Premises EO and OO, being negative, cannot yield a conclusion according to rule 5; similarly, neither can the particulars IO and II because of rule 7.
5. THE DICTUM OF ARISTOTLE.
Aristotle gives an axiom on which all syllogistic inference is based. Indeed from this fundamental principle the significant rules of the syllogism could be derived. The dictum is stated in this wise: “Whatever is predicated, whether affirmatively or negatively, of a term distributed may be predicated in the manner of everything contained under it.” The following statements represent various ways of explaining this dictum:
(1) Whatever is said of a term used in its fullest sense may likewise be said of that term when used only in a partial sense.
(2) What is true of the whole is true of the part.
(3) “What pertains to the higher class pertains also to the lower.” Since this dictum is the basic principleunderlying the important rules of the syllogism, it is unnecessary to dwell longer upon it; because an explanation of the rules is, virtually, an explanation of the dictum.
6. CANONS OF THE SYLLOGISM.
The dictum of Aristotle is ostensibly a self-evident truth, and some logicians have put this truth in the form of three axiomatic statements which are known as the canons of the syllogism. These are as follows:
(1) “Two terms agreeing with one and the same third term agree with each other.”
(2) “Two terms of which one agrees and the other does not agree with one and the same third term, do not agree with each other.”