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An elementary introduction to contemporary symbolic logic is useful in a number of
different ways.
The elements of the language of symbolic logic are introduced to in order
to simply the understanding of many arguments. By using symbolic
notation, we are less likely to error in our assessments of validity or
invalidity due to the difficulties of vagueness, equivocation, amphiboly and
emotive significance.
Some of the uses of symbolic logic are suggested in the exercises accompanying these
topics.
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Links to Lecture Notes …
INTRODUCTION TO SYMBOLIC LOGIC
- The Language of Symbolic Logic
Conventions for translating ordinary
language statements into symbolic notation are outlined.
- Conjunction, Negation,
Disjunction
The logical operations of conjunction,
negation, and disjunction (alteration) are discussed with respect
to their truth-table definitions.
- Conditional
Statements and Material Implication
The reasons for the conventions of
material implication are outlined, and the resulting truth table
for is vindicated.
- How to Construct a
Truth Table
The general principles for the construction
of truth tables are explained and illustrated.
- Argument Forms and
Arguments
Argument forms are introduced and methods
for establishing their validity or invalidity is explained. Common
forms such as modus ponens, modus tollens, disjunctive sylllogism and
hypothetical syllogism are illustrated together with the fallacies
of affirming the consequent and denying the antecedent.
- Statement Forms, Material Equivalence, and
Logical Equivalence
Statement forms are introduced and
characterized as tautologous, contradictory or contingent. Material
and logical equivalence are defined and discussed
- The Paradoxes of Material Implication
Some of the intuitive difficulties with material
implication are outlined and illustrated.
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