Part II: On the Difference between Democritean and Epicurean Physics In Detail
It contradicts the concept of the atom that the atom should have properties, because, as Epicurus says, every property is variable but the atoms do not change.(1) Nevertheless it is a necessary consequence to attribute properties to atoms. Indeed, the many atoms of repulsion separated by sensuous space must necessarily be immediately different from one another and from their pure essence, i.e., they must possess qualities.
In the following analysis I therefore take no account of the assertion made by Schneider and Nürnberger that “Epicurus attributed no qualities to the atoms, paragraphs 44 and 54 of the letter to Herodotus in Diogenes Laertius have been interpolated”. If this were truly so, how is one to invalidate the evidence of Lucretius, Plutarch, and indeed of all other authors who speak of Epicurus? Moreover, Diogenes Laertius mentions the qualities of the atom not in two, but in ten paragraphs: Nos. 42, 43, 44, 54, 55, 56, 57, 58, 59 and 61. The grounds these critics give for their contention — that “they did not know how to reconcile the qualities of the atom with its concept"-are very shallow.”  Spinoza says that ignorance is no argument. [Spinoza, Ethics, Part I, Prop. 36, Appendix] If one was to delete the passages in the ancients which he does not understand, how quickly would we have a tabula rasa!
Through the qualities the atom acquires an existence which contradicts its concept; it is assumed as an externalised being different from its essence. It is this contradiction which mainly interests Epicurus. Hence, as soon as he posits a property and thus draws the consequence of the material nature of the atom, he counterposits at the same time determinations which again destroy this property in its own sphere and validate instead the concept of the atom. He therefore determines all properties in such a way that they contradict themselves. Democritus, on the other hand, nowhere considers the properties in relation to the atom itself, nor does he objectify the contradiction between concept and existence which is inherent in them. His whole interest lies rather in representing the qualities in relation to concrete nature, which is to be formed out of them. To him they are merely hypotheses to explain the plurality . which makes its appearance. It follows that the concept of the atom has nothing to do with them.
In order to prove our assertion it is first of all necessary to elucidate the sources which here seem to contradict one another.
In the treatise De placitis philosophorum we read:
“Epicurus asserts that the atoms have three qualities: size, shape, weight. Democritus only assumed two: size and shape. Epicurus added weight as the third."(2)
The same passage is repeated word for word in the Praeparatio evangelica of Eusebius.(3)
It is confirmed by the testimony of Simplicius(4) and Philoponus,(5) according to whom Democritus attributed to the atoms only difference in size and shape. Directly contrary stands Aristotle who, in the book De generations et corruptions, attributes to the atoms of Democritus difference in weight.(6) In another passage (in the first book of De caelo) Aristotle leaves undecided the question of whether or not Democritus ascribed weight to the atoms, for he says:
"Thus none of the bodies will be absolutely light if they all have weight; but if all have lightness, none will be heavy."(7)
In his Geschichte der alten Philosophie, Ritter, basing himself on the authority of Aristotle, rejects the assertions of Plutarch, Eusebius and Stobaeus.(8) He does not consider the testimony of Simplicius and Philoponus.
Let us see whether these passages are really so contradictory. In the passage cited, Aristotle does not speak of the qualities of the atom ex professo.[as someone who knows their profession] On the other hand, we read in the eighth book of the Metaphysics:
"Democritus assumes three differences between atoms. For the underlying body is one and the same with respect to matter, but it differs in rhysmos, meaning shape, in trope, meaning position, or in diathige, meaning arrangement."(9)
This much can be immediately concluded from this passage . Weight is not mentioned as a property of the Democritean atoms. The fragmented pieces of matter, kept apart by the void, must have special forms, and these are quite externally perceived from the observation of space. This emerges even more clearly from the following passage of Aristotle:
"Leucippus and his companion Democritus hold that the elements are the full and the void.... These are the basis of being as matter. just as those who assume only one fundamental substance generate all other things by its affections, assuming rarity and density as the principles of qualities-in the same way Leucippus and Democritus also teach that the differences between the atoms are the causes of the other things, for the underlying being differs only by rhysmos, diathige and trope .... That is, A differs from N in shape, AN from NA in arrangement, Z from N in position.”(10)
It is evident from this quotation that Democritus considers the properties of the atom only in relation to the formation of the differences in the world of appearances, and not in relation to the atom itself. it follows further that Democritus does not single out weight as an essential property of the atoms. For him weight is taken for granted, since everything corporeal has weight. In the same way, according to him, even size is not a basic quality. It is an accidental determination which is already given to the atoms together with figure. Only the diversity of the figures is of interest to Democritus, since nothing more is contained in shape, position and arrangement. Size, shape and weight, by being combined as they are by Epicurus, are differences which the atom in itself possesses. Shape, position and arrangement are differences which the atom possesses in relation to something else. Whereas we find in Democritus mere hypothetical determinations to explain the world of appearances, in Epicurus the consequence of the principle itself will be presented to us. We shall therefore discuss in detail his determinations of the properties of the atom.
First of all, the atoms have size.(11) And then again, size is also negated. That is to say, they do not have every size;(12) but only some differences in size among them must be admitted.(13) Indeed, only the negation of the large can be ascribed to them, the small,(14) — also not the minimum, for this would be merely a spatial determination, but the infinitely small, which expresses the contradiction.(15) Rosinius, in his notes on the fragments of Epicurus; therefore translates one passage incorrectly and completely ignores the other, when he says:
“In this way Epicurus tried to make plausible the tenuity of the atoms of incredible smallness, by saying, according to Laertius, X, 44, that they have no size.”(16)
Now I shall not concern myself with the fact that, according to Eusebius, Epicurus was the first to ascribe infinite smallness to the atoms,(17) whereas Democritus also assumed atoms of the largest size — Stobaeus says even as large as the world.(18)
This, on the one hand, contradicts the testimony of Aristotle.(19) On the other hand, Eusebius, or rather the Alexandrian bishop Dionysius, from whom he takes excerpts, contradicts himself; for in the same book we read that Democritus assumed as the principles of nature indivisible bodies perceptible through reason.(20) This much at least is clear: Democritus was not aware of the contradiction; he did not pay attention to it, whereas it was the chief interest of Epicurus.
The second property of the Epicurean atoms is shape.(21) But this determination also contradicts the concept of the atom, and its opposite must be assumed. Abstract individuality is abstract identity-to-itself and therefore without shape. The differences in the shape of the atoms cannot, therefore, be determined(22) although they are not absolutely infinite.(23) It is rather by a definite and finite number of shapes that the atoms are differentiated from one another.(24) From this it is obvious that there are not as many different figures as there are atoms,(25) while Democritus assumes an infinite number of figures.(26) If every atom had a particular shape, then there would have to be atoms of infinite — size(27); for they would have an infinite difference, the difference from all the others, in themselves [an sich], like the monads of Leibniz. This leads to the inversion of Leibniz's assertion that no two things are identical, and there are infinitely many atoms of the same shape. This obviously negates again the determination of the shape, because a shape which no longer differs from another is not shape. (28)
Finally, it is highly important that Epicurus makes weight the third quality,(29) for in the centre of gravity matter possesses the ideal individuality which forms a principal determination of the atom. Hence, once the atoms are brought into the realm of presentation, they must also have weight.
But weight also directly contradicts the concept of the atom, because it is the individuality of matter as an ideal point which lies outside matter. But the atom is itself this individuality, as it were the centre of gravity presented as an individual existence. Weight therefore exists for Epicurus only as different weight, and the atoms are themselves substantial centres of gravity like the heavenly bodies. If this is applied to the concrete, then the obvious result is the fact which old Brucker finds so amazing(30) and of which Lucretius assures us, (31) namely, that the earth has no centre towards which everything strives, and that there are no antipodes. Furthermore since weight belongs only to that atom which is different from the other, hence externalised and endowed with properties, then it is clear that where the atoms are not thought of as many in their differentiation from one another, but only in relation to the void, the determination of weight ceases to exist. The atoms, as different as they may be in mass and shape, move therefore with equal speed in empty space.(32) Epicurus thus applies weight only in regard to repulsion and the resulting compositions. This has led to the assertions that only the conglomerations of the atoms are endowed with weight, but not the atoms themselves.(33)
Gassendi already praises Epicurus because, led purely by reason, he anticipated the experimentally demonstrated fact that all bodies, although very different in weight and mass, have the same velocity when they fall from above to below.(34)
The consideration of the properties of the atoms leads us therefore to the same result as the consideration of the declination, namely, that Epicurus objectifies the contradiction in the concept of the atom between essence and existence. He thus gave us the science of atomistics. In Democritus, on the other hand, there is no realisation of the principle itself. He only maintains the material side and offers hypotheses for the benefit of empirical observation.
Part II, Chapter 3: Atomoi archai and atoma stoicheia
((1) Diogenes Laertius, X, 54. For every quality changes, but the atoms do not change.
Lucretius, On the Nature of Things, II, 861-863. They must be kept far apart from the atoms, if we wish to provide the universe with imperishable foundations on which it may rest secure ...
(2) (Plutarch,) On the Sentiments of the Philosophers [I, 3]. Epicurus ... affirms that ... bodies are subject to these three accidents, shape, size and weight. Democritus [acknowledged] but two: size and shape. Epicurus added the third, to wit, weight, for he pronounced that it is necessary that bodies receive their motion from that impulsion which springs from weight Comp. Sextus Empiricus, Against the Professors, p. 421 [X, 240].
(3) Eusebius, Preparation for the Gospel, XIV, p. 749 [141.
(4) Simplicius, 1.c., p. 362. ...giving (i.e., Democritus) them (i.e., the atoms) the difference with regard to size and shape....
(5) Philoponus, ibid. He (Democritus) assigns a unique common nature of the body to all shapes; its parts are the atoms, which differ from each other in size and shape; for they have not only different shape but some of them are bigger, the others smaller.
(6) Aristotle, On Becoming and Decaying, 1, 8 [326, 10]. ...and yet he [Democritus] says “the more any indivisible exceeds, the heavier it is”.
(7) Aristotle, On the Heavens, 1, 7 [276, 1-2, 4-7]. But each piece must, as we assert, have the same motion.... So that if it be weight that all possess, no body is, strictly speaking, light; and if lightness he universal, none is heavy. Moreover, whatever possesses weight or lightness will have its place either at one of the extremes or in the middle region.
(8) Ritter, History of Ancient Philosophy [in German], I, p. 568, Note 2 [2d improved edition, 1836, p. 602, Note 2].
(9) Aristotle, Metaphysics, VIII, 2 [1042, 11-141. Democritus seems to think there are three kinds of difference between things [atoms]; the underlying body, the matter, is one and the same, but they differ either in rhythm, i. e. shape, or in turning, i. e. position, or in inter-contact, i. e. order.
(10) Ibid., I, 4 [985b, 4-191. Leucippus and his associate Democritus say that the full and the empty are the elements, calling the one being and the other non-being-the full and solid being being, the empty non-being (whence they say being no more is than non-being, because the solid no more is than the empty); and they make these the material causes of things. And as those who make the underlying substance one generate all other things by its modifications, supposing the rare and the dense to be the sources of modifications, in the same way these philosophers say the differences in the elements are the causes of all other qualities. These differences, they say, are three-shape and order and position. For they say the real is differentiated only by “rhythm” and “inter-contact” and “turning”; and of these rhythm is shape, inter-contact is order, and turning is position; for A differs from N in shape, AN from NA in order, and Z from, N in position.
(11) Diogenes Laertius X 44. ...atoms have no quality at all except shape, size and weight. ... further, that they are not of any and every size; at any rate no atom has ever been seen by our senses.
(12) Ibid., X, 56. But to attribute any and every size to the atoms does not help to explain the differences of quality in things; moreover, in that case atoms would exist large enough to be perceived by us, which is never observed to occur; nor can we conceive how such an occurrence should be possible, i. e., that an atom should become visible.
(13) Ibid., X, 55. Again, you should not suppose that the atoms have any and every size ... but some differences of size must be admitted.
(14) Ibid., X, 59. On the analogy of things within our experience w e have declared that the atom has size; and this, small as it is, we have merely reproduced on a larger scale.
(15) comp. ibid., X, 58. Stobaeus, Physical Selections, I, p. 27.
(16) Epicurus, Fragments (On Nature, II and XI), collected by Rosinius, ed. By Orefli, p. 26.
(17) Eusebius, Preparation for the Gospel, XIV, p. 773 (Paris ed.). But they differed in that one of them (i.e., Epicurus) assumed that all atoms were infinitely small and could therefore not be perceived, while Democritus assumed that some large atoms existed too.
(18) Stobaeus, Physical Selections, I, 17. Democritus even says ... that an atom is possible as large as the world. Comp. (Plutarch,) On the Sentiments of the philosophers, i, p. 235 11, 31.
(19) Aristotle, On Becoming and Decaying, 1, 8 1324 , 301. ... invisible ... owing to their minuteness....
(20) Eusebius, Preparation for the Gospel, XIV, p. 749. Democritus ... [assumed] as the principles of the things indivisible ... bodies perceptible through reason.... Comp. (Plutarch,) On the Sentiments of the Philosophers, I, p. 235 [31.
(21) Diogenes Laertius, X, 54. Moreover, we must hold that the atoms in fact possess none of the qualities belonging to the world which come under our observation, except shape, weight, and size, and the properties necessarily conjoined with shape. Comp. S. 44.
(22) Ibid., X, 42. Furthermore, the atoms ... vary indefinitely in their shapes.
(23) Ibid., X, 42. ... but the variety of shapes, though indefinitely larger, is not absolutely infinite.
(24) Lucretius, On the Nature of Things, II, 513-514. ...you must acknowledge a corresponding limit to the different forms of matter.
Eusebius, Preparation for the Gospel, XIV, p. 749. Epicurus ... [says] ... that the shapes of the atoms themselves are limited, and not infinite.... Comp. (Plutarch) On the Sentiments of the Philosophers, 1.c.
(25) Diogenes Laertius, X, 42. The like atoms of each shape are absolutely infinite.
Lucretius, On the Nature of Things, 11, 525-528. Since the varieties of form are limited, the number of uniform atoms must be unlimited. Otherwise the totality of matter would be finite, which 1 have proved in my verses is not so.
(26) Aristotle, On the Heavens, III, 4 [303, 3-5, 10-15]. There is, further, another view-that of Leucippus and Democritus of Abdera-the implications of which are also unacceptable.... and further, they say that since the atomic bodies differ in shape, and there is an infinity of shapes, there is an infinity of simple bodies. But they have never explained in detail the shapes of the various elements, except so, far as to allot the sphere to fire. Air, water and the rest...,
Philoponus, 1.c. They have ... not only entirely different shapes....
(27) Lucretius, On the Nature of Things, II, 474-484, 491-492, 495-497. ...the number of different forms of atoms is finite. If it were not so, some of the atoms would have to be of infinite magnitude. Within the narrow limits of any single particle, there can be only a limited range of forms....
... if you wish to vary its form still further ... the arrangement will demand still other parts.... Variation in shape goes with increase in size. You cannot believe, therefore, that the atoms are distinguished by an infinity of forms....
(28) Comp. Note 25).
(29) Diogenes Laertius, X, 44 and 54.
(30) Brucker, Institutions of the History of Philosophy [Latin, 1747], p. 224.
(31) Lucretius, On the Nature of Things, I, 1051-1052. 0, Memmius, here you must give up fully the belief that all things strive — as they say — to the middle of the world.
(32) Diogenes Laertius, X, 43. The atoms move with equal speed, since the void makes way for the lightest and heaviest alike through all eternity.... 61. When they are travelling through the void and meet with no resistance, the atoms must move with equal speed. Neither will heavy atoms travel more quickly than small and light ones, so long as nothing meets them, nor will small atoms travel more quickly than large ones, provided they always find a passage suitable to their size; and provided that they meet with no obstruction.
Lucretius, On the Nature of Things, II, 235-239. But empty space can offer no resistance to any object in any quarter at any time, so as not to yield free passage as its own nature demands. Therefore, through undisturbed vacuum all bodies must travel at equal speed though impelled by unequal weights.
(33) Comp. Ch. 3.
(34) Feuerbach, History of the Newer Philosophy. [1833, quotations from] Gassendi, 1. c., XXXIII, No. 7. Although Epicurus had perhaps never thought about this experiment, he [still] reached, led by reason, the same opinion about atoms that experiment has recently taught us. This opinion is that all bodies.... although very different in weight and bulk, have the same velocity when they fall from above to below. Thus he was of opinion that all atoms, however much they may differ in size and weight, move with an equal velocity.