PHIL& 120 - Symbolic Logic

5 Credits

• Humanities Area I
• Quantitative Skills

Module 1: Basic Concepts

            1.1 Define and use appropriately the following terms:

1.argument

2.statement

3.premises

4.conclusion

5.inference

6.proposition

1.2   Identifying arguments

1.Determine if a group of sentences is an argument.

2.Identify non-inferential passages as examples of

a.Warning

b.Advice

c.Statement of opinion

d.Report

e.Loosely associated statements

f.Expository passage

g.Illustrations

h.Explanation

3.Identify conditional statements.

4.Explain the concepts of necessary condition and sufficient condition.

            1.3   Deduction and Induction

1.Define and use appropriately the following key terms:

a.Deductive argument

b.Inductive argument

c.Argument from definition

d.Categorical syllogism

e.Hypothetical syllogism

f.Disjunctive syllogism

2.Identify inductive argument forms:

a.Prediction

b.Argument from analogy

c.Generalization

d.Argument from authority

e.Argument based on signs

f.Causal inference

1.4  Assessing arguments

1.Define key terms for analyzing deductive arguments:

a.Valid deductive argument

b.Invalid deductive argument

c.Sound argument

d.Unsound argument

2.Define key terms for analyzing inductive arguments:

a.Strong inductive arguments

b.Weak inductive arguments

c.Cogent argument

1.5  Prove the invalidity of arguments using the counterexample method

1.Define  “argument form”

2.Define  “substitution instance”

3.Prove invalidity of an argument using the counterexample method.

Module 2: Categorical Propositions 1

2.1  Components of categorical propositions

1.Identify the quantifier, subject, copula and predicate in a categorical proposition

2.2  Quality, Quantity, Distribution

1.Identify the quality of categorical propositions as affirmative or negative

2.Identify the quantity of categorical propositions as universal or particular

3.Identify categorical propositions using the A,E,I,O system of designation.

4.Identify a term in a categorical proposition as either distributed or non-distributed.

2.3  Venn Diagrams and the Modern Square of Opposition

1.Identify the existential import of  A,E,I, and O statements from the Aristotelian and the Boolean perspectives.

2.Represent  A,E,I, and O statements using Venn diagrams.

3.Interpret Venn diagrams as representing A,E,I and O statements.

4.Use the modern square of opposition to test immediate inferences.

4.4   Conversion, Obversion, Contraposition

1.Construct the converse of any A, E,I. or O statement.

2.Use Venn diagram to test converse statement for logical equivalency with original.

3.Identify the term complement of any term.

4.Construct the obverse of any A,E,I or O statement.

5.Construct the contrapositive of any A,E,I, or O statement.

6.Test statement and it’s contrapositive for logical equivalency using Venn diagrams.

4.5 Traditional Square of Opposition

1.Use the traditional square of opposition to test immediate inferences from a categorical statement.

2.Identify cases of the existential fallacy.

 4.6 Venn Diagrams and the Traditional Standpoint

1.Construct modified Venn diagrams to represent categorical propositions from the traditional standpoint.

2.Use modified Venn diagrams to prove the traditional square of opposition.

3.Use Venn diagrams to test immediate inferences of categorical propositions from the traditional standpoint.

Module 3: Categorical Syllogisms

            3.1 Standard Mood and Figure

1.Define  standard form categorical syllogism.

2.Identify the major, minor, and middle terms of a standard form categorical syllogism.

3.Identify the figure of a standard form categorical syllogism.

4.Identify the mood of a standard form categorical syllogism.

5.Identify standard form categorical syllogisms as valid or invalid from the Boolean and the Aristotelian standpoint.

            3.2 Venn Diagrams

1.Use Venn diagrams to determine validity of categorical syllogisms from the Boolean and Aristotelian standpoint.

Module 4: Propositional Logic 1

4.1  Symbols and Translation

1.Define operator, connective, propositional logic, simple statement, compound statement.

2.Identify statements as examples of conditional statements, negation, conjunction, or disjunction.

3.Identify the operator used to represent negation, conjunction, disjunction, implication, and equivalence.

4.Identify the main operator in a compound statement.

5.Use operators to translate propositional statements.

6.Define sufficient condition, and necessary condition.

7.Use correct placement of parentheses in the translation of propositional statements.

8.Determine if symbolic formulas are well-formed formulas.

            4.2 Truth Functions

1.Use truth tables to define the logical operators: negation, conjunction, disjunction, implication, and equivalence

2.Compute the truth value of compound statement.

            4.3 Truth Tables for Propositions

1.Construct truth tables for simple and compound statement.

2.Use truth tables to determine if a statement is tautologous, contingent, or self-contradictory.

3.Use truth tables to determine if two statements are logically equivalent or contradictory.

4.Use truth tables to determine if two statements are consistent or inconsistent.

Module5: Propositional Logic 2

            5.4 Truth tables for Arguments

1.Construct a truth table for an argument.

2.Use truth table to test the validity of an argument.

1. Indirect Truth Tables

Module 6:  Natural Deduction in Propositional Logic 1

            6.1 Rules of Implication

1.Identify examples of eight rules of implication:

• modus ponens
• modus tollens
• disjunctive syllogism
• pure hypothetical syllogism
• constructive dilemma, simplification
• conjunction
• addition

2.Construct examples of each.

3.Use the eight rules of implication to derive conclusions in symbolized arguments.

Module 7:  Natural Deduction in Propositional Logic 2

            7 .2 Rules of Replacement

1.Identify examples of 10 rules of replacement:

• De Morgan’s Rule
• Commutativity
• Associativity
• Distribution
• Double Negation
• Transposition
• Material Implication
• Material Equivalence
• Exportation
• Tautology

2.Use the 10 rules of replacement to derive the conclusions of symbolized arguments.

Module 8: Natural Deduction in Propositional Logic 2

            8.1 Conditional Proof

1.Use the method of conditional proof (in conjunction with the other rules of inference) to derive the conclusion of a symbolized argument.

            8.2 Indirect Proof

1.Use method of indirect proof to derive the conclusion of symbolized arguments.

            8.3  Proving Logical Truths

1.Use the method of indirect proof to derive tautologies.

Module 9:  Predicate Logic 1

            9.1 Symbols and Translation

1. Translate ordinary language statements using the symbols and conventions of predicate logic.

            9.2 Using the Rules of Inference

1. Apply the rules of universal instantiation and existential instantiation.
2. Use the 18 rules of inference to derive the conclusion of arguments stated in predicate logic.
3. Apply the rules of universal generalization and existential generalization.

    9.3 Change of Quantifier Rule

1. Correctly apply the change of quantifier rule as part of completing proofs in predicate logic.

Module 10: Predicate Logic 2

            10.1 Conditional and Indirect Proof

1. Apply the techniques of conditional proof on arguments in predicate logic.
2. Apply the technique of indirect proof on arguments in predicate logic.