Tutor-Marked Assignment
TUTOR-MARKED ASSIGNMENT 02
This tutor-marked assignment is worth 40% of the final mark for Thinking Critically. The cut-off
date for this assignment is 2355hrs on 11 April 2019.
Submit your solution document in the form of a single MS Word file on or before the cut-off
date shown above.
Additional instructions:
1. You will need to indicate clearly on the front page your name, student ID, course title and
assignment number.
2. You must document all information that you use from another source, or you will be
penalized severely. If you copy from the work of another student, regardless of the course
or programme, you will be severely penalized. You are not permitted to re-use material
from past assignments whether in part or in full. All of the above actions can result in
your failing the TMA.
This TMA assesses the following learning outcomes:
Students should be able to:
Identify the principles that underpin critical thinking and writing.
Explain the rules of legitimate inference.
Distinguish speech or writing that is ‘argumentative’ from that which is descriptive.
Illustrate the structure of any given argument.
Use established principles of inference to evaluate the quality of given arguments.
Recognise, and therefore avoid, common forms of reasoning, which, in spite of their
appeal and popularity, are ultimately fallacious.
Critically develop their own positions on a wide range of issues.
Defend those positions through arguments of their own and at length.
This TMA consists of ELEVEN (11) questions. You must answer ALL of them.
Tutor-Marked Assignment
SECTION A: Propositional Logic (25 marks)
Consider the following argument:
“We should be bothered about climate change only if it will seriously affect us during our
lifetime or we, on our own, can do things to arrest it. Scientists predict (and we have no
reason to believe otherwise) that the serious effects of climate change will be felt more than
100 years from now. If the serious effects of climate change will be felt more than 100 years
from now, then climate change will not seriously affect us during our lifetime. And, it is only
reasonable to suppose that nothing that we do on our own will have any impact on stopping
climate change. So, we shouldn’t be bothered about climate change.”
In the context of this argument, you are required to do the following:
a) Assign a letter of the alphabet to each relevant simple statement in the argument.
(4 marks)
b) Distinguish between and identify the final conclusion, the explicitly stated premises
and the intermediate conclusions of the argument (if any). For any intermediate
conclusion you identify, state the premises you infer this conclusion from, along with
the valid standard argument form used in the inference. Also, state the premises and
intermediate conclusions used in inferring the final conclusion and state the valid
standard argument form (if any) used in the inference [Hint: See Example 5.6.2 in
your textbook for guidance.]
(17 marks)
c) Use standard argument forms to evaluate whether the argument is valid.
(4 marks)
SECTION B: Inductive Arguments (10 marks)
Questions 2 and 3 contain inductive arguments. For each question, identify the arguments by
stating the premises and the conclusion [NOTE: The conclusion might be implicit]. Then,
explain which fact, if known, would make the inductive arguments contained therein
stronger; and which fact, if known, would make the arguments weaker.
Question 2
‘Emma is generally in a happy mood at the end of a work day. It is 9pm now. Emma would
be in a happy mood.’
(100 words max, 5 marks)
Tutor-Marked Assignment
Question 3
‘80% of 5,000 Singaporeans surveyed state that the government was right to deny Ben Davis
exemption from National Service to play Premier League football. So, the government
decision was popular among Singaporeans.’
(100 words max, 5 marks)
SECTION C: Informal Fallacies (10 marks)
In the passages contained in Questions 4 – 8, an informal fallacy may have been committed.
For each passage (argument), if it is fallacious, recognise the fallacy by naming it; if the
passage is not fallacious, state so.
(2 marks each)
Question 4
‘My astrologer claims that climate change is a hoax. So, climate change isn’t happening.’
Question 5
‘Homosexuality is morally wrong because it can’t be right to have carnal relations with
another person of the same sex.’
Question 6
‘I have no proof that my boyfriend cheats on me. So, he doesn’t.’
Question 7
‘Manchester City is a world-class football team. So, every Manchester City football player is
world-class.’
Question 8
‘McDonald’s has delicious food as well as efficient and courteous customer service.
Therefore, McDonald’s is better than KFC.’
Tutor-Marked Assignment
SECTION D: Definitions (10 marks)
Questions 9 and 10 provide definitions of the word/phrase italicised in the question. For each
definition, identify what you consider to be the biggest failing of the definition. If you
consider the definition to be good, state so. Explain your answer.
Question 9
National Service is an institution that requires citizens of a nation state to serve the nation
state.
(50 words max, 5 marks)
Question 10
Terrorism is the practice of using illegal violence against innocent people to achieve deviant
political objectives.
(50 words max, 5 marks)
SECTION E: Evaluating and Writing Argumentative Essays (45 marks)
Question 11
Read the passage “End all immigration controls – They’re a sign we value money more than
people.” This can be retrieved from
https://www.theguardian.com/commentisfree/2017/oct/16/end-immigration-controls-moneypeople-barriers. Answer the following questions.
a) In your own words, identify the final conclusion of the author’s central argument.
(20 words max, 5 marks)
b) In your own words, illustrate the structure of the argument (show how the author
supports his final conclusion). Your response must include a brief evaluation of the
quality of his reasons.
(50 words max, 10 marks)
c) Finally, develop a position of your own in support of or against [but, not both] the
author’s conclusion. Then, defend that position with an argument. Your response
should desirably (and, naturally) use your discussion in b. above as a basis. [NOTE:
Your score for this part will reflect the quality of your argument; the quality of your
writing; use of additional considerations (to the ones discussed in the original paper)
relevant to your conclusion; and your reference to external sources.]
(400 words max, 30 marks)
------END OF TMA02-----
Table of Contents
Table of Contents
Course Guide
1. Welcome.................................................................................................................. CG-2
2. Course Description and Aims............................................................................ CG-3
3. Learning Outcomes..............................................................................................
CG-6
4. Learning Materials................................................................................................ CG-7
5. Assessment Overview.......................................................................................... CG-8
6. Course Schedule.................................................................................................. CG-10
7. Learning Mode.................................................................................................... CG-11
Study Unit 1: The Principles of Reasoning
Learning Outcomes................................................................................................. SU1-2
Overview................................................................................................................... SU1-3
Chapter 1: Basic Concepts of Critical Thought................................................... SU1-4
Chapter 2: Arrow Diagrams: Laying Bare the Structure of an
Argument................................................................................................................
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Formative Assessment.......................................................................................... SU1-19
References............................................................................................................... SU1-30
Study Unit 2: Forms of Arguments
Learning Outcomes................................................................................................. SU2-2
Overview................................................................................................................... SU2-3
i
Table of Contents
Chapter 1: Deductive Arguments......................................................................... SU2-4
Chapter 2: Inductive Arguments......................................................................... SU2-10
Formative Assessment.......................................................................................... SU2-15
References............................................................................................................... SU2-30
Study Unit 3: Additional Principles for Arguing Well
Learning Outcomes................................................................................................. SU3-2
Overview................................................................................................................... SU3-3
Chapter 1: Informal Fallacies................................................................................. SU3-4
Chapter 2: Definitions........................................................................................... SU3-11
Chapter 3: Writing Evaluative and Argumentative Essays............................. SU3-16
Formative Assessment.......................................................................................... SU3-20
References............................................................................................................... SU3-26
ii
List of Lesson Recordings
List of Lesson Recordings
Truth Conditions for Compound Statements......................................................... SU1-10
Quality of Arguments................................................................................................ SU1-13
Drawing an Arrow Diagram.................................................................................... SU1-17
Venn Diagrams and Categorical Statements............................................................ SU2-7
Forms of Deductive Arguments and Validity.......................................................... SU2-8
Inductive Forms and Strength.................................................................................. SU2-13
Defining Love.............................................................................................................. SU3-15
iii
List of Lesson Recordings
iv
Study
Unit
The Principles of Reasoning
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Learning Outcomes
By the end of this unit, you should be able to:
1.
Describe the intended aims of the course.
2.
Distinguish statements from sentences.
3.
Identify types of compound statements, such as disjunctions, conjunctions and
conditionals.
4.
State the truth conditions for compound statements.
5.
Identify the basic structure of an argument.
6.
Categorise ordinary language passages as descriptive or argumentative.
7.
Distinguish deductive from inductive arguments.
8.
Distinguish between concepts such as validity, soundness, strength and cogency.
9.
Distinguish between serial, convergent, linked and divergent reasoning.
10.
Draw an arrow diagram to show the structure of an argument expressed in
ordinary language.
11.
Evaluate the strengths and weaknesses of an argument using an arrow diagram.
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Overview
T
he ability to reason soundly is prized across academic and vocational settings.
Similarly, the degree to which one is professionally successful is founded
on one’s capacity for judicious decision-making and powers of persuasion, which
necessarily demand the skill to think correctly and critically. This natural selection
argument aside, developing the faculty to reason well is an indispensable step towards
fulfilling our uniquely human potential, given that it is the propensity for sophistication
in reasoning that distinguishes us from other species.
In this context, this course attempts to equip students with a tool kit that enables them to
distinguish between truths and falsehoods; justified and unjustified beliefs; coherent and
incoherent claims; and good and bad decisions. In addition, this course provides students
with the rigour, restraint and discipline required for a self-directed understanding of, and
learning about, the world.
All the principles of reasoning presented in this course are developed keeping in mind
how we speak, write and communicate with each other on an everyday basis. There
are two primary advantages of this approach. Firstly, the reasoning skills acquired
become transferable across our students’ academic, professional and personal roles. In
addition, it emphasises that the capacity for and the commitment to critical thought is an
indispensable life skill. This is perhaps the central precept of this course.
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Chapter 1: Basic Concepts of Critical Thought
1.1 Course Overview
Read
You should now read: Mooney et al (2016), Chapter 1 (Section 1.1).
This course has a noble and ambitious goal. It intends, firstly, to teach you to reason.
But, what does reasoning mean? As the opening line of the first chapter of your textbook
suggests, reasoning is giving reasons for any claim (that you might wish to make). You
could broaden the scope of this definition and consider reasoning as having reasons for
any belief (that you might hold).
For example, if you believe that telling a lie is wrong, or that God exists, or that ministers
in Singapore get paid too much, or that you deserve a pay rise or promotion at work, this
course aims to teach you to have reasons for these beliefs. It emphasises the importance of
only having beliefs that you have reasons for. And this is where many of you might object
that this course is going to be a waste of your time, since you already do what I said this
course teaches you to do – reason, that is. You might even claim that the structure of the
ordinary, functional human brain is such as to make the lack of reasoning by an individual
impossible.
If this were to be your objection, I would be happy, because then you would already be a
step closer to achieving the other objective of this course. You see, even if I grant you that
most, if not all, of us engage in reasoning, it does not follow that most of us reason well.
In other words, even if we have reasons for our beliefs, they might not be good reasons.
So, secondly, this course aims to teach you how to reason correctly. Note that whether you
have good reasons for your beliefs is not a matter of interpretation; it is not a subjective
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issue. Rather, there are clear, established and agreed upon criteria based on which, the
‘soundness’ of your reasons can be evaluated.
So, in order to turn you into a ‘good reasoner’, this course will teach you to identify the
different ‘types’ of reasons one might have for one’s beliefs or claims, and to subject such
reasons to the scrutiny of the standards of good reasoning. And, if you are conscientious
and diligent in your study and application of the material prepared for you, then, at the
end of the course, you will be in the happy circumstance of coming as close as possible to:
i.
having only true, or at least, justified beliefs;
ii.
getting others to agree to your claims; and
iii.
making the right decision in your personal and professional lives.
1.2 Statements: ‘Simple’ and ‘Compound’
Read
You should now read: Mooney et al (2016), Chapter 1 (Section 1.2).
1.2.1 Statements versus Sentences
Having read Section 1.1 (Mooney et al, 2016), you should know that the act of reasoning is
the act of giving an argument for a claim or belief. The basic ingredient in any argument
is a statement. Just as a Lego model is constituted by Lego bricks, which are not divisible
further, the indivisible components of an argument are statements. So, your ability to
identify arguments and evaluate them hinges, first and foremost, on your ability to
identify statements. The required reading from your textbook defines statements for you,
and shows you how to distinguish them from sentences. Having familiarised yourself
with that distinction, you should attempt the following exercise:
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Activity 1
Mooney et al (2016), Exercise 1.1, pp.4.
1.2.2 Simple versus Compound Statements
Read
You should now read: Mooney et al (2016), Chapter 9 (Section 9.1).
Section 1.2 (Mooney et al, 2016) also, but very briefly, illustrates the distinction between
simple and compound statements (Section 9.1 is a lot richer). It is easier to make
this distinction by starting with a compound statement. For our purposes, compound
statements take one of the following forms:
a.
Negations
A negation takes the form: “Not [ • ].” Note that any statement can be substituted
for the dot within the brackets to give us a negation. For example, the dot could
stand for: “Jack will ask Jill out.” Then, the negation would be: “Jack will not ask
Jill out” or, to use a more contrived expression, “It is not the case that Jack will
ask Jill out.”
To use another example, the dot could represent: “If a dog wags its tail, it is either
warning you off or being friendly.” Then, the negation would be: “It is not the
case that, if a dog wags its tail it is either warning you off or being friendly.”
b.
Disjunctions
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A disjunction takes the form: “Either [ • ] or [ • ].” As before, the dots, which
are called disjuncts, can stand for any statement. For example, the first dot could
stand for: “Jack will ask Jill out” and the second dot could stand for “Jack will
ask Jane out.” Then, the disjunction would be: “Jack will ask Jill or Jane out,” or
to use a more contrived expression, “Either Jack will ask Jill out or Jack will ask
Jane out.”
To use another example, the first dot could represent: “If it rains, there will be no
game” and the second dot could stand for: “Emma is not coming for the party
tonight.” Then, the disjunction would read: “Either if it rains, there will be no
game, or Emma is not coming for the party tonight.”
You will perhaps (and should) find the last disjunction strange. There appears
to be no ‘relation’ between the disjuncts. However, I have used the example on
purpose, to impress on you the idea that there need not be any ‘relation’ between
the disjuncts in a disjunction. As you will see later, if there is no relation between
the disjuncts, then the disjunction will probably turn out to be false; but it will
still be a disjunct.
c.
Conjunctions
A conjunction takes the form: “[ • ] and [ • ].” The dots, which can represent
any statement, are now called conjuncts. For example, using the dots to represent
the same statements in the first example in (b) above, the conjunction would be:
“Jack will ask Jill and Jane out,” or to use a more contrived expression, “Jack will
ask Jill out and Jack will ask Jane out.”
I will leave you to form the conjunction for the second example in (b) above. Also,
note that the insight of the last paragraph in (b) above applies to conjunctions as
well.
d.
Conditionals
A conditional takes the form: “If [ • ], then [ • ].” The first dot, which can
represent any statement, is called the antecedent of the conditional, while the
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second dot, which can also stand for any statement, is called the consequent. You
have already seen an example of a conditional statement in the examples I have
given you thus far: can you identify it?
Here’s another one though: suppose the first dot stands for: “Ministers in
Singapore are not paid highly” and the second, for: “They will not be corrupt.”
Then, the conditional would read: “If ministers in Singapore are paid highly,
then they will not be corrupt.” Note that the antecedent and the consequent of
the conditional could be either negations or disjunctions, or even conditionals
themselves.
Now that you know what a compound statement is, defining a simple statement is a lot
easier. A simple statement is a statement that does not contain a ‘not,’ or an ‘and,’ or an
‘or,’ or can’t be expressed in the ‘if …, then …’ form. And from now on, throughout the
remainder of your study units, I will refer to a simple statement as some capital letter of
the alphabet (A to Z). Do note that letters of the alphabet can only be assigned to simple
statements, in this context.
1.2.3 Sufficient versus Necessary Conditions
Read
You should now read: Mooney et al (2016), Chapter 5 (Section 5.8).
A conditional statement can also be thought of as the antecedent being a sufficient
condition for the consequent. For example, the conditional in Section 1.2.2 (d) claims that
ministers being paid highly is sufficient for their not being corrupt.
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However, I might, instead, want to claim that high ministerial pay is necessary for
ministers’ abstaining from corruption. Section 5.8 (Mooney et al 2016)1 elaborates on how
to amend the standard conditional statement (the one that expresses a sufficient condition)
to express this idea. Having read this section, you must be familiar with the idea that
the statement, ‘High pay for ministers is necessary to stop them from being corrupt’ in
conditional form would read as: “Only if ministers are paid highly, they will not be
corrupt”. You should also be familiar with alternative ways of claiming ‘Only if A, then
B.’
Although Section 5.8 (Mooney et al, 2016) does not discuss the idea, it is important for
you to be able to understand the relation between necessary and sufficient conditions and
use that understanding to convert an “Only if …, then …” conditional into an “If …, then
…” form. The idea is relatively straight-forward. Let me develop it though the following
example.
Suppose I claim, “If John is wearing a blue shirt, then he is wearing a shirt.” Intuitively,
this statement is true.2 The fact that John is wearing a blue shirt is sufficient for the fact
that he is wearing a shirt. But if that is true, then the fact that John is wearing a shirt is
necessary for the fact that he is wearing a blue shirt. If you get the drift of the example,
you should be able to generalize: ‘A is sufficient for B’ is equivalent to ‘B is necessary for
A.’ In other words, ‘If A, then B’ is equivalent to ‘Only if B, then A.’
There is another more direct approach to developing the relations between ‘Only if …,
then…’ and ‘If …, then …’ conditionals. Suppose I claim: ‘Only if A, then B.’ You already
know this is equivalent to claiming: ‘A is necessary for B.’ Now ask yourself, intuitively,
what does this claim mean? Hopefully, you’ll arrive at my intuition: ‘If A is not true
[A doesn’t happen], then B is not true [B wouldn’t happen].’ In conditional terms, this
intuition is expressed as ‘If not-A, then not-B.’ There we have it: ‘Only if A, then B’ is
equivalent to ‘If not-A, then not-B.’
1
Ignore Example 5.8.9, you can return to it later.
2
I will give you a more formal understanding of truth conditions in Section 1.2.4.
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So, in summary, for reasons that will become obvious to you as the course progresses,
whenever you see an ‘Only if A, then B’ conditional in the context of an argument, you
should convert it to one of the equivalent ‘standard’ conditional forms: ‘If not-A, then notB’ or ‘If B, then A’.
1.2.4 Truth Conditions for Compound Statements
In this section, I am concerned with giving you an intuitive understanding of what makes
negations, disjunctions, conjunctions and conditionals true. This is not discussed in either
Section 9.1 or 5.8 in your textbook (Mooney et al, 2016).3 I will summarise the conditions
for you here; for an intuitive explanation, you must watch the linked video.
a.
‘Not [ • ]’ is true (false) if and only if ‘[ • ]’ is false (true).
b.
‘Either [ • ] or [ • ]’ is true if at least one of the disjuncts is true; otherwise, it
is false.
c.
‘[ • ] and [ • ]’ is true if both conjuncts are true; otherwise, it is false.
d.
‘If [ • ], then [ • ]’ is false if the antecedent is true and the consequent is false;
otherwise, it is true.
Lesson Recording
Truth Conditions for Compound Statements
3
Although your textbook gives you the truth conditions for these statements, more formally, in the
context of truth tables, truth tables are beyond the scope of this course.
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1.3 Arguments: Basic Structure and Types
Read
You should now read: Mooney et al (2016), Chapter 1 (Section 1.3, 1.4, 1.5, 1.6, 1.9 and
1.10).
By now, you know that arguments are constituted by statements. Having read the material
in Chapter 1 of your textbook (Mooney et al, 2016), you should be able to define an
argument as a collection of statements where some of the statements in the collection
operate as reasons for the other statements in the collection. Statements of the former type
are called premises; the latter type are called conclusions.
You should also be able to use inference (premise and conclusion) indicators to identify an
argument when you encounter one and use your judgement and the principle of charity
to do so, when no explicit inference indicators are present.
You must also be able to distinguish between intermediate and final conclusions, and infer
them, where they are not explicitly stated.
Finally, it is extremely important that you are able to distinguish between two types of
arguments, deductive and inductive. Having done your reading, you should be able to
identify a deductive argument as one where the arguer wants to claim his argument to
be guaranteed by his reasons (premises). In addition, you should be able to classify an
argument as inductive if the arguer merely wants to claim his conclusion to be highly
likely, given his premises.
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Activity 2
Mooney et al (2016), Exercise 1.3 (pp.8-9), 1.4 (pp.12-13) and 1.5 (pp.16-17).
1.4 The Quality of Arguments
Read
You should now read: Mooney et al (2016), Chapter 1 (Section 1.8, 1.9 and 1.10).
You are now in a position to consider the criteria by which the quality of an argument is
judged. Having done the required reading, you should be able to see that, regardless of
the type of argument, for one to accept its conclusion, it is necessary that the reasons given
in support of the conclusion be true. In other words, a good argument must, at the very
least, have true premises.
However, true premises are not sufficient for a good argument. It is also necessary that
the premises provide ‘good’ support for the conclusion. What constitutes ‘good’ support?
Your reading should have informed you that this depends on the type of argument being
given. If the argument is deductive, then ‘good’ support is ‘conclusive’ or ‘guaranteed’
support. In other words, if the premises are accepted to be true (regardless of whether
they are, in fact, true), then the conclusion has to be accepted to be true (regardless of
whether it is, in fact, true). Such an (deductive) argument is called valid. Conversely, if
a (deductive) argument is such that even if the premises are accepted as true, it is still
possible that the conclusion is false, then it is an invalid argument.
On the other hand, if the argument is inductive, then ‘good’ support is ‘highly probable’
support. In other words, if the premises are accepted to be true (regardless of whether they
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are, in fact, true), then the conclusion is accepted to be highly likely to be true (regardless
of whether it is, in fact, true). Such an (inductive) argument is called relatively strong.
Conversely, if the conclusion is not very likely to be true, even after accepting the premises
to be true, we categorise the argument as relatively weak.
So, a good deductive argument is one that is valid and has true premises. Such an
argument is called sound; if it is either invalid or has false premises, then it is unsound.
Similarly, a good inductive argument is one that is relatively strong and has true
premises. Such an argument is called cogent; if it is either weak or has false premises, then
it is uncogent.
You should note that the discussion above has the following implications:
a.
Validity and soundness are terms associated only with deductive arguments;
b.
Strength and cogency are terms associated only with inductive arguments;
c.
Validity and strength have nothing to do with whether the premises and
conclusion of the argument are actually true;
d.
The conclusion of a sound argument must be true; and
e.
The conclusion of a cogent argument is highly likely to be true.
Lesson Recording
Quality of Arguments
Activity 3
Mooney et al (2016), Exercise 1.6 (pp.26) and 1.7 (pp.31-32).
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Summary of Key Points
• Thinking implies reasoning, which is the act of giving an argument.
• Every argument consists of (and only of) statements; any statement is ‘a collection
of words’ that can either be true or false, but not both.
• Statements are, usefully, distinguished into two types, simple and compound.
• A compound statement is one that contains an ‘operator’ (not, or, and, if) and is
called a negation, disjunction, conjunction and conditional, respectively; a simple
statement is one that is devoid of an operator.
• A conditional statement claims that the antecedent is sufficient for the consequent;
however, to make the claim that the antecedent is necessary for the consequent, the
‘if’ in a conditional is prefixed by the word ‘only’.
• The truth of a negation, disjunction, conjunction and a conditional is related to the
truth of the negated statement, the truth of the disjuncts, the truth of the conjuncts
and the truth of the antecedent and consequent, respectively.
• An argument is a collection of statements, some of which function as reasons
(premises) for the truth of others in that collection (conclusions).
• Arguments can be classified either as deductive or inductive (but, not both); this
classification depends on how strongly it wants to establish its conclusion.
• A deductive argument intends its conclusion to be certainly true, whereas an
inductive argument intends its conclusion to only be highly likely to be true.
• A good (bad) deductive argument is called a sound (unsound) argument; an
argument is sound if and only if it is valid and has true premises.
• A valid argument is such that the truth of its premises are sufficient for the truth
of its conclusion.
• A good (bad) inductive argument is called a cogent (uncogent) argument; an
argument is cogent if and only if it is strong and has true premises.
• A strong argument is such that the truth of its premises is sufficient for a high chance
that its conclusion is true.
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• Validity and strength are measures of how strongly a set of premises supports the
conclusion; as such, the actual truth or falsity of the premises is irrelevant to whether
an argument is valid/strong.
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Chapter 2: Arrow Diagrams: Laying Bare the Structure
of an Argument
2.1 The Basic Arrow Arrangements
Read
You should now read: Mooney et al (2016), Chapter 2 (Section 2.1, 2.2, 2.3, 2.4, 2.5 and
2.6).
An arrow diagram is an effective and instructive way of identifying the structure of an
argument. This identification of structure is an essential first step towards determining
what the strong and weak points of an argument are (i.e., what features of the argument
make it ‘good’ and what features of the argument make it ‘bad’).
An arrow diagram represents arguments that consist of statements which generally
play exactly one of three roles; a statement could be either an unsupported premise, or
an intermediate conclusion, or a final conclusion. Arrows are drawn from supporting
statements to supported statements (i.e., from premises to either intermediate or final
conclusions, or, from intermediate to final conclusions).
Your readings should make it clear that there are four basic forms of arrow arrangements,
each corresponding to a unique form of reasoning: serial, convergent, linked and
divergent. You should be able to distinguish between arguments expressing these forms
of reasoning and draw corresponding arrow diagrams.
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Activity 4
Mooney et al (2016), Exercise 2.2 (pp.51-52), 2.3 (pp.52-53) and 2.4 (pp.55-56).
2.2 Combining Arrow Arrangements
Read
You should now read: Mooney et al (2016), Chapter 2 (Section 2.7).
Most arguments you will encounter on an everyday basis will combine the different basic
forms of reasoning in a variety of ways. You should read the requisite section in your
textbook to be familiar with how to represent an ordinary language argument in the form
of an arrow diagram. Watch the video for additional guidance.
Lesson Recording
Drawing an Arrow Diagram
Activity 5
Mooney et al (2016), Exercise 2.5 (pp.62-63).
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Summary of Key Points
• An arrow diagram is a useful way of representing any argument because it
illustrates the structure of an argument.
• As the name suggests, an arrow diagram consists of arrows drawn to statements in
the argument that are supported from the statements in the argument that support
them; each arrow represents a mini argument within the larger argument.
• Every statement in an argument is represented in an arrow diagram in exactly one
of three different ways: either it only has arrows drawn from it [in which case, it is
an unsupported premise]; or, it only has arrows drawn to it [in which case, it is a
final conclusion]; or, it has arrows drawn both from and to it [in which case, it is
an intermediate conclusion].
• Arrow diagrams can represent four distinct argument structures: serial, convergent,
linked and divergent.
• In a basic serial structure, one statement supports exactly one other statement; so,
there is exactly one arrow drawn from the supporting statement to the supported
statement.
• In a basic convergent structure, multiple statements independently support exactly
one other statement; so, there is one arrow drawn from each supporting statement
to the supported statement.
• In a basic linked structure, multiple statements jointly support exactly one other
statement; so, there is exactly one arrow drawn from the set of supporting
statements to the supported statement.
• In a basic divergent structure, exactly one statement supports multiple statements;
so, there is one arrow drawn from the supporting statement to each of the supported
statements.
• In general, arguments consist of a variety of combinations of these four basic
structures.
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Formative Assessment
1.
‘If I wear a red shirt to the interview, I will get a job. This is
.
a. a statement
b. an argument
c. (a) and (b)
d. None of the above
2.
Suppose you believe that you have to study hard to do well in this course. Which of
the following conditional statements expresses your belief?
a. If I study hard, then I will do well in this course.
b. If I don’t do well in this course, I did not study hard.
c. If I do well in this course, then I have studied hard.
d. None of the above.
3.
Suppose Emma is married to George. Suppose also that Emma has two children.
Which of the following compound statements is false?
a. Either Emma is married to George or she has two children.
b. Either Emma is not married to George or she has two children.
c. Either Emma is married to George or she does not have two children.
d. Either Emma is not married to George or she does not have two children.
4.
Suppose Emma is married to George. Suppose also that Emma has two children.
Which of the following compound statements is false?
a. If Emma is not married to George, she is childless.
b. If Emma likes wearing red dresses, she has two children.
c. If Emma has two children, then she is married to George.
d. If Emma is married to George, then she is childless.
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Consider the following argument: “Most of the times Roger plays Rafa, Rafa wins.
So, the next time Roger and Rafa play, I think Rafa will win.”
a. This is best read as a deductive argument.
b. This is best read as an inductive argument.
c. Both (a) and (b) are true.
d. None of the above
6.
Consider the following argument: “All flowers are red in colour. A rose is a type of
flower. So, a rose must be red in colour.” Which of the following statements is true?
a. This is a valid, but unsound argument.
b. This is a valid and sound argument.
c. This is an invalid, but sound argument.
d. This is a valid, inductive argument.
7.
Which of the following statements is true?
a. A sound argument can have a false conclusion.
b. A valid argument must have a true conclusion.
c. A cogent argument can have a false conclusion.
d. A strong argument must have true premises.
8.
Consider the following argument: “Mr. Tan has been very active in political work at
the grassroots-level and so he is well-suited to contest the general elections.” Which
of the following arrow diagrams represent this argument?
a. “Mr. Tan has been very active in political work at the grassroots-level” → “He
is well-suited to contest the general elections”.
b. “He is well-suited to contest the general elections” → “Mr. Tan has been very
active in political work at the grassroots-level”.
c. “Mr. Tan has been very active in political work at the grassroots-level” ↔ “He
is well-suited to contest the general elections”.
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d. All of the above.
9.
Consider the following argument, where the statements have been numbered: “(1)
We should go to Hannah’s party because (2) she serves really delicious food. If that
isn’t good enough a reason, remember that (3) she is never miserly with the wine. And
don’t forget, (4) the company is lovely too. Which of the following arrow diagrams
best represent this argument?
a.
b.
c.
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d.
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Solutions or Suggested Answers
Formative Assessment
1.
‘If I wear a red shirt to the interview, I will get a job. This is
a.
.
a statement
Correct. This is a compound statement, referred to as a conditional.
b.
an argument
Incorrect. An argument must have at least two statements such that one of
the two is a premise, and the other, a conclusion.
c.
(a) and (b)
Incorrect. Nothing can be both a statement and an argument.
d.
None of the above
Incorrect. You will know why, when you try again.
2.
Suppose you believe that you have to study hard to do well in this course. Which of
the following conditional statements expresses your belief?
a.
If I study hard, then I will do well in this course.
Incorrect. The ‘have to’ in the statement indicates that you believe that
studying hard is necessary for doing well in this course. But the conditional
in (a) claims that studying hard is sufficient for doing well in this course.
b.
If I don’t do well in this course, I did not study hard.
Incorrect. The ‘have to’ in the statement indicates that you believe that
studying hard is necessary for doing well in this course. But the conditional
in (b) claims that studying hard is sufficient for doing well in this course.
c.
If I do well in this course, then I have studied hard.
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Correct. The ‘have to’ in the statement indicates that you believe that
studying hard is necessary for doing well in this course. This implies that
the fact that you do well for this course is sufficient for the fact that you
studied hard.
d.
None of the above.
Incorrect. Only one of the options above is correct.
3.
Suppose Emma is married to George. Suppose also that Emma has two children.
Which of the following compound statements is false?
a.
Either Emma is married to George or she has two children.
Incorrect. This disjunction is true. For a disjunction to be true, at least one
disjunct must be true; in this case, both disjuncts are true.
b.
Either Emma is not married to George or she has two children.
Incorrect. This disjunction is true. For a disjunction to be true, at least one
disjunct must be true; in this case, the disjunct, ‘Emma has two children’ is
true.
c.
Either Emma is married to George or she does not have two children.
Incorrect. This disjunction is true. For a disjunction to be true, at least one
disjunct must be true; in this case, the disjunct, ‘Emma is married to George’
is true.
d.
Either Emma is not married to George or she does not have two children.
Correct. This disjunction is false. For a disjunction to be true, at least one
disjunct must be true; in this case, both disjuncts are false.
4.
Suppose Emma is married to George. Suppose also that Emma has two children.
Which of the following compound statements is false?
a.
If Emma is not married to George, she is childless.
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Incorrect. This conditional is true. A conditional is true if its antecedent is
false; in this case, the antecedent is false.
b.
If Emma likes wearing red dresses, she has two children.
Incorrect. This conditional is true. A conditional is true if its consequent is
true; in this case, the consequent is true.
c.
If Emma has two children, then she is married to George.
Incorrect. This conditional is true. A conditional is true if its consequent is
true; in this case, the consequent is true.
d.
If Emma is married to George, then she is childless.
Correct. This conditional is false. A conditional is false if its antecedent is
true and its consequent is false; which is the case here.
5.
Consider the following argument: “Most of the times Roger plays Rafa, Rafa wins.
So, the next time Roger and Rafa play, I think Rafa will win.”
a.
This is best read as a deductive argument.
Incorrect. Charitably read, this does not appear to be an argument where the
arguer is trying to claim his conclusion to be guaranteed to be true.
b.
This is best read as an inductive argument.
Correct. Charitably read, this appears to be an argument where the arguer
is trying to claim his conclusion to be highly likely to be true.
c.
Both (a) and (b) are true.
Incorrect. An argument should be read either inductively or deductively, but
not both.
d.
None of the above
Incorrect. An argument has to be read either deductively or inductively.
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The Principles of Reasoning
Consider the following argument: “All flowers are red in colour. A rose is a type of
flower. So, a rose must be red in colour.” Which of the following statements is true?
a.
This is a valid, but unsound argument.
Correct. The argument is valid because if you accept the premises to be
true, you must accept the conclusion to be true; but the premise “All
flowers are red in colour” is false; so, the argument is unsound.
b.
This is a valid and sound argument.
Incorrect. The argument is valid because if you accept the premises to be true,
you must accept the conclusion to be true; but the premise “All flowers are
red in colour” is false; so, the argument is unsound.
c.
This is an invalid, but sound argument.
Incorrect. No argument can be both invalid and sound.
d.
This is a valid, inductive argument.
Incorrect. No argument can be both valid and inductive; validity and
soundness are terms reserved for deductive arguments.
7.
Which of the following statements is true?
a.
A sound argument can have a false conclusion.
Incorrect. A sound argument is both valid (the conclusion is guaranteed by
the premises) and has true premises. So, the conclusion must be true.
b.
A valid argument must have a true conclusion.
Incorrect. The validity of an argument has no link with whether its premises
or conclusion are actually true.
c.
A cogent argument can have a false conclusion.
Correct. A cogent argument must have a conclusion that is highly likely to
be true, but can be false.
d.
A strong argument must have true premises.
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Incorrect. The strength of an argument has no link with whether its premises
are actually true.
8.
Consider the following argument: “Mr. Tan has been very active in political work at
the grassroots-level and so he is well-suited to contest the general elections.” Which
of the following arrow diagrams represent this argument?
a.
“Mr. Tan has been very active in political work at the grassroots-level” →
“He is well-suited to contest the general elections”.
Correct. The word ‘so’ indicates that “Mr. Tan has been very active in
political work at the grassroots-level” is a premise for the conclusion, “He
is well-suited to contest the general elections”. Arrows are drawn from
premises to the conclusion.
b.
“He is well-suited to contest the general elections” → “Mr. Tan has been very
active in political work at the grassroots-level”.
Incorrect. The word ‘so’ indicates that “Mr. Tan has been very active in
political work at the grassroots-level” is a premise for the conclusion, “He
is well-suited to contest the general elections”. Arrows are drawn from
premises to the conclusion.
c.
“Mr. Tan has been very active in political work at the grassroots-level” ↔
“He is well-suited to contest the general elections”.
Incorrect. The word ‘so’ indicates that “Mr. Tan has been very active in
political work at the grassroots-level” is a premise for the conclusion, “He
is well-suited to contest the general elections”. Arrows are drawn from
premises to the conclusion.
d.
All of the above.
Incorrect. There is a unique arrow diagram for every argument.
9.
Consider the following argument, where the statements have been numbered: “(1)
We should go to Hannah’s party because (2) she serves really delicious food. If that
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isn’t good enough a reason, remember that (3) she is never miserly with the wine. And
don’t forget, (4) the company is lovely too. Which of the following arrow diagrams
best represent this argument?
a.
Incorrect. In the given argument, statements (2), (3) and (4) provide
independent reasons for going to Hannah’s party (1); thus, the structure of
the argument is ‘convergent’. (a), however, describes a ‘serial’ structure.
b.
Incorrect. In the given argument, statements (2), (3) and (4) provide
independent reasons for going to Hannah’s party (1); thus, the structure of
the argument is ‘convergent’. (b), however, describes a ‘divergent’ structure.
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c.
Incorrect. In the given argument, statements (2), (3) and (4) provide
independent reasons for going to Hannah’s party (1); thus, the structure of
the argument is ‘convergent’. (c), however, describes a ‘linked’ structure.
d.
Correct. In the given argument, statements (2), (3) and (4) provide
independent reasons for going to Hannah’s party (1); thus, the structure of
the argument is ‘convergent’.
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References
Mooney, T. B., Williams, J. N., & Burik, S. (2016). An introduction to critical and creative
thinking.Singapore: McGraw-Hill Education (Asia).
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Unit
Forms of Arguments
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Learning Outcomes
By the end of this unit, you should be able to:
1.
Identify the basic types of categorical statements.
2.
Identify the types of categorical syllogisms.
3.
Represent categorical statements using Venn diagrams.
4.
Evaluate the validity and soundness of categorical syllogisms.
5.
Identify the different valid deductive forms.
6.
Identify the different invalid deductive forms.
7.
Establish the validity of arguments by determining whether the conclusion is
inferable from the premises via the above forms.
8.
Identify the principles behind the inductive approach and appreciate its
centrality in everyday reasoning.
9.
Identify the four basic forms that an inductive argument might take – statistical
syllogisms; inductive generalisations; arguments from analogy; and arguments
appealing to authority.
10.
Specify conditions under which an inductive argument is relatively strong or
weak.
11.
Evaluate the strength of an ordinary-language inductive argument.
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Overview
T
he first study unit introduced you to the nature of reasoning. There, you
learnt about the basic structure of an argument; a way of representing any
given argument (arrow diagrams); the basic types of arguments (deductive and
inductive); and, given the type, the basic criteria which a good argument must satisfy
(soundness and cogency). You are now prepared for a more sophisticated enterprise: the
task of determining which arguments meet those criteria, and why. Showing you how
to do this is the primary focus of this study unit. We will begin by analysing deductive
arguments and then move on to considering inductive arguments.
A caveat, though, is due here. You’ll recall that the ‘soundness’ of an argument is
constituted by its validity and the truth of its premises. Similarly, a cogent inductive
argument is strong and has true premises. However, our focus will exclusively be on
determining validity and strength; we will ignore considering whether the premises of an
argument are true. The reason for this is because, in principle, determining the truth of a
statement is relatively simple:
i.
you can either appeal to your sensory perceptions (for example, ‘Emma was
wearing a red dress to the party’ is true because I was at the party and I saw her
wearing a red dress); or,
ii.
appeal to your consciousness (for example, ‘I am in pain’ is true because I feel
pain); or,
iii.
appeal to legitimate authority (for example, ‘Changi is in the east of Singapore
because the Atlas tells me so).
Indeed, when controversies about truth arise, they do so because there are conflicts
about sensory perceptions, or about how a particular term should be defined, or among
authorities on a subject.
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Chapter 1: Deductive Arguments
1.1 Categorical Syllogisms
1.1.1 Categorical Statements and Syllogisms
Read
You should now read: Mooney, Williams, & Burik (2016), Chapter 5 and 8 (Section 5.1,
5.2, 5.3, 8.1 and 8.2).
Having read the required material, you should be familiar with the general structure
of a categorical statement. You should, for instance, know that a categorical statement
expresses a relationship between sets or classes or categories of objects. In addition,
you should know that every categorical statement must contain 3 ‘building blocks’: a
quantifier (all, some, or none); a subject category; and, a predicate category. Thus, more
precisely, in a categorical statement, the quantifier tells you how many objects in the
subject category also belong to the predicate category. In fact, your textbook (Mooney et
al., 2016) helpfully classifies the types of categorical statements into A, E, I and O type
statements, depending on the quantifier that is used.
Having familiarised yourself with categorical statements, you should move on to
developing a good understanding of what a categorical syllogism is. Simply put, a
categorical syllogism must have two essential properties: firstly, like all syllogisms, a
categorical syllogism must consist of exactly 2 premises and 1 conclusion; secondly,
the 2 premises and the conclusion must be categorical statements (either A, E, I or O
type). Finally, you must acknowledge that a categorical syllogism, by its very nature, is a
deductive argument. Anyone who puts forward a categorical syllogism is automatically
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assumed to be claiming that his conclusion is guaranteed by the truth of his premises; as
such, whether a categorical syllogism is sound depends on whether it is valid and whether
its premises are true.
I want to conclude this subsection by reiterating an important point that is briefly alluded
to in the ‘preface’ in Chapter 8 of your textbook (Mooney et al., 2016). There are two distinct
approaches to understanding the content of any universal categorical statement (A or E
type statements); on the ‘Aristotelian’ approach, a statement such as ‘All As (for example,
philosophers) are Bs (for example, whisky drinkers)’, is taken to imply that there exists
at least one A (philosopher). In other words, in the ‘world as we know it’, we can ‘find’
at least one A (philosopher). So, on this approach, it would be valid to infer from the
premise, ‘All (No) philosophers drink whisky, the conclusion that ‘A philosopher exists’
or ‘Someone is a philosopher’.
The other approach, the ‘Boolean’ approach denies this claim. On this reading, a universal
categorical statement is silent (or, says nothing) about whether we can ‘find’ at least one
A in the world. So, you cannot validly infer from the premise ‘All (No) philosophers drink
whisky’, the conclusion that ‘Someone is a philosopher’. Although, on the first reading,
you might sympathise with the Aristotelian approach (you might think: who, in his right
mind, would want to claim ‘All philosophers drink whisky’, if there were no philosophers
in the world?), the Boolean approach is not without its merits. Consider for example, the
statements: ‘All unidentified flying objects (UFOs) can fly’ or ‘No queen of Singapore is
a male’. Both of the statements above are true, by the definitions of what ‘UFOs’ and
‘queens’ are. But, does it follow that UFOs exist? Or, that Singapore has a queen?
Now, whatever your persuasions are, in this course, we will read categorical statements
in the ‘Boolean’ way. For us, universal categorical statements will make no existential
claim. Note, finally, that when it comes to particular categorical statements (I or N type
statements), there is no controversy between the Aristotelian and the Boolean approaches.
On both readings, the statements, ‘Some A’s are Bs’ or ‘Some As are not Bs’, imply that at
least one A exists (we can ‘find’ at least one A in the world).
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Activity 1
Mooney, Williams, & Burik (2016), Exercise 8.1, pp.229-230.
1.1.2 Venn Diagrams
Read
You should now read: Mooney, Williams, & Burik (2016), Chapter 8 (Section 8.7).
Our primary focus in this section is to assess whether a given categorical syllogism is valid.
The fool-proof way of doing so is by using Venn diagrams. So, although Section 5.3 of your
textbook (Mooney et al., 2016) gives you a summary of which categorical syllogisms are
valid, when you are asked to determine validity, you must use Venn diagrams. You must
read the required section in the textbook very carefully, and work through the numerous
examples to master how A, E, I and O statements are represented using Venn diagrams.
Having done so, you must also be familiar with how to represent a categorical syllogism
with Venn diagrams and determine its validity. Remember that the simple rule to follow
in this context is to consider whether the conclusion of a categorical syllogism claims more
than what the premises jointly claim. If yes, the syllogism is invalid; otherwise, it is valid.
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Watch the video for additional guidance on this.
Lesson Recording
Venn Diagrams and Categorical Statements
Activity 2
Mooney, Williams, & Burik (2016), Exercise 8.4, pp.259.
1.2 Propositional Logic
Read
You should now read: Mooney, Williams, & Burik (2016), Chapter 5 (Section 5.4-5.6).
Section 5.4 in your textbook introduces you to a second type of deductive argument:
arguments whose validity can be determined by appealing to established rules of
inference. These are arguments in which the premises and the conclusion are either
simple or compound statements, statements that are appended or conjoined by ‘not’,
‘and’, ‘or’ and ‘if …, then …’ (these are called propositional operators). This section also
provides you with a list of 17 valid and invalid inferences in propositional logic. You must
appreciate that the content (and, therefore, truth) of the statement/s is/are immaterial to
the (in)validity of the argument. All that matters is whether the form of the argument takes
one of the 17 forms identified here. Watch the video to strengthen your understanding of
why certain inferences are valid, while others are not.
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Lesson Recording
Forms of Deductive Arguments and Validity
Activity 3
Mooney, Williams, & Burik (2016), Exercise 5.2 (pp.134-136).
Section 5.6 of your textbook provides instruction on how to determine the validity of more
complex arguments in propositional logic – arguments that might need you to employ a
combination of the 17 forms identified in Section 5.4 (and summarised in Section 5.5) to
determine validity. Work through the examples meticulously.
Summary of Key Points
• This chapter introduces you to two different types of deductive arguments as well
as to techniques for determining their validity.
• The first type of deductive argument discussed is the categorical syllogism; this
refers to arguments with two premises and one conclusion, where the premises and
the conclusion are in the form of categorical statements.
• All categorical statements consist of exactly one qualifier (‘all’, ‘none’, or ‘some’),
exactly one subject category and exactly one predicate category.
• We take the Boolean approach to interpreting categorical statements, which states
that universal categorical statements – those containing either the quantifier ‘all’ or
‘non’ – are silent about whether a member of the subject category actually exists.
• Venn diagrams can be used to represent categorical statements; you only need to
be familiar with how universal categorical statements are represented.
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• A statement such as “All As are Bs” is represented by identifying the area
corresponding to the set of As that are not Bs and shading it; shading an area in a
Venn diagram denotes that the shaded area is empty.
• A statement such as “No As are Bs” is represented by identifying a region
corresponding to the set of As that are Bs, and shading it.
• Venn diagrams can also be used to evaluate whether a given categorical syllogism
is valid by following these steps: firstly, each (universal) premise is represented;
secondly, the (universal) conclusion is represented; and finally, the area shaded by
the conclusion is compared to the area shaded by the two premises taken together.
• A categorical syllogism consisting only of universal statements is valid if the area
shaded by the conclusion coincides with or, is contained within the area shaded by
the two premises taken together; otherwise, it is invalid.
• A second type of deductive argument consists of those whose premises and
conclusion are either in the form of simple or compound statements; the study of
the validity of this type of argument is called propositional logic.
• Propositional logic attempts to represent any given argument in a standard
argument form. Some standard argument forms are valid (including, but not
limited to, Modus Ponens, Modus Tollens, Disjunctive Syllogism and Constructive
Dilemma), while others (including, but not limited to, Denying the Antecedent) are
invalid.
• In propositional logic, an argument is valid if it takes a valid standard argument
form; and it is invalid if it follows an invalid standard argument form.
• Generally, arguments within the domain of propositional logic can consist of a
combination of standard argument forms: such arguments are valid if all standard
argument forms in the argument are valid; and they are invalid if at least one
standard argument form is invalid.
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Chapter 2: Inductive Arguments
2.1 The Nature of Induction
In much of your everyday conversation, you might make or come across claims such as
these: ‘It will rain today,’ or ‘Tom won’t be late for the meeting,’ or ‘Let’s not go to Holland
Village; we won’t find parking there.’ These sorts of claims are contingent in nature; they
are fundamentally distinct from absolute or necessary claims such as, ‘Lying is wrong,’ or
‘Only one straight line can be drawn between any two fixed points,’ or ‘God exists.’
When you make a contingent claim, you allow some chance (in other words, a positive
probability) for the claimed proposition to be false. Of course, you don’t think that the
statement you are claiming is likely to be (or has a high probability of being) false –
otherwise, you wouldn’t, in all sincerity, make the claim; you would, for instance, be
surprised if it did rain, or if Tom was late, or that if you drove to Holland Village and
happened to find ample parking space – but that would not change the fact that you
had good reasons for claiming what you did, when you did. If your interlocutor were to
ask you why you made a false claim, you would identify your reasons: ‘It is the rainy
season and it has been raining almost every day,’ or ‘Tom has never been late to a meeting
before,’ or ‘generally, parking is hard to find in Holland Village on weekends and today
is Saturday.’ Indeed, if you were in a similar situation again, you would still be fairly
comfortable (perhaps, a little less than before) in making the claims that you did.
Notice what is going on. You made a claim knowing that it was highly likely, but not
guaranteed, to be true. Your claim was justified by your belief that there are certain
regularities in the world (for instance, the world is such that it invariably rains during
the rainy season), and the belief that these regularities will continue. If the ‘regularity’ is
violated on any one instance, it might affect the confidence with which you make the same
claim on a subsequent occasion; the degree to which your confidence is affected depends
on how you explain away the violation. If you think of the violation merely as random,
you would probably not hesitate in sticking to either your claim or your reasons for the
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claim. For example, if Tom turned up late for the meeting and told you, truthfully, that
a tree had fallen across the road on the way to work – a random occurrence – then you
would still want to maintain that ‘Tom won’t be late for the next meeting.’ Of course, if
your claim starts turning out to be false more frequently, you would suspect that there is
now a ‘new regularity’ in the world and revise your beliefs and claims accordingly.
The process described above is induction. You start with a (probably true, but possible
false) claim that is justified by your knowledge about regularities that have been observed
in the past (evidence); and, you continuously revise the degree of your belief in your claim
in the light of new evidence (in other words, you update the degree of your belief in what
you want to claim). How good the induction is – and that is what we are interested in
determining – depends on the extent to which your evidence makes your claim likely.
We will consider this issue in the next section, but before we do so, I would want you to
appreciate that our day-to-day behaviour – going to the train station at a particular time,
going to a favourite restaurant at lunch time, carrying an umbrella to work, etc. – is all
justified by this process of induction.
2.2 Basic Forms of Inductive Arguments
Read
You should now read: Mooney, Williams, & Burik (2016), Chapter 5 (Section 5.9).
This section in your textbook familiarises you with the 4 basic forms that inductive
arguments take: statistical syllogisms; inductive generalisations; arguments from
inductive analogy; and, appeals to authority. You should carefully consider the general
structure of each of these forms and appreciate how the particular examples follow that
general structure. In addition, you must pay particularly close attention to the factors that
make an inductive argument in each of the 3 forms relatively strong or weak (discussion
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of the fourth form, appeals to authority, is postponed to Study Unit 3). These factors are
specific to the form of the argument.
For example, you should know that the strength of an inductive generalisation depends
on how large and how representative the sample used for the generalisation is. On
the other hand, the strength of any argument from analogy depends on the number of
relevant properties (or characteristics) shared between the objects being compared, and on
whether there are any relevant dissimilarities. Finally, if you have been critically engaging
with the examples in the textbook, then the following subtle point might have struck
you: a statistical syllogism is nothing but an argument from analogy in different clothes.
The former concludes that something or somebody is highly likely to have a particular
property (for example, ‘Sovan is highly likely to be an alcoholic’) based on two premises:
first, that thing/person is a member of a class (or, group) of things/persons (for example,
‘Sovan is a philosopher’ or more facetiously, ‘Sovan belongs to the group of philosophers’);
and second, every thing/one in that class is highly likely to have that particular property
(for example, ‘90% of philosophers are alcoholics’ or ‘Any philosopher has a 90% chance
of being an alcoholic’).
You can easily rewrite the argument above as an argument from analogy:
P1: Steven, John, Bryan, etc. are philosophers.
P2: Sovan is (also) a philosopher.
P3: Steven, John, Bryan, etc. are highly likely to be alcoholics.
C: Sovan is highly likely to be an alcoholic.
There is a moral to this exercise; it is that the factors that determine the strength of an
argument from analogy are also the factors that determine the strength of a statistical
syllogism.
Watch the video for additional guidance.
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Lesson Recording
Inductive Forms and Strength
Finally, note that a more complex inductive argument can be constructed using a
combination of these forms. The strength of that argument will then depend on the
strength of its constituent forms.
Summary of Key Points
• Induction is the act of making contingent claims based on our knowledge of
contingent facts; such as, inductive reasoning is central to much of our everyday
behaviour.
• There are four basic forms of inductive arguments, three of which are discussed
in this chapter – inductive generalisation, statistical syllogism and argument from
analogy.
• An inductive generalisation, as the name suggests, infers a claim about a
population, based on what is known about a sample of the population;
the generalisation is stronger if the sample is relatively large and relatively
representative of the population.
• A statistical syllogism infers a claim about a member (or members) of the
population, based on what is probabilistically known about the population; the
induction is stronger if there are no relevant dissimilarities between the population
at large, and the chosen member(s); what constitutes relevant is determined by what
is claimed.
• An argument from analogy claims that two entities share some properties on
the basis that they are known to share other properties (i.e., are analogous). The
induction is stronger the larger the set of relevant properties the entities are known
to share and the fewer the set of relevant dissimilarities between them.
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• In general, an inductive argument can consist of a variety of the basic inductive
forms; then its strength would depend on the strength of its constituent forms.
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Formative Assessment
1.
Under the ‘Boolean’ interpretation (our chosen interpretation in this course), which
of the following claims are equivalent to claiming, “All elephants are mammals”?
a. There is at least one elephant in the world.
b. There is at least one mammal in the world.
c. Nothing exists in this world that is an elephant, but not a mammal.
d. All of the above.
2.
Which of the following Venn diagrams correctly represents the claim, “All music
composers (Cs) are accomplished players (Ps)”?
a.
b.
c.
d.
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Which of the following Venn diagrams correctly represent the claim, “No music
composers (Cs) are accomplished players (Ps)”?
a.
b.
c.
d.
4.
Suppose the premises of a categorical syllogism are represented as follows:
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Under which of the following representations of the conclusion is the argument
invalid?
a.
b.
c.
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d.
5.
Consider the following argument.
If P, then not Q
Q
Therefore, not P
This standard argument form is called
.
a. Modus Tollens
b. False Dichotomy
c. Hypothetical Syllogism
d. Constructive Dilemma
6.
Consider the following argument.
“Either Modus Ponens is a valid argument form or Hypothetical Syllogism is a valid
argument form. But Hypothetical Syllogism is not a valid argument form. So, Modus
Ponens is a valid argument form.” Which of the following statements is true?
a. This argument is valid and sound.
b. This argument is valid but unsound.
c. This argument is invalid and unsound.
d. This argument is invalid but sound.
7.
Consider the following argument.
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“85% of Singaporeans surveyed are against legalising gay marriage. So, Singaporeans
are against gay marriage.” Knowledge of which of the following would make you
consider this argument to be relatively weak?
a. A thousand Singaporeans were surveyed; men and women were equally
represented.
b. 90% of the Singaporeans surveyed belonged to some religious group and 90%
of all Singaporeans are affiliated to some religious group.
c. All Singaporeans surveyed were above 45 years old.
d. None of the above.
8.
Consider the following argument.
“80% of all unmarried men tend to develop symptoms of depression after they
turn 50. Robert is unmarried. So, he will be depressed when he is older than 50.”
Knowledge of which of the following will make this argument weaker?
a. Like many other unmarried men, Robert has many casual relationships with
women and is sad when they end.
b. Unlike many other unmarried men, Robert stays away from alcohol and is a
fitness enthusiast.
c. Unlike many other unmarried men, Robert prefers driving sedans rather than
convertibles.
d. None of the above
9.
Consider the following argument.
“Jack and Jill both enjoyed their last trip to Singapore. Jack holidayed in Bangkok
last year and enjoyed it. Jill is going there next month, so, I am sure she will love it.”
Which of the following statements will make this argument weaker?
a. Jack and Jill both love sampling the street food in their holiday destinations.
b. Jack loves staying in backpackers’ lodges when on holiday whereas, Jill likes
staying in 5-star hotels.
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c. Jack went to Thailand on a golfing holiday, but Jill does not play golf.
d. None of the above.
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Solutions or Suggested Answers
Formative Assessment
1.
Under the ‘Boolean’ interpretation (our chosen interpretation in this course), which
of the following claims are equivalent to claiming, “All elephants are mammals”?
a.
There is at least one elephant in the world.
Incorrect. Under the Boolean interpretation, a universal categorical statement
such as ‘All As are Bs’ is silent about whether an A exists and whether a B
exists.
b.
There is at least one mammal in the world.
Incorrect. Under the Boolean interpretation, a universal categorical statement
such as ‘All As are Bs’ is silent about whether an A exists and whether a B
exists.
c.
Nothing exists in this world that is an elephant, but not a mammal.
Correct. “All As are Bs” is equivalent to claiming that we can’t have an A
that is not a B.
d.
All of the above.
Incorrect. Under the Boolean interpretation, a universal categorical statement
such as ‘All As are Bs’ is silent about whether an A exists and whether a B
exists.
2.
Which of the following Venn diagrams correctly represents the claim, “All music
composers (Cs) are accomplished players (Ps)”?
a.
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Incorrect. The area shaded in a Venn diagram represents an empty set.
According to the statement, the set that is empty is the set of music composers
who are not accomplished players. What is represented in (a), however, is
that the set of all Cs that are Ps is empty or ‘No Cs are Ps’.
b.
Correct. The area shaded in a Venn diagram represents an empty set.
According to the statement, the set that is empty is the set of music
composers who are not accomplished players.
c.
Incorrect. The area shaded in a Venn diagram represents an empty set.
According to the statement, the set that is empty is the set of music composers
who are not accomplished players. What is represented in (c), however, is
that the set of all Ps that are not Cs is empty or ‘All Ps are Cs’.
d.
Incorrect. The area shaded in a Venn diagram represents an empty set.
According to the statement, the set that is empty is the set of music composers
who are not accomplished players. What is represented in (d), however, is
that the set of Ps is empty or ‘There are no Ps’.
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3.
Forms of Arguments
Which of the following Venn diagrams correctly represent the claim, “No music
composers (Cs) are accomplished players (Ps)”?
a.
Correct. The area shaded in a Venn diagram represents an empty set.
According to the statement, the set of all things that are both Cs and Ps is
empty.
b.
Incorrect. The area shaded in a Venn diagram represents an empty set. What
is represented in (b), however, is that ‘All Cs are Ps’.
c.
Incorrect. The area shaded in a Venn diagram represents an empty set. What
is represented in (c), however, is that ‘All Ps are Cs’.
d.
Incorrect. The area shaded in a Venn diagram represents an empty set. What
is represented in (d), however, is that ‘There are no Cs’.
4.
Suppose the premises of a categorical syllogism are represented as follows:
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Under which of the following representations of the conclusion is the argument
invalid?
a.
Incorrect. An argument represented through a Venn diagram is invalid if and
only if the conclusion shades an area that is not shaded by premises; that is
not the case here.
b.
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Incorrect. An argument represented through a Venn diagram is invalid if and
only if the conclusion shades an area that is not shaded by premises; that is
not the case here.
c.
Incorrect. An argument represented through a Venn diagram is invalid if and
only if the conclusion shades an area that is not shaded by premises; that is
not the case here.
d.
Correct. An argument represented through a Venn diagram is invalid if
and only if the conclusion shades an area that is not shaded by premises;
the shaded intersection of the three circles is such an area.
5.
Consider the following argument.
If P, then not Q
Q
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Therefore, not P
This standard argument form is called
a.
.
Modus Tollens
Correct. Modus Tollens is the name given to the argument form, which
infers the denial of the antecedent from the conditional and the denial of
its consequent.
b.
False Dichotomy
Incorrect. This is not a false dichotomy; check argument form 7 (page 132 in
your textbook).
c.
Hypothetical Syllogism
Incorrect. This is not a hypothetical syllogism; check argument form 13 (page
133 in your textbook).
d.
Constructive Dilemma
Incorrect. This is not a constructive dilemma; check argument form 16 (page
134 in your textbook)
6.
Consider the following argument.
“Either Modus Ponens is a valid argument form or Hypothetical Syllogism is a valid
argument form. But Hypothetical Syllogism is not a valid argument form. So, Modus
Ponens is a valid argument form.” Which of the following statements is true?
a.
This argument is valid and sound.
Incorrect. The argument takes the form, ‘Either P or Q; not Q, So, P’. This is
a disjunctive syllogism, which is a valid standard argument form. However,
the premise ‘Hypothetical Syllogism is not a valid argument form’ is false.
So, the argument is unsound.
b.
This argument is valid but unsound.
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Correct. The argument takes the form, ‘Either P or Q; not Q, So, P’. This is a
disjunctive syllogism, which is a valid standard argument form. However,
the premise ‘Hypothetical Syllogism is not a valid argument form’ is false.
So, the argument is unsound.
c.
This argument is invalid and unsound.
Incorrect. The argument takes the form, ‘Either P or Q; not Q, So, P’. This is
a disjunctive syllogism, which is a valid standard argument form.
d.
This argument is invalid but sound.
Incorrect. No argument can be both invalid and sound
7.
Consider the following argument.
“85% of Singaporeans surveyed are against legalising gay marriage. So, Singaporeans
are against gay marriage.” Knowledge of which of the following would make you
consider this argument to be relatively weak?
a.
A thousand Singaporeans were surveyed; men and women were equally
represented.
Incorrect. A sample of 1,000 is a relatively large sample and the distribution
of men and women in the sample is, largely, representative.
b.
90% of the Singaporeans surveyed belonged to some religious group and 90%
of all Singaporeans are affiliated to some religious group.
Incorrect. Even though the sample is biased towards representing ‘religious’
people, it is still representative of how the population is.
c.
All Singaporeans surveyed were above 45 years old.
Correct. The sample fails to be representative with respect to the agedistribution in the Singapore population.
d.
None of the above.
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Incorrect. One of the options above is correct.
8.
Consider the following argument.
“80% of all unmarried men tend to develop symptoms of depression after they
turn 50. Robert is unmarried. So, he will be depressed when he is older than 50.”
Knowledge of which of the following will make this argument weaker?
a.
Like many other unmarried men, Robert has many casual relationships with
women and is sad when they end.
Incorrect. A similarity between Robert and other unmarried men cannot
make the argument weaker; if it is an irrelevant similarity, it has no effect on
strength, and if it is relevant, it makes the argument stronger.
b.
Unlike many other unmarried men, Robert stays away from alcohol and is
a fitness enthusiast.
Correct. This is a relevant dissimilarity between Robert and other
unmarried men; it is known that lifestyle factors have an influence on
some’s propensity to be depressive.
c.
Unlike many other unmarried men, Robert prefers driving sedans rather
than convertibles.
Incorrect. This is highly likely to be an irrelevant dissimilarity, which should
have no impact on the strength of the argument.
d.
None of the above
Incorrect. One of the options above is correct.
9.
Consider the following argument.
“Jack and Jill both enjoyed their last trip to Singapore. Jack holidayed in Bangkok
last year and enjoyed it. Jill is going there next month, so, I am sure she will love it.”
Which of the following statements will make this argument weaker?
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a.
Jack and Jill both love sampling the street food in their holiday destinations.
Incorrect. This is a relevant similarity which should make the argument
stronger.
b.
Jack loves staying in backpackers’ lodges when on holiday whereas, Jill likes
staying in 5-star hotels.
Incorrect. This is an irrelevant dissimilarity. Bangkok is known to have both
backpackers’ lodges and 5-star hotels.
c.
Jack went to Thailand on a golfing holiday, but Jill does not play golf.
Correct. This is a relevant dissimilarity. Jack might have enjoyed his
holiday purely on account of the good, cheap golf he gets to play, which
Jill would derive no enjoyment from.
d.
None of the above.
Incorrect. One of the above options is correct.
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References
Mooney, T. B., Williams, J. N., & Burik, S. (2016). An Introduction to Critical and Creative
Thinking.Singapore: McGraw-Hill.
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Unit
3
Additional Principles for Arguing
Well
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Learning Outcomes
By the end of this unit, you should be able to:
1.
Describe the relationship between fallacious, invalid and weak arguments.
2.
Identify the commonly committed fallacies and suggest ways of avoiding them.
3.
Describe the role of definitions in achieving consensus over terms used in an
argument.
4.
Identify the criteria for a good definition, and use the criteria to provide
definitions of terms.
5.
Identify the structure of a complex argument.
6.
Evaluate the strengths and weaknesses of a given argument.
7.
Present good, ordinary language arguments for any given conclusion.
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Overview
S
tudy Unit 2 introduced you to some fundamental techniques for reasoning
well. You now know how to determine the validity of a categorical syllogism;
which forms of deductive arguments are valid; and, the criteria that inductive arguments
must satisfy in order to be strong. Now, you are ready to learn how to apply that
knowledge. So, the primary focus of Study Unit 3 is to instruct you how to press all the
conceptual and technical resources studied thus far, to the task of writing a sustained
argument for a conclusion. As a corollary, you will also learn how to evaluate the merits
of relatively long arguments of the sort that routinely appear on the editorial pages of
newspapers, as well as, in much of the academic writing in the social sciences.
To do this however, I will begin by introducing you to certain fallacies; as you will soon
see, fallacies are erroneous ways of reasoning that are common because, at a superficial
and uncritical level, arguments containing these fallacies appear to be good arguments.
It is imperative that you take extra care in watching out for fallacious arguments and,
indeed, avoid fallacies in your own argument.
I will then introduce you to the importance of defining any controversial term (a term,
such that there is no consensus over its meaning) that you might use in your argument.
In addition, we will consider what the criteria for a good definition are. Finally, we will
wrap things up by considering how to critique complex arguments found in relatively
long passages and how to write long argumentative passages that are coherent, internally
consistent and free of fallacies.
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Chapter 1: Informal Fallacies
1.1 The General Nature of Informal Fallacies
Read
You should now read: Mooney, Williams, & Burik (2016), Chapter 7 (Section 7.1).
Your textbook defines fallacies as “mistakes in reasoning,” or “defective pieces of
reasoning” (Mooney et al., 2016). It further distinguishes ‘formal’ fallacies from ‘informal’
ones based on whether the defect is in the structure of the argument, or in the substance
(or “content”) of the argument, while readily admitting that the distinction is slightly
artificial. Given this, it might be better to rename the ‘informal’ fallacy as a ‘popular’
fallacy – a fallacy that is pervasive in everyday, ordinary language arguments and that
goes routinely undetected or unchallenged by an interlocutor who, by the standards
established in Study Unit 2, finds nothing wrong with the argument.
The above characterisation of an informal fallacy is instructive because it tells you that a
fallacy might be lurking in an argument which:
a.
is invalid, even though it does not follow the structure of any of the deductive
forms listed in Section 5.5 of your textbook; or,
b.
is invalid, because it follows the structure of any one of the invalid deductive
forms listed in Section 5.51 ; or,
c.
is unsound, even though it follows the structure of any one of the valid deductive
forms listed in Section 5.5 [in this case, one of the premises has to be untrue]; or,
1 If
you commit this sort of a fallacy, or allow it to pass unchallenged, then you are just being careless
about what you learnt in Study Unit 2.
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d.
is a bad argument, even though it is valid and, perhaps, even sound; or,
e.
is a weak inductive argument.
Let us now look at an example of each of the kinds of fallacies identified above. Begin by
considering Example 7.2.27 in your textbook (Mooney et al., 2016, pp.182) as an example
of (a) above. Here, the argued-for conclusion is: ‘We should not cut down on pesticides
used in growing fruit and vegetables.’ The reason given for the conclusion is that fruit
and vegetables are essential for our health. Note that this argument, as it stands, does not
follow any of the forms listed in Section 5.5. However, a little thought should be sufficient
to convince you that the argument is invalid: accepting the health benefits of consuming
fruit does not allow you to infer that the cultivation of fruit should not use pesticides.
Indeed, there is no connection between the premise and the conclusion.
Next, consider Example 7.4.13 (Mooney et al., 2016, pp.209) as an example for (b) above.
This argument follows the structure of argument 7 in Section 5.5, which is invalid.
Therefore, Example 7.4.13 is straightforwardly fallacious although people routinely
reason in this manner.
Now, look at Example 7.4.11 (Mooney et al., 2016, pp.208) as an example for (c) above. This
argument takes the form of a disjunctive syllogism (argument 6 in Section 5.5), which is
valid. However, Example 7.4.11 is an unsound argument; the disjunctive premise ‘Either
I should explore the tenets of Scientology or continue to lead a meaningless life’ is false.
It could very well be the case that I don’t want to explore the tenets of Scientology and
that I don’t want to lead a meaningless life but that I want to take up the study of music,
instead.
Move on to Example 7.4.5 (Mooney et al., 2016, pp.205) to see an instance of (d) above. The
structure of the argument does not take after any of the valid forms identified in Section
5.5, but is clearly valid. If we accept the premise that we can’t sell medication other than
on a physician’s prescription, then we must accept that we can’t sell medication other
than on a physician’s prescription. Indeed, if any argument is valid, this certainly is. The
greater travesty here is that the argument might also be sound. The pharmacist making
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the argument could be living in a legal jurisdiction where such sale is prohibited. Why
then is this argument ‘bad’ or fallacious? This is because it defeats the implicit purpose of
argumentation: you argue to give independent reasons for a conclusion; in this case, the
reason is not independent. You are only pretending to argue.
Let us now consider fallacies that are erroneous forms of induction. Example 7.3.6
(Mooney et al., 2016, pp.192) is a good example of e. above. The argument takes the form
of an inductive generalisation, but clearly, the small sample (“3 American men that I
dated”) provides weak evidence for the generalised conclusion (that American men are
demanding). Another more innocuous (and so, more dangerous) form of weak induction
is provided by Example 7.3.19 (Mooney et al, 2016, pp.199). Let us bolster the example by
using some numbers: suppose 60% of the students (most of the students) will drink at the
bar on campus; 60% of that lot (most of that lot) will have premarital sex; and 60% of those
having premarital sex (most of those having premarital sex) will end up as single parents.
This does not imply that most of the students will become single parents (the chance of a
student becoming a single parent is only 22%).
I hope that this discussion has put you on firmer ground in terms of understanding what
an informal fallacy is. However, one thing about these fallacies is yet unexplained. Why
are they so frequently committed? I suspect that is, in part, because we are not, ordinarily,
sufficiently scrupulous with our reasoning. Or, there could be a commonly distributed
defect in our neural processes. Whatever the explanation is, it need not detain us any
further; all I am concerned with is that you familiarise yourself with the different types of
fallacies discussed below sufficiently thoroughly, so that you can avoid making them.
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1.2 Types of Informal Fallacies
Read
You should now read: Mooney, Williams, & Burik (2016), Chapter 7 (Section 7.2 to
7.6).
Your textbook helpfully organises the different commonly occurring fallacies into four
categories: fallacies of relevance; of weak induction; of presumption; and, miscellaneous
fallacies. The basis of this organisation is, in part, structural (the fallacies in any of the first
three categories share similarities in their structure, while the last category is a holding
area for fallacies that cannot be accommodated into any of the other categories); the names
chosen for the categories reflect the ‘spirit’, the underlying cause, of the fallacy. Each
category is then subdivided into further groups according to even stronger structural
similarities. I will briefly go over these categories here; it is imperative, however, that
you work through the material and the examples in the textbook to understand what
constitutes the fallacy and how it might be avoided.
1.2.1 Fallacies of Relevance
Fallacious arguments of this sort, invariable, fall into category (a) in Section 1.1 above.
These arguments are such that the premises appear to, but do not, in fact, justify the
conclusion. So, while these arguments are invalid, the misleading appearance of validity
could be grounded in a variety of factors.
As your textbook explains, the conclusion of such arguments might be justified by
appealing to the reason that:
i. There is something pitiable about a person’s circumstance (‘appeal to pity’); or,
ii. The conclusion is popularly believed to be true (‘appeal to popularity’); or,
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Additional Principles for Arguing Well
A contrary conclusion is claimed by a person of objectionable character or a
person who doesn’t practice what he preaches (‘argument against the man’); or,
iv.
It is broadly related to the ‘topic’ of the conclusion without being directly related
to the conclusion (‘red herring’); or,
v.
There is no known evidence against the conclusion (‘appeal to ignorance’); or,
vi.
The argument against the conclusion is unsound/uncogent (‘rejecting the
conclusion of a bad argument’).
You should note that the fallacy of ‘attacking a strawman’ is closely related to the fallacy
committed in vi. above. Fallacy vi. (‘rejecting the conclusion of a bad argument’) arises
when, based on the fact that an argument is bad, you reject its conclusion: the strawman
fallacy arises when you, carelessly or cunningly, provide a bad argument for a conclusion
in order to reject it.
Finally, as you work through the examples in the textbook, be mindful that just because
an argument takes one of the six forms identified above, it is not, by default, fallacious.
Context plays an important role and you must be discerning about whether, in a given
context, a fallacy has been committed.
Activity 1
Mooney, Williams, & Burik (2016), Exercise 7.1, pp.186-188.
1.2.2 Fallacies of Weak Induction
Fallacious arguments of this sort fall into category (e) in Section 1.1 above. In addition,
note that the discussion here complements the discussion in Section 3.2 of Study Unit 2.
You would be guilty of committing this sort of fallacy when you:
i.
Provide a weak inductive generalisation (‘hasty generalisation’); or,
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ii.
Provide a weak statistical syllogism (‘suppressing information); or,
iii.
Provide a weak argument from analogy (‘weak analogy’); or,
iv.
You claim a causal relation based on a correlation (‘with this, so because of this’).
Do note that the fallacy titled ‘Exception proves the rule’ falls under the broad category
i. above. Here, you are generalising from a small sample (indeed, a sample size of one).
Further, the fallacy titled ‘After this, so because of this’ could either be an example of a
weak generalisation (if your sample size is small), or it could be a fallacy that falls under
category iv. above. Thirdly, the fallacy titled ‘Causal slippery slope’ is really an example
of a weak statistical syllogism. I discussed Example 7.3.19 in Section 1.1 of this Study Unit
and showed you that as we build longer syllogistic chains, the strength of the syllogism
diminishes.
Finally, take particular note of the fallacy titled, ‘Appeal to unqualified authority.’ This is
a common enough fallacy for you to take extra care to avoid, although, in my opinion, it
is hard to justify your textbook’s claim that it is a fallacy of weak induction. I would have
placed it under ‘Miscellaneous Fallacies.’
Activity 2
Mooney, Williams, & Burik (2016), Exercise 7.2, pp.202-203.
1.2.3 Fallacies of Presumption
Although we really have a mixed bag of fallacies here, the common strand running
through them is that the conclusion in these arguments is justified by a premise that is
presumed to be true; however, that presumption is, itself, unjustified. The fallacy ‘Begging
the question’ falls under category d. in Section 1.1 above, while the fallacy titled ‘False
dichotomies’ would fall under category (a) or category (c), depending on whether it is a
case of “overlapping alternatives” or “overlooking alternatives” respectively.
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1.2.4 Miscellaneous Fallacies
I will leave you to work through these fallacies on your own. As an exercise, for each type
and example of fallacy that you encounter under this heading in the textbook, ask yourself
which of the categories (category [a] to [e] in Section 1.1 above) it falls under.
Activity 3
Mooney, Williams, & Burik (2016), Exercise 7.3, pp.216-218.
Summary of Key Points
• Fallacies are especially pernicious arguments because the flaws in the argument
(whether invalidity, weakness, false premises or others) are not immediately
apparent.
• For ease of exposition, fallacies can be categorised as fallacies of relevance; fallacies
of weak induction; fallacies of presumption and miscellaneous fallacies.
• Fallacies of relevance (such as, but not limited to, Ad Populum, Ad Hominem and
Red Herring) are, in fact, invalid, but masquerade as valid arguments.
• Fallacies of weak induction (such as, but not limited to, Hasty Generalisation and
Slippery Slope) are, in fact, weak arguments, which appear strong.
• Fallacies of presumption comprise Begging the Question and False Dichotomies.
The former is an instance of bad (but, sound!) reasoning because the conclusion is
assumed by the premises; the latter is an instance of unsound reasoning because
the premises, even though they appear true, are actually false.
• Miscellaneous fallacies consist of fallacies (such as, but not limited to, Composition,
Division and False Appeal to Authority) have no common diagnosis of why they
are fallacious.
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Chapter 2: Definitions
2.1 The Importance of Definitions
Read
You should now read: Mooney, Williams, & Burik (2016), Chapter 10 (Section 10.1 and
10.2).
Language makes communication between us possible precisely because the signs and
sounds that comprise it have a shared meaning for the interlocutors. The ‘codification’ of
this shared meaning is a ‘definition.’ Suppose, for instance, I was suggesting to Emma that
we should have pasta for lunch at this new Italian restaurant. Emma would understand
me perfectly well because she would know exactly what I meant by ‘pasta’ or ‘lunch’ or
‘new Italian restaurant.’
However, there are terms (words or phrases, if you wish) in ordinary language that are
vague; these are terms over whose meaning there is no consensus. Examples of such terms
are: ‘tall,’ ‘hot,’ ‘bald,’ ‘heap,’ etc. The ambiguity in the meaning of these terms arises due
to the fact that the meaning of such words depend also on the context in which they are
used (I might be tall in a community of pygmies, but certainly not among professional
basketball players). Another way of saying, more or less, the same thing is that the word
‘tall’ has no precise definition.2
In addition to vague terms, ordinary language also consists of words (let us call them
‘licentious words’), where their meaning, even though not context dependent, has a
2
In fact, while preparing this discussion for you, I checked up ‘tall’ in a dictionary and was told, ‘tall’ is
‘something above average height’. Note that, ‘average height’ is context dependent.
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‘subjective’ element to it. These words (or, phrases) such as, ‘God,’ ‘love,’ ‘morally right,’
provide their users the license to give a personal, private meaning to them. For example,
when I claim, ‘There’s no good reason to believe in the existence of God,’ I am really
claiming that, ‘There’s no good reason to believe in the existence of what I consider to
be God.’ The trouble is, our everyday usage of licentious terms generally happens to be
presumptuous: we presume, without warrant, that our meaning for the term is shared by
the person(s) we are speaking to.
When conversation consists of vague or licentious terms, disagreements may result, which
are of a superficial nature. For example, if during the course of our Italian lunch, I were to
tell Emma that I love her, Emma might respond, “No, you don’t. Because, if you did, you
wouldn’t have flings with all these other women.” To which, I might respond, “D...
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