A syllogism, in the original sense, must have three distinct terms. It must be deductive, and it must consist of three statements, two of which are the premise and the third of which is the conclusion. It states necessary and sufficient conditions for a syllogism. This more precise account is rooted in Aristotle’s logic of the syllogism. Any argument that contains these ingredients is a syllogism.” (Beardsley 1950, p. (2) It contains exactly three distinct terms, each of which appears exactly twice (but not twice in the same statement). , logically speaking, are of two kinds: (1) The argument consists of exactly three atomic statements, two of which are premises and one the conclusion. 316.)īeardsley offered a more precise account of the syllogism, as follows: Monroe Beardsley, writing in 1950, said, “A syllogism is a simple kind of deductive argument.” He then added, “The study of syllogisms is the heart of what is usually called ‘Aristotelian logic,’ to distinguish the work of Aristotle (who was the first systematic logician, and who first formulated the rules of the syllogism) from the work of modern and contemporary logicians.” (See Beardsley, Practical Logic, p. Borchert (Detroit: Thomson Gale, 2006), vol. Brody, “Logical Terms, Glossary of,” in Encyclopedia of Philosophy,” 2nd ed., ed. “A valid deductive argument having two premises and a conclusion.” -Baruch A. I reserve the right to stipulate, along with various philosophers and logicians, that syllogisms are deductive arguments.Ĭonsider this definition from the Encyclopedia of Philosophy, 2nd ed.: See also “What Is “What Is Modus Ponens?” Modus tolendo ponens is an argument of the following form: “Always infer not- A from the conjunction of two premises, if one premise is a conditional statement of the form ‘If A, then B,’ and the other premise denies B.” (The order of the premises doesn’t matter.)īe careful not to confuse modus ponens with modus tolendo ponens. (It also turns out that Casey does have four legs so premise 2 is false, also.)īecause modus tollens arguments are always valid, we may extrapolate from this argument form a rule of inference as follows: But this generalization, unfortunately, is not true. The above argument about Casey is valid, but it’s not sound. First, it must be valid second, it must have true premises. For an argument to be sound, it must meet two requirements. But not every argument of this form is sound. Premise 2: Casey does not have four legs.Ĭonclusion: Therefore, Casey is not a dog.Īny argument of this form is valid. Premise 1: If Casey is a dog, then Casey has four legs. For example, suppose A = ‘Casey is a dog’ and B = ‘Casey has four legs.’ We can substitute as follows, for a valid argument: Shown schematically, this form of argument looks like this:Īrguments of this form are produced by substituting statements in English for A and for B. The Latin phrase ‘ modus tollens‘, translated literally, means ‘mode of denying’. (A syllogism is any deductive argument with two premises and a conclusion.) Because the form is deductive and has two premises and a conclusion, modus tollens is an example of a syllogism.
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