhaps easiest to illustrate these two conditions by considering what is wrong with
statistical generalizations that fail to meet one or more of these conditions. First, consider a
case in which the sample size is too small (and thus the adequate sample size condition is not
met). If I were to sit in front of my house for only fifteen minutes from 12:00-12:15 and saw only
one car, then my sample would consist of only 1 automobile, which happened to be a car. If I
were to try to generalize from that sample, then I would have to say that only cars (and no
trucks) drive down my street. But the evidence for this universal statistical generalization (i.e.,
“every automobile that drives down my street is acar”) is extremely poor since I have sampled
only a very small portion of the total population (i.e., the total number of automobiles that drive
down my
street). Taking this sample to be representative would be like going to Flagstaff, AZ for one day
and saying that since it rained there on that day, it must rain every day in Flagstaff. Inferring to
such a generalization is an informal fallacy called “hasty generalization.” One commits the
fallacy of hasty generalization when one infers a statistical generalization (either universal or
partial) about a population from too few
instances of that population. Hasty generalization fallacies are very common in everyday
discourse, as when a person gives just one example of a phenomenon occurring and implicitly
treats that one case as sufficient evidence for a generalization. This works especially well when
fear or ractical interests are involved. For example, Jones and Smith are talking about the
relative quality of Fords versus Chevys and Jones tells Smith about his uncle’s Ford, which
broke down numerous times within the first year of owning it. Jones then says that Fords are
just unreliable and that that is why he would never buy one. The generalization, which is here
ambiguous between a universal generalization (i.e., all Fords are unreliable) and a partial
generalization (i.e., most/many Fords are unreliable), is not supported by just one case,
however convinced Smith might be after hearing the anecdote about Jones’s uncle’s Ford.
The non-biased sample condition may not be met even when the adequate sample size
condition is met. For example, suppose that I count all the cars on my street for a three hour
period from 11-2 pm during a weekday. Let’s assume that counting for three hours straight give
us an adequate sample size. However, suppose that during those hours (lunch hours) there is a
much higher proportion of trucks to cars, since (let’s suppose) many work trucks are coming to
and from worksites during those lunch hours. If that were the case, then my sample, although
large enough, would not be representative because it would be biased. In particular, the number
of trucks to cars in the sample would be higher than in the overall population, which would make
the sample unrepresentative of the population (and hence biased).
Another good way of illustrating sampling bias is by considering polls. So consider candidate X
who is running for elected office and who strongly supports gun rights and is the candidate of
choice of the NRA. Suppose an organization runs a poll to determine how candidate X is faring
against candidate Y, who is actively anti gun rights. Busuppose that the way the organization
administers the poll is by polling subscribers to the magazine, Field and Stream. Suppose the
poll returned over 5000 responses, which, let’s suppose, is an adequate sample size and out of
those responses, 89% favored candidate X. If the organization were to take that sample to
support the statistical generalization that “most voters are in favor of candidate X” then they
would have made a mistake. If you know anything about the magazine Field and Stream, it
should be obvious why. Field and Stream is a magazine whose subscribers who would tend to
own guns and support gun rights. Thus we would expect that subscribers to that magazine
would have a much higher percentage of gun rights activists than would the general population,
to which the poll is attempting to generalize. But in this case, the sample would be
unrepresentative and biased and thus the poll would be useless. Although the sample would
allow us to generalize to the population, “Field and Stream
subscribers,” it would not allow us to generalize to the population at large.
Let’s consider one more example of a sampling bias. Suppose candidate X were running in a
district in which there was a high proportion of elderly voters. Suppose that candidate X favored
policies that elderly voters were against. For example, suppose candidate X favors slashing
Medicare funding to reduce the budget deficit, whereas candidate Y favored maintaining or
increasing support to Medicare. Along comes an organization who is interested in polling voters
to determine which candidate is favored in the district. Suppose that the organization chooses to
administer the poll via text message and that the results of the poll show that 75% of the voters
favor candidate X. Can you see what’s wrong with the poll—why it is biased? You probably
recognize that this polling method will not produce a representative sample because elderly
voters aremuch less likely to use cell phones and text messaging and so the poll will leave
out the responses of these elderly voters (who, we’ve assumed make up a large segment of the
population). Thus, the sample will be biased and unrepresentative of the target population. As a
result, any attempt to generalize to the general population would be extremely ill-advised.
Before ending this section, we should consider one other source of bias, which is a bias in the
polling questionnaire itself (what statisticians call the “instrument”). Suppose that a poll is trying
to determine how much a population favors organic food products.We can imagine the
questionnaire containing a choice like the following:
Which do you prefer?
a. products that are expensive and have no FDA proven advantage over the less
expensive products
b. products that are inexpensive and have no FDA proven disadvantage over more
expensive products
Because of the phrasing of the options, it seems clear that many people will choose option “b.”
Although the two options do accurately describe the difference between organic and nonorganic products, option “b” sounds much more desirable than option “a.” The phrasing of the
options is biased insofar as “a” is a stand-in for “organic” and “b” is stand-in for “non-organic.”
Even people who favor organic products may be more inclined to choose option “b” here. Thus,
the poll would not be representative because the responses would be skewed by the biased
phrasing of the options. Here is another example with the same point:
Which do you favor?
a. Preserving a citizen’s constitutional right to bear arms
b. Leaving honest citizens defenseless against armed criminals
Again, because option “b” sounds so bad and “a” sounds more attractive, those responding to a
poll with this question might be inclined to choose “a” even if they don’t really support gun rights.
This is another example of how bias can creep into a statistical generalization through a biased
way of asking a question.
Random sampling is a common sampling method that attempts to avoid any kinds of sampling
bias by making selection of individuals for the sample a matter of random chance (i.e., anyone
in the population is as likely as anyone else to be chosen for the sample). The basic justification
behind the method of random sampling is that if the sample is truly random (i.e., anyone in the
population is as likely as anyone else to be chosen for the sample), then the sample will be
representative. The trick for any random sampling technique is to find a way of selecting
individuals for the sample that doesn’t create any kind of bias. A common method used to select
individuals for a random sample (for example, by Gallup polls) is to call people on either their
landline or cell phones. Since most voting Americans have either a landline or a cell phone, this
is a good way of ensuring that every American has an equal chance of being included in the
sample. Next, a random number generating computer program selects numbers to dial. In this
way, organizations like Gallup are able to get something close to a random sample and are able
to represent the whole U.S. population with a sample size as small as 1000 (with a margin of
error of +/- 4). As technology and social factors change, random sampling techniques have to
be updated. For example, although Gallup used to call only landlines, eventually this method
became biased because many people no longer owned landlines, but only cell phones. If some
new kind of technology replaces cell phones and landlines, then Gallup will have to adjust the
way it obtains a sample in order to reflect the changing social reality.
Exercise 8.1: What kinds of problems, if any, do the following statistical generalizations have?
If there is a problem with the generalization,specify which of the two conditions (adequate
sample size, non-biased sample) are not met. Some generalizations may have multiple
problems.If so, specify all of the problems you see with the generalization.
1. Bob, from Silverton, CO drives a 4x4 pickup truck, so most people from Silverton,
drive 4x4 pickup trucks.
Answer: Hasty generalization (you can’t infer something general from just one case
here—the sample size is way too small). There is also a sampling bias present: even if
many others people from Silverton, CO drove pickups, itdoesn’t follow that people
generally do. There is a high percentage of
trucks in Silverton because the rough roads there almost require trucks.
2. Tom counts and categorizes birds that land in the tree in his backyard every morning
from 5:00-5:20 am. He counts mostly morning doves and generalizes, “most birds that
land in my tree in the morning are morning doves.”
3. Tom counts and categorizes birds that land in the tree in his backyard every morning
from 5:00-6:00 am. He counts mostly morning doves and generalizes, “most birds that
land in my tree during the 24-hour day are morning doves.”
4. Tom counts and categorizes birds that land in the tree in his backyard every day from
5:00-6:00 am, from 11:00-12:00 pm, and from 5:00- 6:00 pm. He counts mostly morning
doves and generalizes, “most birds that land in my tree during the 24-hour day are
morning doves.”
Tom counts and categorizes birds that land in the tree in his backyard every evening
from 10:00-11:00 pm. He counts mostly owls and generalizes, “most birds that land in
my tree throughout the 24-hour day are owls.”
6. Tom counts and categorizes birds that land in the tree in his backyard every evening
from 10:00-11:00 pm and from 2:00-3:00 am. He counts mostly owls and generalizes,
“most birds that land in my tree throughout the night are owls.”
Answer: This seems to be a good generalization, assuming that he keeps up this
regimen on multiple days. The difference, of course, is that instead of
making his generalization cover the whole day, his generalization is only
about the birds that land in his tree during the night.
A poll administered to 10,000 registered voters who were homeowners showed that
90% supported a policy to slash Medicaid funding and decrease property taxes.
Therefore, 90% of voters support a policy to slash Medicaid funding.
8. A telephone poll administered by a computer randomly generating numbers to call,
found that 68% of Americans in the sample of 2000 were in favor of legalizing
recreational marijuana use. Thus, almost 70% of Americans favor legalizing recreation
marijuana use.
9. A randomized telephone poll in the United States asked respondents whether they
supported a) a policy that allows killing innocent children in the womb or b) a policy that
saves the lives of innocent children in the womb. The results showed that 69% of
respondents choose option “b” over option “a.” The generalization was made that “most
Americans favor a policy that disallows abortion.”
10. Steve’s first rock and roll concert was an Ani Difranco concert, in which most of the
concert-goers were women with feminist political slogans written on their t-shirts. Steve
makes the generalization that “most rock and roll concert-goers are women who are
feminists.” He then applies this generalization to the next concert he attends (Tom Petty)
and is greatly surprised by what he finds.
8.2 Explanation and the seven explanatory virtues
Explanations help us to understand why something happened, not simply convince us that
something happened However,there is a common kind of inductive argument that takes the
best explanation of why x occurred as an argument for the claim that x occurred. For example,
suppose that your car window is broken and your iPod (which you left visible in the front seat) is
missing. The immediate inference you would probably make is that someone broke the window
of your car and stole your iPod. What makesthis a reasonable inference? What makes it a
reasonable inference is that this
explanation explains all the relevant facts (broken window, missing iPod) and does so better
than any other competing explanation. In this case, it is perhaps possible that a stray baseball
broke your window, but since (let us suppose) there is no baseball diamond close by, and
people don’t play catch in the parking garage you are parked in, this seems unlikely. Moreover,
the baseball scenario doesn’t explain why the iPod is gone. Of course, it could be that some
inanimate object broke your window and then someone saw the iPod and took it. Or perhaps a
dog jumped into the window that was broken by a stray baseball and ate your iPod. These are
all possibilities, but they are remote and thus much less likely explanations of the facts at hand.
The much better
explanation is that a thief both broke the window and took the iPod. This explanation explains all
the relevant facts in a simple way (i.e., it was the thief responsible for both things) and this kind
of thing is (unfortunately) not uncommon—it happens to other people at other times and places.
The baseball-dog scenario is not as plausible because it doesn’t happen in contexts like this
one (i.e., in a parking garage) nearly as often and it is not as simple (i.e.,we need to posit two
different events that are unconnected to each other—stray baseball, stray dog—rather than just
one—the thief). Inference to the best explanation is a form of inductive argument whose
premises are a set of observed facts, a hypothesis that explains those observed facts, and a
comparison of competing explanations, and whose conclusion is that the hypothesis is true. The
example we’ve just been discussing is an inference tothe best explanation. Here is its form:
1. Observed facts: Your car window is broken and your iPod is gone.
2. Explanation: The hypothesis that a thief broke the window and stole your iPod
provides a reasonable explanation of the observed facts.
3. Comparison: No other hypothesis provides as reasonable an explanation.
4. Conclusion: Therefore, a thief broke your car window and stole your iPod.
Notice that this is an inductive argument because the premises could all be trueand yet the
conclusion false. Just because something is reasonable, doesn’t mean it is true. After all,
sometimes things happen in the world that defy our reason. So perhaps the baseball-dog
hypothesis was actually true. In that case, the premises of the argument would still be true (after
all, the thief hypothesis is still more reasonable than the baseball-dog hypothesis) and yet the
conclusion would be false. But the fact that the argument is not a deductive argument isn’t a
defect of the argument, because inference to the best explanation arguments are not intended
to be deductive arguments, but inductive arguments. Inductive arguments can be strong even if
the premises don’t
entail the conclusion. That isn’t a defect of an inductive argument, it is simply a
definition of what an inductive argument is!
As we’ve seen, in order to make a strong inference to the best explanation, the favored
explanation must be the best (or the most reasonable). But what makes an explanation
reasonable? There are certain conditions that any good explanation must meet. The more of
these conditions are met, the better the explanation. The first, and perhaps most obvious
condition, is that the hypothesis proposed must actually explain all the observed facts. For
example, if, in order to explain the facts that your car window was broken and your iPod was
missing, someone were to say offer the hypothesis that a rock thrown up from a lawnmower
broke the window of your car, then this hypothesis wouldn’t account for all the facts because it
wouldn’t explain the disappearance of your
iPod. It would lack the explanatory virtue of explaining all the observed facts. The baseball-dog
hypothesis would explain all the observed facts, but it would lack certain other explanatory
virtues, such as “power” and “simplicity.” In the remainder of this section, I will list the seven
explanatory virtues and then I will discuss each one in turn. The seven explanatory virtues are:
1. Explanatoriness: Explanations must explain all the observed facts.
2. Depth: Explanations should not raise more questions than they
3. Power: Explanations should apply in a range of similar contexts, not
just the current situation in which the explanation is being offered.
4. Falsifiability: Explanations should be falsifiable—it must be possible
for there to be evidence that would show that the explanation is
5. Modesty: Explanations should not claim any more than is needed to
explain the observed facts. Any details in the explanation must relate
to explaining one of the observed facts.
6. Simplicity: Explanations that posit fewer entities or processes are
preferable to explanations that posit more entities or processes. All
other things being equal, the simplest explanation is the best. This is
sometimes referred to as “Ockham’s razor” after William of Ockham
(1287-1347), the medieval philosopher and logician.
7. Conservativeness: Explanations that force us to give up fewer wellestablished
beliefs are better than explanations that force us to give
up more well-established beliefs.
Suppose that when confronted with the observed facts of my car window being broken and my
iPod missing, my colleague Jeff hypothesizes that my colleague, Paul Jurczak did it. However,
given that I am friends with Paul, that Paul could easily buy an iPod if he wanted one, and that I
know Paul to be the kind of person who has probably never stolen anything in his life (much less
broken a car window), this explanation would raise many more questions than it answers. Why
would Paul want to steal my iPod? Why would he break my car window to do so? Etc. This
explanation raises as many questions as it answers and thus it lacks the explanatory virtue of
Consider now an explanation that lacks the explanatory virtue of “power.” A good example
would be the stray baseball scenario which is supposed to explain, specifically, the breaking of
the car window. Although it is possible that a stray baseball broke my car window, that
explanation would not apply in a range of similar contexts since people don’t play baseball in or
around parking garages. So not many windows broken in parking garages can be explained by
stray baseballs. In contrast, many windows broken in parking garages can be explained by
thieves. Thus, the thief explanation would be a more powerful explanation, whereas the stray
baseball explanation would lack the explanatory virtue of power.
Falsifiability can be a confusing concept to grasp. How can anything having to do with being
false be a virtue of an explanation? An example will illustrate why the possibility of being false is
actually a necessary condition for any good empirical explanation.Consider the following
explanation. My socks regularly disappear and then sometime reappear in various places in the
house. Suppose I were to explain this fact as follows. There is an invisible sock gnome that lives
in our house. He steals my socks and sometimes he brings them back and sometimes he
doesn’t. This explanation sounds silly and absurd, but how would you show that it is false? It
seems that the hypothesis of the sock gnome is designed such that it cannot be shown to be
false—it cannot be falsified. The gnome is invisible, so you can never see it do its thing. Since
there is no way to observe it, it seems you can never prove nor disprove the existence of the
sock gnome. Thus, you can neither confirm nor disconfirm the hypothesis. But such a
hypothesis is a defective hypothesis. Any empirical hypothesis (i.e., a hypothesis that is
supposed to explain a set of observed facts) must at least be able to be shown false. The sock
gnome hypothesis lacks this virtue—that is, it lacks the explanatory virtue of being falsifiable. In
contrast, if I were to hypothesize that our dog, Violet, ate the sock, then this hypothesis is
falsifiable. Falsifiability requires only that it be possible to show that the hypothesis is false. If we
look for evidence that would show that the hypothesis is false, but we won’t find that evidence,
then we have confirmed that hypothesis. In contrast, an unfalsifiable hypothesis cannot be
confirmed because we cannot specify any evidence that would show false, so we can’t try to
look for such evidence (which is what a rigorous scientific methodology requires).
The explanatory virtue of “simplicity” tells us that all other things being equal, the simplest
explanation is the better explanation. More precisely, an explanation that posits fewer entities or
processes in order to explain the observed facts is better than a explanation that posits more
entities and processes to explain that same set of observed facts. Here is an example of an
explanation that would lack the virtue of simplicity. Suppose that all three of our cars in our
driveway were broken into one night and that the next morning the passenger’s side rear
windows of each car were broken out. If I were to hypothesize that three separate, unrelated
thieves at three different times of the night broke into each of the cars, then this would be an
explanation that lacks the virtue of simplicity. The far simpler explanation is that it was one thief
(or one related group of thieves) that broke into the three cars at roughly the same
time. In the domain of science, upholding simplicity is often a matter of not positing new entities
or laws when we can explain the observed facts in terms of existing entities and laws. My earlier
example of the sock gnome stealing the socks vs. our dog Violet taking the socks is a good
example to illustrate this. Sock gnomes would be a new kind of entity that we don’t have any
independent reason to think exists, but our dog Violet clearly already exists and since the
observed facts can be explained by Violet’s actions rather than that of a sock gnome, the Violet
explanation possesses the explanatory virtue of simplicity, whereas the sock gnome explanation
lacks the explanatory virtue of simplicity. However, sometimes science requires that we posit
new kinds of entities or
processes, as when Copernicus and Galileo suggested that the sun, rather than the earth, was
at the center of the “solar system” in order to explain certain astronomical observations. In
physics new entities are often posited in order to explain the observations that physicists make.
For example, the elementary particle dubbed “the Higgs boson” was hypothesized by Peter
Higgs (and others) in 1964 and was confirmed in 2012. Much earlier, in 1897, J.J. Thompson
and his collaborators, drawing on the work of earlier German physicists, discovered the
electron—one of the first elementary particles to be discovered. So there is nothing wrong with
positing new laws or entities—that is how science progresses. Simplicity doesn’t say that one
should never posit new entities; that would be absurd. Rather, it tells us that if the observed
facts can
be explained without having to posit new entities, then that explanation is preferable to an
explanation that does posit new entities (all other things being equal). Of course, sometimes the
observations cannot be explained without having to change the way we understand that world.
This is when it is legitimate to posit new entities or scientific laws.
The last explanatory virtue—conservativeness—tells us that better explanations are ones that
force us to give up fewer well-established beliefs. Like simplicity, conservativeness is an
explanatory virtue only when we are considering two explanations that each explain all the
observed facts, but where one conflicts with well-established beliefs and the other doesn’t. In
such a case, the former explanation would lack the explanatory virtue of conservativeness,
whereas the latter explanation would possess the virtue of conservativeness. Here is an
example to illustrate the virtue of conservativeness. Suppose that there are some photographs
that vaguely seem to indicate a furry, bipedal humanoid creature that does not look human. My
friend Chris offers the following explanation: the creature in those photos is Bigfoot, or
Sasquatch. In contrast, I maintain that the creature in the photos is a person in a Bigfoot suit.
Given justthis evidence (the blurry photos), Chris’s explanation lacks the virtue
ofconservativeness since his explanation requires the existence of Bigfoot, which is
contrary to well-established beliefs that Bigfoot is merely folklore, not a real creature. In
contrast, my explanation possesses the virtue of conservativeness since there is nothing about
someone dressing up in a costume and being caught on camera (or even someone doing so to
play a practical joke or to perpetuate a false belief in a certain population) that conflicts with
wellestablished beliefs. My explanation doesn’t require the existence of Bigfoot,but just the
existence of human beings dressed up to look like Bigfoot.
8.2 Exercise : Identify which explanatory virtues, if any, the following
explanations lack and explain why it lacks that particular virtue. If there is
a better explanation, suggest what it might be.
1. Bob explains the fact that he can’t remember what happened yesterday by
saying that he must have been kidnapped by aliens, who performed surgery on
him and then erased his memory of everything that happened the day before
returning him to his house.
Answer: This could be any number of them, including: depth (why would the aliens
have kidnapped him and then returned him to his home?), power (this
explanation cannot be used in a range of different circumstances—a better
explanation is simply that he has some kind of amnesia), or simplicity (if we don’t
have any other reason to admit there are aliens, then we should simply chalk it
up to some kind of amnesia).
2. Mrs. Jones hears strange noises at night such as the creaking of the floor
downstairs and rattling of windows. She explains these phenomena by
hypothesizing that there is a 37-pound badger that inhabits the house and that
emerges at night in search of Wheat Thins and Oreos.
3. Edward saw his friend Tom at the store in their hometown of Lincoln, Nebraska
just an hour ago. Then, while watching the World Cup on television, he saw
someone that looked just like Tom in the crowd at
the game in Brazil. He hypothesizes that his friend Tom must have an
identical twin that Tom has never told him about.
4. Edward’s friend Tom died two years ago. But just yesterday Tom saw
someone who looked and spoke exactly like Tom. Edward hypothesizes that Tom
must have come back to life.
5. Edward’s friend Tom died twenty years ago when Tom was just 18. But just
yesterday Edward saw someone who looked and spoke exactly like Tom.
Edward hypothesizes that Tom must have had a son that he did not know about
and that this person must have been Tom’s son.
6. Elise has the uncanny feeling that although her family members look exactly the
same, something just isn’t right about them. She hypothesizes that her family
members have been replaced with imposters who look and act exactly like her
real family members and that no one can prove that this happened.
8.4 Analogical arguments
Another kind of common inductive argument is an argument from analogy. In an argument from
analogy, we note that since something x shares similar properties to some thing y, then since y
has characteristic A, x probably has characteristic A as well. For example, suppose that I have
always owned Subaru cars in the past and that they have always been reliable and I argue that
the new car I’ve just purchased will also be reliable because it is a Subaru. The two things in the
analogy are 1) the Subarus I have owned in the past and 2) the current Subaru I have just
purchased. The similarity between these two things is just that they are both Subarus. Finally,
the conclusion of the argument is that this Subaru will share the characteristic of being reliable
with the past Subarus I have owned. Is this argument a strong or weak inductive argument?
Partly itdepends on how many Subarus I’ve owned in the past. What this illustrates is that better
arguments from analogy will invoke more relevant similarities between the things being
compared in the analogy. This is a key condition for any good argument from analogy: the
similar characteristics between the two things citedin the premises must be relevant to the
characteristic cited in the conclusion.
Here is an ethical argument that is an argument from analogy.1 Suppose that Bob uses his life
savings to buy an expensive sports car. One day Bob parks his car and takes a walk along a set
of train tracks. As he walks, he sees in the distance a small child whose leg has become caught
in the train tracks. Much to his alarm, he sees a train coming towards the child. Unfortunately,
the train will reach the child before he can (since it is moving very fast) and he knows it will be
unable to stop in time and will kill the child. At just that moment, he sees a switch near him that
he can throw to change the direction of the tracks and divert the train onto another set of tracks
so that it won’t hit the child. Unfortunately, Bob sees that he has unwittingly parked his car on
that other set of tracks and that if he throws the switch, his expensive car will be destroyed.
Realizing this, Bob decides not to throw the switch and the train strikes and kills the child,
leaving his car unharmed. What should we say of Bob? Clearly, that was a horrible thing for Bob
to do and we would rightly judge him harshly for doing it. In fact, given the situation described,
Bob would likely be criminally liable. Now consider the following situation in which you, my
reader, likely findyourself (whether you know it or not—well, now you do know it). Each week
youspend money on things that you do not need. For example, I sometimes buy $5 espressos
from Biggby’s or Starbuck’s. With the money that you could save from forgoing these luxuries,
you could, quiteliterally, save a child’s life.
Given these facts, and comparing these two scenarios (Bob’s and your own), the argument from
analogy proceeds like this:
1. Bob chose to have a luxury item for himself rather than to save the life of a child.
2. “We” regularly choose having luxury items rather than saving the life of a child.
3. What Bob did was morally wrong.
4. Therefore, what we are doing is morally wrong as well.
The two things being compared here are Bob’s situation and our own. The argument then
proceeds by claiming that since we judge what Bob did to be morally wrong, and since our
situation is analogous to Bob’s in relevant respects (i.e., choosing to have luxury items for
ourselves rather than saving the lives of dying children), then our actions of purchasing luxury
items for ourselves mustbe morally wrong for the same reason.
One way of arguing against the conclusion of this argument is by trying to argue that there are
relevant disanalogies between Bob’s situation and our own. For example, one might claim that
in Bob’s situation, there was something much more immediate he could do to save the child’s
life right then and there. In contrast, our own situation is not one in which a child that is
physically proximate to us is in imminent danger of death, where there is something we can
immediately do about it. One might argue that this disanalogy is enough to show that the two
situations are not analogous and that, therefore, the conclusion does not follow.
So we’ve seen that an argument from analogy is strong only if the following two
conditions are met:
1. The characteristics of the two things being compared must be similar in relevant respects to
the characteristic cited in the conclusion.
2. There must not be any relevant disanalogies between the two things being compared.
Arguments from analogy that meet these two conditions will tend to be strongerinductive
Exercise 8.3 : Evaluate the following arguments from analogy as either strong or weak. If the
argument is weak, cite what you think would be a relevant disanalogy.
1. Every painting by Rembrandt contains dark colors and illuminated faces, therefore the
original painting that hangs in my high school is probably by Rembrandt, since it contains dark
colors and illuminated faces.
Answer: Weak: if the painting is hanging in your high school, it probably isn’t a
Rembrandt. That is the disanalogy: even if the colors are very similar,
almost all Rembrandts hang in galleries, not in high schools.
2. I was once bitten by a poodle. Therefore, this poodle will probably bite me too.
3. Every poodle I’ve ever met has bitten me (and I’ve met over 300poodles). Therefore this
poodle will probably bite me too.
4. My friend took Dr. Van Cleave’s logic class last semester and got an A. Since Dr. Van
Cleave’s class is essentially the same this semester and since my friend is no better a student
than I am, I will probably get an A as well.
5. Bill Cosby used his power and position to seduce and rape women. Therefore, Bill Cosby
probably also used his power to rob banks.
6. Every car I’ve ever owned had seats, wheels and brakes and was also safe to drive. This
used car that I am contemplating buying has seats, wheels and brakes. Therefore, this used car
is probably safe to drive.
8.4 Causal reasoning
When I strike a match it will produce a flame. It is natural to take the striking of the match as the
cause that produces the effect of a flame. But what if the matchbook is wet? Or what if I happen
to be in a vacuum in which there is no oxygen (such as in outer space)? If either of those things
is the case, then the striking of the match will not produce a flame. So it isn’t simply the striking
of the match that produces the flame, but a combination of the striking of the match together
with a number of other conditions that must be in place in order for the striking of the match to
create a flame. Which of those conditions we call the “cause” depends in part on the context.
Suppose that I’m in outer space striking a match (suppose I’m wearing a space suit that
supplies me with oxygen but that I’m striking the match in space, where there is no oxygen). I
continuously strike it but no flame appears (of course). But then someone (also in a space suit)
brings out a can of compressed oxygen that they spray on the match while I strike it. All of a
sudden a flame is produced. In this context, it looks like it is the spraying of oxygen that causes
flame, not the striking of the match. Just as in the case of the striking of the match, any cause is
more complex than just a simple event that produces some other event. Rather, there are
always multiple conditions that must be in place for any cause to occur. These conditions are
called background conditions. That said, we often take for granted the background conditions in
normal contexts and just refer to one particular event as the cause. Thus, we call the striking of
the match the cause of the flame. We don’t go on to specify all the other conditions that
conspiredto create the flame (such as the presence of oxygen and the absence of water).
But this is more for convenience than correctness. For just about any cause, there are a number
of conditions that must be in place in order for the effect to occur. These are called necessary
conditions. For example, a necessary condition of the match lighting is that there is oxygen
present. A necessary condition of a car running is that there is gas in the tank. We can use
necessary conditions to diagnose what has gone wrong in cases of malfunction. That is, we can
consider each condition in turn in order to determine what caused the malfunction. For example,
if the match doesn’t light, we can check to see whether the matches are wet. If we find that the
matches are wet then we can explain the lack of the flame by saying something like, “dropping
the matches in the water caused the matches not to light.” In contrast, a sufficient condition is
one which if present will always bring about the effect. For example, a person being fed through
an operating wood chipper is sufficient for causing that person’s death (as was the fate of Steve
Buscemi’s character in the movie Fargo).
Being able to determine when causal generalizations are true is an important part of becoming a
critical thinker. Since in both scientific and every day contexts we rely on causal generalizations
in explaining and understanding our world, the ability to assess when a causal generalization is
true is an important skill.
For example, suppose that we are trying to figure out what causes our
dog, Charlie, to have seizures. To simplify, let’s suppose that we have a set of potential
candidates for what causes his seizures. It could be either:
A) eating human food,
B) the shampoo we use to wash him,
C) his flea treatment,
D) not eating at regular intervals,or some combination of these things.
Suppose we keep a log of when these things occur each day and when his seizures (S) occur.
In the table below, I will represent the absence of the feature by a negation. So in the table
below, “~A” represents that Charlie did not eat human food on that day; “~B” represents that he
did not get a bath and shampoo that day; “~S” represents that he didnot have a seizure that
day. In contrast, “B” represents that he did have a bath and shampoo, whereas “C” represents
that he was given a flea treatment that day. Here is how the log looks
How can we use this information to determine what might be causing Charlie to have seizures?
The first thing we’d want to know is what feature is present every time he has a seizure. This
would be a necessary (but not sufficient) condition. And that can tell us something important
about the cause. The necessary condition test says that any candidate feature (here A, B, C, or
D) that is absent when the target feature (S) is present is eliminated as a possible necessary
condition of S.3 In the table above, A is absent when S is present, so A can’t be a necessary
condition (i.e., day 1). D is also absent when S is present (day 4) so D can’t be a necessary
condition either. In contrast, B is never absent when S is present—that is every time S is
present, B is also present. That means B is a necessary condition, based on the data that we
have gathered so far. The same applies to C since it is never absent when S is present. Notice
that there are times when both B and C are absent, but on those days the target feature (S) is
absent as well, so it doesn’t matter.
The next thing we’d want to know is which feature is such that every time it is present, Charlie
has a seizure. The test that is relevant to determining this is called the sufficient condition test.
The sufficient condition test says that any candidate that is present when the target feature (S)
is absent is eliminated as a possible sufficient condition of S. In the table above, we can see
that no one candidate feature is a sufficient condition for causing the seizures since for each
candidate (A, B, C, D) there is a case (i.e. day) where it is present but that no seizure occurred.
Although no one feature is sufficient for causing the seizures (according to the data we have
gathered so far), it is still possible that certain features are jointly sufficient. Two candidate
features are jointly sufficient for a target feature if and only if there is no case in which both
candidates are present and yet the target is absent. Applying this test, we can see that B and C
are jointly sufficient for the target feature since any time both are present, the target feature is
always present. Thus, from the data we have gathered so far, we can say that the likely cause
of Charlie’s seizures are when we both give him a bath and then follow that bath up with a flea
treatment. Every time those two things occur, he has a seizure (sufficient condition); and every
time he has a seizure, those two things occur (necessary condition). Thus, the data gathered so
far supports the following causal conditional: Any time Charlie is given a shampoo bath and a
flea treatment, he has a seizure.
Although in the above case, the necessary and sufficient conditions were the same, this needn’t
always be the case. Sometimes sufficient conditions are not necessary conditions. For example,
being fed through a wood chipper is a sufficient condition for death, but it certainly isn’t
necessary! (Lot’s of people die without being fed through a wood chipper, so it can’t be a
necessary condition of dying.) In any case, determining necessary and sufficient conditions
is a key part of determining a cause. When analyzing data to find a cause it is important that
we rigorously test each candidate. Here is an example to illustrate rigorous testing. Suppose
that on every day we collected data about Charlie he ate human food but that on none of the
days was he given a bath and shampoo, as the table below indicates.
Given this data, A trivially passes the necessary condition test since it is always present (thus,
there can never be a case where A is absent when S is present). However, in order to rigorously
test A as a necessary condition, we have to look for cases in which A is not present and then
see if our target condition S is present. We have rigorously tested A as a necessary condition
only if we have collected data in which A was not present. Otherwise, we don’t really know
whether A is a necessary condition. Similarly, B trivially passes the sufficient condition test since
it is never present (thus, there can never be a case where B is present but S is absent).
However, in order to rigorously test B as a sufficient condition, we have to look for cases in
which B is present and then see if ourtarget condition S is absent. We have rigorously tested B
as a sufficient condition only if we have collected data in which B is present. Otherwise, we don’t
really know whether B is a sufficient condition or not. In rigorous testing, we are actively looking
for (or trying to create) situations in which a candidate feature fails one of the tests. That is why
when rigorously testing a candidate for the necessary condition test, we must seek out cases in
which the candidate is not present, whereas when rigorously testing a candidate for the
sufficient condition test, we must seek out cases in which the candidate is present. In the
example above, A is not rigorously tested as a necessary condition and B is not rigorously
tested as a sufficient condition. If we are interested in finding a cause, we should always
rigorously test each candidate.
This means that we should always have a mix of different situations where the candidates and
targets are sometimes present and sometimes absent. The necessary and sufficient conditions
tests can be applied when features of the environment are wholly present or wholly absent.
However, in situations where features of the environment are always present in some degree,
these tests will not work (since there will never be cases where the features are absent and so
rigorous testing cannot be applied). For example, suppose we are trying to figure out whether
CO2 is a contributing cause to higher global temperatures. In this case, we can’t very well look
for cases in which CO2 is present but high global temperatures aren’t (sufficient condition test),
since CO2 and high temperatures are always present to some degree. Nor can we look for
cases in which CO2 is absent when high global temperatures are present (necessary condition
test), since, again, CO2 and high global temperatures are always present to some degree.
Rather, we must use a different method, the method that J.S. Mill called the method of
concomitant variation. In concomitant variation we look for how things vary vis-à-vis each
other. For example, if we see that as CO2 levels rise, global temperatures also rise, then this is
evidence that CO2 and higher temperatures are positively correlated. When two things are
positively correlated, as one increases, the other also increases at a similar rate (or as one
decreases, the other decreases at a similar rate). In contrast, when two things are negatively
correlated, as one increases, the other decreases at similar rate (or vice versa). For example, if
as a police department increased the number of police officers on the street, the number of
crimes reported decreases, then number of police on the street and number of crimes reported
would be negative correlated. In each of these examples, we may think we can directly infer the
cause from the correlation—the rising CO2 levels are causing the rising global temperatures
and the increasing number of police on the street is causing the crime rate to drop. However, we
cannot directly infer causation from correlation. Correlation is not causation. If A and B are
positively correlated, then there are four distinct possibilities regarding what the cause is:
1. A is the cause of B
2. B is the cause of A
3. Some third thing, C, is the cause of both A and B increasing
4. The correlation is accidental
In order to infer what causes what in a correlation, we must rely on our general background
knowledge (i.e., things we know to be true about the world), our scientific knowledge, and
possibly further scientific testing. For example, in the global warming case, there is no scientific
theory that explains how rising global temperatures could cause rising levels of CO2 but there is
a scientific theory that enables us to understand how rising levels of CO2 could increase
average global temperatures. This knowledge makes it plausible to infer that the rising CO2
levels are causing the rising average global temperatures. In the police/crime case, drawing on
our background knowledge we can easily come up with an inference to the best explanation
argument for why increased police presence on the streets would lower the crime rate—the
more police on the street, the harder it is for criminals to get away with crimes because there
are fewer places where those crimes could take place without the criminal being caught. Since
criminals don’t want to risk getting caught when they commit a crime, seeing more police around
will make them less likely to commit a crime. In contrast, there is no good explanation for why
decreased crime would cause there to be more police on the street. In fact, it would seem to be
just the opposite: if the crime rate is low, the city should cut back, or at least remain stable, on
the number of police officers and put those resources somewhere else. This makes it plausible
to infer that it is the increased police officers on the street that iscausing the decrease in crime.
Sometimes two things can be correlated without either one causing the other. Rather, some
third thing is causing them both. For example, suppose that Bob discovers a correlation
between waking up with all his clothes on and waking up with a headache. Bob might try to infer
that sleeping with all his clothes on causes headaches, but there is probably a better
explanation than that. It ismore likely that Bob’s drinking too much the night before caused him
to pass out in his bed with all his clothes on, as well as his headache. In this scenario, Bob’s
inebriation is the common cause of both his headache and his clothes being on in bed.
Sometimes correlations are merely accidental, meaning that there is no causal relationship
between them at all. For example, Tyler Vigen4 reports that the per capita consumption of
cheese in the U.S. correlates with the number of people who die by becoming entangled in their
bed sheets:
And the number of Mexican lemons imported to the U.S. correlates with the
number of traffic fatalities5
Clearly neither of these correlations are causally related at all—they are accidental correlations.
What makes them accidental is that we have no theory that would make sense of how they
could be causally related. This just goes to show that it isn’t simply the correlation that allows us
to infer a cause, but, rather, some additional background theory, scientific theory, or other
evidence that establishes one thing as causing another. We can explain the relationship
between correlation and causation using the concepts of necessary and sufficient conditions:
correlation is a necessarycondition for causation, but it is not a sufficient condition for causation.
Our discussion of causes has shown that we cannot say that just because A precedes B or is
correlated with B, that A caused B. To claim that since A precedes or correlates with B, A must
therefore be the cause of B is to commit what is called the false cause fallacy. The false cause
fallacy is sometimescalled the “post hoc” fallacy. “Post hoc” is short for the Latin phrase, “post
hoc ergo propter hoc,” which means “before this therefore because of this.” As we’ve seen, false
cause fallacies occur any time someone assumes that two events that are correlated must be in
a causal relationship, or that since one event precedes another, it must cause the other. To
avoid the false cause fallacy, one must look more carefully into the relationship between A and
B to determine whether there is a true cause or just a common cause or accidental correlation.
Common causes and accidental correlations are more common than one might think.
Exercise 8.4 : Determine which of the candidates (A, B, C, D) in thefollowing examples pass
the necessary condition test or the sufficient condition test relative to the target (G). In addition,
note whether there are any candidates that aren’t rigorously tested as either necessary or
sufficient conditions.
Answer: C is sufficient since any time it is present, the target G is present. Both C
and D are necessary, since any time the target G is present, they are present.
Critical Thinking and Decision Making
3 Hours
Show how critical thinking leads to better decisions.
Distinguish the different decision making techniques.
Examine the crucial role of decision makers in an organization.
Show the mutual relation between decision making and critical thinking.
READINGS AND VIDEOS (Please see the digital copies of the materials.)
Reading 9.1
Turan, U., Fidan, Y., & Yıldıran, C. (2019). Critical Thinking as a Qualified
Decision-Making Tool in Journal of History Culture and Art Research, 8(4), 1-18.
Reading 9.2
Noel, L. Pierre, S. & Watson, J. (2017) Critical Thinking, Decision Making and
Mindfullness in Fischler College of Education: Student Articles. 16. Retrieved
from https://nsuworks.nova.edu/fse_stuarticles/16
Video 9.1
Webinar: The Case of Critical Thinking in Business in
The Importance of Critical Thinking in
Critical Thinking Skills in https://www.youtube.com/watch?v=9PsLktb7HTA
Video 9.2
Video 8.3
Exercise 9.1 Write a reflection paper (150-200 words) on the impact and
importance of critical thinking in the different decision making techniques.
9.0 Critical Thinking as a Qualified Decision-Making Tool
Uğur Turan 1 , Yahya Fidan 2 , Canan Yıldıran3
Critical thinking is an important requirement for individuals to make better decisions, while
various decision-making techniques also contribute positively to the quality of critical thinking of
individuals. It is very important for individuals who want to make more successful decisions both
in their personal and professional lives, in order to improve their critical thinking capacities and
to benefit from decision techniques in making high importance decisions. For today's and
tomorrow's executives who influence the lives of countless people with their decisions,
developing critical thinking skills will be an approach that requires determination and
commitment as an indication of their respect for their profession
Every business and management invests in human resources to improve the decision quality of
senior executives, especially those who make strategic decisions. Undoubtedly, one of the most
prominent investments in business resources is the investments made in the training and
development of managers. Every effort to improve the decision quality of the managers will
increase the quality of the decision in parallel with the increase of the qualifications of the
Management scientist Daft described the decision as a choice among the existing alternatives.
Decision-making is the process of identifying problems and opportunities and then providing
solutions to them (Daft R. L., 2008, p. 272).
There are many techniques that can be used at various stages of the decision process and
make it easier to make more accurate decisions. Some of the most used ones are the following:
Decision Trees:
Six Thinking Hats
Nominal Group Technique
Delphi Technique
9.1 Relationship between Decision-Making and Critical Thinking
Usually, a threat or an opportunity arises when managers need to make a decision (Daft &
Marcic, 2009, p. 207). In such cases, managers should first become aware of the threat or
opportunity. The main thing that is necessary to recognize a threat or opportunity situation is
knowledge. Information needed by managers can be obtained from printed sources such as
financial reports, performance reports or reports on activities carried out within the enterprise, or
informally through communication with other managers, employees or internal and external
stakeholders of the entity (Daft & Marcic, 2009, p. 208).
In the process of defining the problem, which is another stage in the decision-making process, a
critical thinking manager needs to analyse or examine the situation or opportunity he/she
encounters. The best way to do this is to ask questions that will clarify the situation and clarify
the definition of threats or opportunities. Kepner and Tregoe stated that it is necessary to ask a
series of questions to better define the problem and to reveal the underlying causes of the
problem: i) What is the situation affecting us, ii) When, iii) Where did it happen, iv) How did it
happen, v) Urgency of the situation vi) whether the situation is related to other situations or
events (Kepner & Tregoe, 1965, p. 41-42).
At the stage of developing alternatives, alternative methods that can be used to solve the
problem should be found. At this stage, it was stated that limiting the alternative search had a
negative effect on the success of the decision (Nutt, 2004, p. 27). A critical thinker should be
able to present possible alternative solutions by evaluating the problem situation from different
perspectives. In addition, managers who are based on a critical approach should be aware of
the need to apply innovative thinking methods for alternative solutions.
Another step in the decision-making process is the selection of one of the alternatives. Decision
selection is the selection of the most promising alternative action. The best alternative is
generally the solution that best fits the overall goals and values of the enterprise and provides
the desired results using the least resources (Daft & Marcic, 2009, p. 210). In addition, moral
and ethical consequences of the decision should be taken into consideration when making
decisions (Fisher, 2011, p. 175).
In the implementation of the decision, it is necessary to use the managerial, administrative and
persuasive skills of the managers to ensure that the selected alternative is fulfilled.
Implementation of the decision may require negotiation with people affected by the decision.
Communication, motivation and leadership skills should be used to see the decision being
implemented. Employees are committed to more positive actions when they see that managers
follow the decisions made by following the success of the implementation (Daft & Marcic, 2009,
p. 211).
Managers should observe the implementation of the decision and examine the positive and
negative impacts they believe will be achieved and whether the results they have achieved
during the decision making process are achieved. As a result of these observations, they should
make an effort to improve their own thinking processes by reviewing the stages of thinking
applied in the decision-making process in the light of the information they have acquired.
Since programmable decisions are often for repetitive situations and the steps to be taken are
often specific, there is limited space for critical thinking for such decisions. In any case, from a
critical point of view, such decisions can be evaluated to determine the reasons for their
emergence and to find out if there is a solution that can eliminate the problem situation.
Unprogrammable decisions are made in unique, ambiguous cases. Usually, such decisions
have important consequences for the business. Many unprogrammable decisions require
strategic planning because uncertainty is high and decisions are complex (Daft, 2008, p. 272).
Critical thinking skills are the most needed decisions. In such a decision-making process, as
much information as possible should be obtained and important criteria should be determined
for an effective decision. Critical thinking is based on rational thought, and rational thinking will
be more reliable than decisions based on emotion, intuition or belief (Tittle, 2011, p. 11).
The techniques used in the decision-making process offer various benefits to decision-makers
and help them to make more dominant decisions. The goals of critical thinking include thinking
and making decisions with as many and necessary information as possible (Ennis, 2015, p. 32).
Decision-making techniques aim to help decision-makers in decision-making by providing them
with different perspectives and reviewing information in a specific order.
It is often difficult to decide on a complex issue involving many options and outcomes that
interact in all ways. In such cases, decision trees are a useful tool to see the whole problem
(Lau, 2011, p. 211). Taking the whole situation into consideration is among the tendencies of a
critical thinker (Ennis, 2011, p. 6). Decision trees present the entire problem to the decisionmaker's assessment, but a critical perspective is also needed during the formation of the
decision tree in order to undertake an ideal decision process. The tendency to approach
different views in an open-minded manner and to be aware of and evaluate the alternatives
(Facione, 1990, p. 28) should be implemented in the decisionmaking process and ensure that
all available data is contained in the decision-tree. Only after such a decision tree forming
process can a knowledgeable and logical decision-making process be completed, which is a
requirement of critical thinking. Another feature of decision trees is that they reveal the
situations that will arise after the decision. According to Paul, a thinker should take into
consideration the reflections that will occur after making a decision and should what
consequences will arise when he transforms his thoughts into reality (Gambrill & Gibbs, 2009, p.
Six thinking hats, which is another method to support the decision-making process, becomes
more valuable when critical thinking is considered. According to De Bono, the biggest enemy of
thinking is complexity, because complexity leads to confusion. When thinking is clear and
simple, it becomes more enjoyable and more effective. De Bono stated that thinking with six
hats had two purposes. The first is to simplify thinking by allowing the thinker to deal with one
thing each time. Instead of dealing with different perspectives such as emotions, logic,
knowledge, hope and creativity at the same time, the thinker can think about them separately.
The second objective is to provide a transition in thinking. Focusing only on emotions or
information only leads to the same type of information (Bono, 2000, p. 133). Different hats
enable us to come up with different kinds of perspectives and protect us from onesided
perspectives. In addition, addressing a subject from one perspective at a time is an effective
way to avoid overlooking different perspectives in the decision-making process.
Lack of knowledge, prejudices, emotions or other factors that limit one's objectivity or rationality
are factors that hinder critical thinking. Individual's self-monitoring and evaluation, which is an
important critical thinking skill, include the consideration of the extent to which an individual's
ideas are influenced by these factors and refine themselves from it (Facione, 1990, p. 93).
De Bono's six-hats thinking metaphor represents six different cognitive approaches to critical
thinking and analysis in understanding a situation or problem and trying to find a suitable
solution. The white hat focuses on the data, information and questions that need to be asked.
Lack of information is also identified at this stage. The red hat provides a clear expression of
emotions and feelings. Black hats are important for a careful critical approach. Interrogation,
revealing negative approaches and revealing weaknesses in propositions are among the
features of this perspective. The yellow hat has an optimistic perspective and reveals the
strengths in assessing the situation at hand. The green hat combines critical and creative
thinking and focuses on finding new ways to solve problems. The blue hat, on the other hand,
requires analysis of the situation and awareness of the ideas and situations uncovered. An
important benefit of the six-hat thinking technique is that it shows that there is no single method
for problem-solving or decision-making (Kivunja, 2015).
In order to find a solution to a problem, it is necessary to first identify and understand the causes
of the problem. According to Okes, businesses and managers often feel that they do not have
time to carry out the deep analysis needed to solve the problems and turn to solutions that
temporarily eliminate the problem at hand. However, this problem then repeats itself, leading to
a recurring cycle. Recurring problems can lead to the interpretation that managers are not doing
their job well enough or diligently. According to the author, root cause analysis is necessary to
overcome such situations, but this is not widely known by most managers (Okes, 2009, p. 1416). Tools that help groups and individuals to identify root causes of problems are known as root
cause analysis tools. Root cause analysis or fishbone diagram is the process of identifying
problem-causing factors using a structured approach with techniques designed to focus on
identifying and solving problems (Istikomah, et al., 2017, p. 84).
The most important aspect of the fishbone technique, which is developed by Japanese quality
expert Dr. Kaoru Ishikawa and is one of the basic techniques used in root cause analysis, is to
visually reveal the causes of the problem and to facilitate the solution. It is clear that the
fishbone technique will be very useful in asking questions that lead to reasons and explanations
in the first stage of the critical thinking process (Cottrell, 2005, p. 2; Tittle, 2011, p. 17; Ennis,
1996, p. 2). In addition, with the fish bone technique revealing the root causes of the problem
visually and clearly, situations that can be quite complicated when not handled carefully will be
easily clarified. This situation is in line with ‘orderliness in working with complexity and diligent in
seeking relevant information' approaches of critical thinking (Facione, 1990, p. 25), suggesting
that this technique will be useful. On the other hand, in a study conducted in 2017, it was
revealed that the development of critical thinking skills was positively affected when a problembased teaching technique, which aims to develop students' critical thinking skills, is supported
by fishbone technique (Istikomah, et al., 2017, p. 89).
The brainstorming technique, first described by Alex Osborn, is a useful method designed to be
used in problem solving as a group, but it’s also useful for individuals (Halpern, 2014, p. 492).
Osborn described brainstorming as an organized way of letting the mind produce ideas without
trying to judge the value of ideas (Ghabanchi & Behrooznia, 2014, p. 514).