ABSTRACT
So far, discussion of each type of problem has started with a brief analysis of the main ways in which it may be varied. Discussion of the formal variants of the syllogism is traditionally a task for the textbooks of logic and no attempt will be made to usurp their function. But there are four types of variation (not all of them logical or formal ones) which are of particular interest here.
The first concerns the number of premisses in the argument and thus raises the question of the distinction between the syllogism proper and the sorites. Quine (1952) defines syllogisms as ‘arguments wherein a categorical statement is derived as conclusion from two categorical statements as premisses, the three statements being so related that there are altogether just three terms, each of which appears in two of the statements’. The sorites is an argument of the same kind but with one or more additional premisses — that is to say, with four or more related terms instead of three. This difference will be illustrated later when the problems used are quoted.
The second variable is that of content, and here the main issues are two in number:
whether the terms of the premisses are symbols such as a, b, c, or whether they are the names of objects and classes of objects;
if the latter is the case, whether the premisses are true or false.
The third variable is that of the form in which the premisses are stated, and particularly whether they are in conditional or categorical form. It must be noted at this point that to state the premisses of an ordinary categorical syllogism in hypothetical form — that is, simply to preface them by the word ‘if’ — is not to turn the syllogism into what is traditionally described as a conditional syllogism. The latter has the form: ‘If A, then B. But A. Therefore B’. Consequently, it is different in its structure from the ordinary or categorical syllogism.
The fourth variable is that of the form in which the answer is to be given: whether the subject has to draw a conclusion for himself; or say of one stated conclusion whether it is valid or invalid; or select a valid conclusion from a number of offered alternatives.
