Syllogisms
Syllogism is the deductive solution of a pervasive scientific problem: what is the relationship between the two classes A and C, given that I know the relation of both A and C to the third class B?
Aristotle loved syllogisms. He systematized them, developed rules for and patterns among them, and promoted them as the foremost tool for analysis of arguments. But what is a syllogism? Let us examine the syllogism using Aristotle’s own example:
All men are mortal. Socrates is a man. Therefore Socrates is mortal.
This argument is recognizable as a syllogism by these characteristics:
- the argument consists of three statements;
- two of the statements (in this case the first and second) are premises and the third is a conclusion that is claimed to follow from the premises.
In so-called standard form such as the Socrates syllogism, the third statement is the conclusion, containing a subject (‘Socrates’) and predicate (‘mortal’), the first statement is a premise dealing with the predicate, and the second statement is a premise dealing with the subject.
Syllogisms are of three types: categorical, hypothetical, and disjunctive. We will consider hypothetical syllogisms briefly later in this chapter. The Socrates syllogism is categorical: three classification statements, each beginning explicitly or implicitly with one of the three words ‘all’, ‘no’, or ‘some’, with two terms in each statement, and with each term used a total of twice in the argument. Each term must be used in exactly the same sense both times. For example, man cannot refer to mankind in one use and males in the second; this is the fallacy of equivocation, described in a later section.
Chambliss [1954] succinctly comments:
“The syllogism does not discover truth; it merely clarifies, extends, and gives precision to ideas accepted as true. It is, according to Aristotle, ‘a mental process in which certain facts being assumed something else differing from these facts results in virtue of them.’”
Aristotle's description that “something else differing from these facts results” is a bit misleading in its hint of getting something for nothing. The conclusion does not really transcend the premises; instead it is really immanent, an implication of the premises that may or may not be obvious. Rather than discover truth, the syllogism reveals the implications of our assumptions. As such, it is a fundamental step in the hypothetico-deductive method (better known as the scientific method).
Syllogisms can be difficult to recognize in everyday language. Formal analysis of syllogistic logic requires a translation from everyday language into the so-called standard syllogism form. This translation may involve reorganizing the statements, recognizing that a term can be much longer than one word, using logical equivalences to reduce terms, supplying an omitted (but implied) premise or conclusion, or breaking apart a compound argument into its component syllogisms. This translation is useful to learn but beyond the scope of this book; the reader is encouraged to consult a textbook on logic and practice translation of the many examples therein. Here we focus on the analysis of standard-form syllogisms, because familiarity with standard-form syllogisms has a fringe benefit: invalid syllogisms will sound dubious and invite closer scrutiny, even if they are couched in everyday language.
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