Philosophy 9, Introduction to Symbolic Logic, 3 units

**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**

- The student should be able confidently to assess, for the vast majority of non-ambiguous arguments, whether or not their conclusions follow from premises.
- Students should be able to apply techniques of logical analysis to their own thinking, so that their arguments become more precise, powerful, and persuasive.
- Students should be able to demonstrate advanced levels of proficiency in the formal techniques for establishing the validity of deductive arguments. They should also be able to apply these techniques to questions of consistency, tautology, and contradiction, when appropriate.
- The student should be able to explicate the connections between symbolic logic and other branches of science and mathematics.

**Course Content**

I. BASIC NOTIONS OF LOGIC 2 weeksThe concept of an argumentDistinguishing arguments from non-argumentsComplex argumentsInductive vs deductive logicValidity and soundnessFormal systems: vocabulary, grammar, semantics, syntaxDeductive logic as a formal systemII. LOGIC OF TRUTH FUNCTIONS 4 weeksHow the concept of a truth function is related to the ordinary concept of a functionOrdinary sentential connectives and truth-functional sentential connectivesTruth tablesThe redundancy of connectivesUsing truth tables to determine validityNatural language, formal language, and meta-language -- logical form and substitution instancesCommon valid argument forms: modus ponens, modus tollens, disjunctive syllogism, hypothetical syllogism, dilemmas, etc.Logical equivalence; proving it using truth tablesCommon 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 argumentsUsing the complete set of truth-functional valid argument forms and equivalences to construct complex proofs of validity of truth-functional argumentsProving tautology and contradictionValidity and tautologyProving consistencyValidity and consistency(Optional) The truth tree methodTruth tables and computersIII. QUANTIFICATIONAL LOGIC 6 weeksPropositional functions and quantifiersSingular and general propositionsQuantificational logical equivalencesExpanding the set of truth-functional valid forms and equivalences to include quantificational rules and equivalencesConstructing proofs in predicate logic(Optional) The tree method for quantification IV. THE LOGIC OF RELATIONS 2 weeksSymbolizing relationsComplex translationsSymbolizing identity and definite descriptionsConstructing formal proofs of validity of arguments involving relationsV. META-LOGIC 3 weeksProving that the validity and invalidity of all arguments in truth-functional logic is mechanically decidableConsistency and completenessGodel'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. |||

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Page last modified: April 30, 1999