Nicomachus, Introduction to Arithmetic

Book I, Chapter 1

The ancients, who under the leadership of Pythagoras first made science systematic, defined philosophy as the love of wisdom. Indeed, the name itself means this, and before Pythagoras, all who had knowledge were called ‘wise’ indiscriminately—a carpenter, for example, a cobbler, a helmsman, and in a word, anyone who was versed in any art or handicraft. Pythagoras, however, restricting the title so as to apply to the knowledge and comprehension of reality, and calling the knowledge of the truth in this the only wisdom, naturally designated the desire and pursuit of this knowledge philosophy, as being the desire for wisdom.

He is more worthy of credence than those who have given other definitions since he makes clear the sense of the term and the thing defined. This ‘wisdom’ he defined as the knowledge, or science, of the truth in real things, conceiving ‘science’ to be a steadfast and firm apprehension of the underlying substance, and ‘real things’ to be those which continue uniformly and the same in the universe and never depart even briefly from their existence; these real things would be things immaterial, by sharing in the substance of which everything else that exists under the same name and is so called is said to be ‘this particular thing,’ and exists.

For bodily, material things are, to be sure, forever involved in continuous flow and change—in imitation of the nature and peculiar quality of that eternal matter and substance which has been from the beginning, and which was all changeable and variable throughout. The bodiless things, however, of which we conceive in connection with or together with matter, such as qualities, quantities, configurations, largeness, smallness, equality, relations, actualities, dispositions, places, times, all those things, in a word, whereby the qualities found in each body are comprehended—all these are of themselves immovable and unchangeable, but accidentally they share in and partake of the affections of the body to which they belong.

Now it is with such things that ‘wisdom’ is particularly concerned, but accidentally also with things that share in them, that is, bodies.

Book I, Chapter 2

Those things, however, are immaterial, eternal, without end, and it is their nature to persist ever the same and unchanging, abiding by their own essential being, and each one of them is called real in the proper sense. But what are involved in birth and destruction, growth and diminution, all kinds of change and participation, are seen to vary continually, and while they are called real things, by the same term as the former, so far as they partake of them, they are not actually real by their own nature; for they do not abide for even the shortest moment in the same condition, but are always passing over in all sorts of changes. To quote the words of Timaeus, in Plato, “What is that which always is, and has no birth, and what is that which is always becoming but never is? The one is apprehended by the mental processes, with reasoning, and is ever the same; the other can be guessed at by opinion in company with unreasoning sense, a thing which becomes and passes away, but never really is.”

Therefore, if we crave for the goal that is worthy and fitting for man, namely, happiness of life—and this is accomplished by philosophy alone and by nothing else, and philosophy, as I said, means for us desire for wisdom, and wisdom the science of the truth in things, and of things some are properly so called, others merely share the name—it is reasonable and most necessary to distinguish and systematize the accidental qualities of things.

Things, then, both those properly so called and those that simply have the name, are some of them unified and continuous, for example, an animal, the universe, a tree, and the like, which are properly and peculiarly called ‘magnitudes’; others are discontinuous, in a side-by-side arrangement, and, as it were, in heaps, which are called ‘multitudes,’ a flock, for instance, a people, a heap, a chorus, and the like. Wisdom, then, must be considered to be the knowledge of these two forms. Since, however, all multitude and magnitude are by their own nature of necessity infinite—for multitude starts from a definite root and never ceases increasing; and magnitude, when division beginning with a limited whole is carried on, cannot bring the dividing process to an end, but proceeds therefore to infinity—and since sciences are always sciences of limited things, and never of infinites, it is accordingly evident that a science dealing either with magnitude, per se, or with multitude, per se, could never be formulated, for each of them is limitless in itself, multitude in the direction of the more, and magnitude in the direction of the less. A science, however, would arise to deal with something separated from each of them, with quantity, set off from multitude, and size, set off from magnitude.