By Joseph Gerard Brennan
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In the syllogism illustrated, the major term is "vertebrates," the minor term "wallabies," and the middle "marsupials. " RULES OF THE CATEGORICAL SYLLOGISM Some syllogisms are valid; others are not. The following rules are given by means of which we may determine the validity of categorical syllogisms: I. The syllogism must have three and only three terms. The following syllogism violates this rule: Cats like cream. Kittens are pets. · .. Kittens like cream. " In certain syllogisms, the middle term is ambiguous or double-meaninged, thereby creating what is in effect the fallacy of four terms.
3. Republicans are not rascals. Some non-Republicans are rascals. 4. Hammerhead sharks wear false teeth. Some non wearers of false teeth are not hammerhead sharks. 5. Some unicorns are registered. Some who are nonregistered are nonumcorns. Inferences from Simple Propositions 47 6. Some oysters have Oedipus complexes. Some non oysters do not have Oedipus complexes. 7. Martinis are not intoxicating. Nothing that is intoxicating is a Martini. 8. Some who repent are among those who are saved. Some who are saved fall outside the class of those who fall outside the class of those who repent.
We may now draw up a table showing the distribution of subject and predicate terms for A, E, I, and 0 propositions: Subject Term A. distrihuted E. distributed I. undistributed O. undistributed Predicate Term undistributed distributed undistributed distributed Singular propositions are considered by most modern logicians to be closely related to particulars. Both types, it is claimed, assert existence. ] The predicate of a singular affirmative proposition is undistributed, while that of a singular negative is distributed.
A handbook of logic by Joseph Gerard Brennan