CHAPTER 3: MAKING SENSE OF
ARGUMENTS
• Exploring in more depth the nature of
arguments
• Evaluating them
• Diagramming them
Wednesday, July 20, 2011
ARGUMENT BASICS
• Arguments allow us to support claims
and to evaluate claims
• 2 Forms: Deductive and Inductive
• Deductive: to deduce means to draw out
or distill
• Intended to provide CONCLUSIVE support
Wednesday, July 20, 2011
ARGUMENTS
• Inductive: to broaden out
• Intended to provide PROBABLE support
Wednesday, July 20, 2011
More on Deductive Arguments
• Validity: if premises are true, then
conclusion must be true.
• Guaranteed conclusion (All or nothing)
• Necessity
• Truth Preserving: The conclusion
cannot be false if the premises are true.
Wednesday, July 20, 2011
Examples: Deductive
• Socrates is a man
All men are mortal
Therefore, Socrates is mortal
• Example in invalid argument with
same form:
• All dogs are mammals
All cows are mammals
Therefore, all dogs are cows
Wednesday, July 20, 2011
More Examples: Deductive
• If Socrates is a man, then he is mortal
Socrates is a man
Therefore, Socrates is mortal
Invalid form:
• If Socrates has horns, he is mortal.
He is mortal
Therefore he has horns
Wednesday, July 20, 2011
INDUCTIVE ARGUMENTS
• probable logical support
• Strong and Weak
• Structure of Inductive Arguments
cannot guarantee that if the premises
are true the conclusion must also be
true
• Implies: premises can be true, and
Wednesday, July 20, 2011
Slippage/free play
• Conclusion always goes a bit beyond
what is contained in premises
• The idea of Gap:
• It is always possible to go to another
conclusion, sometimes even an opposite
one with weak arguments
• Principle helps us Evaluate arguments
Wednesday, July 20, 2011
Degrees of Strength
• varying from weak, to modestly weak,
to modestly strong and to strong
• eg. Most dogs have fleas
My dog Bowser, therefore, probably
has fleas
What about the premise here?
Wednesday, July 20, 2011
DEDUCTIVE PATTERNS
3 types
conditional
disjunctive
categorical
Wednesday, July 20, 2011
CONDITIONAL ARGUMENT PATTERNS
• Hypothetical syllogism or conditional
• 3 valid forms, 2 invalid
e.g If the job is worth doing, then it’s
worth doing well.
The job is worth doing.
Therefore, it is worth doing well.
Wednesday, July 20, 2011
CONDITIONAL PATTERNS
• Antecedent: the job is worth doing
• Consequent: the job is worth doing well.
• Antecedent: p
• Consequent: q
• ps and qs: like variables, but...
Wednesday, July 20, 2011
Specific Standard Forms
• 2 Valid Forms: modus ponens and
modus tollens
• Modus Ponens
• Affirming the antecedent
if p, then q
p
therefore , q
Wednesday, July 20, 2011
STANDARD FORMS, cont.
Modus Tollens (Denying the consequent!)
E.G:
If Austin is happy, then Barb is happy
Barb is not happy.
Therefore, Austin is not happy.
Wednesday, July 20, 2011
Pure Hypothetical Syllogism
If polar bears thrive, then they eat more
seals.
If they eat more seals, they will gain
more weight.
Therefore,
If polar bears thrive, they will gain more
weight.
Wednesday, July 20, 2011
STANDARD FORM OF PurE
HYPOTHETICAL SYLLOGISM
if p, then q
if q, then r
if p, then r
Wednesday, July 20, 2011
INVALID CONDITIONAL FORMS
• eg. If Dogbert commits one more
fallacy, I will eat my hat.
Dogbert did not commit one more fallacy.
Therefore, I did not eat my hat.
DENYING THE ANTECEDENT:
why invalid?
Wednesday, July 20, 2011
AFFIRMING THE CONSEQUENT
IF DOGBERT COMMITS ONE MORE FALlACY ,
THEN I WILL EAT MY HAT.
I ATE MY HATE
DOGBERT COMMITTED ONE MORE FALLACY
Wednesday, July 20, 2011
DISJUNCTIVE SYLLOGISMS
• eg. Either Casey Anthony will go to jail
for a long time, or her lawyer will do
a good job to get her exonerated.
Casey Anthony will not go to jail for a
long time.
Therefore, her lawyer did a good job to
get her exonerated.
Disjuncts
Wednesday, July 20, 2011
Standard Form of Disjunctive
Syllogisms
either p or q
not P (or not q)
q (or P)
Denying one of the disjuncts
Validity and 2 senses of “or”: Inclusive and
exclusive
Wednesday, July 20, 2011
CATEGORICAL SYLLOGISMS
classification: relating classes of things
categorical statements
All professors are sadistic
Some professors are sadistic
no professors are sadistic
Wednesday, July 20, 2011
CATEGORICAL SYLLOGISMS AND
VALIDITY
ALL ALIENS ARE INTELLIGENT
ALL INTELLIGENT THINGS ARE STRANGE
ALL ALIENS ARE STRANGE
CLASSES AND MEMBERSHIP: IDEA OF
INCLUSION AND EXCLUSION
Exercises 3.2
Wednesday, July 20, 2011
SOUNDNESS
• Applied to deductive arguments. When
arguments have true premises and true
conclusions (to be sure)
• It is possible to have valid deductive
arguments while having false premises
and false conclusions
• Page 69 in text
• Undetermined soundness
Wednesday, July 20, 2011
COGENCY
• applies to inductive arguments
• When inductive arguments have true
premises
• Good inductive arguments are both
strong and cogent
Wednesday, July 20, 2011
Important Distinctions
Deductive
Valid/
Invalid
Sound/
Unsound/
Undetermined
Inductive
Stong/
Weak
(Degree)
Cogent/not
cogent/
undetermined
Table
Wednesday, July 20, 2011
JUDGING AND EVALUATING ARGUMENTS
• Skills to start
• Always start by looking for deductive
patterns or forms
• If not deductive by form, treat as
inductive
• if deductive, determine validity based
on pattern
• Then, determine soundness if possible
Wednesday, July 20, 2011
EVALUATING INDUCTIVE ARGUMENTS: IMPLIED
PREMISES
• What are they? Premises essential to
the argument that are left unstated or
unspoken.
Implied statements vs implied premises
most important in inductive arguments
In deductive arguments they are usually
called missing premises
Implied conclusions:
Wednesday, July 20, 2011
Implied Premises Examples
• Text: P. 80
• “Handguns are rare in Canada, but the
availability of shotguns and rifles poses a
risk of death and injury. Shotguns and
rifles should be banned, too!”
• Implied premise: Anything or most ...
Wednesday, July 20, 2011
IMPLIED PREMISES
• The Point: We need to evaluate also this
implied premise.
• How plausible or contestable is this
premise?
• Other examples. Page 81.
Wednesday, July 20, 2011
SOME IMPORTANT TIPS
• 1. It is best always to identify missing
premises. We cannot take them for
granted.
• 2. Formulate the implied premise with as
much charity as possible.
• 3. Premise should be plausible (or, as
strong as possible)
• 4. Premise should fit author’s intent
•
Wednesday, July 20, 2011
FORMULATING THEM: A STRATEGY
• USING THE PRINCIPLE OF CONNECTING TERMS
NOT CONNECTED IN ARGUMENT
• COACH JOHNSON ONCE FELL ASLEEP DURING
THE GAME.
• HE IS PROBABLY NOT A VERY GOOD COACH
• TERMS: 1. COACH JOHNSON (CJ) 2. FELL ASLEEP
• 3. NOT A VERY GOOD COACH.
• FIRST PREMISE 1 CONNECTS WITH 2
• CONCLUSION: 1 CONNECTS WITH 3
Wednesday, July 20, 2011
EVALUATED INDUCTIVE ARGUMENTS
• IDENTIFYING IMPLIED PREMISE FILLS THE GAP
BUT ALSO HELPS US MEASURE THE GAP
• FILLING THE GAP MAKES THE ARGUMENT
APPEAR NOW DEDUCTIVE (SEE EXERCISE 3.4)
• Degree of controversy: Do we need other
premises and/or evidence for us to accept
this premise?
• MEASURING GAP AND ALTERNATE AND
OPPOSITE CONCLUSIONS
Wednesday, July 20, 2011
EVALUATION cont.
• More complex arguments and mixed
arguments
• Evaluate each aspect (deductive and nondeductive) of the the argument
• If several steps in argument,
concentrate on weakest step
• If several independent premises or
clusters, focus on strongest premise(s)
• REMEMBER SCALE: STRONG ----------- WEAK
Wednesday, July 20, 2011
DIAGRAMMING ARGUMENTS
• 1. Underline indicator words, if present
• 2. Number all statements (or propositions)
in sequential order.
• 3. Break down compound statements
(statements using connectives ‘and,’
‘but,’ ‘or.’) into single statements.
Wednesday, July 20, 2011
EVALUATION PROTOCOL
DEDUCTIVE
NONDEDUCTIVE
(INDUCTIVE)
Wednesday, July 20, 2011
ASSESS
VALIDITY
ASSESS
STRENGTH
USE FORM AND
TYPE
MEASURE THE
GAP
FORMULATE AND
ASSESS ACCEPTABILITY
OF IMPLIED PREMISES:
IDENTIFY ALTERNATE OR
OPPOSITE CONCLUSION
USE
ASSESS
DIAGRAM
SOUNDNESS
TO
CONFIRM
ASSESS
COGENCY
USE
DIAGRAM
TO
CONFIRM
REVISED STEPS FOR ARGUMENT
IDENTIFICATION AND EVALUATION
STEP ONE: USE RECOGNITION OF DEDUCTIVE
PATTERNS TO DETERMINE TYPE.
STEP TWO: IF NOT DEDUCTIVE, THEN INDUCTIVE.
STEP THREE: IF DEDUCTIVE PATTERN, VALIDITY OR
NON-VALIDITY WILL FOLLOW THE
IDENTIFICATION. DIAGRAM THE ARGUMENT TO
CONFIRM.
STEP FOUR: DETERMINE SOUNDNESS/
UNSOUNDNESS/UNDETERMINED SOUNDNESS
EVEN WHEN ARGUMENT IS INVALID.
Wednesday, July 20, 2011
REVISED STEPS FOR ARGUMENT
STEP FIVE: DIAGRAM THE NON-DEDUCTIVE
ARGUMENT. THIS WILL CONFIRM ALSO.
STEP SIX: PROCEED TO EVALUATE BASED ON
IDENTIFYING IMPLIED PREMISES AND HOW
CONTROVERSIAL THEY ARE, AND WHETHER
ALTERNATE CONCLUSIONS ARE CONTRADICTORY.
STEP SEVEN: DETERMINE COGENCY OF
ARGUMENT.
Wednesday, July 20, 2011
DIAGRAMMING ARGUMENTS
NUMBER ALL PREMISES AND CONCLUSIONS BY
ASSIGNING A NUMBER TO THE STATEMENTS.
I DO THIS AT THE SIDE OF THE PAPER AND USE
ELLIPSES TO ABBREVIATE THE STATEMENT.
IT IS BEST TO IDENTIFY CONCLUSION FIRST.
WRITE THE NUMBER OF THE CONCLUSION AT THE
BOTTOM, LEAVING ROOM ABOVE FOR THE
PREMISES.
YOU CAN USE BRACKETS INSTEAD OF CIRCLES
AND SQUARES AROUND THE NUMBERS.
Wednesday, July 20, 2011
DIAGRAMMING ARGUMENTS
DETERMINE WHETHER PREMISES ARE DEPENDENT,
OR INDEPENDENT.
PROCEED TO PLACE THEM ABOVE THE
CONCLUSION AND DETERMINE HOW THEY
RELATE.
IF PREMISES ARE DEPENDENT, USE AN
UNDERLINE TO CAPTURE THIS. DRAW AN AROW
FROM THE UNDERLINE TO THE CONCLUSION.
IF PREMISES ARE INDEPENDENT, USE
CONVERGING ARROWS TO THE CONCLUSION TO
CAPTURE THIS.
Wednesday, July 20, 2011
DIAGRAMMING ARGUMENTS
• Caution sometimes ‘or.’ should not be
broken down.
• 4. Cross out extraneous or irrelevant
statements, None-premises or conclusions.
Preludes, redundant statements, or
background information.
• PATTERNS: EXERCISE 3.8
Wednesday, July 20, 2011