Arguments III
Basic Logical Concepts
RECAP
• Critical thinking involves distinguishing ‘argument’ from
other kinds of information as follows:
– introductions
– descriptions
– explanations
– background information
– summaries
– other extraneous materials
Learning Outcomes
• Distinguish between deductive and inductive
arguments
• Determine the common patterns of deductive
and inductive arguments
Evaluating Arguments
In evaluating any argument, one should
always ask two key questions.
1. Are the premises true? Accuracy
2. Do
the
premises
support
conclusion? Logic
the
1. Are the Premises True?
When Is A Premise True?
• A statement is true when what it says about the
world is accurate.
• A statement is false when what it says about the
world is inaccurate.
• A good premise is based on facts and experience,
not opinions and assumptions.
2. Do the Premises Support the
Conclusion?
• What does it mean to say that an argument’s premises
provide good reasons to accept the conclusion?
• Before we can effectively evaluate an argument, we
need to understand what type of argument is offered.
• Two of the major types of argument forms are deductive
arguments and inductive arguments.
Deductive and
Inductive Arguments
• Because the standards for evaluating deductive and
inductive arguments are quite different, it is important to
understand the difference between these two types of
arguments.
• Deductive argument (Deductive reasoning)
PROVES their conclusion with logical premises
• Inductive argument (Inductive reasoning)
show that their conclusion is LIKELY through the
premises
Deductive Arguments
Definition
• A deductive argument is an argument that is intended to be
completely true and certain.
• If your premises are true, your reasoning will lead you to a
logically certain conclusion.
• Each conclusion of an argument follows necessarily from
the premises.
Example:
Premise 1 : All humans are mortal. True
Premise 2 : I am a human. True
Conclusion : Therefore, I am mortal. Certain
Deductive Arguments
Examples, 1
More Examples
P1
P2
C
: All humans have brains.
: I am a human.
: I have a brain.
P1
: If the president lives in the White House,
he lives in Washington, D.C.
: The president does live in the White House.
: So, the president lives in Washington, D.C.
P2
C
If the premises are true, the conclusion must be true. (Truth-preserving
structure)
Deductive Arguments
Examples, 2
More Examples
P1
P2
C
: All mothers are females.
: Jane is a mother.
: Jane is female.
P1
P2
C
: If you are in Selangor, then you are in Malaysia.
: You are in Selangor.
: So, you are in Malaysia.
Premises based on logic – conclusion must be true – Deductive
Inductive Arguments, 1
Definition
• Inductive arguments, on the other
hand, simply claim that their
conclusions are likely or probable,
given the premises offered.
Inductive Arguments, 2
Examples:
Premise 1
Premise 2
Conclusion
: Most Rottweilers make good watchdogs.
: My dog, Coco is a Rottweiler.
: Coco is probably a good watchdog.
Premise
: Every ruby so far discovered has been red.
Conclusion
: So probably all rubies are red.
Inductive Arguments, 3
More Examples:
Premise
Conclusion
: John rarely eats out.
: Therefore, he probably declines invitations
to dine out.
Premise 1
Premise 2
: Polls show that 87% of 5-year-olds believe in the
tooth fairy.
: Martha is five years old.
Conclusion
: Martha most likely believes in tooth fairies.
Key Differences Between Deductive and
Inductive Arguments
Key: deductive / inductive
• If the premises are true the conclusion is
necessarily / probably true.
• The premises provide conclusive / good
evidence for the conclusion.
• It is impossible / unlikely for the premises to
be true and the conclusion to be false.
• It is logically inconsistent / consistent to
assert the premises but deny the conclusion.
Determining the Types of Arguments?, 1
• Test 1: Indicator Word Test
• Deductive: certainly, definitely, absolutely,
logical, conclusively, must be the case
• Inductive: probably, likely, chances are,
plausible, reasonable to assume
• Note: Not fool-proof as many
arguments without indicator words &
some indicator words might be used
improperly
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Determining the Types of Arguments?, 2
• Test 2: The Strict Necessity Test – either an
argument’s conclusion follows with strict logical
necessity from its premises or it does not.
– If it does, the argument should always be treated as deductive.
– If it doesn’t, the argument should be treated as inductive.
• Joyce is a mother. Therefore, Joyce is a female. (Conclusion
follows with strict necessity from the premise – Deductive
argument).
• Bobby is 70 years old. Therefore, Bobby cannot be a breakdancer.
(Premise is true but possible that conclusion might not be true –
Inductive argument)
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Determining the Types of Arguments?, 3
• Test 3: Common Pattern Test –
Argument has a pattern which is
characteristically deductive or inductive
– E.g. the pattern of a deductive pattern is as follows
(Three-line arguments):
• If A, then B.
• A.
• Therefore B.
– If Garfield is a cat, then it must be an animal.
– Garfield is a cat.
– Therefore, Garfield is an animal.
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Determining the Types of Arguments?, 4
• Test 4: Principle of Charity Test – Give the benefit
of the doubt to make it the most favourable to the
arguer.
• When interpreting an unclear argument or passage,
always give the speaker or writer the benefit of the
doubt.
– Never attribute to an arguer a weaker argument
when the evidence reasonably permits us to
attribute to them a stronger one.
– Never interpret a passage as a bad argument
when the evidence reasonably permits us to
interpret it as not an argument at all.
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Determining the Types of Arguments?, 5
Example: Andy told me that he ate at Maxine Restaurant
yesterday. But Maxine Restaurant was destroyed by fire
last month. It is certain, therefore that Andy is lying or
mistaken.
• Test 1 - Indicator word: certain – Deductive
• Test 2 – Strict necessity: conclusion doesn’t follow the
premises with strict necessity as it is probable that the
restaurant has been rebuilt in less than a month –
Argument could be inductive
• Test 3: Pattern: Not applicable
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Determining the Types of Arguments?, 6
Andy told me that he ate at Maxine Restaurant
yesterday.
But Maxine Restaurant was
destroyed by fire last month. It is certain,
therefore that Andy is lying or mistaken.
• Test 4: Charity – If we treat it as deductive, it
would be a bad deductive argument since the
conclusion does not follow with strict necessity.
If we treat it as inductive, strong premises make
conclusion likely. Thus, interpret argument as
inductive.
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Common Patterns of Deductive Reasoning
1. Hypothetical syllogism
a. Modus ponens
b. Chain arguments
c. Modus Tollens
2. Categorical syllogism
3. Argument by elimination
4. Argument based on mathematics
5. Argument from definition
Common Patterns of Deductive Reasoning
1. Hypothetical Syllogism – Three line arguments (Two
premises and one conclusion)
– A.Modus ponens – If A, then B. A. Therefore B
• If Joyce is a nun, then Joyce must be a female. Joyce
is a nun. Therefore, Joyce is a female.
– Chain Arguments – If A, then B. If B, then C. Therefore,
if A then C.
• If we don’t study, we won’t pass the examinations. If
we don’t pass the examinations, then we won’t
graduate in December. Therefore, if we don’t study,
we won’t be graduating in December.
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Common Patterns of Deductive Reasoning
1. Hypothetical Syllogism – Three line arguments
– Modus tollens – If A then B. Not B. Therefore, not
A.
• Modus ponens, chain arguments and modus tollens are
logically reliable pattern of deductive reasoning.
• Any argument that has one of these patterns is
absolutely guaranteed to have a true conclusion if the
premises are true.
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Common Patterns of Deductive
Reasoning
Modus Tollens – ‘denying the consequence’
P1 : If Michael were a really good friend, he would lend me his car over
the weekend.
P2 : Michael refuses to lend me his car over the weekend.
C : Therefore, he is not really a good friend.
Structure
P1 : If A (Michael were a really good friend), then B (he would lend me his
car over the weekend.
P2 : Not B Michael refuses to lend me his car over the weekend.
C : Therefore, not A he is not really a good friend.
Common Patterns of Deductive Reasoning
2. Categorical Syllogism – Three line arguments
with the word ‘all’, ‘some’ or ‘no’
– All animals are living things.
– All living things need food to survive.
– Therefore, all animals need food to survive.
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Common Patterns of Deductive
Reasoning
Categorical Syllogism – Three line arguments
with the word ‘all’, ‘some’ or ‘no’
B Mortal
P1 : All men are mortal.
P : Socrates is a man
C : Socrates is a mortal.
Structure
P1: All A (men) are B (mortal)
P2: S is an A (Socrates is a man)
C: Therefore, S is B
A Men
B Mortal
S Socrates
Common Patterns of Deductive Reasoning
3. Argument by Elimination: Logically rule out various
possibilities until only one remains.
Either Jane or Jack ate the cookie.
Jane didn’t eat the cookie.
Therefore, Jack ate it.
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Common Patterns of Deductive Reasoning
4. Based on Mathematics: Logical, step by
step reasoning.
– Eight is greater than four.
– Four is greater than two.
– Therefore, eight is greater than two.
– The fastest I can walk is at 2 km in an hour.
– My house is 2.5 km away.
– Therefore, I could not reach my house in an hour
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Common Patterns of Deductive Reasoning
5. Argument from Definition: Conclusion is
presented as being true by definition.
A bachelor is an unmarried man.
John is an unmarried man.
Therefore, John is a bachelor.
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Common Patterns of Inductive Reasoning
1. Inductive generalisation
2. Predictive argument
3. Augment from authority
4. Causal argument
5. Statistical argument
6. Argument from analogy
Common Patterns of Inductive Reasoning
1. Inductive generalisation: attributes some characteristics to
all, most or some members of a group.
– Most men are so unromantic.
unromantic.
So, Bob is probably
– All doctors I know have bad handwriting. Chris is a
doctor, so he probably has bad handwriting.
– I have observed five swans in this park, and all of them
are white. Therefore, all swans are likely to be white.
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Common Patterns of Inductive Reasoning
2. Predictive argument: Drawing conclusion
based on established principles/trend.
– Most US presidents have been male. So,
the next president will probably be male.
– It has rained every morning since last week.
It will probably rain tomorrow morning too.
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Common Patterns of Inductive Reasoning
3. Argument from authority: Support of a claim from a
presumed authority of the subject.
My doctor, who has been practicing cardiology for over 20
years, said that regular exercise is crucial for maintaining good
heart health. Therefore, regular exercise is crucial for
maintaining good heart health.
*Experts can be wrong. Relying solely on authority without
considering other evidences can be a weakness in CT.
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Common Patterns of Inductive Reasoning
4. Causal argument: Asserts or denies that
something is the cause of another happening.
– The government implemented a new tax policy last
year, and since then, the unemployment rate has
significantly decreased. Therefore, the new tax policy
caused the decrease in the unemployment rate.
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Common Patterns of Inductive Reasoning
5. Statistical argument: Uses statistics as evidence
– A recent survey of 500 randomly selected residents in
Sepang found that 78% of respondents reported
feeling safer after the implementation of the new
community policing program. Therefore, it is highly
likely that a significant majority of all residents in
Sepang feel safer due to the new community policing
program.
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Common Patterns of Inductive Reasoning
6. Argument from Analogy
– Analogy – argues that because two things are
similar in some known respects, they are likely to
be similar in some other unknown respects.
• A car needs regular oil changes to run
smoothly and avoid engine problems. Similarly,
the human body is a complex machine that also
needs regular 'maintenance' like exercise and
proper nutrition to function optimally and
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prevent health issues.
SUMMARY
Types of Argument
• Deductive vs. inductive
• Tests to determine type of argument
– Indicator word
– Strict necessity test
– Common pattern test
– Principle of charity test
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SUMMARY
Types of Argument
•
Common patterns of deductive reasoning
1. Hypothetical syllogism
2. Categorical syllogism
3. By elimination
4. Based on mathematics
5. Argument from definition
•
Common patterns of inductive reasoning
1. Inductive generalisation
2. Predictive
3. From authority
4. Causal
5. Statistical
6. From analogy
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