First, as to the term or name, which may be in one word or in The okl logicians drew the distinction between a name used as "timid; denoting an external object, such as might be thought of as oilstone without any mind to think of it, and the name used as thinking of Os object his its mental relation to other objects. A man, thought of a an individual pointed out, or a quality, an white, the white of a par titular white ball, were called names of first intention, or first motion, Ent nuts as a clam, or an individual thought of as a member of a class and white, as an attribute of classes, were names of second intention, o second motions.. The distinction in precisely that now known a objective and subjective : and accordingly, we propose to conside thiege—not material things only—and the qualities residing in their as besnigiug to the objective use of names ; and classes, and the atte butes by which we define classes, as belonging to the subjective we Now though the logicians have always professed to cultivate intentions, or subjective uses, the form, and the language of th syllogism have been strictly fashioned on the objective use, and alhowe t J remain so.
Next, it is clear that a name excludes as well as includes : every objet of thought la related to man, for lustance, either as in the name or on The logician hos 'assays excluded tho privative name, not-man, fs instance, as all but itmelone : a certain practice of his own really maks it so. For he will have no nnirerse—or total sphere of thought—exeei tho whole universe of passible existence; or, at narrowest, the whol universe of objective reality, lie forgets that, more often than no the universe of the cxist.iog topic of thought is limited. IV° as of animals, for example, amid nothing else : not-man becomes definitely migulticative that we have a separate name for it, brut Logic imeht to give us that commend of thought which will our mental vision from being obstructed by the casual absence of name ; sird it ought to investigate the (lama/ term of thought, as we as possible scientific generalleation.
Thirdly, two names may be joined either as separate parte of common whole, or OA jointly separating the common part of to Lfferent wholes. Thus the class anima/ boa the two separate suleclasees, an and brute : but MGM, under the name rational animal, is seen as ,longing to the common part of the two wholes, rational bring and Rinsed being. We call the first procedure aggregation, the second imposition. The first process is mathematical: animal is made up of an and brute after the same law of thought by which a square is made p of two triangles. The second process is deep in the nature of lingo, metaphysical : the combination of rational and anima/ into a sing such as man is not conceivable as oggregation or addition, and no lore. Nevertheless the logician does not admit this : Ile announces
a object as the sum of all its attributes. The preceding distinction hides logic' into two parts, which we call the mathematical and the ietaphysical; not meaning that one part of logic is mathematics, and nether metaphysics, but that the distinctive features of the two sides !logic are of prominent account, the one in mathematics, aud the other metaphysics.
The distinction of composition and aggregation was conveyed and nplied in a few remarkable words of Aristotle, contained in his letaphysies " The genus is said to be part of the species ; but in reAlier point of view the species is part of the genus." Animal is art of man : the lthole notion (all the attributes) of animal forms part component) of the notion man. But man is part of animal : the whole lass (all the individuals) of man form part (aggregant) of the class This is the heading of a chapter in logic which only begins to se written in full in our own day : the logicians always threw the idea if attributes compounded of attributes into metaphysics, and retained he mathematical notion of class aggregated of classes for logic. Thu Stributes which compound into an attribute were said to form its ntension : the classeswhich aggregate into a clam were said to form is extension. This distinction of extension and intension—or extent nd intent—is now often styled that of extension and comprehension ; he Mills, father and son, call it that of denotation and connotation ; lamilton, that of breadth and depth. The revival of the distinction, n logic, and as a separation of the two sides of logic, is mainly due to Ilamiltou : but he and his followers have made a singular inisconcep. ion. In the above explanation it appears clearly that the logical inantities change terms in the opposed modes of speaking. All animal all the attributes) forms part of the notion man : all man (the whole A the class) forms part of the class animal. According to Hamilton, he quantities do not change places. lie affirms that when we say All men are some animals," we speak * in dePth ; and that when we say " Some animals are all men" we speak in breadth. We shall not 3nlarge upon this distinction : we do not think it necessary to impress it length upon the reader that Hamilton's distinction is not the great :distinction of the Laws of thought. And such discussion would be the snore inappropriate at this time, because Hamilton's logical lectures are on the eve of publication by Mr. Maned, who may be expected to defend his principal well, if defence be possible, and who must either defend ur surrender. And we are glad of the opportunity of calling tho reader's anticipation to a work which will most surely contain a vast breadth and depth of thought.