1. INTRODUCTION: THE PROBLEM

Both W.D. Ross's and J. Brunschwig's editions of Aristotle's Topics contain the following passage:

The passage is translated in the revised Oxford translation as follows: ‘Moreover, if in any character one thing exceeds and another falls short of the same standard; also, if the one exceeds something which possesses the character, while the other exceeds something which does not, then clearly the first thing exhibits that character in a greater degree’.Footnote ¹

However, in most manuscripts the second, problematic, sentence of this passage runs as follows:

This was clearly the text read by Boethius when he wrote his translation:

As is already evident in Boethius’ literal translation, the Greek expression τὸ δὲ μὴ τοιούτου τοιοῦτον is not straightforward. The deletion of τοιοῦτον after τὸ δὲ μὴ τοιούτου, which was first proposed by H. Bonitz and is indirectly attested in a manuscript (P) of Alexander of Aphrodisias’ commentary on the Topics, seems beneficial and is indeed accepted in both Ross's and Brunschwig's editions. This emendation certainly makes the expression less difficult, but does not help the reader to understand the exact meaning of the passage, which remains problematic.

The aim of this short paper is to present a philosophical and philological discussion of the above passage: we will show that (almost) all available translations are unsatisfactory and that most of them are unsound, and will propose our own translation and interpretation.

Moreover, we will show that this passage was understood in the same way that we understand it by some ancient commentators of Aristotle, such as Alexander of Aphrodisias and the scholiast, whose gloss was incorporated in the text that was preserved by some medieval manuscripts.

Finally, on the basis of a linguistic analysis of elliptical contrasts in Aristotle, we will claim that Aristotle's text as printed by Ross and Brunschwig does indeed support our interpretation, but at the same time we propose a simple emendation which would avoid ambiguities.

2. MODERN TRANSLATIONS

The interpretation implied by the Oxford translation is widespread in modern versions of Aristotle's Topics.

For instance, Jacques Brunschwig translates as follows: ‘en outre, si une chose est plus telle, une autre moins telle qu'un même terme de référence; ou encore (avec deux termes de référence) si l'une est plus telle qu'un terme lui-même tel, l'autre plus telle qu'un terme lui-même non tel, il est clair que c'est la première qui est plus telle’.Footnote ³

Similarly, Giorgio Colli has: ‘Inoltre, se un oggetto è più siffatto di un qualcosa e l'altro oggetto è meno siffatto del medesimo qualcosa, come pure, se un oggetto è più siffatto di un siffatto qualcosa e l'altro oggetto è più siffatto di un qualcosa non siffatto, sarà evidente che il primo oggetto è più siffatto del secondo’.Footnote ⁴

Finally, in their recent edition Wagner and Rapp translate: ‘Ferner, wenn gegenueber demselben das eine mehr und das andere weniger so beschaffen ist. Auch wenn das eine mehr so und so beschaffen ist als ein so und so Beschaffenes, das andere aber (lediglich mehr so und so beschaffen ist) als ein nicht so und so Beschaffenes, dann ist klar, dass das erste mehr so und so beschaffen ist’.Footnote ⁵

These translations, which all take μὴ as negating τοιούτου (‘something which does not [possess the character]’, ‘non tel’, ‘un qualcosa non siffatto’, ‘als ein nicht so und so Beschaffenes’), might seem linguistically correct, but they fail to understand Aristotle's point: they solve some of the obscurities of the Greek original text, but the resulting argument is logically flawed.Footnote ⁶ The flaw is implicitly observed by T. Waitz in his commentary on Aristotle's Topics. In his note ad loc. he construes the passage in the same way as modern translators do, adding that this is the first attestation of this problematic rule: ‘ei loco quem habemus vs. 21 nullus est similis eorum qui praecesserunt: nam si eum transferas ad τὸ αἱϱετόν, sic se habebit: εἰ τὸ μὲν αἱϱετοῦ αἱϱετώτεϱον, τὸ δὲ μὴ αἱϱετοῦ αἱϱετώτεϱον, καὶ ἐκεῖνο τούτου ἔσται αἱϱετώτεϱον’.Footnote ⁷

In order to better understand the problems of this interpretation, it is now useful to recall what Aristotle is expounding in these chapters of the third book of the Topics.

3. THE CONTEXT

In the sections preceding our passage, Aristotle has been expanding his comparative logic,Footnote ⁸ and has already presented some of the properties of the relations ‘more than’, ‘less than’ and ‘equal to’ (cf. Top. B 114 b37 − 115 a26).

These properties are expanded further by the τόποι concerning comparative relations; the τόποι should be understood as schemes of arguments, which can be used in a dialectical disputation.Footnote ⁹ Even though Aristotle states at the beginning of the Topics that dialectic makes use of syllogisms, and syllogisms are defined as they were defined in the Prior Analytics (A 24 b18-20), the τόποι do not have the structure of a syllogism, but seem rather to be other forms of argument.Footnote ¹⁰

The relations ‘more than’ and ‘less than’ are intuitively transitive, and Aristotle clearly maintains that these relations have this property of being transitive in Top. Γ 119 a20-2.

The logical argument introduced by the first sentence of our passage states that if A is more ϕ than B, and C is less ϕ than B, then A is more ϕ than C (ἔτι εἰ τοῦ αὐτοῦ τινος τὸ μὲν μᾶλλον τὸ δὲ ἧττον τοιοῦτο […] δῆλον ὅτι τὸ πϱῶτον μᾶλλον τοιοῦτο, Top. Γ 119 a20-2), a rule which is logically correct.

However, the second sentence (καὶ εἰ τὸ μὲν τοιούτου μᾶλλον τοιοῦτο, τὸ δὲ μὴ τοιούτου, δῆλον ὅτι τὸ πϱῶτον μᾶλλον τοιοῦτο), as it has been understood by most translators and commentators (see above), would state the following rule:

This rule is plainly wrong. An example will make this clearer: the moon (A) is brighter than this candle (B), and both of them are bright; on the other hand, the sun (C) is brighter than a piece of coal (D), and whilst the sun is certainly bright, coal is not. Now, from this it should follow by the above rule that the moon is brighter than the sun—and this is clearly not the case. Therefore, the rule by means of which we have inferred this conclusion must be wrong.

It is possible that Aristotle suggested a logically incorrect rule: his corpus is scattered with notions that modern science has proved to be mistaken, and we should not be surprised if quandoque bonus dormitat Aristoteles. However, mistakes are not all of the same sort, and if we accept this interpretation, we have to accept the idea that Aristotle has endorsed a rule which is patently wrong: this seems to be at odds with the careful descriptions of the other (correct) rules which govern the logic of comparatives, and which are found in the third book of the Topics.

4. SOME PROBLEMATIC SOLUTIONS

A first solution to the problems of rule 1 involves an interpretation of the passage as shown by the following translation:

This translation interprets the text as stating the following rule:

According to this ‘charitable’ interpretation, the not-ϕ term (D) compared to C is not just any example of a not-ϕ, but the best case one can provide in which C is more ϕ than something; in this way the counterexample of the sun, mentioned above, would be ruled out, as the bright thing referred to in the second premise (C) would be more bright only than a non-bright thing (D), thus never being more bright than another bright thing.

The main problem with this interpretation is that the logical component on which the soundness of rule 2 relies upon, and which indeed distinguishes rule 2 from rule 1, is expressed by a linguistic element (the adverb ‘at best’ or ‘only’) which the Greek text does not display.

Another way to solve the problem, envisaged by some scholars, involves a simplification of the logic of the passage. An example of this is found in Rolfes's translation: ‘Ferner, wenn das eine bestimmte Beschaffenheit in höherem, das andere in niederem Grade hat als eine und dasselbe Dritte; und wenn das eine sie in höherem, das andere nicht in höherem Grade hat als ein gleichbeschaffenes Dritte, so hat offenbar das erste die betraffende Beschaffenheit in höherem Grade’.Footnote ¹¹

However, both this translation and the resulting interpretation are problematic. Apart from the fact that Rolfes's version hardly corresponds to the Greek, the rule which Aristotle would have suggested, if these were his words, would be a truism:

Rolfes's reading would entail a repetition in the second sentence of what Aristotle has just said in the first. As a consequence, one might be tempted to think that the second sentence was simply a gloss. In other words, quite apart from its linguistic problems, this alternative interpretation does not improve our understanding of the passage, although it is logically correct.

5. ALEXANDER OF APHRODISIAS

There is yet another way to solve the problem, without stretching the Greek or simplifying the logic. This interpretation has been strangely neglected by modern scholars, but was apparently clear to ancient commentators.

In his note commenting on the passage, Alexander of Aphrodisias quotes the rule of Aristotle, in a form slightly different from those discussed above, and then presents an exemplifying argument, which proves to be logically correct:

In his τόπος Alexander is clearly suggesting the following rule:

This rule presupposes that the degrees according to which a property is shared by its subjects are ordered in a rigid way, namely that for every a, for every b, if a and b are different items and share the same property ϕ, either a is more ϕ than b, or b is more ϕ than a. Footnote ¹² This is compatible with the common understanding of comparative relations.

What is worth noting is that, at first sight, Alexander's interpretation does not seem to be compatible with the wording of Aristotle's lemma, and in particular with the problematic second premise, which is here given in yet another form (τὸ δὲ μὴ τοιοῦτον, i.e. τὸ δὲ μὴ τοιοῦτο),Footnote ¹³ which we have, for the moment, left in Greek as it is textually problematic.

One might be tempted to emend Aristotle's text by inserting into the second premise the same μηδενός, which Alexander uses in his τόπος (μηδενὸς δὲ ἀγαθοῦ μεῖζον), and which unequivocally introduces the property of trichotomy for comparative relations.

If we were to accept this tempting emendation, Aristotle's passage would look something like this (following Ross's and Brunschwig's editions):

This minor emendation, although it would explicitly state rule (4), is not palaeographically satisfactory, because it is difficult to admit that a copyist could have misread μηδενός as μή. Moreover, Alexander did not read μηδενός, but he nevertheless understood the passage as referring to the trichotomy of comparative relations (cf. rule 4). The only possibility is therefore to verify whether Aristotle's text (in either of its variants) may actually be interpreted in the same way as Alexander interpreted it, that is, as expressing rule (4), which is most satisfactory from a logical point of view, although it is widely neglected by modern translators and commentators.

6. ELLIPTICAL NEGATIONS IN ARISTOTLE AND THE POSITION OF μή

A good starting point is to analyse what would be the most explicit and clear form of the second premise of rule (4) without the emendation μηδενός. This would probably be something like one of the following:

We do not try here to establish which of the above word orders, if any, would be most idiomatic in Greek, nor which one would be most appropriate in the context, given the parallelism with the first premise, but we simply note that most of them seem to be paralleled in the corpus of Aristotle.Footnote ¹⁴

However, none of the above clauses is likely to have been used by Aristotle; in contrastive comparisons of this kind, in which a sentence is followed by a second sentence that is an exact negative copy of the first, the verb of the second sentence is normally dropped. Cf. for example An. Post. A 73 b10-12: ἔτι δ’ ἄλλον τϱόπον τὸ μὲν δι’ αὑτὸ ὑπάϱχον ἑκάστῳ καθ’ αὑτό, τὸ δὲ μὴ δι’ αὑτὸ συμβεβηκός, οἷον εἰ βαδίζοντος ἤστϱαψε, συμβεβηκός.Footnote ¹⁵ In particular, the verb ἐστι is hardly ever found in contrastive comparisons of this kind: cf. for instance An. Pr. A 30 a23-4: εἰ δὲ τὸ μὲν Α Β μὴ ἔστιν ἀναγκαῖον, τὸ δὲ Β Γ ἀναγκαῖον.Footnote ¹⁶

If we eliminate the verb ἐστι from the above sentences, we are left with only three options:

However, if options (f) and (g) are still straightforward and would state rule (4) in clear terms, option (h) would be ambiguous. Indeed, the adverb μή could also be taken as negating not the whole predicate phrase τοιούτου μᾶλλον τοιοῦτο(ν) or the implied ἐστι (‘not possessing the character to a greater degree than another thing that possesses the same character’) but only the (nominalized) adjective τοιούτου (‘[possessing the character to a greater degree than] another thing that does not possess the same character’).Footnote ¹⁷

This construction of μή preceding a complex phrase and negating only the word directly following it (in our case a noun phrase with τοιούτου as a head) can be easily paralleled.Footnote ¹⁸ Cf. for example Top. Θ 162 a3-5: εἴη δ’ ἄν ποτε λόγος καὶ συμπεπεϱασμένος μὴ συμπεπεϱασμένου χείϱωνFootnote ¹⁹ (μή is negating συμπεπεϱασμένου, not συμπεπεϱασμένου χείϱων); Top. Γ 119 a16-17: τὸ ϕύσει τοιοῦτο τοῦ μὴ ϕύσει τοιούτου μᾶλλον τοιοῦτοFootnote ²⁰ (μή is negating ϕύσει, not ϕύσει τοιούτου).

In contrast to these types of cases, when the adverb μή is meant to negate the whole phrase, it tends to be attached to the head: cf. for instance Eth. Nic. घ 1139 b34-5: εἰ γὰϱ μὴ μᾶλλον τοῦ συμπεϱάσματος, κατὰ συμβεβηκὸς ἕξει τὴν ἐπιστήμην.Footnote ²¹

Consequently, the fact that in sentence (h) the adverb μή is detached from the head of the phrase ([μᾶλλον] τοιοῦτο) might be taken as suggesting that it is negating the adverb τοιούτου (‘[that possesses the character more than any other thing] that does not possess the character’) and not the whole phrase τοιούτου μᾶλλον τοιοῦτο (or the implied ἐστι or the whole clause)Footnote ²² (‘not possessing the character to a greater degree than another thing that possesses the same character’): consequently, sentence h might be construed as expressing rule 1, which, as we have shown, is logically incorrect.

On the other hand, although it has significant syntactic plausibility, the interpretation above (taking μή as negating τοιούτου) is not the only one possible: there are parallels for the use of the adverb μή used to negate a complex noun phrase with the head in last position. Cf. for example Arist. De An. Α 403 b9-15:

In the passage above, the adverb μή preceding the phrase τοιούτου σώματος πάθη is not negating only the adjective τοιούτου (‘regarded as properties [that are] belonging to a body not of a given sort’, i.e. ‘attributes [that are] belonging to a different body’) but rather the whole phrase (‘regarded not as properties [that are] belonging to a body of a given sort’). The phrase τοιούτου σώματος πάθη is a simplified form of the phrase τοῦ τοιουδὶ σώματος καὶ τῆς τοιαύτης ὕλης ἔϱγα καὶ πάθη stated in the previous sentence, with which it is contrasted by means of the adverb μή. Indeed, the contrast between the two phrases is the reason for the fact that in the second phrase μή is placed in the first position detached from the head, and that no ambiguity is possible.Footnote ²⁴

Therefore, it is not syntactically inconceivable that in the clause (h) the adverb μή is negating the whole phrase τοιούτου μᾶλλον τοιοῦτο(ν) (or the implied ἐστι or the whole clause),Footnote ²⁵ and thus that the sentence could still be construed as expressing rule 4 (‘not possessing the character to a greater degree than another thing that possesses the same character’).

Interestingly, option (h) is actually found in this form in two manuscripts of Aristotle (Vaticanus Barberinianus 87 and Parisinus 1843) and is printed by Forster in his Loeb edition (with an elliptical but correct translation; cf. n. 28): this reading is probably a simplification of the original text, originating from the insertion of an explanatory gloss of the scholiast in the text. Consequently, the reading could be considered as evidence for another ancient commentator interpreting the passage in the same way as Alexander, an interpretation which, as we have seen, seems to be the correct one.

Going back to sentences (f), (g) and (h), it must be pointed out that it is still unlikely that they represent the original text of Aristotle. Indeed, the readings of the majority of the manuscripts and of Alexander suggest that the original text displayed a further degree of ellipsis. In particular, it seems evident that the adverb μᾶλλον was not repeated in the second sentence. The omission of μᾶλλον would produce the following sentence:

and, with a further degree of simplification,

Sentence (j) is the text transmitted in most manuscripts of Aristotle and probably lying behind the corrupt reading τοιούτως τοιοῦτον found in MS B of Alexander (also printed in the Aldine edition); sentence (k) is transmitted in one branch of the tradition of Alexander (MSS A and D) and printed by his editors; sentence (l) is transmitted in another of Alexander's manuscripts (MS P) and printed by several editors of Aristotle. Again, all these sentences would not be at variance with the usus scribendi of Aristotle. Indeed, the simplification of the wording of the second member of a contrastive comparison is not limited to the omission of the verb.

It is difficult to determine which of these readings (i, j, k and l) was the original one, since all present some problems and all could be explained palaeographically as corruptions of another reading (k and l as deriving from each other by confusion of final ν/υ, or from i or j by haplography; i and j as deriving from insertion in the text of k, to be construed as a marginal or interlinear variant of l, or vice versa).

However, options (i) and (j) are not satisfactory from a linguistic point of view: given the fact that the adverb μᾶλλον functions as a syntactic bridge between τοιοῦτο(ν) and τοιούτου, through its individual bond with each of them (μᾶλλον τοιοῦτο(ν) ‘the same character to a greater degree’; μᾶλλον τοιούτου ‘to a greater degree than another thing that possesses the same character’), its omission would be problematic in a context where τοιοῦτο(ν) and τοιούτου would both be present.

Option (k) is linguistically more sound, but only if one takes τοιοῦτο(ν) as having not the meaning it has in the previous sentence (‘of such sort’, ‘possessing the character/quality’), but rather the anaphoric meaning of ‘such as this’, with reference to what has just been said, i.e. τοιούτου μᾶλλον τοιοῦτο(ν); the resultant translation would be:

This option is advantageous in many respects, since the reading μὴ τοιοῦτο(ν) is well attested in manuscripts and the text would express unambiguously rule 4. The only problem with this reading is the fact that in the context the adjective τοιοῦτο(ν) is being constantly used (more than fifteen times in section 119a alone) in the non-anaphoric indefinite sense of ‘possessing a certain quality’, ‘possessing such-and-such a quality’ (or similar), and not in the anaphoric sense of ‘such as this [i.e. what has just been said]’): such a sudden change of meaning within a sentence, from the non-anaphoric (εἰ τὸ μὲν τοιούτου μᾶλλον τοιοῦτον) to the anaphoric sense of τοιοῦτο (τὸ δὲ μὴ τοιοῦτον) would be unexpected and difficult to defend.

We are thus left with option (l), which is the reading printed by modern editors of Aristotle and already found in one branch of the tradition of Alexander (MS P). As we have seen above, this sentence (l) is problematic since it displays some degree of ambiguity, as the adverb μή may seem to negate only the adjective.

Nevertheless, this sentence (l) could still be construed as a simplified form of sentences (a)−(h), i.e. as expressing, in an elliptic form, rule 4. This would be possible if one took the adverb μή as negating the implied copula or the predicate phrase τοιούτου [μᾶλλον τοιοῦτο(ν)], whose omitted head (μᾶλλον τοιοῦτο) would be implied by the contrast of the second premise with the preceding sentence. There are parallels of a similar use of μή in elliptic sequences, attached to a complement but negating some omitted material. Cf. for example An. Pr. A 29 a6-9:

In the sentence above, the adverb μὴ (in bold) is not negating only the word παντί (‘it applies to the not-whole’) but the whole verb phrase παντὶ ὑπάϱχῃ (‘it does not apply to the whole’), whose omitted head (ὑπάϱχῃ) is implied, in a sequence of contrastive sentences.

Therefore, even reading (l), found in most editions, could be construed as expressing, although in a very elliptic form, rule 4. Reading (l) seems preferable to the other options, and, if accepted in Aristotle's text, should also be printed as such in Alexander's text, thus introducing the reading of manuscript P.Footnote ²⁷

There is however, a final degree of simplification, which would entail ellipsis of the whole phrase:

Editors have not yet suggested this reading, but it might be suitable from both a syntactic and palaeographic point of view.

To begin with, complete simplification of the second member of a contrastive comparison to an elliptical phrase with τὸ δὲ μή (or similar) is very common in Aristotle. Cf. for example:

All these sentences display an ellipsis of one or more phrases in the second member of a contrastive comparison introduced by μή, which would be the same construction which we find in sentence (m).

However, it is easy to imagine how this elliptical construction could have created some problems of interpretation for later readers of the text, who presumably opted for inserting some of the material omitted, as testified to by the various readings found in the manuscripts (τοιούτου τοιοῦτο, τοιούτου, τοιοῦτο(ν) or τοιούτου μᾶλλον τοιοῦτο). These attempts at clarifying the Aristotelian obscuritas did not greatly benefit Aristotle in so far as they created a dangerous ambiguity (μή negating τοιούτου), which, if our reconstruction is correct, was not present in the original text, where the adverb μή could only negate the whole of the omitted material (τοιούτου μᾶλλον τοιοῦτο).