The following sections of this BookRags Literature Study Guide is offprint from Gale's For Students Series: Presenting Analysis, Context, and Criticism on Commonly Studied Works: Introduction, Author Biography, Plot Summary, Characters, Themes, Style, Historical Context, Critical Overview, Criticism and Critical Essays, Media Adaptations, Topics for Further Study, Compare & Contrast, What Do I Read Next?, For Further Study, and Sources.
(c)1998-2002; (c)2002 by Gale. Gale is an imprint of The Gale Group, Inc., a division of Thomson Learning, Inc. Gale and Design and Thomson Learning are trademarks used herein under license.
The following sections, if they exist, are offprint from Beacham's Encyclopedia of Popular Fiction: "Social Concerns", "Thematic Overview", "Techniques", "Literary Precedents", "Key Questions", "Related Titles", "Adaptations", "Related Web Sites". (c)1994-2005, by Walton Beacham.
The following sections, if they exist, are offprint from Beacham's Guide to Literature for Young Adults: "About the Author", "Overview", "Setting", "Literary Qualities", "Social Sensitivity", "Topics for Discussion", "Ideas for Reports and Papers". (c)1994-2005, by Walton Beacham.
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Implication is a binary propositional connective read most often as an "if-then" statement. An "If-then" statement is composed of an antecedent (what comes after the "if"), and a consequent (what comes after the "then"). Implication is defined as follows: the antecedent S implies the consequent P if and only if it is impossible for S to be true while P is false. For example, the proposition "If there are objects, then there is space" expresses an implication. Space is implied by objects. If it is true that there are objects, then it must also be true that there is space, since space is a necessary condition of the existence of objects. This type of implication is called material implication, and it can also be expressed as a necessary implication, as it is with respect to validity.
Implication is a form of inference closely related to the concept of validity. In an argument, a set of true propositions that implies or entails another true proposition with necessity is a valid argument. However, whereas validity is a feature of certain deductive arguments, implication expresses the relationship between propositions and sets of propositions.
Not all "if-then" propositions express material or necessary implication. For example, "If Lee Harvey Oswald had not killed Kennedy, then someone else would have killed Kennedy," expresses a counter-factual implication--that is, an "if-then" statement whose antecedent is false. The implication is only probable at best, because if it is false that Lee Harvey Oswald had killed Kennedy, then it is only probable that someone else would have killed Kennedy. There is no good reason to infer that someone necessarily would have killed Kennedy if Oswald had not.