This is called the AXIOM OF SYLLOGISM. The most common form of it in Logic is that known as the _Dictum_, or _Regula de Omni et Nullo:_ "Whatever is predicated of All or None of a term, is predicated of whatever is contained in that term". It has been expressed with many little variations, and there has been a good deal of discussion as to the best way of expressing it, the relativity of the word best being often left out of sight. _Best_ for what purpose? Practically that form is the best which best commands general assent, and for this purpose there is little to choose between various ways of expressing it. To make it easy and obvious it is perhaps best to have two separate forms, one for affirmative conclusions and one for negative. Thus: "Whatever is affirmed of all M, is affirmed of whatever is contained in M: and whatever is denied of all M, is denied of whatever is contained in M". The only advantage of including the two forms in one expression, is compendious neatness. "A part of a part is a part of the whole," is a neat form, it being understood that an individual or a species is part of a genus. "What is said of a whole, is said of every one of its parts," is really a sufficient statement of the principle: the whole being the Middle Term, and the Minor being a part of it, the Major is predicable of the Minor affirmatively or negatively if it is predicable similarly of the Middle. This Axiom, as the name imports, is indemonstrable. As Aristotle pointed out in the case of the Axiom of Contradiction, it can be vindicated, if challenged, only by reducing the challenger to a practical absurdity. You can no more deny it than you can deny that if a leaf is in a book and the book is in your pocket, the leaf is in your pocket. If you say that you have a sovereign in your purse and your purse is in your pocket, and yet that the sovereign is not in your pocket: will you give me what is in your pocket for the value of the purse? II.--THE MINOR FIGURES OF THE SYLLOGISM, AND THEIR REDUCTION TO THE FIRST. The word Figure ([Greek: schema]) applies to the form or figure of the premisses, that is, the order of the terms in the statement of the premisses, when the Major Premiss is put first, and the Minor second. In the First Figure the order is M P S M But there are three other possible orders or figures, namely:-- Fig. ii. Fig. iii. Fig. iv. PM MP PM SM MS MS. It results from the doctrines of Conversion that valid arguments may be stated in these forms, inasmuch as a proposition in one order of terms may be equivalent to a proposition in another. Thus No M is in P is convertible with No P is in M: consequently the argument No P is in M All S is in M, in the Second Figure is as much valid as when it is stated in the First-- No M is in P All S is in M.