These fallacies, called fallacies of ambiguity, arise when the conclusion is achieved through an improper use of words. The principal instances are as follows: (1) Equivocation occurs when a word or phrase is used in one sense in one premise and in another sense in some other needed premise or in the conclusion (example: “The loss made Jones mad [= angry]; mad [= insane] people should be institutionalized; so Jones should be institutionalized.”). The figure-of-speech fallacy is the special case arising from confusion between the ordinary sense of a word and its metaphorical, figurative, or technical employment (example: “For the past week Joan has been living on the heights of ecstasy.” “And what is her address there?”). (2) Amphiboly occurs when the grammar of a statement is such that several distinct meanings can obtain (example: “The governor says, ‘Save soap and waste paper.’ So soap is more valuable than paper.”). (3) Accent is a counterpart of amphiboly arising when a statement can bear distinct meanings depending on which word is stressed (example: “Men are considered equal.” “Men are considered equal.”). (4) Composition occurs when the premise that the parts of a whole are of a certain nature is improperly used to infer that the whole itself must also be of this nature (example: a story made up of good paragraphs is thus said to be a good story). (5) Division—the reverse of composition—occurs when the premise that a collective whole has a certain nature is improperly used to infer that a part of this whole must also be of this nature (example: in a speech that is long-winded it is presumed that every sentence is long). But this fallacy and its predecessor can be viewed as versions of equivocation, in which the distributive use of a term—i.e., its application to the elements of an aggregate (example: “the crowd,” viewed as individuals)—is confused with its collective use (“the crowd,” as a unitary whole); compare “The crowd were filing through the turnstile” with “The crowd was compressed into the space of a city block.”

Formal fallacies

Formal fallacies are deductively invalid arguments that typically commit an easily recognizable logical error. A classic case is Aristotle’s fallacy of the consequent, relating to reasoning from premises of the form “If p₁, then p₂.” The fallacy has two forms: (1) denial of the antecedent, in which one mistakenly argues from the premises “If p₁, then p₂” and “not- p₁” (symbolized ~ p₁) to the conclusion “not- p₂” (example: “If George is a man of good faith, he can be entrusted with this office; but George is not a man of good faith; therefore, George cannot be entrusted with this office”), and (2) affirmation of the consequent, in which one mistakenly argues from the premises “If p₁, then p₂” and “ p₂” to the conclusion “ p₁” (example: “If Amos was a prophet, then he had a social conscience; he had a social conscience; hence, Amos was a prophet”). Most of the traditionally considered formal fallacies, however, relate to the syllogism. One example may be cited, that of the fallacy of illicit major (or minor) premise, which violates the rules for “distribution.” (A term is said to be distributed when reference is made to all members of the class. For example, in “Some crows are not friendly,” reference is made to all friendly things but not to all crows.) The fallacy arises when a major (or minor) term that is undistributed in the premise is distributed in the conclusion (example: “All tubers are high-starch foods [undistributed]; no squashes are tubers; therefore, no squashes are high-starch foods [distributed]”).