At some time in the course of his life Plato acquired such thorough knowledge of mathematics that he was able to associate in the Academy on easy terms with the finest mathematicians of his time, sharing and abetting their enthusiasm for their work. The Academicorum Philosophorum Index Herculanensis (ed. Mekkler, p. 17) goes so far as to picture Plato as “masterminding” (ἀρχιτεκτον) the researches of his mathematical colleagues. This we may discount as eulogistic blow-up. Not so its further statement that Plato “set problems” to the mathematicians. Elsewhere I have argued for the credibility of the well-known report in Simplicius:

There is no good reason to doubt that Plato had been the first to project the idea that the apparently inconstant motions of the planets could be accounted for by compositions of invariantly constant circular motions proceeding in different planes, directions, and angular velocities. If Plato could hit on this powerful and fertile notion which “under the name of the Platonic axiom was to dominate theoretical astronomy for twenty centuries” and could propound it in a form which would strike Eudoxus and other practicing mathematical astronomers not as a pretty fancy but as a workable hypothesis, he must have been accepted by them as no dabbler in their business but as a student of their subject who understood it so well that his vision of progress in it might even be at certain points ahead of theirs.

At the start of the preceding chapter I staked out the claim that through a “Socrates” in Plato we can come to know the thought of the Socrates of history. By the end of the present chapter the reader should be in a fair position to judge if I am making that claim stick.

Let this much be agreed before I start: much as I need Plato's witness, I could not do the job if I had only his. The most we could learn from his writings is that in different periods of his life he puts into the mouth of Socrates philosophies which are not only different but, in important respects, antithetical. And that of itself would not give a particle of support to my claim. For there is no intrinsic reason why both of these philosophies, despite their polar differences, could not have been Plato's own original creations at different periods of his life. Within the present century we have seen a spectacular illustration of such a shift. In his Tractatus Wittgenstein produced a startlingly original philosophy and published it with the confidence that it would be his last word – indeed the last word – on the subject, announcing in the Preface: “The truth of the thoughts communicated in this work seems to me uncontestable and definitive.

A second inquiry by Arnim rivalled Lutoslawski's for the title of the most maligned work in the history of the stylistic method. This seems rather ironical in view of the fact that its express aim was to endow the chronological conclusions previously arrived at by the stylistic method with such a conclusive force that ‘any opposition would be impossible’. As it was, they did not have this force, simply because they were not absolute. In other words, while they showed that it was probable that certain dialogues belonged together by reason of a common possession of particular stylistic features, they did not show that different groupings according to other features were impossible. Although scholars had found, for instance, that a large number of features connected Soph, and Pol. to the Phil., Tim. and Laws and had consequently assumed their temporal proximity, they had never thought of investigating how many features connected these same two dialogues to, say, Hipp. Mi., Phdo and Crat. Yet it was theoretically possible that such an investigation would unearth a larger number of features than in the former case, and the whole chronological order would have to be revised.

This was the doubt which Arnim wished to eliminate. It meant that every dialogue would have to be compared with every other dialogue, a task which would occupy the lifetimes of several investigators, if the material were to be every possible feature of style. However, it did not have to be, since there existed a smaller, yet self-contained body of material to work on in the reply formulae.

Before the true genesis of the stylistic method in Germany at the hands of Dittenberger, an isolated but important observation was made which, like Campbell's, appears to have passed for the most part unnoticed. In his work on rhetoric1 Blass remarked almost incidentally that in striking contrast to his earlier practice Plato eventually adopted Isocrates’ principle of avoiding hiatus.

It is in the Phdr., at least in the dialogue part, that this avoidance of hiatus first becomes noticeable, since scarcely half as many instances occur as, for example, in the Symp. and Rep. At the same time, Blass pointed out, there is no need to put the Phdr. among Plato's last works, since a certain leaning towards Isocrates, who is mentioned in the dialogue, was only to be expected.

In the Laws, however, hiatus is very definitely avoided, so that in book i for example there are only just over ioo instances on 34 pages (Teubner). Next comes the Phil, with hardly on average 2 instances per page. Finally, in Tim. (87 pages) there are about 50, in Crit. only 5, in Soph. (82 pages) 20, and in Pol. (83 pages) 11.

Blass inferred that Soph., Pol., Phil., Tim. and Crit. belong with the Laws to the last period of Plato's literary career. Both his statistics and his deductions were later confirmed in their broad lines by G. Janell (q.v.) who drew up exact figures of hiatus for the majority of the dialogues.

A comparison of Blass's results with Campbell's makes it immediately apparent that they provide mutual support. The two investigators employed entirely different methods, yet arrived at exactly the same conclusion.

Tiemann's articles have already been referred to in the chapter on Ritter, with whose work they are closely connected, the third being a review of his book. The second, relating to certain reply formulae investigated by Ritter, was intended partly to clarify the statistics for individual formulae which Ritter had combined in groups, partly to correct his figures (Table i I.I p. 88). For the reason mentioned previously (p. 56), it is difficult in the case of reply formulae to declare categorically that one investigator's data are correct, another's incorrect, but Tiemann appears to have been more consistent than Ritter in his specifications.

There are, Tiemann said, three things worth noting in the statistics.

1. (a) Formulae with ὀρθῶς are very rare in the first period, only ὀρθῶς λέγεις being found, 5 times in all. The same formulae are more frequent in the second period, still more so in the third.

2. (b) Almost only the formulae with λέγεις are used in the first period. In the dialogues of the other two periods the percentage of formulae without λέγεις in relation to the total is as follows: Theaet. 58, Phdr. 20, Rep. 74, Soph. 76, Pol. 87, Phil. 65, Laws 41.

3. The small percentage in the Phdr.> Tiemann explained, is of no significance, since the total of 5 formulae hardly permits any comparison. On the other hand the considerable decrease in the Laws is very remarkable, and we should perhaps recognise it as a sign of increasing prolixity of expression.

4. […]

In an article which was the first contribution to the stylistic method from France and the last example of unwitting repetition of work already done Baron expressed surprise that no one had thought of investigating Plato's use of the anastrophe πέρι. Ironically enough, the book which would have informed him of Lina's earlier research on this subject was actually in the process of being published.

Whereas Lina drew no chronological conclusions from his material, Baron intended to do so by measuring the total number of πέρι in each dialogue against that of πɛρί on the basis that each occurrence of πɛρί represented an opportunity for the use of anastrophe. Obviously, however, if the ratios thus obtained were to be truly accurate, any instances of πɛρί which did not afford an opportunity for the substitution of πέρι would first have to be deducted from the total. Such instances, according to Baron, were as follows:

1. The expression, πɛρὶ πολλοῦ, πλείονος, πλείστου ποιεῖσθαι etcc., for which not a single instance of anastrophe can be quoted.

2. The use of πɛρί in a phrase qualifying either a substantive (e.g. ὁ πɛρὶ τῆς ψυχῆς λόγος) or a substantival article (e.g. τὰ πɛρὶ τῆς ψυχῆς) Instances of anastrophe in these cases do occur, but only rarely and mostly in works of the last period. There are certainly none at all in dialogues of the first period, the earliest example perhaps being Rep.iii 39206, τὰ μὲν δὴ λόγων πέρι.

Finally Baron also declared his intention of discounting all instances of πɛρι occurring in myths on the grounds that the anastrophe is ‘never once found in a myth’.

The present book originates from my Ph.D. thesis, a critical survey of attempts to determine the order of composition of Plato's works by analysing their style, which has been brought up to date by the inclusion of two investigations carried out since that time. On the other hand, several investigations in the thesis have now been omitted, as they seemed to be of only slight significance. The idea of including an account of research on questions of authenticity was rejected as likely to lead to a volume of increased complexity and unmanageable proportions; although closely connected with the problem of chronology, that of authorship provides sufficient material to justify separate treatment.

In a work of this nature the accuracy of the statistics is of paramount importance, and the opportunity has been taken to check them, wherever feasible, with the Word Index which is now available. It should be remembered, however, that this relates to Burnet's Oxford text, which did not exist when most of the research described was carried out, so that some statistical discrepancies may have arisen from different textual readings rather than from careless observation. Nevertheless, as anyone will know who has tried to record by hand the incidence of words or phrases in a text, complete accuracy is almost impossible to attain, and the fact that checks generally revealed only small errors is a tribute to the painstaking diligence and dedication of the scholars concerned.

By a strange coincidence the two other investigations published in 1888 both introduced the same new material independently, as it seems, of one another. The surprising thing is that it took the scholars of Germany seven years to hit upon this rich linguistic field of reply formulae, even though Dittenberger had previously touched its brink with his observations on τί μήν; The works were those of H. Siebeck and C. Ritter, the latter's being by far the larger and more accurate.

Siebeck's was not an independent article but an appendix (pp. 253ff.) to the second edition of his book. Moreover its results were not intended to stand by themselves, merely to support where possible those obtained by the comparison of the dialogues’ contents, which were presented earlier in the book in the chapter on Plato. Just as the value he placed on his language statistics was of a secondary nature, so too apparently was the care with which he produced them.

The rules which he laid down for the application of these statistics to the determination of the chronological order of the dialogues were practical and precise. The subject of his inquiry was twofold; (a) simple, direct questions, i.e. those that can be answered by ‘yes’ or ‘no’, (b) answers conveying assent. His method was to take the total number of instances of each particular expression in a dialogue, then calculate the percentage of its occurrence in relation to the aggregate of all the instances in that particular category, either (a) or (b). On the differences between these percentages in the various dialogues were based the conclusions regarding chronology.

The year 1889 saw the appearance of a second stylistic inquiry. It is fairly slight, concerning the forms of verbs used to refer to something already said in the dialogue, and not all of these, but only certain past tenses of the passive. There are five types: (a) ἐρρήθη and ῥηθείς (Table 12.1 on p. 93, where these forms are also expressed as a percentage of the total number of references, (b) ἐλέχθη and λεχθείς, (c) προερρήθη and προείρηται together with their participles, (d) λεχθείς and λεχθεῖσα used as an adjective, (e) the perfect passive of λέγω. In the case of the last two types, however, not just instances in references, but all occurrences are reckoned, including the imperative of the perfect passive of λέγω. A further point which should be made is that the reference totals are composed solely of references to the argument, and do not include any except such as go back to full, complete statements of the persons engaged in the discussion. Thus all words are omitted which refer to quotations of poetry, of tradition, or of any composition not original to the speakers of the dialogue. The only exception is the oration of Lysias in the Phdr. This is regarded as a component part of the dialogue, because it is read in full by Phaedrus and plays a prominent part in the succeeding discussion. In the whole argument Phaedrus himself acts as a passive listener and the opinions considered belong either to Socrates or Lysias.

The statistics can probably be accepted as accurate; at least a check of those for the five types in the Phil, showed them to be all correct.

Dittenberger's research, as novel in Germany as Campbell's in Britain, provoked an immediate and sarcastic retort from A. Frederking in an article bearing the same title. In his view the stylistic method was a dangerous weapon requiring proper application, if it was to be of any service, and this was exactly what it had not received. It is by no means a foregone conclusion, he remarked, that an author's language has such a symmetrical development and is in every single work so perfectly in harmony with this development at its particular stage as Dittenberger was inclined to assume. It changes not only in accordance with the different period of the composition of individual works, but also within the same period according to the content and form of the work, the degree of logical and artistic perfection, and the character of the persons taking part in the dialogue, as well as for various other reasons which may conveniently be collected under the one name of ‘chance’.

This applies especially to particles, he said; if a particle is not used in some work, above all a small one, nothing at all can be deduced from its absence; nor can anything be gathered about the frequency of a particle in general from its more or less frequent occurrence in a single work; the opportunity for using it could be either entirely lacking or seldom offered. Frederking proceeded to illustrate his argument from some of the observations made by his predecessor.

Ritter was the first to write a book on the stylistic method and its use in determining the chronology of the dialogues. All previous investigations were either articles in periodicals or parts of theses and other works on Plato of a general character. Not only was it the first book, but also the largest collection of linguistic data up till that time.

His main inquiry, as mentioned in the chapter on Siebeck, was into answer formulae, but in addition to this he investigated the use of well over a hundred expressions of different kinds, though many of these turned out to be of no value for chronological purposes, and he did not therefore trouble to publish the actual statistics. As the number of facts presented is so large, the best arrangement will be to reverse Ritter's procedure of discussing the individual items and finally reproducing them all in statistical tables; that is to say, to give these tables first (pp. 58–62) and leave the examination of their results till afterwards. The first table contains the reply formulae, the second other expressions which Ritter believed to be chronologically noteworthy. In the latter are also included the phrases and words which were investigated by Ritter's two most important predecessors, Dittenberger and Schanz.

The first question is whether the statistics are accurate or not. As in the case of Siebeck, answering it is rather difficult, only this time it is not so much the problem of classifying the reply formulae into three acceptable groups, but of deciding the exact constitution and limit of each formula to be counted.

It will be convenient at this point to depart from the chronological order of research, in order to treat together two investigators both of whom examined the rhythm of Plato's prose and arrived at similar conclusions. A separate account of each can then be followed by a common appreciation of their results.

The aim of Kaluscha's investigation was to ascertain which dialogues exhibited a clear prose rhythm or rhythms, then to deduce from a comparison of these their temporal relation to one another. For this purpose his concept of rhythm was a purely practical one; he confined himself to investigating the part of the sentence considered in antiquity to be the most important rhythmically, namely the clausula, which he interpreted as the end of a period or colon. Furthermore this was regarded as consisting of five syllables only, thus producing thirty-two different types, into which all the sentence endings were to be classified. Lastly, in order to make his data as unobjectionable as possible, he observed the following principles.

1. Clausulae containing a word ending in a long vowel before a word beginning with a vowel were omitted.

2. Similarly those in which a short vowel was followed by a combination of mute and liquid consonants.

3. The last syllable of the clausula was not regarded as anceps.

4. Two short syllables together were not reckoned as the equivalent of a long one.

The investigation fell into two parts. The first examined the clausulae of the Laws to establish the truth or otherwise of Blass's belief that under Isocrates’ influence Plato began to prefer certain rhythms to others.

The next contribution to the progress of the stylistic method was rather slight, the reason being that it came from the author of a dissertation, whose interest, primarily philological, was only incidentally concerned with the chronology of Plato's dialogues. Kugler's criticism of Dittenberger has already been mentioned, but in addition to this he made use of the statistics of τoι which he had compiled to attempt his own solution of the problem. The chronological divisions marked in his tables (pp.29–30) are those of Dittenberger, the three dialogues omitted by the latter being added at the top. At the same time an advance is made over previous work in the separate treatment of individual books of the Rep. and Laws, though the way had already been pointed out by Frederking.

Kugler's figures have not all been verified, but a sample test (Thesis p. 53) showed them to be reasonably accurate. Referring to his tables he noted:

1. The ratio of μέντοι to τοινυν varies considerably.

2. This reaches its extreme in Rep. vni and Laws v, vm, xi, where μέντοι is missing altogether.

3. In some dialogues there is a greater variety in the combinations of xoi than in others. In Tim. and Crit. there is only one type, in Laws books I, V, VI, XI, XII only two, in Rep. VIII and Laws VIII, IX three; in the Gorg. by contrast there are eight.

4. […]

Following closely on Baron's article came an account of stylistic research carried out by the Polish scholar W. Lutoslawski in conjunction with his study of Plato's logic. Starting in 1891 he revealed from time to time details of his work, originally in Polish, but afterwards in periodicals of other countries. Later the fruits of his various labours were collected and published in one book. The greater part of it deals with the subject of the title; of concern here is only chapter 3 (pp. 64–193), entitled ‘The style of Plato’, which contains his investigation into the chronological order of the dialogues.

Lutoslawski's interest being primarily in Plato's logic and only incidentally in his style, he excluded from his inquiry not only suspected works, but also those ‘of no logical importance’. There remained twenty-two dialogues, the same as those accepted by Ritter as authentic together with the Parm., to be arranged in their order of composition. In contrast to earlier investigators he was acquainted with the achievements of all his predecessors, his own work being in fact a compendium of their inquiries. Knowing, therefore, that Campbell, Dittenberger, Schanz, Ritter and Arnim generally agreed on this, he regarded it as proven that Soph., Pol., Phil., Tim., Crit. and Laws constituted the last chronological group. His procedure was based on that of Ritter, the calculation of the number of ‘late’ linguistic characteristics in each dialogue, but whereas the latter used a mere 40 criteria, Lutoslawski aimed to amass 500.

In his final article on the subject Ritter said that he had hoped to leave the problem of Plato's earlier works to younger hands, but since none had appeared willing to take on the task, had finally resolved to attack it himself. The results of his research were published, despite incompleteness, in the belief that they indicated the possibility of a solution and in the hope that they would be verified and completed by others.

The investigation comprised five main items: μήν, ὡς with a superlative adjective or adverb, ᾄλλος and ἔτερος, ὄσος, and ὥσπερ and οἰον each of which according to Ritter provided significant evidence on the question of chronology within the early group of works.

μήν

For this particle he re-classified and added to the material already made use of by Dittenberger. Whereas the latter had reckoned all occurrences of ἀλλὰ … μήν together as the same, Ritter pointed out that they were to be distinguished according to their sense, there being no relationship between the asseverative ἀλλ' οὐ(δὲ) μήν, ἀλλ' ἔστι μήν etc. and the interrogative ἀλλὰ τί(ς) μήν; A distinction likewise had to be made between the use of ἀλλὰ τί μήν; as a true interrogative and as a rhetorical question to form an affirmative reply.