Catalog Description
This course is an introduction to the concepts and methods of modern symbolic logic, both sentential and quantificational. The student will learn to do truth value analysis of statements, translate complex natural-language arguments into both sentential and quantificational logic, construct advanced formal proofs of validity in both sentential and quantificational logic, and explore the meta-logical issues of consistency and completeness of formal systems. The relevance of symbolic logic to areas such as set theory and computer science will also be explored.
Prerequisite
None. Philosophy 2 recommended.
Text
No department requirement
Course Objectives
Course Content
I. BASIC NOTIONS OF LOGIC 2 weeks
The concept of an argument
Distinguishing arguments from non-arguments
Complex arguments
Inductive vs deductive logic
Validity and soundness
Formal systems: vocabulary, grammar, semantics, syntax
Deductive logic as a formal system
II. LOGIC OF TRUTH FUNCTIONS 4 weeks
How the concept of a truth function is related to the
ordinary concept of a function
Ordinary sentential connectives and
truth-functional sentential connectives
Truth tables
The redundancy of connectives
Using truth tables to determine validity
Natural language, formal language, and meta-language --
logical form and substitution instances
Common valid argument forms:
modus ponens, modus tollens,
disjunctive syllogism, hypothetical
syllogism, dilemmas, etc.
Logical equivalence; proving it using truth tables
Common logical equivalences:
DeMorgan's laws, double
negation, commutative law, etc.
Using common valid argument forms
and common logical equivalences to construct
simple formal proofs of validity of
truth-functional arguments
Using the complete set of truth-functional
valid argument forms and equivalences
to construct complex proofs of
validity of truth-functional arguments
Proving tautology and contradiction
Validity and tautology
Proving consistency
Validity and consistency
(Optional) The truth tree method
Truth tables and computers
III. QUANTIFICATIONAL LOGIC 6 weeks
Propositional functions and quantifiers
Singular and general propositions
Quantificational logical equivalences
Expanding the set of truth-functional valid
forms and equivalences to include
quantificational rules and equivalences
Constructing proofs in predicate logic
(Optional) The tree method for quantification
IV. THE LOGIC OF RELATIONS 2 weeks
Symbolizing relations
Complex translations
Symbolizing identity and definite descriptions
Constructing formal proofs of validity of
arguments involving relations
V. META-LOGIC 3 weeks
Proving that the validity and invalidity of all
arguments in truth-functional logic
is mechanically decidable
Consistency and completeness
Godel's proof and the limits of axiomatic method
General Requirements
Completion of required reading and final exam. Other requirements are determined by instructor; these may include homework, quizzes, other exams,
class participation, class attendance, etc.
Evaluation
Generally, evaluation is based primarily on written examinations. The exams are primarily "objective" skill demonstration. Students do not write essays in this class.
Suggested Instructional Methods and Materials
Primarily lecture, problem-solving, and discussion. Computer-aided instructional materials are available. Guest speakers, class debates, etc., may be used as appropriate according to the preference of the individual instructor.