Argument Basics
• When an argument shows that its conclusion is
worth accepting we say that the argument is good.
• When an argument fails to do so we say that the
argument is bad.
• But there are different ways for an argument to be
good or bad because there are different types of
arguments.
Two types of arguments
1) Deductive Argument
2) Inductive Argument
(1) Deduction:
Reasoning from general principles to
particular cases
1. The sum of the interior angles of any triangle is
180 degrees.
2. ABC is a triangle.
3. Angle A = 50 degrees.
4. Angle B = 40 degrees.
Therefore
C. Angle C = 90 degrees.
•
In deductive arguments, the premises entail the
conclusions.
– This is a very powerful form of reasoning.
– If the premises are true and the form is valid, then
conclusion must be true.
(2) Induction:
Reasoning from particular cases to
general principles
1. Helium is a gas and it has a low density at 1ATM & 22C.
2. Oxygen is a gas and it has a low density at 1ATM & 22C.
3. Nitrogen is a gas and it has a low density at 1ATM &
22C.
…
Therefore
C. All gases have a low density at 1ATM and 22C.
• In inductive reasoning the premises support the
conclusion in direct proportion to the extent and
comprehensiveness of the available data.
A philosophical aside …
In praise of induction and risk …
“Valid [deductive] arguments are risk free. Inductive logic studies risky
arguments. A risky argument can be a very good one, and yet its
conclusions can be false, even when the premises are true. Most of our
arguments are risky.”
Ian Hacking, Introduction to Probability and Inductive Logic, 11.
“A inference rule is amended it yields an inference we are unwilling to
accept; and inference rule is amended if it violates a rule we are unwilling to
amend. … All this applies equally well to [deduction and] induction. …
Predictions are justified if they conform to valid canons of induction; and the
canons are valid if they accurately codify accepted inductive practice.”
Nelson Goodman, Fact, Fiction and Forecast, 64.
Important Note:
(i) No inductive argument meets the standard of deductive validity.
(ii) No deductive argument meets the standard of inductive validity.
(3) Analogical reasoning:
Similar cases ought to be treated similarly
•
•
•
•
1. A is relevantly similar to B.
2. A has property P.
Therefore
C. B has property P.
• Meeting the G condition here is different from
either deduction or induction. (Assuming that
Premise 2 is acceptable) it all comes down to
the claim of ‘relevant similarity’.
(4) Conductive Reasoning:
Weighing pros and cons, arguments and
counterarguments
• Conductive arguments can typically involve a blend of
the above three. You strengthen a conductive argument
by explicitly conceding and attempting to address
counter-considerations.
• E.g., the question of affirmative action
• Again, here, meeting the G condition is not simply
deductive validity, sufficient inductive support, or a
strongly compelling analogy; this a a fourth (and most
complex) way of meeting the G condition.
Interpreting Arguments
(i) Standardizing Arguments
– What is the C? What are the P’s?
(ii) Patterns of Premises
– How exactly are the P’s organized and interrelated?
(iii) Unstated Premises and Conclusions
– Filling in what is left unsaid (and left for you to fill in).
(iv) Charity in Interpretation
– Be kind! Avoid the temptation to portray an argument
poorly.
Argument Structure
• In order to evaluate an argument, it is
obviously crucial to first understand
exactly what the argument is.
• Step 1: identify premises and conclusions
• Step 2(a): identify the content of the
premises and conclusion
• Step 2(b): identify the form or structure of
the argument
Standardizing Arguments (I)
• To standardize an argument is to explicitly set apart its
conclusion and its premises.
– Standardizing arguments should not be confused with
formalizing or schematizing arguments.
• Procedure:
(i) Find the conclusion.
•
What is the passage trying to make me believe?
(ii) Find the premises.
•
What claims are being offered to support the
conclusion.
Standardizing Arguments (II)
• Be careful! Be thoughtful!
• In written and spoken exchanges, conclusions are often
scattered among premises and irrelevant material in the
passage you are evaluating.
– Conclusions may be asserted first, last or in the
middle of a passage.
– This makes arguments difficult to evaluate.
• In good editorials, conclusions are asserted first.
• In good analytical writing, conclusions are asserted last.
• In general, it is a sign of bad writing that conclusions are
asserted in the middle.
Example (I)
“Research by Professor Fizzbane has shown
conclusively that all humdingers are zipwags.
Interestingly, our research at Gentech labs has
shown that the rare spittleburg collected from
Amazonia is also a humdinger. We conclude,
uncontroversially, that the spittleburg is a
zipwag.”
Hermione Granger, “Recent Gentech Research”
Example (I) – Analysis
• Here is the standardized argument.
Premise 1: All humdingers are zigwags.
Premise 2: This spittleburg is a humdinger.
Conclusion: This spittleburg is zigwag.
• We would formalize the argument as follows:
Premise 1: All P are Q
Premise 2: R is P
Conclusion: Therefore, R is Q
Example (II)
• “At Stalingrad, General Chuikov faced an
unhappy dilemma. On the one hand, he
could order a further retreat in the face of
the German advance. This would result in
significant losses to the 62nd army. On the
other hand, he could order the army to
stand its ground at Stalingrad. That, too,
would result in heavy losses.”
Example (II) – Analysis
• Here is the standardized argument:
1: Either we retreat further or we stand our ground.
2: If we retreat, then we will suffer heavy losses.
3: If we stand our ground, then we will suffer heavy losses.
4: Therefore, we will suffer heavy losses.
• Here is the formalized argument:
Premise 1:
Either P or Q.
Premise 2:
If P then R.
Premise 3:
If Q then R.
Conclusion:
R.
Scope
• The scope of a claim can be understood as the coverage
of the claim.
(i) Universal claims.
• Cover all.
• “All toddlers love toy cars.”
• “Every toddler loves toy cars”
• “There is no toddler that does not love toy cars.”
(ii) Particular claims
•
•
•
•
Cover some.
“Some toddlers love toy cars.”
“A few toddlers love toy cars.”
“There is a toddler that loves toy cars.”
Degrees of Commitment
• People’s commitment to their conclusions vary.
– They may be more or less committed to a conclusion.
–
–
–
–
–
–
“It is certain that …”
“It is indubitable that …”
“It is probable that …”
“It is likely that …”
“It might be true that …”
“It could be true that …”
Organization of Premises
• Premises may be organized in different
ways.
• There are (i) convergent premises, and (ii)
linked premises
– Sometimes called convergent support, and
linked support.
Convergent Premises
• Convergent premises (also convergent support)
are completely independent, and each
individually adds to the case in favor of the
conclusion.
– The failure of an individual premise does not
necessarily indicate the failure of the whole argument.
• Convergent premises:
P1 P2
P3
↓
↓
↓
C1
Example of Convergent Premises
David Dangoor, Phillip Morris in a “Rolling Stone”
interview
“I’ll tell you what I like about this business.
First, there are no surprises. There is nothing
more to be said or discovered about
cigarettes. … Second, no new company wants
to get into the tobacco business. That’s great.
Third, we have the best partners in the world:
the governments. In a lot of countries, the
taxes from our product are incredibly important
to the whole welfare state. So, no matter how
you look at it, this is a great business to be in –
if you can handle the fact that some people
are not going to like you.”
Example Standardized
P1: There is no more negative evidence forthcoming
about tobacco.
P2: No one today wants to get into the tobacco business.
P3: Tobacco companies have the best partners in the
world.
Therefore
C1: The tobacco business is a great business to be in – if
you can handle the fact that some people are not
going to like you.
Linked Premises
• Linked premises (also linked support) are
interdependent in their support for the
conclusion.
• Linked Premises
P1 + P2 + P3  C1
• Linked arguments are only as strong as
their weakest link. If any link fails, then the
argument fails.
Example of Linked Support
“Anyone who uses weapons that
predictably injure civilians is acting
immorally. Cluster bombs predictably
injure civilians. Those jerks are still today
using cluster bombs. Therefore, they are
acting immorally.” [p.41]
Example Standardized
P1: Anyone who uses weapons that
predictably injure civilians is acting
immorally.
P2: Cluster bombs predictably injure
civilians.
P3: A group of people is using cluster
bombs.
C1: That group is acting immorally.
Subarguments
• Arguments often proceed in stages. A
statement that serves as the conclusion of
one argument becomes a premise in
another argument.
• Subarguments may be provided to support
controversial premises.
Example of Subargument (I)
“A computer cannot cheat in a game,
because cheating requires deliberately
breaking the rules in order to win. A
computer cannot deliberately break rules
because it has no freedom of action.”
Example of Subargument (I)
P1: A computer has no freedom of action
C1 (P2): A computer cannot deliberately
break rules.
P3: Cheating requires deliberately breaking
rules.
C2: A computer cannot cheat.
Example of Subargument (I)
1. A computer has no freedom of action.
Thus
2. A computer cannot deliberately break rules.
3. Cheating requires deliberately breaking rules.
Therefore
C. A computer cannot cheat
1
↓
2+3
↓
C
Unstated Conclusions
• Sometimes conclusions are left implicit. This is
often an effective rhetorical device as it forces the
listener to contribute to, and thereby participate in,
the argument.
• Consider the following cases:
– “The law does not permit suicide, and whatever the
law does not explicitly permit it forbids.” Aristotle
– “Could evolution ever account for the depth of intellect
that Carl Sagan possesses? Not in a billion years.”
(p.51)
Supplementing Unstated Material
P1. The law does not permit suicide.
P2. Whatever the law does not explicitly permit it
forbids.
Therefore
C. Suicide is illegal.
P1. Evolution cannot account for the depth of
intellect that Carl Sagan possesses.
Therefore
C. The theory of evolution is false.
Unstated Premises
• The question of unstated premises gets us into more
subtle terrain, because all communication relies on a
vast implicit background of shared beliefs and values.
• In general, in any conversation, we do not explicitly
articulate everything that is relevant.
• Sometimes, one of these implicit background beliefs
must be explicitly added when standardizing an
argument, on the grounds that:
(i) The author clearly seems to be committed to it
(ii) Explicitly adding it greatly improves the force or clarity of the
argument
Example (I)
[P0: Freedom of action is required to
deliberately break rules.]
P1: A computer has no freedom of action
C1 (P2): A computer cannot deliberately
break rules.
P3: Cheating requires deliberately breaking
rules.
C2: A computer cannot cheat.
Former US President Jimmy Carter, “Just War—or a
Just War?” from The New York Times (9 March 2003).
“Profound changes have been taking
place in American foreign policy,
reversing consistent bipartisan
commitments that for more than two
centuries have earned our nation
greatness. These commitments have
been predicated on basic religious
principles, respect for international law,
and alliances that resulted in wise
decisions and mutual restraint. Our
apparent determination to launch a war
against Iraq, without international
support, is a violation of these
premises.”
Standardized
• 1. America’s reputation was staked on commitment to
certain key principles.
• 2. These principles are based on religious principles,
respect for international law, and important alliances.
• 3. Adherence to these principles has usually resulted in
wise decisions.
• 4. Attacking Iraq without international support would
violated these principles.
• Therefore
• C. America should not attack Iraq without international
support
Be Careful!
• No supplementation without justification
• Guidelines for when to add missing premises
1) Logical gaps indicative of missing
premise(s).
2) Additional premise is implicitly or explicitly
accepted by the arguer.
3) Statements of missing premises should be
as plausible as possible.
Be Charitable!
• The Principle of Charity:
– Bend over backwards to be fair to the arguer.
– Reid on Hume: “Temper, moderation, and good
manners.”
• In other words:
– Begin with the assumption that the argument is
cogent.
– Do not add material to an argument that makes it
a worse argument.
– Assume that the arguer will be responsive to
reasoned counter-arguments.
Wisdom from your textbook!
“On the presumption that people who offer
arguments are seeking to be reasonable,
and to provide information supported by
logically connected ideas, we should not
represent their argument as implausible or
unreasonable unless there is compelling
evidence for doing so.” [p.60]
Final Example III –
Mill, On Liberty (1859)
“The peculiar evil of silencing the
expression of an opinion is that it is
robbing the human race; posterity as
well as the existing generation; those
who dissent from the opinion still
more than those who hold it. If the
opinion is right, they are deprived of
the opportunity of exchanging error
for truth. If it is wrong, they lose what
is almost as great a benefit, the
clearer perception and livelier
impression of truth, produced by its
collision with error.”
1. If an opinion that is right is censored, then those who
mistakenly think that it is wrong are deprived of the
opportunity of exchanging error for truth.
2. If an opinion that is wrong is censored, then those who
correctly think that it is wrong are robbed of almost as great
a benefit …
Thus
3. Those who dissent from a censured opinion are wronged to
an even greater extent than those who agree with the
censured opinion.
4. If an opinion that is right is censored, then those who
correctly agree with the censored opinion are also
wronged.
Thus
5. Silencing the expression of an opinion robs the human
race, both present and future generations.
Therefore
C. Censorship is wrong.
Example III – Diagram
1 2
↓↓
3 4
↓ ↓
5
↓
C
A counter-argument
Sometimes opinions are particularly volatile, and
can have harmful consequences. This is why we
have laws against hate literature. We are not free
simpliciter, but rather, only free to the extent that
our actions do not impinge the freedoms of
others. Whenever opinions can predictably have
the consequence of impinging on the rights and
freedoms of others, they should be censured.
Standardized
1. Like all rights and freedoms, freedom of expression
of opinion is essentially qualified and restricted.
2. One is only entitled to a certain right or freedom to
the extent that it does not impinge on the rights and
freedoms of others.
3. Some opinions impinge on the rights of others.
Therefore
C: Whenever opinions can predictably have the
consequence of impinging on the rights and
freedoms of others, they should be censured.
Three Key Logical Terms
(1) Cogency
(2) Soundness
(3) Validity
(1) Cogency
• Cogency: A general property of arguments that reflects the
extent to which an argument compels or constraints.
– A cogent argument satisfies the ARG conditions.
– An argument may be said to be “cogent” or “lack cogency”.
• Does admitting that an argument is “cogent” commit you to
the conclusion?
– In some cases “yes” and in others “no.” It depends on
the mode of reasoning at work!
– Strangely, as a matter of style and convention, we usually
don’t use the term “cogent” in cases where admitting the
cogency of the argument would, in fact, absolutely commit
us to the conclusion.
– Typically, the use of “cogent” to describe an argument
often indicates a tentative commitment to the argument.
(2) Soundness
• Soundness: An argument is sound if the premises of the
argument are true and the conclusion is implied by the
premises.
– A sound argument satisfies the ARG conditions.
– Committing to the soundness of an argument is to commit to the truth
and relevance of the premises as well as the acceptability of the form of
the argument.
• Deductive arguments have the highest standard of cogency.
• Thus, we seldom describe deductive arguments, involving
deductive entailment, as “cogent.” We usually described them
as “sound.”
– A sound argument has true premises that deductively entail the
conclusion.
– A sound argument is an argument that has the highest standard of
cogency.
(3) Validity
• In day-to-day life, we talk about a valid driver’s license, or the
validation of software serial number.
• Validity is a technical term in deductive logic.
• If an argument has an appropriate deductive form, then we say
that the argument is valid.
• Recall: deductive logic is just one mode of reasoning, though it is
a very powerful form of reasoning.
• An argument is either “valid” or “invalid”.
•
•
When we say that an argument is invalid we mean that we are rejecting
the argument because it doesn’t have the right deductive form.
When we say this, we don’t care about the content of the premises.
• That is, we don’t care what the premises are about.
(3) Validity (more)
• If an argument has a valid form and the premises are true, then the
conclusion of the argument must be true.
– The conclusion is deductively entailed.
• But, an argument may be valid (have the right form or structure) but
not be true. It’s premises could be false.
• Important: Committing to the validity of an argument, does not necessarily
commit you to the truth conclusion.
– Likewise, asserting the invalidity of an argument, does not necessarily
commit you to rejecting the conclusion. (You might accept the
conclusion, but reject the form of the argument given for the
conclusion.)
Validity Illustrated
P1: If it’s whirly-gig then smack-gurgle.
P2: This is a whirly-gig.
C1: This is also a smack-gurgle.
•
This is a valid argument. We recognize the form as being valid. All
arguments of this form are valid:
P1: If P then Q.
P2: P
C1: Therefore, Q
•
But, not all arguments of this form necessarily produce true conclusions. In
this case, we don’t know if the premises are true or false.
• We only know that argument is valid. We know nothing about its truth!
Important!
Validity and Truth are Different.
Example 1:
P1: All men are mortal.
P2: Socrates is a man.
C1: Socrates is mortal.
Valid and True.
Example 2:
P1: All men are purple.
P2: Socrates is a man.
C1: Socrates is purple.
Valid but false.
Note that Example 1 and Example 2 have exactly the same form or
structure of argument.
A Practical Aside
•
•
•
•
•
Sometimes you will hear “valid” applied to other modes of reasoning.
– For example, you might hear: “That’s a valid analogy.”
– This is generally a mistake or error.
As a matter of style and convention, we reserve the word “valid” for
deductive arguments that have an appropriate form.
Sometimes you will hear “sound” applied to other modes of reasoning.
– For example, you might hear: “That’s a sound analogy.”
– This is generally an mistake or error.
Likewise, we also usually reserve the term “sound” for deductive arguments
that have true premises and entail the conclusion.
– “Cogence” is usually the positive term used to describe arguments that
use modes of reasoning other than deduction.
In technical discussion you might here someone refer to “a sound induction”
or a “valid induction.”
– This is often simply a mistake but sometimes a controversial
philosophical point is being made …