Approved by Faculty Senate

University Studies Course Approval:

**Department Program:** Philosophy Department

**Course Number: **250

**Number of Credits:** 3

**Course Title: **Symbolic Logic

Catalog Description:

**250 - Symbolic Logic - 3 S.H.**

An examination of methods for putting ordinary deductive reasoning into symbols in order to test its validity. Topics include ways to translate English into symbols, uses of truth tables, rules for deduction in propositional and predicate logic, models for showing invalidity, and strategies for constructing proofs. Offered as appropriate.

This is an existing course that has previously been approved by A2C2.

**Department Contact Person for this course: **Ed Slowik

**Email: **eslowik@winona.edu

**Unity and Diversity—Critical Analysis**

SYMBOLIC LOGIC

PHIL 250

University Studies—Critical Analysis

**Critical Analysis courses in the University Studies program are devoted to teaching
critical thinking or analytic problem-solving skills. These skills include the ability to
identify sound arguments and distinguish them from fallacious ones. The objective of these
courses is to develop student's abilities to effectively use the process of critical
analysis. Disciplinary examples should be selected to support the development of critical
analysis skills.**

Symbolic Logic 250 introduces the student to many of the fundamental concepts and methods of deductive logic; in particular, propositional logic, natural deduction, and predicate logic.

These courses must include requirements and learning activities that promote students' abilities to...

**1. evaluate the validity and reliability of information.**

While all aspects of Philosophy 250 are devoted to evaluating the reliability of information as it pertains to correct argument form, the introductory section of the course (Basic Concepts) examines reliability in general by exploring the role of premises, and soundness/cogency, in deductive and inductive arguments.

**2. analyze modes of thought, expressive works, arguments, explanations, or theories.**

Philosophy 250 *is* the critical examination of deductive argument forms and
reasoning (in the modern guise of a natural deduction system with predicates and
quantifiers).

**3. recognize possible inadequacies or biases in the evidence given to support arguments
or conclusions; **

While Philosophy 250 does not examine the content of any specific piece of evidence in the use of arguments, the course centers upon the structural form of deductive arguments—that is, given that the premises in an argument are true, what conclusions can be reached from those premises that preserve truth? In this manner, the correct use, and misuse, of evidence in argument forms is exhaustively examined.

**4. advance and support claims.**

Since Philosophy 250 examines the valid and invalid use of arguments, especially in deductive reasoning, students will gain appreciable knowledge of how to properly advance and support claims.

SYMBOLIC LOGIC

PHIL 250

Curriculum, Outcomes, Policies, and Requirements

University Studies—Critical Analysis

**Sample Syllabus**

SYMBOLIC LOGIC

PHILOSOPHY 250 (Course # 001009)

WSU Spring 1999

Instructor: Dr. Ed Slowik

Office: 325 Minne Hall/Office phone: 457-5663/Office Hours: MWF 12-1, 3-4 PM

__Text:__

P. Hurley, *A Concise Introduction to Logic,* 6th edition (Wadsworth, 1997)

__Course Objectives:__

The course objective is to introduce the student to many of the fundamental concepts and methods of deductive logic; in particular, propositional logic, natural deduction, and predicate logic.

__Course Requirements:__

Class requirements are 4 tests, a midterm, and a final. The dates are given below: The final is comprehensive. The breakdown of the grade is as follows: tests, 30% total; Midterm, 35%; Final, 35%. I will drop the lowest of the four tests and average your grade for the remaining three (that is your extra-credit). The dates for the tests and midterm are provided below. I will regularly assign homework problems from the book. Logic is very much like math, you need to do a lot of problems to get the hang of it. The logic lab will also be available to practice propositional logic problems (see me if you would like to use this nice resource).

__Class Meetings:__

The class meets for lecture/discussion on Mondays, Wednesdays, and Fridays, from
11:00-12:00 AM, in Minne 110.

__Schedule: __

The actual day-to-day progress and reading/homework assignments will be announced in class, but the general schedule is as follows:

Week 1 (Jan. 13-15): Introduction, chap. 1

Week 2-6 (Jan. 21-Feb. 17): chap. 6; Tests, Friday, Jan. 29/Wednesday, Feb. 17

Week 7-11 (March 1-April 9): chap. 7; Midterm, Friday, March 5; Test, April 9

Week 12-16 (April 12-May 14): chap. 8; Test, Wednesday, May 12

Final Exam: Thursday, May 20, 8-10 AM

**Course Outline:**

I. Basic Concepts

A. Arguments, Premises, Conclusions

B. Recognizing Arguments

C. Deduction and Induction

D. Validity, Truth, Soundness, Strength, Cogency

E. Argument Forms

II. Propositional Logic

A. Symbols and Translation

B. Truth Functions

C. Truth Tables for Propositions

D. Truth Tables for Arguments

E. Argument Forms

III. Natural Deduction in Propositional Logic

A. Rules of Implication

B. Rules of Replacement

C. Conditional Proof

D. Indirect Proof

E. Proving Logical Truths

IV. Predicate Logic

A. Symbols and Translations

B. Rules of Reference

C. Change of Quantifier Rules

D. Conditional and Indirect Proof

E. Proving Invalidity

F. Relational Predicates and Overlapping Quantifiers

G. Identity

**All course activities and assignments simultaneously address all University Studies
required course outcomes in Philosophy of Science 240 in the following ways:**

**Critical Analysis courses in the University Studies program are devoted to teaching
critical thinking or analytic problem-solving skills. These skills include the ability to
identify sound arguments and distinguish them from fallacious ones. The objective of these
courses is to develop student's abilities to effectively use the process of critical
analysis. Disciplinary examples should be selected to support the development of critical
analysis skills.**

Symbolic Logic 250 introduces the student to many of the fundamental concepts and methods of deductive logic; in particular, propositional logic, natural deduction, and predicate logic.

These courses must include requirements and learning activities that promote students' abilities to...

**1. evaluate the validity and reliability of information.**

While all aspects of Philosophy 250 are devoted to evaluating the reliability of information as it pertains to correct argument form, the introductory section of the course (Basic Concepts) examines reliability in general by exploring the role of premises, and soundness/cogency, in deductive and inductive arguments.

**2. analyze modes of thought, expressive works, arguments, explanations, or theories.**

Philosophy 250 *is* the critical examination of deductive argument forms and
reasoning (in the modern guise of a natural deduction system with predicates and
quantifiers).

**3. recognize possible inadequacies or biases in the evidence given to support arguments
or conclusions; **

While Philosophy 250 does not examine the content of any specific piece of evidence in the use of arguments, the course centers upon the structural form of deductive arguments—that is, given that the premises in an argument are true, what conclusions can be reached from those premises that preserve truth? In this manner, the correct use, and misuse, of evidence in argument forms is exhaustively examined.

**4. advance and support claims.**

Since Philosophy 250 examines the valid and invalid use of arguments, especially in deductive reasoning, students will gain appreciable knowledge of how to properly advance and support claims.