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).