A
Very Brief Outline of Critical Thinking
William
S. Larkin
_________________________________
I.
Critical Thinking
A.
Thinking
=df Processes by means of which creatures like us construct, maintain,
and employ a system of beliefs and attitudes.
B.
Critical
=df Rational and reflective; conscious and controlled.
C.
The
Philosophic Virtue
1.
Philosophy:
The love (philo) of wisdom (sophia)
2.
Object
of Wisdom: Maximize true/reliable/useful beliefs and attitudes while at the
same time minimizing false/unreliable/harmful beliefs and attitudes.
3.
Extreme
Open-Mindedness: Believing or accepting everything is a good strategy for
maximizing good beliefs and attitudes, but it also maximizes bad ones.
4.
Extreme
Skepticism: Not believing or accepting anything is a good strategy minimizing false
beliefs and attitudes, but it also minimizes the good ones.
5.
The
Philosophic Virtue: A golden mean between extreme skepticism and extreme
open-mindedness.
II.
Arguments
A.
Statement
=df a sentence that can be true or false
B.
Argument
=df set of statements one of which (the conclusion) is intended to be
supported by the others (the premises).
C.
Form
vs. Content
1.
Form
is determined by certain logical (syntactic) expressions and a pattern of
repetition of non-logical (semantic) parts.
EX. P1:
All S are M.
P2: Some M are not P.
C: So, no S are P.
2.
Content
is determined by the specific non-logical (semantic) expressions that are
‘plugged into’ the form.
EX. Let S = dogs, M = mammals, P = cats; then the above
argument form becomes:
P1: All dogs are mammals.
P2: Some mammals are not cats.
C: So no dogs are cats.
[This argument has good content but bad form. It has all true premises, but it is invalid
(see below)]
III.
Argument Form
A.
Deductive
vs. Inductive
1.
Deductive
argument =df Premises are intended to provide conclusive reasons for the
conclusion.
2.
Inductive
argument =df Premises are intended to provide compelling but not
conclusive reasons for conclusion.
3.
R
is a conclusive reason for S =df The truth of R guarantees the truth of
S—if R is true, then S must be true.
4.
R
is a compelling reason for S =df The truth of R makes the truth of S
more likely—if R is true, then S is probably true.
B.
Deductive
Arguments
1.
Validity
=df Good deductive structure
2.
An
argument is valid =df It is not possible for all premises to be
true but conclusion false.
3.
Soundness
=df Good overall deductive argument—i.e., good deductive structure plus
good content.
4.
An
argument is sound =df The argument is valid and has all true
premises.
C.
Inductive
Arguments
1.
Strength
=df Good inductive structure
2.
An
argument is strong =df It is not probable that all the premises
are true but the conclusion false.
3.
Cogency
=df Good overall inductive argument—i.e., good inductive form plus good
content.
4.
An
argument is cogent =df The argument is strong and has all true
premises.
IV.
Argument Content
A.
Some
Distinctions
1.
Semantic
a.
Analytic
=df True or false solely in virtue of the meanings of the terms
involved.
[EX: All bachelors are unmarried.]
b.
Synthetic
=df Not analytic.
[EX:
All bachelors are happy slobs.]
2.
Metaphysical
a.
Necessarily
True =df True in all possible worlds.
b.
A
statement S is necessarily true =df S is true and could not have been
false.
[EX: 2 + 2 = 4.]
c.
Contingently
True =df True in the actual world but false in some possible world.
d.
A
statement S is contingently true =df S is true but could have been
false.
[EX: My name is ‘William’.]
3.
Possibility
a.
Logically
Possible =df Consistent with the formal laws of logic.
b.
Logical
Necessity =df True in all logically possible worlds.
[EX: Either it is raining here and now or it
is not.]
c.
Nomologically
(Physically) Possible =df Consistent with the (physical) laws of nature.
d.
Nomological
Necessity =df True in all nomologically possible worlds.
[EX: Force equals mass times acceleration.]
4.
Epistemological
a.
A
Priori =df Can be known before (prior to) sense-experience.
b.
A
statement S is a priori =df S can be known without relying on any more
empirical investigation than is necessary to understand S.
[EX: I am not in two places at the same
time.]
c.
A
Posteriori =df Can be known only after (posterior to) sense-experience.
d.
A
statement S is a posteriori =df S cannot be known without relying on
more empirical investigation than is necessary to understand S.
[EX: There is a table in front of me.]
B.
Truth
Functional Statements
1.
Atomic
Propositions: True if and only if subject(s) has (or are in) the states
property (relation).
2.
Negations:
Have the opposite truth-value of atomic constituent.
3.
Conjunctions:
True only when all atomic constituents are true.
4.
Disjunctions
a.
Inclusive: True when at least one, and maybe
all, atomic constituents are true.
b.
Exclusive:
True when at least one, but not all, atomic constituents are true.
5.
Conditionals
a.
Material:
False only when antecedent is true but consequent is false in the actual world.
b.
Subjunctive:
False only when antecedent is true but consequent is false in some close
possible world.
c.
Causal:
False only when antecedent is true but consequent is false in some
nomologically possible world.
d.
Entailment:
False only when antecedent is true but consequent is false in some logically
possible world.
C.
Categorical
Statements
1.
Basic
Forms:
a.
Universal
Affirmative: All S are P
[Falsified by one S that is not a P]
b.
Universal
Negative: No S are P
[Falsified by one S that is a P]
c.
Particular
Affirmative: Some S are P
[Verified by one S that is a P]
d.
Particular
Negative: Some S are not P
[Verified by one S that is not a P]
2.
P
and Q are contradictories =df P and Q have opposite truth-values.
[EX: All trees are evergreens / Some trees
are not evergreens]
3.
P
and Q are contraries =df P and Q cannot both be true, but they can both
be false.
[EX: All trees are evergreens / No trees are
evergreens]
4.
P
and Q are sub-contraries =df P and Q cannot both be false, but they can
both be true.
[EX: Some trees are evergreens / Some trees
are not evergreens]
D.
Definitions
1.
Stipulative
vs. Analytical
a.
Stipulated
definitions recommend a usage for a term—they are judged on the basis of their
utility.
b.
Analytical
definitions attempt to explicate pre-established usage of a term—they are
judged on the basis of how well they correspond to that usage (the intuitions
of competent users of the term).
2.
Necessary
vs. Sufficient Conditions: Explicit definitions of a term T claim that some
conditions are both necessary and sufficient for something to be a T.
a.
P
is a necessary condition for Q =df P is a condition that must be met in
order for Q to be true—i.e., if Q is true, then P is true.
[EX:
Wining some LCS is necessary but not sufficient for wining the WS.]
b.
P
is a sufficient condition for Q =df P is a condition that is enough to
bring about the truth of Q—i.e., if P is true, then Q is true.
[EX:
Wining the ALCS is sufficient but not necessary for being in the WS.]
V.
Fallacies
A.
Relevance
1.
Appeal
to Force:
P: If you do not do/believe
X I will harm you.
C: So you should do/believe X.
2.
Appeal
to Inappropriate Authority
P1: S says you should do/believe X.
P2: S is an expert (though not about X).
C: So you should do/believe P.
3.
Ad
Hominem
P1: S says that you should
do/believe X.
P2: But S is a jerk/an idiot/has an ulterior
motive/etc.
C: So you should not do/believe P.
4.
Ad
Populum
P1: Most people do/believe
X.
C: You should do/believe X.
5.
Argument
from Ignorance
P1: There is no proof that X is not true.
C: So X is true.
B.
Presumption
1.
Begging
the Question: Circular reasoning, committed when an argument presumes the very
thing it is trying to establish.
2.
Accident:
P: Generally, S’s are F.
C: So this S (which is in fact an atypical case) is F.
3.
Converse
Accident (Hasty Generalization):
P: These S’s (which are in fact atypical cases) are F.
C: So all S’s are F.
C.
Ambiguity
1.
Equivocation:
Committed when some semantically ambiguous term is used in different ways in
different statements of an argument.
2.
Amphiboly:
Committed when some syntactically ambiguous phrase is used in different ways in
different statements of an argument.
3.
Composition:
P: All the parts of W have
property F.
C: So W has F.
4.
Division:
P: W has property F.
C: So all the parts of W have F.
Common
Deductive Argument Forms
|
Valid
Form |
|
Invalid
Cousin |
|
|
Modus
Ponens |
If
P, then Q. P. __________ Q. |
Affirming
the Consequent |
If
P, then Q. Q. __________ P. |
|
Modus
Tollens |
If
P, then Q. Not-Q. ___________ Not-P. |
Denying
the Antecedent |
If
P, then Q. Not-P. __________ Not-Q. |
|
Disjunctive
Syllogism |
Either
P or Q. Not-P. _____________ Q. |
Dysfunctional
Syllogism |
Either
P or Q. Q. ____________ Not-P. |
|
Hypothetical
Syllogism |
If
P, then Q. If
Q, then R. _____________ If
P, then R. |
Illegitimate
Syllogism |
If
P, then Q. If
R, then Q. __________ If
P, then R. |
|
Dilemma |
Either
P or Q. If
P, then R. If Q, then R. ___________ R. |
False
Dichotomy |
Either
P or Q (or S). If
P, then R. If
Q, then R. __________ R. |
|
Contraposition |
If
P, then Q. ___________ If
not-Q, then not-P. |
Conversion |
If
P, then Q. __________ If
Q, then P. |
|
Simplification |
P
and Q. _______ P. |
Conjunction |
P. ________ P
and Q. |
|
Addition |
P. _______ P
or Q. |
Subtraction |
P
or Q. ________ P. |
Common
Inductive Argument Forms
I.
Testimonial Arguments
A.
Form
P: S (a person or a faculty) claims that F.
C: So, F.
B.
Evaluation
1.
How
reliable is S? Under what
circumstances? Are the present
circumstances favorable?
2.
Are
there other reliable sources that contradict S?
II.
Argument by Enumeration
A.
Form
P1: In N
observed cases F has been the case.
C: So F is
always the case.
B.
Evaluation
1.
Sample
Size: How many observed cases N? How
large of a percentage is N of total number of cases?
2.
Sample
Representation: How representative is N
of total cases?
III.
Argument by Analogy
A.
Form
P1: A and B
are alike with respect to features F.
P2: A has
property X.
C: So, B has
property X.
B.
Evaluation
1.
Strength
of Analogy: How many features are part of F?
2.
Relevance
of Analogy: How relevant are the F-features to property X?
IV.
Argument to the Best Explanation
A.
Form
P1: F is an
observed fact.
P2: The best
available explanation for F is E.
C: So E is
true.
B.
Evaluation
1.
Explanatory
power of E: How many more facts does E explain as compared to rival
hypotheses? Does E make better
predictions than rivals? Does E fit
better with other beliefs than rival hypotheses?
2.
Simplicity:
Does E postulate any radically new types of entities/forces/events/etc.? How far beyond past experiences/theories
does E venture?