Part 1 of 2
Addenda to Volume I
I. Plato and Geometry (1957)
In the second edition of this book, I made a lengthy addition to note 9 to chapter 6 (pp. 248 to 253). The historical hypothesis propounded in this note was later amplified in my paper 'The Nature of Philosophical Problems and Their Roots in Science' (British Journal for the Philosophy of Science, 3, 1952, pp. 124 ff.; now also in my Conjectures and Refutations). It may be restated as follows: (1) the discovery of the irrationality of the square root of two which led to the breakdown of the Pythagorean programme of reducing geometry and cosmology (and presumably all knowledge) to arithmetic, produced a crisis in Greek mathematics; (2) Euclid's Elements are not a textbook of geometry, but rather the final attempt of the Platonic School to resolve this crisis by reconstructing the whole of mathematics and cosmology on a geometrical basis, in order to deal with the problem of irrationality systematically rather than ad hoc, thus inverting the Pythagorean programme of arithmetization; (3) it was Plato who first conceived the programme later carried out by Euclid: it was Plato who first recognized the need for a reconstruction; who chose geometry as the new basis, and the geometrical method of proportion as the new method; who drew up the programme for a geometrization of mathematics, including arithmetic, astronomy, and cosmology; and who became the founder of the geometrical picture of the world, and thereby also the founder of modern science — of the science of Copernicus, Galileo, Kepler, and Newton.
I suggested that the famous inscription over the door of Plato's Academy (p. 248, (2)) alluded to this programme of geometrization. (That it was intended to announce an inversion of the Pythagorean programme seems likely in view of Archytas, fragment A, Diels-Kranz.)
In the middle of the last paragraph on p. 249 I suggested 'that Plato was one of the first to develop a specifically geometrical method aiming at rescuing what could be rescued ... from the breakdown of Pythagoreanism'; and I described this suggestion as 'a highly uncertain historical hypothesis'. I no longer think that the hypothesis is so very uncertain. On the contrary, I now feel that a re-reading of Plato, Aristotle, Euclid, and Proclus, in the light of this hypothesis, would produce as much corroborating evidence as one could expect. In addition to the confirming evidence referred to in the paragraph quoted, I now wish to add that already the Gorgias (451a/b; c; 453e) takes the discussion of 'odd' and 'even' as characteristic of arithmetic, thereby, clearly identifying arithmetic with Pythagorean number theory, while characterizing the geometer as the man who adopts the method of proportions (465b/c). Moreover, in the passage from the Gorgias (508a) Plato speaks not only of geometrical equality (cp. note 48 to chapter 8) but he also states implicitly the principle which he was later to develop fully in the Timaeus: that the cosmic order is a geometrical order. Incidentally, the Gorgias also proves that the word 'alogos' was not associated in Plato's mind with irrational numbers, since 465a says that even a technique, or art, must not be alogos; which would hold a fortiori for a science such as geometry. I think we may simply translate 'alogos' as 'alogical'. (Cp. also Gorgias 496a/b; and 522e.) The point is important for the interpretation of the title of Democritus's lost book, mentioned earlier on p. 249.
My paper on 'The Nature of Philosophical Problems' (see above) contains some further suggestions concerning Plato's geometrization of arithmetic and of cosmology in general (his inversion of the Pythagorean programme), and his theory of forms.
Added in 1961
Since this addendum was first published in 1957, in the third edition of this book, I have found, almost by accident, some interesting corroboration of the historical hypothesis formulated above, in the first paragraph under (2). It is a passage in Proclus' commentaries to the First Book of Euclid's Elements (ed. Friedlein, 1873, Prologus ii, p. 71, 2-5) from which it becomes clear that there existed a tradition according to which Euclid's elements were a Platonic cosmology, a treatment of the problems of the Timaeus.
II. The Dating of the Theaetetus (1961)
There is a hint in note 50 (6), to chapter 8, p. 281, that 'the Theaetetus is perhaps (as against the usual assumption) earlier than the Republic'. This suggestion was made to me by the late Dr. Robert Eisler in a conversation not long before his death in 1949. But since he did not tell me any more about his conjecture than that it was partly based on Theaetetus 174e, f. — the crucial passage whose post-Republican dating did not seem to me to fit into my theory — I felt that there was not sufficient evidence for it, and that it was too ad hoc to justify me in publicly saddling Eisler with the responsibility for it.
However, I have since found quite a number of independent arguments in favour of an earlier dating of the Theaetetus, and I therefore wish now to acknowledge Eisler's original suggestion.
Since Eva Sachs (cp. Socrates, 5, 1917, 531 f.) established that the proem of the Theaetetus, as we know it, was written after 369, the conjecture of a Socratic core and an early dating involves another — ^that of an earlier lost edition, revised by Plato after Theaetetus' death. The latter conjecture was proposed independently by various scholars, even before the discovery of a papyrus (ed. by Diels, Berlin, Klassikerhefte, 2, 1905) that contains part of a Commentary to the Theaetetus and refers to two distinct editions. The following arguments seem to support both conjectures.
(1) Certain passages in Aristotle seem to allude to the Theaetetus: they fit the text of the Theaetetus perfectly, and they claim, at the same time, that the ideas there expressed belong to Socrates rather than to Plato. The passages I have in mind are the ascription to Socrates of the invention of induction (Metaphysics 1078b 17-33; cp. 987b1 and 1086b3) which, I think, is an allusion to Socrates' maieutic (developed at length in the Theaetetus), his method of helping the pupil to perceive the true essence of a thing through purging his mind of his false prejudices; and the further ascription to Socrates of the attitude so strongly expressed again and again in the Theaetetus: 'Socrates used to ask questions and not to answer them; for he used to confess that he did not know' (Soph. EL 183b7). (These passages are discussed, in a different context, in my lecture On the Sources of Knowledge and of Ignorance, Proceedings of the British Academy, 46, 1960 (see especially p. 50) which is also separately published by Oxford University Press and is now included in my Conjectures and Refutations.)
(2) The Theaetetus has a surprisingly inconclusive ending, even though it turns out that it was so planned and prepared almost from the beginning. (In fact, as an attempt to solve the problem of knowledge which it ostensibly tries to do, this beautiful dialogue is a complete failure.) But endings of a similarly inconclusive nature are known to be characteristic of a number of early dialogues.
(3) 'Know thyself is interpreted, as in the Apology, as 'Know how little you know'. In his final speech Socrates says 'After this, Theaetetus . . . you will be less harsh and gentler to your associates, for you will have the wisdom not to think that you know what you do not know. So much my art [of maieutic] can accomplish; nor do I know any of the things that are known by others . . . '
(4) That ours is a second edition, revised by Plato, seems likely, especially in view of the fact that the Introduction to the dialogue (142a to the end of 143c) which might well have been added as a memorial to a great man, actually contradicts a passage which may have survived the revision of the earlier edition of this dialogue; I mean its very end which, like a number of other early dialogues, alludes to Socrates' trial as imminent. The contradiction consists in the fact that Euclid, who appears as a character in the Introduction and who narrates how the dialogue came to be written down, tells us (142c/d, 143a) that he went repeatedly to Athens (from Megara, presumably), using every time the opportunity of checking his notes with Socrates, and making 'corrections' here and there. This is told in a way which makes it quite clear that the dialogue itself must have taken place at least several months before Socrates' trial and death; but this is inconsistent with the ending of the dialogue. (I have not seen any reference to this point, but I cannot imagine that it has not been discussed by some Platonist.) It may even be that the reference to 'corrections', in 143a, and also the much discussed description of the 'new style' in 143b-c (see for example C. Ritter's Plato, vol. I, 1910, pp. 220 f.) were introduced in order to explain some deviations of the revised edition from the original edition. (This would make it possible to place the revised edition even after the Sophist.)
III. Reply to a Critic (1961)
I have been asked to say something in reply to the critics of this volume. But before doing so, I should like to thank again those whose criticism has helped me to improve the book in various ways.
Of the others — those I have come across — I feel reluctant to say much. In attacking Plato I have, as I now realize, offended and hurt many Platonists, and I am sorry for this. Still, I have been surprised by the violence of some of the reactions.
I think most of the defenders of Plato have denied facts which, it seems to me, cannot be seriously denied. This is true even of the best of them: Professor Ronald B. Levinson in his monumental book (645 closely printed pages) In Defense of Plato.
In trying to answer Professor Levinson I have before me two tasks of very unequal importance. The less important task — defending myself against a number of accusations — ^will be tackled first (in section A), so that the more important task — replying to Professor Levinson's defence of Plato (in section B) — will not be too much obscured by my personal defence.
A
The portrait of myself painted by Professor Levinson has caused me to doubt the truth of my own portrait of Plato; for if it is possible to derive from a living author's book so distorted an image of his doctrines and intentions, what hope can there be of producing anything like a true portrait of an author born almost twenty-four centuries ago?
Yet how can I defend myself against being identified with the supposed original of the portrait painted by Professor Levinson? All I can do is to show that some at least of the mistranslations, misrepresentations, and distortions of Plato with which Professor Levinson charges me are really non-existent. And even this I can only do by analysing two or three representative samples, taken at random from hundreds: there seem to be more such charges in the book than there are pages. Thus all I can do is to prove that some at least of the most violent accusations levelled against me are baseless.
I should have liked to do this without raising any counter-accusation of misquotation, etc.; but as this has turned out to be impossible, I wish to make it quite clear that I now see that Professor Levinson, like other Platonists, must have found my book not only exasperating, but almost sacrilegious. And since I am that man by whom the offence cometh, I must not complain if I am bitterly denounced.
So let us examine a few of the relevant passages. Professor Levinson writes (p. 273, note 72) of me: 'As with others of whom he disapproves, so here with Critias, Popper has further blackened his character by exaggeration. For the verses cited represent religion, though a fabrication, as being aimed at the general good of society, not at the selfish benefit of the cunning fabricator himself.
Now if this means anything, it must mean that I have asserted, or at least hinted, in the passages quoted by Professor Levinson (that is, pp. 179 and 140 of A, which corresponds to pp. 183-184, and pp. 142-143 of E[1]) that Critias' verses which I have quoted represent religion not only as a fabrication, but as a fabrication 'aimed ... at the selfish benefit of the cunning fabricator himself.'
I deny that I either asserted, or even hinted at, anything of the kind. On the contrary, my concern has been to point out that the 'general good of society' is one of the dominant preoccupations of Plato, and that his attitude in this respect 'is practically identical with that of Critias'. The basis of my criticism is clearly announced at the beginning of chapter 8 (second paragraph) where I write: '"For the benefit of the city", says Plato. Again we find that the appeal to the principle of collective utility is the ultimate ethical consideration. '
What I assert is that this moral principle which posits 'the general good of society' as a moral aim, is not good enough as a basis of ethics; for example, that it leads to lying — 'for the general good of society' or 'for the benefit of the city'. In other words, I try to show that ethical collectivism is mischievous, and that it corrupts. But I nowhere interpret Critias' quoted verses in the sense alleged by Professor Levinson. I should be inclined to ask 'Who blackens whose character by exaggeration?', were it not for the fact that I recognize that the severity of my attack was a provocation which excuses Professor Levinson's charges. But it does not make them true.
A second example is this. Professor Levinson writes (pp. 354 f.): 'One of Popper's most extravagant assertions is that Plato had viewed as a "favourable circumstance" the presence in Athens of Spartan troops, summoned to assist the Thirty in maintaining themselves and their iniquitous regime and had felt no other emotion than approval at the thought of Athens beneath the Spartan yoke; he would have been prepared, we are led to suppose, to summon them again, if their presence could aid him in achieving his neooligarchical revolution. There is no text which Popper can cite in support of such a charge; it arises solely from his picture of Plato as a third head upon the double-headed monster he has created, called "the Old Oligarch and Critias"; it is guilt by association, the very ultimate example of the witch-hunt technique.'
To this my reply is: if this is one of my 'most extravagant assertions', then I cannot have made any extravagant assertions. For this assertion was never made by me; nor does it fit into the picture which I have of Plato, and which I have tried — not wholly successfully, it seems — to convey.
I do believe that Plato was led, by his distrust of the common man, and by his ethical collectivism, to approve of violence; but I simply never have made any assertion about Plato even faintly similar to the one which Professor Levinson here asserts, somewhat extravagantly, that I have made. There is therefore no text which Professor Levinson can cite in support of his charge that I have made this assertion: it arises solely from his picture of Popper as a third head upon the double-headed monster of Otto Neurath and J. A. Lauwerys which Professor Levinson has created; and as to 'guilt by association', I can only refer to Professor Levinson's p. 441. There he is 'helped towards answering this question' — the question of 'the predisposing cause that leads Popper chronically to indulge these sinister imaginings' — by associating me with 'an older compatriot of Popper's, the late versatile Austrian philosopher and sociologist, Otto Neurath'. (In fact neither Neurath nor I had any sympathy for the other's philosophy, as emerges only too clearly from Neurath's and my own writings; Neurath, for example, defended Hegel, and attacked both Kantianism and my own praise of Kant. Of Neurath's attack on Plato I heard for the first time when I read about it in Professor Levinson's book; and I have not yet seen Neurath's relevant papers.)
But to return to my alleged 'extravagant assertion': what I actually said (p. 195E = 190A) about Plato's feelings is almost the opposite of what Professor Levinson (p. 354) reports. I did not at all suggest that Plato viewed as a 'favourable circumstance' the presence in Athens of Spartan troops, or that he 'felt no other emotion than approval at the thought of Athens beneath the Spartan yoke'. What I tried to convey, and what I said, was that the Thirty Tyrants had failed 'in spite of favourable circumstances in the shape of powerful support from victorious Sparta'; and I suggested that Plato saw the cause of their failure — just as I do — in the moral failure of the Thirty. I wrote: 'Plato felt that a complete reconstruction of the programme was needed. The Thirty had been beaten in the realm of power politics largely because they had offended the citizens' sense of justice. The defeat had been largely a moral defeat.'
This is all I say here of Plato's feelings. (I say twice 'Plato felt'.) I suggest that the failure of the Thirty induced a partial moral conversion in Plato — though not a sufficiently far-reaching one. There is no suggestion here of those feelings which Professor Levinson makes me attribute to Plato; and I would never have dreamt that anybody could read this into my text.
I certainly do attribute to Plato a measure of sympathy with the Thirty Tyrants and especially with their pro- Spartan aims. But this is of course something completely different from the 'extravagant assertions' which Professor Levinson attributes to me. I can only say that I did suggest that he admired his uncle Critias, the leader of the Thirty. I did suggest that he was in sympathy with some of Critias' aims and views. But I also said that he considered the oligarchy of the Thirty as a moral failure, and that this led him to reconstruct his collectivist morality.
It will be seen that my answer to two of Professor Levinson' s charges has taken up almost as much space as the charges themselves. This is unavoidable; and I must therefore confine myself to only two further examples (out of hundreds), both connected with my alleged mistranslations of Plato's text.
The first is Professor Levinson's allegation that I worsen, or exaggerate, Plato's text. 'Popper, however, as before, employs the unfavourable word "deport" in his translation, in place of "send out",' writes Professor Levinson on p. 349, note 244. But this is simply a mistake — Professor Levinson's mistake. If he looks at the passage again, he will find that I employ the word 'deport' where his translation — or rather Fowler's — uses 'banish'. (The part of the passage in which Fowler's translation uses 'send out' simply does not occur in my quotation but is replaced by dots.)
As a consequence of this mistake, it turns out that, in this context. Professor Levinson's remark 'as before' is highly appropriate. For before the passage just discussed he writes of me (p. 348, note 243): 'Popper reenforces his interpretation [p. 166E = p. 162A] of the Platonic passage [Rep. 540e/541a] by slight inaccuracies in the translation, tending to give the impression of greater scorn or violence in Plato's attitude. Thus he translates "send away" (apopempo) as "expel and deport" . . . ' Now first of all, there is another of Professor Levinson's slips here (which makes two in two consecutive footnotes); for Plato does not use here the word 'apopempo', but the word 'ekpempo'. This certainly does not make much difference; yet 'ekpempo' has, at any rate, the 'ex' of ' expel'; and one of its dictionary meanings is 'to drive away' and another 'to send away in disgrace' (or 'to send away with the collateral notion of disgrace' as my edition of Liddell and Scott has it). The word is a somewhat stronger form of 'pempo' — 'to send off, 'to dispatch' — which, if used in connection with Hades ('to send to Hades') 'commonly means to send a living man to Hades, i.e. to kill him'. (I am quoting Liddell and Scott. Nowadays some people might even 'commonly' say 'to dispatch him'. Closely related is the meaning intended when Phaedrus tells us in Plato's Symposium 179e — a passage referred to by Professor Levinson on p. 348 — that the gods, redeeming and honouring Achilles for his valour and his love of Patroclus, 'sent him to the Islands of the Blessed' — while Homer sent him to Hades.) It seems obvious that neither of the translations 'expel' or 'deport' is open to criticism here on scholarly grounds. Yet Professor Levinson is open to criticism when he quotes me as writing 'expel and deport' for I do not use the words in this way. (He would have been at least technically correct had he quoted me 'must be expelled ... and deported': the three dots make some difference here, for to write 'expel and deport' could be an attempt to exaggerate, by way of 're- enforcing' the one expression with the other. Thus this slight inaccuracy tends to re-enforce my alleged misdeed — my alleged re-enforcing of my interpretation of this Platonic passage by slight inaccuracies in my translation.)
But anyhow, this case amounts to nothing. For take the passage in Shorey's translation. (Shorey is, rightly, accepted as an authority by Professor Levinson.) 'All inhabitants above the age of ten', Shorey translates, 'they [the 'philosophers' who have become 'masters of the state'] will send out into the fields, and they will take over the children, remove them from the manners and habits of their parents, and bring them up in their own customs and laws which will be such as we have described.' Now does this not say exactly what I said (though perhaps not quite as clearly as I did on my p. 166E = 162A)? For who can believe that the 'sending out' of 'all the inhabitants above the age of ten' can be anything but a violent expulsion and deportation? Would they just meekly go, leaving their children behind, when 'sent out', if they were not threatened, and compelled, by the 'philosophers' who have become 'masters of the state'? (Professor Levinson's suggestion, p. 349, that they are sent to 'their . . . country estates, outside the city proper' is supported by him, ironically enough, with a reference to the Symposium 179e and the 'Islands of the Blessed', the place to which Achilles was sent by the gods — or more precisely by Apollo's or Paris 's arrow. Gorgias, 526c, would have been a more appropriate reference.) In all this, there is an important principle involved. I mean the principle that there is no such thing as a literal translation', that all translations are interpretations; and that we always have to take the context into account, and even parallel passages.
That the passages with which (on p. 166E = p. 162A) I have associated the one just quoted may indeed be so associated is confirmed by Shorey's own footnotes: he refers, especially, to the passage which I have called the 'canvas-cleaning' passage, and to the 'kill-and-banish' passage from the Statesman, 293 c-e. 'Whether they happen to rule by law or without law, over willing or unwilling subjects; ... and whether they purge the state for its good, by killing or by deporting [or, as Professor Levinson translates with Fowler, 'by killing or banishing'; see above] some of its citizens . . . this form of government must be declared to be the only one that is right.' (See my text, p. 166E = p. 162A.)
Professor Levinson quotes (p. 349) part of this passage more fully than I do. Yet he omits to quote that part which I quoted as its commencement, 'Whether they happen to rule by law or without law, over willing or unwilling subjects'. The point is interesting, because it fits Professor Levinson's attempt to make the kill-and-banish passage appear in an almost innocent light. Immediately after quoting the passage. Professor Levinson writes: 'Fair interpretation of this stated principle [I do not see any 'principle' here stated, unless it is that all is permitted if it is done for the benefit of the state] requires at least a brief indication of the general pattern of the dialogue.' In the course of this 'brief indication' of Plato's aims and tendencies, we hear — without a direct quotation from Plato — that 'Other traditional and currently accepted criteria, such as whether rule be exercised ... over willing or unwilling subjects, or in accord or not in accord with law, are rejected as irrelevant or non-essential'. The words from Professor Levinson's passage which I have here italicized will be seen to be a near-quotation of the commencement (not quoted by Professor Levinson) of my own quotation from Plato's kill-and-banish passage. Yet this commencement appears now in a very harmless light: no longer are the rulers told to kill and banish 'with or without law,' as I indicated; and Professor Levinson's readers get the impression that this question is here merely dismissed as a side issue — as 'irrelevant' to the problem in hand.
But Plato's readers, and even the participants in his dialogue, get a different impression. Even the 'Younger Socrates', who intervened just before (after the commencement of the passage as quoted by me) with the one exclamation 'Excellent!' is shocked by the lawlessness of the proposed killing; for immediately after the enunciation of the kill-and-banish principle (perhaps it really is a 'principle', after all) he says, in Fowler's translation (the italics are of course mine): 'Everything else that you have said seems reasonable; but that government [and such hard measures, too, it is implied] should be carried out without laws is a hard saying.'
I think that this remark proves that the commencement of my quotation — 'by law or without law' — is really meant by Plato to be part of his kill-and-banish principle; that I was right in commencing the quotation where I did; and that Professor Levinson is simply mistaken when he suggests that 'with or without law' is here merely intended to mean that this is a question which is here 'rejected as irrelevant' to the essence of the problem in hand.
In interpreting the kill-and-banish passage, Professor Levinson is clearly deeply disturbed; yet at the end of his elaborate attempt to defend Plato by comparing his practices with our own he arrives at the following view of the passage: 'Looked at in this context, Plato's statesman, with his apparent readiness to kill, banish, and enslave, where we should prescribe either the penitentiary, at one end, or psychiatric social service, at the other, loses much of his sanguinary coloration.'
Now I do not doubt that Professor Levinson is a genuine humanitarian — a democrat and a liberal. But is it not perturbing to see that a genuine humanitarian, in his eagerness to defend Plato, can be led to compare in this fashion our admittedly very faulty penal practices and our no less faulty social services with the avowedly lawless killing and banishing (and enslaving) of citizens by the 'true statesman' — a good and wise man — 'for the benefit of the city'? Is this not a frightening example of the spell which Plato casts over many of his readers, and of the danger of Platonism?
There is too much of this — all mixed with accusations against a largely imaginary Popper — for me to deal with. But I wish to say that I regard Professor Levinson's book not only as a very sincere attempt to defend Plato, but also as an attempt to see Plato in a new light. And though I have found only one passage — and quite an unimportant one — which has led me to think that, in this place, I interpreted Plato's text (though not his meaning) somewhat too freely, I do not wish to create the impression that Professor Levinson's is not a very good and interesting book — especially if we forget all about the scores of places where 'Popper' is quoted, or (as I have shown) slightly misquoted, and very often radically misunderstood.
But more important than these personal questions is the question: how far does Professor Levinson's defence of Plato succeed?
B
I have learnt that when faced with a new attack on my book by a defender of Plato it is best to disregard the smaller points and to look for answers to the following five cardinal points.
(1) How is my assertion met that the Republic and the Laws condemn the Socrates of the Apology (as pointed out in chapter 10, second paragraph of section vi)? As explained in a note (note 55 to chapter 10) the assertion was in effect made by Grote, and supported by Taylor. If it is fair — and I think it is — then it supports also my assertion mentioned in my next point, (2).
(2) How is my assertion met that Plato's anti-liberal and anti-humanitarian attitude cannot possibly be explained by the alleged fact that better ideas were not known to him, or that he was, for those days, comparatively liberal and humanitarian?
(3) How is my assertion met that Plato (for example in the canvas-cleaning passage of the Republic and in the kill-and-banish passage of the Statesman) encouraged his rulers to use ruthless violence 'for the benefit of the state'?
(4) How is my assertion met that Plato established for his philosopher kings the duty and privilege of using lies and deceit for the benefit of the city, especially in connection with racial breeding, and that he was one of the founding fathers of racialism?
(5) What is said in answer to my quotation of the passage from the Laws used as a motto for The Spell of Plato on p. 7 (and, as announced at the beginning of the Notes on p. 203, 'discussed in some detail in notes 33 and 34 to chapter 6')?
I often tell my students that what I say about Plato is — necessarily — merely an interpretation, and that I should not be surprised if Plato (should I ever meet his shade) were to tell me, and to establish to my satisfaction, that it is a misrepresentation; but I usually add that he would have quite a task to explain away a number of the things he had said.
Has Professor Levinson succeeded on Plato's behalf in this task, regarding any of the five points mentioned above?
I really do not think he has.