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# Introduction to Symbolic Logic

“Portion of Babbage's Difference Engine” woodcut, B.H. Babbage, del. (June, 1853).[1]

The elements of the language of symbolic logic are introduced in order to simply the understanding of many arguments.

Since the arguments are evaluated according to their form only, arguments put into symbolic notation are less likely to be misinterpreted in our assessments of validity or invalidity due to their absence of vagueness, equivocation, amphiboly and emotive significance.

Errors in argument evaluation usually are due to the issues of translation from ordinary language into symbolic forms

Some uses of symbolic logic are suggested in the exercises accompanying these topics.

#### Notes

1. “Portion of Babbage's Difference Engine” from “Recreations of a Philosopher,” Harper's New Monthly Magazine 30 no. 175 (December, 1864), 34.

Ada Lovelace, Lord Byron's daughter, remarked about Babbage's subsequent design, “[T]he Analytical Engine weaves algebraic patterns just as the Jacquard loom weaves flowers and leaves.” “Translator's Notes,” in L.F. Menabrea, Sketch of the Analytical Engine (London: Richard and John E. Taylor, 1843), 696.

• ### 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 syllogism 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. [Lecture Notes are under construction]

• ### The Paradoxes of Material Implication

Some of the intuitive difficulties with material implication are outlined and illustrated. [Lecture Notes are under construction]

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