QUANTITY. There is little here to add to what has been said in the article 31A0NITUVE, so far as the mathematical notion is concerned. The quantity of anything is the answer to quantize i (how much I ) and the considerations under RATIO are necessary to the precise answer. Mr. Mill, in Ilia Elements of the limzum Mind, has invented the word tastily, since quantal (how much) is answered by tants, (so much); and ho therefore uses' quantity and tantity as correlative words. But in truth the meaning of quantity, as generally received, does net refer to the question, but to the answer : so that the word tastily, if intro duced, could only mean the same thing as quantity, unless the meaning of the latter word were changed. If any one were to propose that quantity should signify what it does at present, with the addition of a reference to seeking, requiring, or asking, and that tantity should involve the same notion, its object being considered as found, given, or determined, undoubtedly the proposition would be a good one, con sidered apart from the difficulty of altering established meanings. The word quantuplicity, as distinguished from quantity, means the answer to how many times, as distinguished from how much. [RATIO.
The notion attached to the word quantity in the middle ages varied between two extremes. At one end it signified the abstract idea of that about which quantize can be asked : and in this sense it necessitated the startling maxim that "quantity does not admit of more and less." Thus we have not more right to say of a mile than of a foot that it is the proper subject of the question quantus, or has quantitas. At the other end, quantity was a " thing which is per at divisible into ]arts" : thus making the quantity to be the thing from which the notion arises, which some called the rca quanta. This idiom is common in all time ; and it has sometimes created confusion, and that in every line of thought, from agriculture to logic. We should perfectly well under
stand what a person meant who said that he had bought a hundred weight of sugar from Smith, and had sold as much to Jones, but not the same quantity : and we should also understand the charge of having made a blunder which might be brought against the speaker. But there is no blunder at ail : the phrase has always been in use, and has lasted from the time of the schoolmen, of whom many defined quantity as being res per se dirisibilis in partes. Blunder begins when a person confuses this old concrete sense with the modern one, in which quantity is tho propor answer to home much! on a thing which admits of the notion of more and less.
Quantity admits another important division. In sonic quantities (now meaning me quanta!) we hold the parts in joint and separate existence at once, as in length, area, solidity, angle, time, number. In others we have not the separate perception of parts, though sensible of a whole which we are conscious might be more or less, Thus when we see a foot, we see the inches: but when we feel a pound, we do not feel the ounces. Some of the old writers say that it is essential to quantity to have parks extra pastes : that is, to be of the first kind now under discussion. But they cannot help admitting quantities which do nut satisfy this so-called essential condition. The truth seems to be that only is the fundamental notions of mathematics, space, time, and number, do we feel cognisant of the separate existence of parts in a whole by the same means which make us cognisant of the whole. In other things we learn by instruments, material or solely mental. We should never have divided weight into parts, if it had not been for the invention of the balance : nor belief, if it had not been for the calculus of probabilities, aided, in the first instance, by the definite ness of the cases which are on the cards or on the dice.