Proposal for General Education Program
1. Course/Department/Representative: PHIL 250 Symbolic Logic / Philosophy /
Kevin Possin kpossin@winona.edu
2. Proposed WSU GEP Goal Area: Goal 4—Math/Logical Reasoning
This course currently meets Goal 4 at all the other Minnesota State Universities
that have abandoned Goal 2 as a separate requirement
3-4. WSU GEP Goal Area 4: Goal and Student Competencies and
Documentation:
GEP Goal: To increase students’ knowledge about mathematical and logical modes
of thinking. This will enable students to appreciate the breadth of applications of
mathematics, evaluate arguments, and detect fallacious reasoning. Students will
learn to apply mathematic, logic, and/or statistics to help them make decisions in
their lives and careers.
Symbolic Logic PHIL 250 Goal Documentation: This is an introductory logic
course focused on both symbolic arguments and arguments found in natural
language. Identification of formal fallacies, i.e., invalid arguments is also studied.
The goal is to help students develop logically reasoning skills for universal
application.
Two systems of logic are extensively studied in historical progression: propositional
logic and predicate logic, each having its own notation, methods of proof, and
limitations.
Within propositional logic, truth-tables are used to formally define logical
connectives and test the validity of arguments. Either the short truth-table method
or the truth-tree method of testing validity of arguments is introduced. The natural
deduction method of proof is also studied and its application to, e.g., computer
programming is discussed.
This ultimately provides the student with the two basic approaches to logical
proof—semantic and syntactic.
The enhanced powers of predicate logic [i.e., quantification] are then studied,
involving its unique notation and its capacities to represent more complex relations
than can propositional or categorical.
Practical applications of these logical systems are demonstrated and practiced
throughout the course.
Goal Area 4 Student Competencies:
Students will be able to:
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Illustrate historical and contemporary applications of mathematics/logical
systems.
Clearly express mathematical/logical ideas in writing.
Explain what constitutes a valid mathematical/logical argument (proof).
Apply higher-order problem-solving and/or modeling strategies.
Symbolical Logic PHIL 250 Student Competencies Documentation:
Students will acquire, practice, and demonstrate the ability to:
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Illustrate historical and contemporary applications of logical systems by
Illustrating and applying the logical systems of (historically) first
propositional and then (more contemporary) predicate logic, to assess the
validity of arguments and do natural deduction proofs.
Clearly express logical ideas in writing by clearly demonstrating the
concepts and methods of propositional logic and predicate logic in writing
and proofs, by means of truth tables, truth trees, and natural deduction
proofs.
Explain what constitutes a valid logical argument (proof) by explaining what
constitutes a valid and an invalid logical argument and proof in both
propositional and predicate logic, by means of truth tables, truth trees, and
natural deduction proofs.
Apply higher-order problem-solving and/or modeling strategies by doing
natural deduction proofs and proving the validity or invalidity of arguments
in symbolic form and ordinary language, by means of truth tables, truth trees,
and natural deduction proofs.
5. Course Outline:
1. Propositional logic
a. Symbolization and translation
b. Standard propositional form
c. Truth functions
d. Logical connectives
e. Truth-functional definitions of the connectives
f. Truth tables
g. Testing arguments for validity using truth tables
h. Short truth tables
i. Argument forms
2. Natural deduction
a. Rules of implication
b. Rules of replacement
c. Conditional proofs
d. Indirect proofs
3. Predicate logic
a. Symbolization and translation
b. Quantifiers
c. Rules of inference
d. Conditional proofs
e. Indirect proofs
f. Proving invalidity
g. Identity statements
All course contents and requirements satisfy Goal Area 4 competencies.
Current Catalog Description: An examination of methods for putting ordinarylanguage 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.
6. Assessment Plan:
Various means are employed to verify that students have acquired and can
demonstrate all of the Goal Area 4 Student Competencies, such as homework
exercises and computer-assisted, in-class, and/or take-home exams, whereby
students demonstrate their understanding and application of all the individual logic
skills listed in the course outline.