§ 2. On examining, then, these two general formulæ, we find that in both of them, one premiss, the major, is an universal proposition; and according as this is affirmative or negative, the conclusion is so too. All ratiocination, therefore, starts from a _general_ proposition, principle, or assumption: a proposition in which a predicate is affirmed or denied of an entire class; that is, in which some attribute, or the negation of some attribute, is asserted of an indefinite number of objects distinguished by a common characteristic, and designated, in consequence, by a common name.
The other premiss is always affirmative, and asserts that something (which may be either an individual, a class, or part of a class) belongs to, or is included in, the class respecting which something was affirmed or denied in the major premiss. It follows that the attribute affirmed or denied of the entire class may (if there was truth in that affirmation or denial) be affirmed or denied of the object or objects alleged to be included in the class: and this is precisely the assertion made in the conclusion.
Whether or not the foregoing is an adequate account of the constituent parts of the syllogism, will be presently considered; but as far as it goes it is a true account. It has accordingly been generalized, and erected into a logical maxim, on which all ratiocination is said to be founded, insomuch that to reason, and to apply the maxim, are supposed to be one and the same thing. The maxim is, That whatever can be affirmed (or denied) of a class, may be affirmed (or denied) of everything included in the class. This axiom, supposed to be the basis of the syllogistic theory, is termed by logicians the _dictum de omni et nullo_.
This maxim, however, when considered as a principle of reasoning, appears suited to a system of metaphysics once indeed generally received, but which for the last two centuries has been considered as finally abandoned, though there have not been wanting, in our own day, attempts at its revival. So long as what were termed Universals were regarded as a peculiar kind of substances, having an objective existence distinct from the individual objects classed under them, the _dictum de omni_ conveyed an important meaning; because it expressed the intercommunity of nature, which it was necessary on that theory that we should suppose to exist between those general substances and the particular substances which were subordinated to them. That everything predicable of the universal was predicable of the various individuals contained under it, was then no identical proposition, but a statement of what was conceived as a fundamental law of the universe. The assertion that the entire nature and properties of the _substantia secunda_ formed part of the properties of each of the individual substances called by the same name; that the properties of Man, for example, were properties of all men; was a proposition of real significance when man did not _mean_ all men, but something inherent in men, and vastly superior to them in dignity. Now, however, when it is known that a class, an universal, a genus or species, is not an entity _per se_, but neither more nor less than the individual substances themselves which are placed in the class, and that there is nothing real in the matter except those objects, a common name given to them, and common attributes indicated by the name; what, I should be glad to know, do we learn by being told, that whatever can be affirmed of a class, may be affirmed of every object contained in the class? The class _is_ nothing but the objects contained in it: and the _dictum de omni_ merely amounts to the identical proposition, that whatever is true of certain objects, is true of each of those objects. If all ratiocination were no more than the application of this maxim to particular cases, the syllogism would indeed be, what it has so often been declared to be, solemn trifling. The _dictum de omni_ is on a par with another truth, which in its time was also reckoned of great importance, "Whatever is, is;" and not to be compared in point of significance to the cognate aphorism, "It is impossible for the same thing to be and not to be;" since this is, at the lowest, equivalent to the logical axiom that contradictory propositions cannot both be true. To give any real meaning to the _dictum de omni_, we must consider it not as an axiom, but as a definition; we must look upon it as intended to explain, in a circuitous and paraphrastic manner, the meaning of the word _class_.