Quantity

“ And so the balance sways and the story runs—here a gain, there a loss, and Nature’s great average struck across the two, whereof the sum total forms one of the factors in that mighty equation in which the result will equal the unknown quantity of her purpose. ”

“ Though proportion be measurable in its own nature, and therefore hath proper quantity, yet as things cannot have proportion which have not quantity of some other kind, it follows that whatever has quantity must have it in one or other of these three kinds, extension, duration, or number. ”

“ Whatever has quantity, or is measurable, must be made up of parts, which bear proportion to one another and to the whole; so that it may be increased by addition of like parts, and diminished by subtraction, may be multiplied and divided, and, in a word, may bear any proportion to another quantity of the same kind, that one line or number can bear to another. That this is essential to all mathematical quantity, is evident from the first elements of algebra, which treats of quantity in general, or of those relations and properties which are common to all kinds of quantity. ”

“ Therefore, one has much to say for the thesis that the whole logical value of the quantitative conceptions in science is due, not to any peculiar advantage of the concept of quantity, as such, but to the exactness of the forms of serial order which are discoverable in case of any quantitative realm of facts. ”

“ Measurement owes its existence to Earth; Estimation of quantity to Measurement; Calculation to Estimation of quantity; Balancing of chances to Calculation; and Victory to Balancing of chances. ”

“ Strictly speaking, only the things which I have mentioned belong to the category of quantity: everything else that is called quantitative is a quantity in a secondary sense. It is because we have in mind some one of these quantities, properly so called, that we apply quantitative terms to other things. We speak of what is white as large, because the surface over which the white extends is large; we speak of an action or a process as lengthy, because the time covered is long ”

“ But as a measure of quantity, such as the natural foot, fathom, or handful, which is continually varying in its own quantity, can never be an accurate measure of the quantity of other things; so a commodity which is itself continually varying in its own value, can never be an accurate measure of the value of other commodities. ”

“ What is the use of giving, for instance, an unestablished, and perhaps preposterous, notion of corporeal quantity to him who has as yet to learn what is the essential composition of bodies? Is a student prepared to realize the true nature of the quantity of mass, or of the quantity of volume, who has never yet explored either the mysterious attributes of formal continuity or the intimate constitution of material substance? ”

“ In quantity (a translation of the Greek ‘posotes’—‘how-muchness’—and seemingly formed by Aristotle on the analogy of Plato’s ‘poiotēs’, from which we have quality) we can perhaps see the beginning of that interest in the calculable aspect of the objects of the visible world from which the exact sciences have arisen. The human mind had now begun to weigh and measure, to examine and compare; and that weighing and measuring has gone on—with intervals—for twenty-three centuries. ”

“ The quantity theory, in its usual formulations, is a theory, not of the value of money, in the absolute sense of value, but of the general price-level, the average price of goods exchanged for money. It is not a psychological theory. ”

“ Now that quantity which is apprehended only as unity, and in which plurality can be represented only by approximation to negation = 0, I call an intensive quantity. Every reality, therefore, in a phenomenon has intensive quantity, that is, a degree. ”

“ At first, no doubt, looking at the nature of quantity as an indifferent and external character of Being, we are disposed to answer these questions in the negative. And yet, as we must admit, this indifferent increase and diminution has its limit: a point is finally reached, where a single additional grain makes a heap of wheat; and the bald-tail is produced, if we continue plucking out single hairs. ”

“ Furthermore, quantitative distinctions in the material world, i.e. distinctions of position, shape, and the like, are all of them primarily known to us in universal form, — not as individual but as specific characters of the object that we have before us. Quantity is no more and no less individuated for our reason than is any other object of thought. This place, this shape, this size, and this definite matter, are just as hard to define in an individual way as this angelic nature, or this immaterial soul. ”

“ When treating of quantity, we have already said that it consists in number and dimension, in so far as some thing possesses such a quantity, that is, in the number of material things, and in the extension of the subject.380 Here indeed we are not treating of abstract quantity, but of a quantity which causes a piece of wood to measure three feet, or that horses are five952 in number. ”

“ If we assume the quantity of goods on sale, and the number of times those goods are resold, to be fixed quantities, the value of money will depend upon its quantity, together with the average number of times that each piece changes hands in the process. ”

“ It is not easy to say how many kinds of improper quantity may in time be introduced into mathematics, or to what new subjects measures may be applied; but this, I think, we may conclude, that there is no foundation in nature for, nor can any valuable end be served by, applying measure to anything but what has these two properties. ”

“ We say that a man is tall, or heavy, or that the room is hot—qualitative statements; or we may say exactly how tall, or how heavy, or how hot—quantitative statements. The distinction between qualitative analysis and quantitative analysis in chemistry implies the same idea. Thus we may speak of a piece of wealth as having a definite quantity of value, or say that the value of the piece of wealth is a definite quantity. ”

“ Of the things that are quantities by their own nature some are so as substances, e.g. the line is a quantity (for 'a certain kind of quantity' is present [37] in the formula which states what it is) , and others are modifications and states of this kind of substance, e.g. much and little, long and short, broad and narrow, deep and shallow, heavy and light, and the other terms of the sort. And also great and small, and greater and smaller, both in themselves and when taken relatively to each other, are by their own nature attributes of quantity ”

“ Bodily quantity has something as quantity, and something else, in so far as it is an accidental form. As quantity, it is distinguishable in respect of position or number, and in this way we have the increase of magnitude by addition, as may be seen in animals. ”

“ Size, on the other hand, and its alteration regarded merely as size, is for the qualitative determination, when it is unable to assert itself in terms of measure, an indifferent determination. That is to say, measure is quantity, precisely in so far as it can give to itself an aspect which qualifies it, and thereby a qualitative determination is united to the purely quantitative one. ”

“ Proportion is the measure of relative quantity. Since all quantity is divisible, it is evident that every distinct part, into which any quantity is divided, must bear some relation to the other parts, or to the whole. These relations give an origin to the idea of proportion. They are discovered by mensuration, and they are the objects of mathematical inquiry. ”

“ Now, exactly as the height at which a person stands may be calculated from any one object on his horizon as well as from a hundred, so one of these superior thoughts is in itself proof sufficient of an elevated mind. For quantity is the measure of low things, but quality of high. ”

“ But the conception of continuous quantity has a great office to fulfill, independently of any attempt at precision. Far from tending to the exaggeration of differences, it is the direct instrument of the finest generalizations. ”

“ He is thus led to recognize a classification of quantities on a new principle, according to which the physical nature of the quantity is subordinated to its mathematical form. ”

“ If the quantity theory is not valid here, if the price-level is not absolutely fixed, helpless to change, with these assumptions, then the quantity theory, even as a minor tendency, must be surrendered, and the quantity theorist must admit that the whole line of thought has been fallacious. ”

“ and it is from this absolute indifference and tranquillity of the mind, that mathematical speculations derive some of their most considerable advantages; because there is nothing to interest the imagination; because the judgment sits free and unbiassed to examine the point. All proportions, every arrangement of quantity, is alike to the understanding, because the same truths result to it from all; from greater, from lesser, from equality and inequality. ”

“ Consequently, the value of the variable quantity of produce which, under different circumstances, forms the wages of a given number of men, being composed of the values of the two elements, labour and profits, varying as above described, must be constant, and may therefore, with propriety, be proposed as a standard measure. ”

“ It is said in the Bible that God has ordered all things according to weight, number and measure. Omnia in pondere et numero et mensura disposuit Deus. Weight is equilibrium, number is quantity, measure is proportion—these three, and these are the eternal or divine basis of the science of Nature. Here now is the formula of equilibrium: Harmony results from the analogy of contraries. Number is the scale of analogies, the proportion of which is measure. The entire occult philosophy of the Zohar might be termed the science of equilibrium. ”

“ The first fact presented is, that equal quantities, when coming together, produce monotony, and, if at all admissible, are only so when absolutely needed, at a proper distance, to echo back or recall the theme, which would otherwise be lost in the excess of variety. We speak of quantity here as of a mass, not of the minutiae; for the essential components of a part may often be equal quantities, (as in a piece of architecture, of armour, &c.,) which are analogous to poetic feet, for instance, a spondee. ”

“ Dimensions of quantity are accidents consequent to the corporeity which belongs to the whole matter. Wherefore matter, once understood as corporeal and measurable, can be understood as distinct in its various parts, and as receptive of different forms according to the further degrees of perfection. ”

“ So if the quantity of money is large, the total value of the property of the world will be correspondingly large as expressed in dollars or money units. If the quantity of money is small, the total value of the property of the world will be correspondingly reduced. ”

“ So much for the theses to be maintained. The detailed proof of these contentions will best be given in connection with a critical account of various versions of quantity theory doctrine. Attention will be given in this summary to the expositions of Nicholson, Mill, Taussig, and Kemmerer, and very special attention to I. Fisher, though some other writers will also be taken into account. ”

“ Quantity is the reciprocal of something else which is usually called quality, but in the course of this discussion it will be found that the term quality is badly chosen, that the real reciprocal of quantity is kind or class. ”

“ Weights and measures.—Another important growth in the machinery of trade is found in standards of quantity,—weights and measures of every kind. It is scarcely possible to realize the uncertainty of exchange without exact weights and measures. ”

“ Yet each of these is not called a quantity by itself, for if a man should explain the quantity of an action, he will define it by time, describing it as yearly, or something of the sort; and if he were to explain the quantity of whiteness, he will define it by the superficies, for as the quantity of the superficies, so he would say is the quantity of the whiteness ”

“ In the same manner as an exponent expresses one operation on quantity, namely, the multiplication of it by itself a certain number of times, or raising it to the power expressed by that exponent, so the term Function, which has been introduced into modern analysis, is intended to express generally the results of all the various operations that can be performed upon quantity. ”

“ A cent is the representative of a certain quantity of corn or other commodity. ”

“ Quantity, therefore, is a very fruitful possession, and, unlike quality, may be directly reënforced by wholesome conditions—by physical education, and by the promotion of healthy and rapid digestion, assimilation, and excretion. ”

“ If the quantity of labour realized in commodities, regulate their exchangeable value, every increase of the quantity of labour must augment the value of that commodity on which it is exercised, as every diminution must lower it. ”

“ It is not by the absolute quantity of produce obtained by either class, that we can correctly judge of the rate of profit, rent, and wages, but by the quantity of labour required to obtain that produce. ”

“ That a fixed quantity A is the cause of, or produces another fixed quantity B, is a proposition which, though convenient for scientific purposes, is apt to damage all inquiry, in so far as it leads us completely to ignore the innumerable conditions lying at the back of a phenomenon. ”

“ You must, however, be aware that the reward for labour, and quantity of labour, are quite disparate things. ”