In Metaphysics A Aristotle criticises the Platonic identification of the Forms with numbers. ‘If the Forms are numbers, how can they be causes,’ he asks (991b9). Speaking of himself as a Platonist, he says: ‘When we wish to reduce substances to their principles (boulomenoi de tas ousias anagein eis tas archas), we state that lines come from short and long (i. e. from a kind of small and great), and the plane from the broad and narrow, and body from the deep and shallow (992a10-13) … from what principle will the presence of the points in the line be derived (hai stigmai ek tinos enuparxousin)? Plato even used to object to this class of things (toutȏi men oun tȏi genei kai diemacheto Platȏn) as being a geometrical fiction (hȏs onti geȏmetrikȏi dogmati). He gave the name of principle of line (all ekalei archên grammês) – and this he often posited (touto de pollakis etithei) – to the indivisible lines (tas atomous grammas) (992a19-22, tr. W. D. Ross).’
Ross comments: ‘The imperfects diemacheto (‘used to object’), ekalei (‘gave the name’), etithei (‘posited’) indicate that Aristotle is thinking of frequently repeated oral teaching of Plato … The imperfects probably also indicate that Book A was written after Plato’s death in 348-347.’ (Aritotle’s Metaphysics, A revised text with Introduction and Commentary by W. D. Ross, Oxford, Clarendon Press, 1997, vol. I, p. 207). Pace Ross, the imperfects may equally well indicate that Plato left his Academy having gone to Sicily on his third journey, where he intended to stay to the end of his days.
The same can be said of the aorist ȏiêthê (‘thought’) and the imperfect elege (‘agreed in saying’) in an earlier passage in Book A where Aristotle speaks of Plato’s oral teaching: ‘Since the Forms were the causes of all other things (epei d’ aitia ta eidê tois allois), he thought (ȏiêthê ) their elements were the elements of all things. As matter, the great and small were principles; as essential reality, the One; for from the great and the small, by participation in the One, come the Numbers. But he agreed with the Pythagoreans in saying (paraplêsiȏs tois Puthagoreiois elege) that the One is substance and not a predicate of something else’ (987b22-24, tr. Ross).
Concerning Plato’s rejection of points as a geometrical fiction Ross remarks: ‘The point, if it was to be real, should have been a combination of form and matter. Now a matter could be assigned to the line, the plane, and the solid (the long and short &c.), but no such matter could be assigned to the point, since it had no dimensions at all. We have, however, no evidence to show that this difficulty was in Plato’s mind.’ (Ross, p. 207)
Aristotle’s tithemen (‘we state’) at 992a11 clearly indicates that Plato at the time of writing Book A considered himself as a member of the school. In the same vein, using the first person plural, Aristotle speaks as a Platonist throughout his critical remarks on the views prevalent in the Academy at that time. At 990b8-17 he says: ‘Of the ways in which we prove that the Forms exist (kath’ hous tropous deiknumen hoti esti ta eidê), none is convincing (kat’ outhena phainetai toutȏn); for from some no inference necessarily follows, and from some arise Forms even of things of which we think there are no Forms (ex eniȏn de kai ouch hȏn oiometha toutȏn eidê gignetai) … according to the ‘one over many’ (kai kata to hen epi pollȏn) argument there will be Forms even of negations … of the more accurate arguments (hoi akribesteroi tȏn logȏn), some lead to Ideas of relations (hoi men tȏn pros ti poiousin ideas), of which we say there is no independent class (hȏn ou phamen einai kath’ hauto genos), and others introduce ‘the third man’ (hoi de triton anthrȏpon legousin).’ (Tr. Ross)
Ross notes ‘It is quite clear that Platonism soon departed from the doctrine of the Republic (596 A) that there is an Idea answering to every group of things.’ At 596 A Socrates tells Glaukon: ‘Let us begin the enquiry (arxȏmetha episkopountes) in our usual manner (ek tês eiȏthuias methodou): We posit a Form, one each (eidos gar pou ti hen hekaston eiȏthamen tithesthai), for each group of many things (peri hekasta ta polla) to which we give the same name (hois t’auton onoma epipheromen).’ For the Forms of negations Ross refers to Republic 402 C where Socrates refers to virtues, such as sȏphrosunê (temperance, prudence, self-control), andreia (courage), eleutheriotês (liberality, generosity) and megaloprepeia (magnificence) and their opposites (ta toutȏn au enantia), as Forms (eidê). – Concerning this point, one might argue against Ross that the opposites of virtues are vices, such as aphrosunê, aneleutheriotês, which have a specific force in determining behaviour; they are not just negations.
Concerning the Forms of relations Ross refers to Phaedo 74 A where Socrates speaks of ‘the equal itself’ (auto to ison), 75 C where he speaks of ‘the equal’, the ‘greater’, ‘the smaller’, and 100 E where he points to ‘largeness’ by which large things are large and larger things are larger, and to ‘smallness’ by which smaller things are smaller. To this may be added Parmenides 129d8 where we find homoiotês ‘likeness’ and anomoiotês ‘unlikeness’, 131c12 auto to megethos ‘largeness itself’, 131d5 auto to ison ‘the equal itself’, d7 to smikron ‘the small’.
At 990b17-22 Aristotle writes: ‘And in general the arguments for the Forms destroy the things for whose existence we are more zealous than for the existence of the Ideas (ha mallon boulometha tou tas ideas einai); for it follows (sumbainei gar) that not the dyad but number is first (mê einai tên duada prȏtên alla ton arithmon), and that the relative is prior to the absolute (kai to pros ti tou kath’ hauto), – besides all the other points on which certain people (kai panth’ hosa tines) by following out the opinions held about the Ideas (akolouthêsantes tais peri tȏn ideȏn doxais) have come into conflict with the principles of the theory (ênantiȏthêsan tais archais).’ (Tr. Ross)
When Aristotle wrote Metaphysics A, the theory of Forms appears to have been hotly discussed, criticised, and profoundly modified even by those Platonists, who accepted the Forms. On the dating that I propose for Metaphysics A – after Plato went on his last journey to Sicily and before he returned to Athens – we may presume that the picture of the Academy he gives in it reflects on the situation in the school not only during Plato’s last stay in Sicily, but even prior to it. Plato went on his second journey to Sicily in 367-6, just at the time when the 17 years old Aristotle entered Plato’s Academy. When Plato was leaving Sicily in 366, his departure was to be short, as he says in the Seventh Letter: ‘I urged Dionysius by all means possible to let me go, and we both made a compact that when peace was concluded (for at that time there was war in Sicily) Dionysius, for his part, should invite Dion and me back again, as soon as he had made his own power more secure; and he asked Dion to regard the position he was now in not as a form of exile but rather as a change of abode; and I gave a promise that upon these conditions I would return. When peace was made he kept sending for me; but he asked Dion to wait still another year, although he kept demanding most insistently that I should come. Dion, then, kept urging and entreating me to make the voyage.’ (338a3-b5, tr. Bury)
It thus appears that after his return from his second journey to Sicily Plato’s thoughts were mainly preoccupied with Dion, with Dionysius, with the prospect of establishing a state in which a philosopher rules, Dionysius becoming a philosopher. In the Seventh Letter Plato says that from his youth he was strongly attracted to politics, looked for a possibility to take part in establishing a true aristocracy, the rule of the best citizens for the good of the whole city: ‘As regards political action I kept constantly waiting for an opportune moment; until, finally … in my praise of the right philosophy (epainȏn tên orthên philosophian) I was compelled to declare (legein te ênangkasthên) that by it (hȏs ek tautês) one is enabled to discern all forms of justice both political and individual (estin ta te politika dikaia kai ta tȏn idiȏtȏn panta katidein). Wherefore the classes of mankind (I said) will have no cessation from evils (kakȏn oun ou lêxein ta anthrȏpina genê) until (prin an) either the class of those who are right and true philosophers (ê to tȏn philosophountȏn orthȏs genos) attains political supremacy (eis archas elthêi tas politikas), or else the class of those who hold power in the States (ê to tȏn dunasteuontȏn en tais polesin) becomes, by some dispensation of Heaven, really philosophic (ek tinos moiras theias ontȏs philosophêsêi). This was the view I held when I went to Italy and Sicily, at the time of my first arrival.’ (325e3-326b6, tr. Bury) It was on that occasion, that he ‘associated with Dion, who was then a youth, instructing him verbally in what I believed was the best for mankind and counselling him to realise it in action’ (327a1-4, tr. Bury).
During the time Plato spent in Athens after his return from Sicily he did his best to keep Dion quiet (hêsuchian agein) and prevent him from attempting any revolution (kai mêden neȏterizein) and from saying anything evil against him to the Greeks (Plutarch, Dion, xvi. 6). Plutarch says that Plato ‘kept Dion with him in the Academy, where he turned his attention to philosophy … Plato desired that Dion’s disposition should be tempered and sweetened by association with men of charming presence who indulged seasonably in graceful pleasantries. And such a man was Speusippus [Plato’s nephew who after Plato’s death succeeded him as the head of the Academy]; wherefore Timon, in his Silli spoke of him as “good at jest”. And when Plato himself was called upon to furnish a chorus of boys, Dion had the chorus trained and defrayed all the expense of its maintenance … ‘(Plutarch, Dion xvii. 1-5, tr. Bernadotte Perrin)
As can be seen from Aristotle’s Metaphysics A, the theory of Forms as such was exposed to criticism, and as can be seen from the Parmenides, instead of attempting to defend the Forms by arguments, he simply believed that those who are by nature capable of seeing the Forms, will in the end see them in spite of all the arguments against their existence and knowability. On the testimony of the Second Letter Plato avoided discussing the Forms with Dionysius, for he does not mention them when he speaks of the nature of the First where we might expect them mentioned: ‘The matter stands thus: Related to the King of All are all things, and for his sake they are, and of all things fair He is the cause (kai ekeino aition hapantȏn tȏn kalȏn). And related to the Second are the second things; and related to the Third are the third. About these, then, the human soul strives to learn, looking to the things that are akin to itself, whereof none is fully perfect. But as to the King and the objects I have mentioned (tou dê basileȏs peri kai hȏn eipon), they are of quite different quality (ouden esti toiouton). In the next place the soul inquires – “Well then, what quality have they (alla poion ti mên)?” But the cause of all the mischief, O son of Dionysius and Doris, lies in this very question, or rather in the travail which this question creates in the soul; and unless a man delivers himself from this he will never attain the truth. You, however, declared to me in the garden, under the laurels, that you had formed this notion yourself and that it was a discovery of your own.’ (312e1-313b1, tr. Bury).
When Plato speaks here of all things fair of which the King/the Good is the cause – ‘the objects I have mentioned’ (peri hȏn eipon) at 313a1 refers to ‘all things fair’ at 312e3 – we are reminded of the passage in Republic VI where he says that the Good is not only the cause of knowing the entities that can be known (only the Forms can be known in this sense) but is the cause of their being and there substance (alla kai to einai te kai tên ousian hup’ ekeinou autois einai, 509b6-8). But while in the Republic passage Plato clearly speaks about the Forms, in the Second Letter passage he avoids speaking about them, as he did in his discussion with Dionysius in the garden under the laurels to which he refers; had he discussed the Forms, Dionysius would hardly have claimed that it was his own discovery.
All this can help us to better understand and take more seriously the passage ‘I myself have never yet written on these subjects, and no treatise by Plato exists or will exist, but those which now bear his name belong to a Socrates who became fair and young (314c2-4, tr. Bury)’ in the Second Letter. On this passage Bury notes: ‘This curious statement seems based on Ep. vii. 342c, combined perhaps with an allusion to the Parmenides.’
Plato’s primary concern in writing this statement was to prevent Dionysius from publishing what he told him during their discussion ‘on the nature of the First’ and the passage in the Seventh Letter to which Bury refers was motivated by similar concerns. Speaking of ‘the test’ to which he subjected Dionysius on his last stay with him, Plato says: ‘I did not expound the matter fully (panta men oun out egȏ diexêlthon), nor did Dionysius ask me to do so (oute Dionusius edeito)… And I am even told that later on (husteron de kai akouȏ) he himself wrote a treatise (gegraphenai auton) on the subjects in which I then instructed him (peri hȏn tote êkouse)… I know indeed that certain others have written on these same subjects (allous men tinas oida gegraphotas peri tȏn autȏn toutȏn) … it is impossible, in my judgement at least, that these men should understand anything about this subject (toutous ouk estin kata ge tên emên doxan peri tou pragmatos epaiein ouden). There does not exist, nor will there ever exist, any treatise of mine dealing therewith (oukoun ge peri autȏn estin sungramma oude mêpote genêtai). For it does not at all admit of verbal expression like other studies (rêton gar oudamȏs estin hȏs alla mathêmata), but, as a result of continued application to the subject itself and communion therewith (all’ ek pollês sunousias gignomenês peri to pragma auto kai tou suzên), it is brought to birth in the soul (en têi psuchêi genomenon) on a sudden, as light that is kindled by a leaping spark (exaiphnês hoion apo puros pêdêsantos exaphthen phȏs), and thereafter nourishes itself (auto heauto êdê trephei).’ (341a8-d2, tr. Bury) At 342a8-343a4 Plato makes it then clear that the ineffable subject to which he thus refers are the Forms; it is in the very nature of the Forms that they cannot be verbally expressed.
The passage 341a8-d2 in the Seventh Letter is closely related to Parmenides 133b4-c1, as I have pointed out in my entry of January 10 ‘Plato’s defence of the Forms in the Parmenides’ in which I expanded on my view that Plato wrote the Parmenides in preparation for his third journey to Sicily, which I expressed in my entry of October 16, 2014 ‘A note on the 3rd book of Aristotle’s Metaphysics’. In the Parmenides Plato presents us a young Socrates discussing a theory of Forms, and Bury is probably right when he believes that there is a connection between it and ‘a Socrates who became fair and young’ in the Second Letter. But if it is so, it does in no way negatively affect the authenticity of the Second Letter; on my dating of the Parmenides, Plato was most likely in the middle of writing it when he composed the Second Letter. The difficulties raised there against the theory of Forms by Parmenides are closely connected with Aristotle’s criticism of the Forms in Metaphysics A. On the dating that I have proposed, Plato’s Second and Seventh Letter, his Parmenides, and Aristotle’s Metaphysics A allow us an insight into Plato’s own thoughts and those of his disciples in the Academy after Plato left Athens for his second and before he returned from his third journey to Sicily.