Syllogisms may be hypothetical disjunctive (as: S is either P or Q; but S is P; ergo,S is not Q), or dilemmatic, a combination of !lie two. Sometimes one proposition does not .s.mpear, forming- the enthymeme; and agaih, several syllogisms may bo linked together, the whole being termed the chain or sorites. Still another form is the epichirema, where the reason for each premise is given with it.
Fallacies are errors resulting from the improper use of words or mental processes in argument. They are variously classified. Among the most important are: generaliza tion, or the attributing to a class individual limitations, as "S is a clergyman and a hypocrite—ergo, all clergymen are hypocrites:" equivocation, where a word is used in two senses; the non vera pro vera, where a premise is false; ac6dent, where an acciden tal property is made to appear as a substantial attribute. For others and a more com plete treatment of the subject, see F_kLLACY. An ancient Greek fallacy, which appears perennially as a modern joke, is the case of a man who says, " I lie. Does he lie or not? If he lie, he tells the truth; if he speak truly, he lies.
The study of formal logic in the monastic schools and universities of the middle ages was carried to an extent more recondite than profitable, the result being a not unmerited contempt for the science as then limited by the scholastic method. A classi
fication and discussion of syllogisms in which no attention is given to the orig-in of the concepts which form the premises or to the process of induction, resembles rather a series of mathematical permutations than fruitful intellectual investigation. In fact, in our day, prof. Jevons has constructed what he calls a logical machiue, which will per form many of the operations of syllogistic reasoning. In modern tiines the study has been in a measure reinstated; but it has been through the enlargement of the ground allotted it and the installment of induction as a. most important factor. Thus widened in its scope, there may be derived from it laws of reasoning of the greatest value as forming the basis of all investigation physical, philosophical, and moral science.
Among numerous authors who may be consulted on this topic are, besides Hamilton aud Mill, archbishop Whately, Wallace, Jeremy Bentham (essays), William Stanley Jevons; and of American writers, profs. Bowen of Harvard, Wilson of Cornell, and Schuyler of Baldwin,