It will doubtless be objected by most of the present period, who believe in nothing beyond the information of their senses, that plants, animals, and stones, no longer possess those wonderful sympathetic powers, which are mentioned by Proclus in the above extract. In answer to any such objector, whose little soul, (in the language of the Emperor Julian) is indeed acute, but sees nothing with a vision healthy and sound, it must be said, that this is not at all wonderful at a period, when, as the author of the Asclepian dialogue justly observes, “there is a lamentable departure of divinity from man, when nothing worthy of heaven, or celestial concerns, is heard or believed, and when every divine voice is by a necessary silence dumb.”[102] But to the philosophic reader, it must be observed, that as in the realms of generation, or in other words, the sublunary region, wholes, viz. the spheres of the different elements, remain perpetually according to nature; but their parts are sometimes according, and sometimes contrary to nature; this must also be true of the parts of the earth. When those circulations therefore take place, during which the parts of the earth subsist according to nature, and which are justly called, by Plato, fertile periods, the powers of plants, animals, and stones, magically sympathize with superior natures, in consequence of a more abundant participation of them, through a greater degree of aptitude to receive, and alliance to the participated powers. But during those circulations, in which the parts of the earth subsist contrary to nature, as at present, and which Plato calls barren periods, the powers of plants, animals, and stones, no longer possess a magic sympathy, and consequently are no longer capable of producing magical operations.

[P. 106.] The eternal essence of number is the most providential principle of the universe, &c.

The following account of the manner in which the Pythagoreans philosophized about numbers, is extracted from my Theoretic Arithmetic, and the information contained in it is principally derived from the great Syrianus.

“The Pythagoreans, turning from the vulgar paths, and delivering their philosophy in secret to those alone who were worthy to receive it, exhibited it to others through mathematical names. Hence, they called forms, numbers, as things which are the first separated from impartible union; for the natures which are above forms, are also above separation.[103] The all-perfect multitude of forms, therefore, they obscurely signified through the duad; but they indicated the first formal principles by the monad and duad, as not being numbers; and also by the first triad and tetrad, as being the first numbers, the one being odd, and the other even, from which by addition the decad is generated; for the sum of 1, 2, 3, and 4, is ten. But after numbers, in secondary and multifarious lives, introducing geometrical prior to physical magnitudes; these also they referred to numbers, as to formal causes and the principles of these; referring the point indeed, as being impartible, to the monad; but a line, as the first interval, to the duad; and again, a superficies, as having a more abundant interval, to the triad; and a solid to the tetrad. They also called, as is evident from the testimony of Aristotle, the first length the duad; for it is not simply length, but the first length, in order that by this they might signify cause. In a similar manner also, they denominated the first breadth, the triad; and the first depth the tetrad. They also referred to formal principles all psychical knowledge. And intellectual knowledge indeed, as being contracted according to impartible union, they referred to the monad; but scientific knowledge, as being evolved, and as proceeding from cause to the thing caused, yet through the inerratic, and always through the same things, they referred to the duad; and opinion to the triad, because the power of it is not always directed to the same thing, but at one time inclines to the true, and at another to the false. And they referred sense to the tetrad, because it has an apprehension of bodies; for in the duad, indeed, there is one interval from one monad to the other; but in the triad there are two intervals from any one monad to the rest; and in the tetrad there are three. They referred, therefore, to principles every thing knowable, viz. beings, and the gnostic powers of these. But they divided beings not according to breadth, but according to depth; into intelligibles, objects of science, objects of opinion, and sensibles. In a similar manner, also, they divided knowledge into intellect, science, opinion, and sense. The extremity, therefore, of the intelligible triad, or animal itself, as it is called by Plato in the Timæus, is assumed from the division of the objects of knowledge, manifesting the intelligible order, in which forms themselves, viz. the first forms and the principles of these, are contained, viz. the idea of the one itself, of the first length, which is the duad itself, and also the ideas of the first breadth and the first depth; (for in common the term first is adapted to all of them), viz. to the triad itself, and the tetrad itself.

“Again, the Pythagoreans and Plato did not denominate idea from one thing, and ideal number from another. But since the assertion is eminently true, that all things are similar to number, it is evident that number, and especially every ideal number, was denominated on account of its paradigmatic peculiarity. If any one, however, wishes to apprehend this from the appellation itself, it is easy to infer that idea was so called, from rendering as it were its participants similar to itself, and imparting to them form, order, beauty, and unity; and this in consequence of always preserving the same form, expanding its own power to the infinity of particulars, and investing with the same species its eternal participants. Number also, since it imparts proportion and elegant arrangement to all things, was allotted this appellation. For the ancients, says Syrianus,[104] call to adapt or compose αρσαι arsai, whence is derived αριθμος arithmos number. Hence αναρσιον anarsion among the Greeks signifies incomposite. Hence too, those Grecian sayings, you will adapt the balance, they placed number together with them, and also number and friendship. From all which number was called by the Greeks arithmos, as that which measures and orderly arranges all things, and unites them in amicable league.

“Farther still, some of the Pythagoreans discoursed about inseparable numbers alone, i. e. numbers which are inseparable from mundane natures, but others about such as have a subsistence separate from the universe, in which as paradigms they saw those numbers are contained, which are perfected by nature. But others, making a distinction between the two, unfolded their doctrine in a more clear and perfect manner. If it be requisite, however, to speak concerning the difference of these monads, and their privation of difference, we must say that the monads which subsist in quantity, are by no means to be extended to essential numbers; but when we call essential numbers monads, we must assert that all of them mutually differ from each other by difference itself, and that they possess a privation of difference from sameness. It is evident also, that those which are in the same order, are contained through mutual comparison, in sameness rather than in difference, but that those which are in different orders are conversant with much diversity, through the dominion of difference.

“Again, the Pythagoreans asserted that nature produces sensibles by numbers; but then these numbers were not mathematical but physical; and as they spoke symbolically, it is not improbable that they demonstrated every property of sensibles by mathematical names. However, says Syrianus, to ascribe to them a knowledge of sensible numbers alone, is not only ridiculous, but highly impious. For they received indeed, from the theology of Orpheus, the principles of intelligible and intellectual numbers, they assigned them an abundant progression, and extended their dominion as far as to sensibles themselves.”

Again, their conceptions about mathematical and physical number, were as follow:

“As in every thing, according to the doctrine of Aristotle, one thing corresponds to matter, and another to form, in any number, as for instance the pentad, its five monads, and in short its quantity, and the number which is the subject of participation, are derived from the duad itself; but its form, i. e. the pentad itself, is from the monad; for every form is a monad, and unites its subject quantity. The pentad itself, therefore, which is a monad, proceeds from the principal monad, forms its subject quantity, which is itself formless, and connects it to its own form. For there are two principles of mathematical numbers in our souls: the monad, which comprehends in itself all the forms of numbers, and corresponds to the monad in intellectual natures; and the duad, which is a certain generative principle of infinite power, and which on this account, as being the image of the never-failing and intelligible duad, is called indefinite. While this proceeds to all things, it is not deserted in its course by the monad, but that which proceeds from the monad continually distinguishes and forms boundless quantity, gives a specific distinction to all its orderly progressions, and incessantly adorns them with forms. And as in mundane natures, there is neither any thing formless, nor any vacuum among the species of things, so likewise in mathematical number, neither is any quantity left innumerable; for thus the forming power of the monad would be vanquished by the indefinite duad, nor does any medium intervene between the consequent numbers, and the well-disposed energy of the monad.

“Neither, therefore, does the pentad consist of substance and accident, as a white man; nor of genus and difference, as man of animal and biped; nor of five monads mutually touching each other, like a bundle of wood; nor of things mingled, like a drink made from wine and honey; nor of things sustaining position, as stones by their position complete the house; nor lastly, as things numerable, for these are nothing else than particulars. But it does not follow that numbers themselves, because they consist of indivisible monads, have nothing else besides monads, (for the multitude of points in continued quantity is an indivisible multitude, yet it is not on this account that there is a completion of something else from the points themselves); but this takes place because there is something in them which corresponds to matter, and something which corresponds to form. Lastly, when we unite the triad with the tetrad, we say that we make seven. The assertion, however, is not true: for monads conjoined with monads, produce indeed the subject of the number 7, but nothing more. Who then imparts the heptadic form to these monads? Who is it also that gives the form of a bed to a certain number of pieces of wood? Shall we not say that the soul of the carpenter, from the art which he possesses, fashions the wood, so as to receive the form of a bed, and that the numerative soul, from possessing in herself a monad which has the relation of a principle, gives form and subsistence to all numbers? But in this only consists the difference, that the carpenter’s art is not naturally inherent in us, and requires manual operation, because it is conversant with sensible matter; but the numerative art is naturally present with us, and is therefore possessed by all men, and has an intellectual matter which it instantaneously invests with form. And this is that which deceives the multitude, who think that the heptad is nothing besides seven monads. For the imagination of the vulgar, unless it first sees a thing unadorned, afterwards the supervening energy of the adorner, and lastly, above all the thing itself, perfect and formed, cannot be persuaded that it has two natures, one formless, the other formal, and still further, that which beyond these imparts form; but asserts, that the subject is one, and without generation. Hence, perhaps, the ancient theologists and Plato ascribed temporal generations to things without generation, and to things which are perpetually adorned, and regularly disposed, privation of order and ornament, the erroneous and the boundless, that they might lead men to the knowledge of a formal and effective cause. It is, therefore, by no means wonderful, that though seven sensible monads are never without the heptad, these should be distinguished by science, and that the former should have the relation of a subject, and be analogous to matter, but the latter should correspond to species and form.