It is necessary to observe the artifice, to which we are obliged to have recourse, to name, and even to distinguish, the different modifications, not of kind but of degree, included under the word quantity. We are obliged to take some one object, with which we are familiar, and to distinguish other objects, as differing or agreeing with that object. Thus, we take some well-known line, the length of the foot, or the length of the arm, and distinguish and name all other lengths by that length; which can be divided or multiplied so as to correspond with them. In like manner, we take some well-known object as a standard weight, which we call, for example, a pound, and distinguish and name all other weights, as parts or multiples of that known weight.
Now it will be recognised, that, in applying the relative terms equal, equal, or in calling two objects equal, no one of them is marked as the standard. Both are taken on the same footing. The one is equal to the other; and the other is equal to that. But when we say that one thing is tantus, quantus another; or one so great, as the other is great; the first is referred to the last, the tantus to the quantus; the first is distinguished and named by the last. The quantus is the standard.
It is this which gives its peculiar meaning to the word Quantity, and has recommended it for that very 53 comprehensive and generical acceptation, in which it is now received.
Our word Quantity, is the Latin word Quantitas; and Quantitas is the abstract of the concrete Quantus. We have no English words, corresponding to Tantus, Quantus. We form an equivalent, by aid of the relative conjunctions; we say, So Great, As Great. But these concrete terms do not furnish abstracts; we do not say, As-greatness; in the first place, because it is an awkward expression; and in the next place, because the relative, “as,” is not steady in its application, since we use “as great” not for quantus only, but frequently also for tantus. As greatness, therefore, does not readily suggest the idea of the abstract of Quantus.
On what account, then, is it we give to any thing the name Quantus? As a standard by which to name another thing Tantus. The thing called Quantus, is the previously known thing, the ascertained amount, by which we can mark and define the other amount. Leaving out the connotation of Quantus, which is some one individual body, Quantitas merely denotes such and such an amount of body. Quantitas, if it was kept to its original meaning, would still connote Tantitas; just as paternity connotes filiality. But in the case of Quantity, even this connotation is dropped; it is used not as a relative abstract term, but an absolute abstract term; and is employed as a generical name for any portion of extension, any portion of weight, of heat, or any thing else, which can be measured by a part of itself.[14]
[14] After analysing Position and Extension under the head of Relative Terms, the author now, under the same head, gives the analysis of Quantity and Quality. To what he says on the subject of Quantity it does not appear necessary to add anything. He seems to have correctly analysed the phenomenon down to a primitive element, beyond which we have no power to investigate. As Likeness and Unlikeness appeared to be properties of our simple feelings, which must be postulated as ultimate, and which are inseparable from the feelings themselves, so may this also be said of More and Less. As some of our feelings are like, some unlike, so there is a mode of likeness or unlikeness which we call Degree: some feelings otherwise like are unlike in degree, that is one is unlike another in intensity, or one is unlike another in duration; in either case one is distinguished as more, or greater, the other as less. And the fact of being more or less only means that we feel them as more or less. The author says in this case, as he had said in the other elementary cases of relation, that the more and the less being different sensations, to trace them and to distinguish their difference are not two things but one and the same thing. It matters not, since there the difference still is, unsusceptible of further analysis. The author’s apparent simplification amounts only to this, that differences of quantity, like all other differences of which we take cognizance, are differences merely in our feelings; they exist only as they are felt. But (as we have already said of [resemblance], and of [antecedence and consequence]) they must be postulated as elements. The distinction of more and less is one of the ultimate conditions under which we have all our states of consciousness.—Ed.
54 4. After tracing the sensations and ideas, which are marked when we apply relative terms to objects, as agreeing or disagreeing in quantity; we have now to trace the sensations and ideas, which are marked, when we apply relative terms to objects, on account of their agreeing or disagreeing in quality.
First of all, the learner must take note of what he 55 means by Quality. We ascribe qualities to an object on account of our sensations. We call an object green, on account of the sensation green; hard, on account of the sensation hard; sounding, on account of the sensation sounding. The names of all qualities of objects, then, are names of sensations. Are they any thing else? Yes; they are the names of our sensations, with connotation of a supposed unknown cause of those sensations. As far, however, as our knowledge goes, they are names of sensations, and nothing else. The supposed cause is never known; the effects alone are known to us.
We ascribe qualities to objects, in two cases, which require to be distinguished: on account of the sensations which we have from them primarily; on account of those which we have from them secondarily. The first we call their sensible qualities; as green, hot, hard, sweet, scented, and so on: the second we more frequently call their powers; as the power of the loadstone to draw iron, the power of water to melt sugar. In this latter case, the sensations marked are not those which are derived from the loadstone, or from water; but those which are derived from the changes in the iron, and the sugar; of which changes, we call the loadstone, and the water, the cause. In the latter case, the train of antecedents and consequents is longer than it is in the former. When I see an object green; there is the object, the antecedent; and myself sentient of green, the consequent. When I see a loadstone draw iron, there is the following train; the loadstone, antecedent; iron drawn, first consequent; myself seeing it drawn, second consequent. When I see water melt sugar, there is the 56 antecedent water; sugar melting, first consequent; myself seeing it, second consequent. What I call the powers of an object, then, are its order in respect to certain of my sensations, the order of antecedence, not proximate, but more or less remote.
When I say that grass is green, I trace my sensation green, no farther than to the grass. When I say, the sugar is melting, I trace my sensations (for they are several) called sugar melting, first to the sugar, and then to the water. My word green, therefore, is the notation of a sensation, and connotation of an unknown cause; my name melting, is the notation of a compound of sensations, and connotation of two causes, an antecedent and a consequent: the first, an unknown cause in the sugar; the second, the cause of that unknown cause, namely, the water.