argument which may happen to be before us, or another similar to it.

Speaking of such self-evident truths, Locke remarks, "they are known in particular instances before these general maxims are ever thought on, and draw all their force from the discernment of the mind employed about particular ideas."*

Mr. Stewart, who concurred in this view with the illustrious author of the Essay on Human Understanding, gives the following lucid exposition of his doctrine.

"It was long ago remarked by Locke, of the axioms of geometry as stated by Euclid, that although the proposition be at first enunciated in general terms, and afterwards appealed to, in its particular applications, as a principle previously examined and admitted, yet that the truth is not less evident in the latter case than in the former. He observes further that it is in some of its particular applications, that the truth of every axiom is originally perceived by the mind; and, therefore, that the general proposition, so far from being the ground of our assent to the truths which it comprehends, is only a verbal generalisation of what, in particular instances, has been already acknowledged as true."†

* On the Understanding, book iv. chap. vii. § 4.

+ Elements of the Philosophy of the Human Mind, vol. ii. p. 29. 2d ed.

Another writer, eminent both as a mathematician and a philosopher, I mean D'Alembert, gives his sanction to the same view, and remarks, that so far are axioms from holding the first rank in philosophy, that there is no necessity even to enunciate them. He afterwards terms them barren

and puerile truths.*

Taking with us these considerations regarding the value and position of self-evident maxims, let us turn to the celebrated dictum of Aristotle.

The dictum de omni et nullo, viz. that "whatever is predicated universally of any class of things, may be predicated in like manner of any thing comprehended in that class," is not only stated by logicians to be a general maxim, of the application of which every direct syllogism is a particular instance, but proclaimed to be the universal principle of reasoning.

If we closely scrutinise the meaning of this maxim, undazzled by the somewhat magnificent and imposing phraseology in which it has been spoken of, we shall find it an obviously simple and undeniable proposition, namely, whatever is asserted of a class may be asserted of any species or individual of that class. A class, however, we must bear in mind, is not a collective or corporate whole, which, as a whole, possesses pro

Elémens de Philosophie, chap. iv.; also Discours Préliminaire de l'Encyclopédie.

perties or attributes different from those of the individuals composing it; but what is predicated of it is predicated of every separate individual ranked under it. The proposition "all men are fallible" affirms that every individual man is fallible, while the proposition" the army is large" affirms of the body collectively something which it does not affirm of any single individual in it. If a class were such a collective body, the Aristotelian maxim could not be true.*

The dictum, therefore, it is plain, means neither more nor less than that whatever is predicated of every individual of a class may be predicated of any individual, or any number of individuals of that class. As, however, what can be truly predicated of any thing must be a property or attribute actually possessed, we may, if we choose, leave out predication altogether, and then the maxim will appear in a still simpler shape, as follows: What belongs to every individual of a class must belong to any individual of that class. However it may be expressed, it is obviously a selfevident and indisputable truth, like the other maxims we have just been considering; and this

* Lord Kames was sharply taken up by Dr. Gillies for having blundered on this point, he having represented the dictum to be, "Whatever is true of a number of particulars joined together, holds true of every one separately." — See ARISTOTLE'S Ethics and Politics, translated by John Gillies, LL.D., vol. i. p. 76.

F

view of its co-ordinate character is sufficient of itself to determine the accuracy of the doctrine which proclaims it as the universal principle of reasoning.

To this point I must draw the reader's particular attention, for here lies the grand error of the Aristotelian theory; and it is really astonishing that a mistake of such magnitude should have been so implicitly admitted.

If the doctrine were true, every act of reasoning would be an exemplification of this one maxim, and might be ranged under it in other words, all reasoning without exception would consist in concluding that an attribute belongs to some individual of a class, because it belongs to every individual of that class. No other reason, according to this theory, can possibly exist or be assigned, The sole ground on which we can argue that an individual thing possesses any attribute is, that the thing belongs to a class all the members of which possess the attribute. The only kind of implication possible consists in generic facts implying individual facts.

In contradiction to all this, it has been shown above, that there are many other general principles or maxims of which particular acts of reasoning are exemplifications; such as, "things equal to

* Or is excluded from it. I have thought it needless to take into separate consideration the de nullo part of the maxim, as it would lead only to repetitions: negative propositions may, as Mr. Walker says, be considered at pleasure as affirmative.

the same thing are equal to each other;" " a body cannot be in two places at one time;" "if equals are taken from equals the remainders are equal." When I affirm that two things, A and B, are equal to each other because they are severally equal to c, or that a man could not commit a crime at a specified time in London because he was at that precise moment in Edinburgh, I reason just as much as I do when I affirm that this man is fallible because all men are fallible, or that the three angles of the triangle before me are together equal to two right angles, because the three angles of every triangle are equal to two right angles.

The dictum, then, is obviously one of those self. evident maxims which we have above described, and it may be exhibited in the same manner.

Arguments.

Implying fact: All horned

animals are ruminant. Implied fact: This horned animal is ruminant. Implying fact: The three

angles of every triangle are together equal to two right angles.

Implied fact: The angles of

this triangle are together

equal to two right angles.

General Principle.

Whatever is predicated of a class may be predicated of any individual of that class.

The same.

If we compare these instances of one fact or proposition implying another with the others already referred to, we shall at once discern the true place and value of this renowned maxim; we.