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Critical Thinking 1290 Summary and Review.
Exam prep
Review course notes.
Review assigned text material.
Compare your notes with others.
Review Term work, identify errors and
omissions.
Attend review session.
Study old exams –
◦ Don’t seek answer key. Make it!
Note no natural deduction proofs.
Final Exam
40 Multiple Choice Questions.
Bubble Sheet.
Fill in Name, Student Number.
Bring HB pencil & Eraser, Photo ID.
Don’t bring Valuables, Electronics.
Exam Format
3 hrs. (average writing time = 1hr.)
Multiple choice Questions.
Each desk has:
◦ Question sheet (2 sided).
◦ Bubble Sheet.
◦ Scrap Paper.
Examination Hall
◦ ? other courses writing same room.
◦ Please be quiet and courteous when leaving.
Content Review
Basic Concepts
Statements or Claims.
Arguments.
‘Valid’.
Fallacies.
Counter-examples.
Arguments
Combinations of Claims that have an
rational relationship.
One or more Claims is support for one
claim.
Premises: the supporting claims.
Conclusion: the supporting claims.
Valid
Defn:
An argument is valid when (AND ONLY
WHEN)
…if the premises are true, the conclusion
must be true.
Fallacies
Informal Fallacies vs. Formal Fallacies.
Informal fallacies.
◦ Mistakes in reasoning not precisely
formulated by logical rules or requirements.
Formal Fallacies.
◦ Mistakes in reasoning precisely formulated by
logical rules or requirements.
Inductive fallacies…
◦ Mistakes in reasoning typical in inductive logic.
Counter-examples
Refutation by Counter-example.
A form of argument by analogy.
◦ Creating an analogous argument that clearly violates the definition of ‘Valid’.
◦ A counter-example is considered an acceptable proof of invalidity because every argument with the same form is equally valid (or invalid).
Informal Fallacies
Fallacies of Relevance.
Fallacies of Presumption.
Fallacies of Ambiguity.
Misc (Phil’s) Fallacies.
Fallacies of presumption
Complex Question.
False cause.
Begging the question.
Accident.
Converse Accident.
Suppressed Evidence.
False Dichotomy.
Fallacies of Relevance
◦ Ignorance
◦ Illegitimate authority
◦ Abuse
◦ Emotion
◦ Pity
◦ Force
◦ Irrelevant conclusion.
Fallacies of Ambiguity
Equivocation Ambiguity in words.
Amphiboly Ambiguity in grammar or sentence construction.
Accent Ambiguity in emphasis.
Composition
Division
Misc. Fallacies
Naturalistic fallacy.
Gambler’s Fallacy
Reverse Gambler’s Fallacy
Texas sharpshooter fallacy
Wishful Thinking.
The fallacy fallacy.
Syllogistic Logic
Logic of set membership.
Restrictive language: only verb = “to be”
Restrictive number(s): “some, none, all”.
Four Standard Statement forms A, E, I, O.
Direct Inferences
There are clear relationships between
different forms of statements with the
same subject and predicate.
If All A’s are B’s then…
◦ No A’s Are B’s is false. (contrary)
◦ Some A’s are B’s is true. (contradiction)
◦ Some A’s are not B’s is false. (sub-alternate).
Direct inferences summary
Square of opposition…
You should be able to rely on memory.
Evaluating Categorical Arguments
Categorical Arguments must be in the
form of a Standard Syllogism:
Exactly two premises.
Exactly one conclusion.
All statements in standard Form.
Categorical arguments may be valid or
invalid
Demonstrate using a Venn diagram
Demonstrate using Rules for Valid Syllogisms
Venn Diagrams
Labeling a Venn diagram
Minor
Term
Major
Term
Middle
Term
Anatomy of a Venn diagram
All cats are mammals.
All mammals are animals.
All cats are animals.
What does each section represent?
How to Draw Venn Diagrams
Step 1: State the argument as a standard form
categorical syllogism.
Step 2: Draw and label three intersecting circles.
Step 3: Shade the sections to represent the
universal premises.
Step 4: Place an X in the section or on the line
to represent any particular premises.
Step 5: Determine validity by checking whether
the conclusion is represented in the diagram.
Distribution
A subject or predicate term is
distributed if the claim refers to every
member of the group.
A claim: All S are P.
E claim: No S are P.
I claim: Some S are P.
O claim: Some S are not P.
Rules for Valid Syllogisms
1. Avoid 4 Terms.
2. The middle term must be distributed at least once.
3. Any term that is distributed in the conclusion must be distributed in a premise.
4. If a premise is negative, the conclusion must be negative, and vice-versa.
5. A valid argument cannot have two negative premises.
6. A valid argument cannot have two universal premises when the conclusion is particular.
Syllogistic Fallacies
Rule 1: 4 term fallacy.
Rule 2: Undistributed Middle.
Rule 3: Illicit Major / Minor.
Rule 4: Negative Conclusion from positive
premises.
Rule 5. Two negative premises (Fallacy of exclusive
premises).
Rule 6. Existential Fallacy.
Propositional Logic
Atomic Propositions.
◦ Propositions that make only one truth value,
and have no logical connectives.
Compound Propositions.
◦ Atomic propositions combined with logical
connectives.
Logical Operators:
◦ Symbols that represent logical operations
such as “and”, “or”, “if-then” and “not”.
Truth Tables
Complete proof procedure.
Compiles every possible permutation of
truth-values.
Assessment procedure for Statements or
Arguments.
◦ Statements are: tautologies, contradictions or
truth-functional
◦ Arguments are: valid or invalid.
Standard Argument forms.
Modus Ponens
Modus Tollens
Disjunctive Syllogism
Constructive dilemma.
Hypothetical syllogism.
Propositional Fallacies
Affirming the consequent.
Denying the antecedent.
Affirming the disjunct.
Induction and Scientific Reasoning
Nature of induction.
◦ Strength of inductive arguments
◦ Inductive fallacies
Problem of induction.
Mill’s methods.
Falsification (and confirmation problem).
Supra-empirical virtues and inference to
the best explanation.
Main Inductive Fallacies
False Analogy.
◦ Know an example of each…
Biased Statistics / Sample
Insufficient Sample Size
Supra-Empirical Virtues
◦ Simplicity (Occam's razor) (copi’s H4)
◦ explanatory power (copi’s H3)
◦ Consistency (H5)
◦ Fruitful (H6)
◦ testability (H1) as per popper.
◦ confirmation (H2) “survival of the fittest”
◦ Try to think of WHY for each virtue, as well
as WHY this is so lame!
Course Evaluation.
Please feel free to comment on E-Text,
Quiz Design, Assignment Design, Course
Content.
Thank you!
Remember Review Sessions.
April 15th and 22nd @ 1:30 PM
My office (311 SPC).