(1) The I proposition distributes neither subject nor predicate, hence the premises “II” would distribute no term. (2) But the middle term must be distributed at least once according to rule 3. (3) Therefore no conclusion can be drawn from “II.” A valid conclusion from “OO” is impossible according to rule 5. (8) _If one premise be particular the conclusion must be particular._ Proof: The possible combinations conditioned by rule 8 are AI, AO, EI, EO, IO, II, OO. “AI” considered. (1) Proposition A distributes its subject, proposition I neither; hence “AI” together distribute but one term. (2) According to rule 3 this one term must be the middle term. (3) The minor term must, therefore, be undistributed in the minor premise, and in consequence undistributed in the conclusion. (4) But this undistributed minor term is the subject of the conclusion; hence said conclusion must be particular, as only particulars have an undistributed subject. “AO” and “EI” considered. Proof: (1) “AO” distribute two terms; so do “EI.” (2) Both “AO” and “EI” must have negative conclusions according to rule 6. (3) A negative conclusion distributes its predicate which is the major term. (4) The major term and the middle term must be distributed in the premises. Rules 4 and 3. (5) Thus the third term, which is the minor, cannot be distributed in the minor premise and, consequently, the minor cannot be distributed in the conclusion. (6) This necessitates a particular conclusion. 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 principle underlying 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: