ABSTRACT
In this chapter we study arguments that have two or more premises. Any argument consists of n statements (a conclusion and n-I premises). An argument is called a syllogism if it has as many terms as it has statements, each term appearing twice in different statements. Here are two examples of syllogistic arguments:
Al all baboons are apes all apes are primates I all baboons are primates
A2 no primate is a reptile some reptiles are herbivores all baboons are primates Isome herbivores are not baboons
Al is a syllogism with three recurrent terms and three statements. A2 is a syllogism with four recurrent terms and four statements. (Syllogisms with more than two premises are often referred to as polysyllogisms or sOrites.)
Logicians are especially interested in two kinds of syllogism:
1. Those containing only universal statements. (AI is an example.) 2. Those containing exactly two particular statements one of which is the conclusion. (A2 is an example.)
All other syllogisms are irregular. The reason for being interested in regular
syllogisms is simple: only regular syllogisms are valid. (A 1 is U-regular; A2 is P-regular.)
Logicians speak of the mood of a syllogism. A syllogism that is of type 1 or type 2 is said to have a regular mood. If its mood is irregular, the syllogism is invalid. So the first question we ask when looking at a syllogism is: What is its mood? If its mood is regular, it may be valid. If its mood is irregular we may dismiss it forthwith as invalid. For example, looking at the argument:
A· Some cats are tigers some tigers are striped Isome cats are striped
we know at once that, despite its plausible appearance, it does not have a valid form, being neither U-regular nor P-regular. The form of A· is:
some X isY someYisZ IsomeX is Z
(Since the form is invalid, there will be counter-instances. After a moments reflection we may think of a counter-instance like
some cats are mangy animals some mangy animals are dogs Isome cats are dogs)
A second question we ask is: Do the premises add up to the conclusion? The answer to this question is again crucial. For only those syllogism that add up are valid.
