Corps de l’article

In spite of his cardinal role in late antique philosophy, much of the extant work of Ammonius, the son of Hermias, remains inaccessible to the Greekless reader.[1] This state of affairs, though understandable insofar as Ammonius himself has only recently emerged from obscurity, is still disconcerting when we consider the immense historical importance of one of these ignored works, namely, his In Porphyrii Isagogen. Not only is this work the earliest surviving commentary on Porphyry’s hugely influential introduction to philosophy, but it is also the source of at least one doctrine of enduring philosophical importance. This doctrine, of course, is that of the three states of universal, which are described by Ammonius as πρὸ τῶν πολλῶν, ἐν τοῖς πολλοῖς and ἐπὶ τοῖς πολλοῖς, or prior to the many, in the many and posterior to the many.[2] This doctrine is offered by the Alexandrian in response to what was, by his time, an already ancient debate concerning the ontological status of genera and species (or universals in general), a debate whose main positions are rapidly summarized by Porphyry in the following lines from the Isagoge :

For example, concerning both genera and species — whether they subsist, whether they actually depend on bear thought alone, whether if they actually subsist they are bodies or incorporeal and whether they are separate or are in perceptible things and subsist about them.[3]

Through various byways, Ammonius’ doctrine became central to the thirteenth century response to the controversy concerning the status of universals, thereby setting the stage for the radical positions which emerged in the following century.[4] Having played such a seminal role in the history of philosophy, it is only just that this doctrine’s paternity has been made widely known, thanks in large part to the work of Alain de Libera. Over the past two decades, de Libera has not only trumpeted Ammonius’ importance with respect to ‘la querelle des universaux’, but has also liberally cited the locus classicus of his doctrine. Indeed, a French translation of In Porphyrii Isagogen 41, 10-20 appears in at least three of his major publications,[5] although in each instance, the citation states that he has translated lines 41, 10-42, 26 of Adolf Busse’s edition[6] of the text, whereas he in fact offers no more than the above stated ten lines from this four page section of the commentary.[7]

De Libera can hardly be faulted for his concentration on these ten lines, in which Ammonius introduces his solution to the third question by means of the image of the signet ring. Nevertheless, as is the case with any excerption from so rich a text as Ammonius’ commentary, much of both historical and philosophical interest is left behind. What follows may be seen as equally wanting insofar as it is little more than a slightly larger excerpt, in which not only the crucial passage, but the entire section of commentary in which it occurs, is translated. It is likewise impoverished for want of the whole whence it comes, but equally enriching in that it presents the reader with at least some part of what is otherwise only accessed with difficulty. It also shares in the goal of all excerpts, which is to entice the reader to consult the text as a whole, and in this case, to perhaps inspire someone to offer something more than an excerpt.

I. Ammonius’ Interpretation of the Questionnaire

It is Ammonius’ position that Porphyry offers the series of questions at Isagoge, 1.9-12 as proof of the potential depth of the inquiries which his subject matter could elicit and has indeed elicited in the past. Upon citing the Porphyrian passage, our commentator immediately sets about probing these depths, beginning with what is commonly interpreted as the first question, namely, whether genera and species either a) subsist (i.e. have a real existence) or b) simply depend on bear thought alone. This common interpretation, however, tends to overlook the fundamental ambiguity of Porphyry’s wording. We are right to ask, as Jonathan Barnes points out,[8] whether Porphyry is here presenting us with two clear alternatives (a or b ?), or two separate questions (a ? b ?). Moreover, Barnes is also correct in signalling an additional ambiguity in the very alternatives/questions themselves. Is Porphyry asking us whether genera and species “are natural items rather than creations of the mind” (or natural items ? creations of the mind ?) or “real items rather than fantasies” (or real items ? fantasies ?) ?[9] Barnes sees these as two very different sets of alternatives/questions, as the first concerns the origin of something which has real existence, while the latter concerns the existing things and things which have no real existence (fantasies).

The polysemous nature of this first question comes across clearly in Ammonius’ interpretation. He seems to grasp both of the Barnesian ambiguities, but treats of them, in typical Neoplatonic fashion, as simply matters of perspective. Porphyry therefore offers us two separate questions, insofar as both, in both of their senses, may be answered in the affirmative. Universals can either exist as real beings or as the fantasies within a certain mind (contra Barnes, who would deny fantasies any form of existence).[10] They can also be either natural in origin (such as a goat or a stag), or purely mental creations (such as a goat-stag). Therefore, though it is a creation of the mind which depends on bare thoughts alone, we may still say that the goat-stag does in some way exist.

This first question, however, also represents two distinct alternatives for Ammonius, insofar as we view it historically. As the commentator sees it, the Porphyrian questions are not simply a summary of possible philosophical positions dreamed up by Porphyry himself, but also a historical survey of the real positions held in this debate. The first question therefore represents, with regard to the history of philosophy, nothing less than the quintessence of the great Socratic schism. Whether or not Socrates concerned himself with the status of universals, it was a question that deeply occupied his successors and effectively divided the two most influential amongst them, namely Plato and Antisthenes. Ammonius sees this historic division embodied in the two alternatives, the former being the Platonic response to the problem of universals, the latter being the Antisthenian. As proof of the second alternative’s Antisthenian pedigree, Ammonius furnishes us with two famous statements attributed to the first Cynic,[11] which scholars[12] generally accept as confirmation that Antisthenes was indeed the proponent of a sort of proto-nominalism and accordingly held (as the second alternative states) genera and species to be nothing more than bare thoughts.[13]

The second Porphyrian question, according to Ammonius, rests upon the assumption that subsisting things, such as genera and species, may be divided into the corporeal and the incorporeal. Yet, under which heading then do the aforementioned universals belong ? The ancients, according to Ammonius, were particularly divided over this question. Furthermore, those who held the latter position, that universals are incorporeal, were divided into three rival camps : those who held them to subsist according to themselves, those who held them to subsist in other things and those who hold them to exist, as Porphyry explicitly mentions, “about the things which subsist (περὶ τὰ ὑφεστῶτα)”, in the manner of place and time. The second group, a historical fact which Porphyry’s account seems to overlook, may be further divided into those who held the universals to exist “throughout the whole (δι’ ὅλου)” in the manner of whiteness in white lead, those who held them to exist “according to appearance (κατὰ τὴν ἐπιφάνειαν)” in the manner of a spherical figure.

Despite this confrontation with an embarrassment of historical positions, Porphyry, as Ammonius takes his third question to imply, clearly held that genera and species both subsist and are incorporeal. Both of these responses would be fairly evident to anyone professing to be a student of Plato. The answer to the third question, however, is unclear. Porphyry, according to Ammonius, presents us with two historical options for what an incorporeal universal might be. It might be either separate from the corporeal world, or exist in and about perceptible things. This question alone, perhaps, (as far as a Platonist is concerned) is justification of Porphyry’s warnings about the depths of such an investigation. It therefore, with due reason, occupies the rest of Ammonius’ exegesis.

In order to broach such a difficult problem and explain the apparent discord amongst the ancients on this subject, Ammonius follows the Platonic practice of first offering his solution in the form of an illustration. He turns to one with a distinguished philosophical pedigree, namely, the image of a signet ring making an impression in a waxen tablet. This image was first used by Plato in the Theaetetus (191c-195a)[14] in his discussion of perception and memory. It was conserved by Aristotle, who used it in the same context in both his De anima (II.12, 424a19-24) and De memoria (I.1, 450a32). Chrysippus later inherited this image from the Platonists and through him it became one of the key images of stoic psychology.[15]

The image recurs yet again in the context of sensation and memory in the writings of Plotinus (41 [IV 6], 1, 20), but was also used earlier by the Egyptian (8 [IV 9], 4, 20) as a means of illustrating the resemblance of all souls to one another. This latter use of the image marks its first transposition beyond the domain of psychology to the richer and wider field of metaphysics, and will set a precedent which Ammonius will follow to great effect in his discussion of the three states of the universal.

The celebrated image runs as follows : a signet ring bearing a relief of Achilles as its seal is used to make multiple impressions on several waxen tablets. After the event, another man chances upon the same waxen tablets, and concluding that the several impressions upon the tablet are the product of the same seal, he attains the impression of the same figure in relief of Achilles in his reasoning faculty (ἐν τῇ διανοίᾳ). This image, according to Ammonius, illustrates how the seal of Achilles can exist in three different states. The first state is as figure in relief upon the signet ring itself, where it may be called prior to the many (i.e. prior to the multiple impressions in wax). The second is its existence in the wax as the multiple impressions, where it may be called in the many. The third is in the reasoning faculty of the viewer who beholds the tablets and concludes that the images are derived from the same seal, where it may be called posterior to the many. It is these three possible states of the seal, as Ammonius goes on to show, which correspond to the three possible states of universal.

In order to apply this extremely mundane image to the cosmic level of the universals, we need only, according to Ammonius, imagine the bearer of the signet ring as the demiurge rather than a man and the seal to be not a figure in relief of Achilles, but the form of humanity itself. Of course, one might initially object to the fact that such an analogy presupposes that the demiurge has the forms with himself. This objection is foreseen by Ammonius and refuted on the basis that if the demiurge is not to be considered as less of a craftsman than his human counterpart, he must possess an idea of what he is making.[16]

Therefore, with regard to the universals, the form is in the demiurge just as the relief is in signet-ring (prior to the many), it exists separately in each human being (in the many), and for the man who beholds multiple human beings and concludes that they all partake in a common form of humanity, it exists in his reasoning faculty (posterior to the many).[17] Thus, we have Ammonius’ answer to Porphyry’s third question, which is no less than an affirmation of all three options. A universal, such as a genus or a species, may exist in any of the three states described by Porphyry. The first possible state of the universal (prior to the many) is clearly “separate”, while the second (in the many) is clearly inseparable and permanently “in perceptible things”. The third state (posterior to the many) must therefore account for those universals which exist “about perceptible things”, specifically, about the mind which has created them.

Each of these three states can easily be related to an earlier theory of universals, be it Platonic idealism, Aristotelian hylomorphism or the more enigmatic Aristotelian theory of logical or abstracted universals.[18] This third theory, Ammonius makes clear, was unknown to Plato, who assumed that even the demiurge had to look outside of himself to grasp the forms. Such an opposition between the Platonic and Aristotelian conceptions of universals raises the spectre of disharmony between the two thinkers, something which later Neoplatonism was generally loath to tolerate. Ammonius concludes this section of commentary, however, by stating that it is not the appropriate place to plunge into a discussion of the principle of homodoxia,[19] though he does hint at a potential solution, according to which Aristotle should be taken as pronouncing on one aspect of reality and Plato on another.

II. The universals ‘posterior to the many’ and the problem of abstraction

Having examined the basic structure of Ammonius’ solution, we now propose to examine in greater depth one particular aspect of his solution, namely, his conception of the universal posterior to the many. This state of the universal is especially intriguing in that it is the only one which is produced by an act of the mind. What exactly this act is, however, is cause for question.

Ammonius’ initial description of how the universal posterior to the many is formed runs as follows :

But later, someone coming and beholding the wax tablets, having established that all [the impressions] are from one figure in relief, now has within himself the impression which is the figure in relief in his reasoning faculty. Therefore the seal on the signet ring is said to be prior to the many, but in the wax tablets it is in the many, and in the reasoning faculty of the impression taker it is posterior to the many and posterior in order of being.[20]

According to this description, there seem to be three steps in the production of this particular type of universal. The viewer first beholds the waxen tablets after (ὕστερον) the multiple impressions have been made upon them by the ring-bearer. He then establishes that these many impressions must come from a single seal. Upon establishing this,[21] the viewer acquires a knowledge of the seal which has made these many impressions in his reasoning faculty, as if it had left its impression there as well as in the wax. This ‘mental impression’ of the seal in the reasoning faculty of the viewer[22] is further qualified by Ammonius as not only ‘posterior to the many’, but also as ‘posterior in order of being (ὑστερογενής)’,[23] meaning that this type of universal is a later production modeled upon the other two types.

The production of this particular type of universal seems to be a case of abstraction as described by Aristotle, though which of the two modes of Aristotelian abstraction Ammonius intends it to represent, whether the inductive abstraction (ἐπαγωγή) described at Posterior analytics II.19 or the geometrical abstraction (ἀφαίρεσις) described at De anima III.7, is unclear. The issue is further complicated by de Libera’s assertion that “nombre de commentateurs anciens, comme Ammonius, ont manifestement cherché à absorber le modèle géométrique dans le modèle inductif de l’abstraction”.[24] We therefore find ourselves confronted with three possibilities for describing the production of this particular type of universal. It seems that it must either be a case of inductive abstraction, a case of geometrical abstraction, or, as de Libera proposes, a conflation of the two.

As it turns out, de Libera’s assertion is correct, though only partially so. It is incorrect insofar as there is evidence to suggest that Ammonius did not always conflate the two modes of abstraction. Although Ammonius does employ the nouns ἐπαγωγή and ἀφαίρεσις, as well as the verbs ἐπάγειν and ἀφαιρεῖσθαι, in his four surviving works, he does so very rarely in the technical sense of abstraction. Moreover, even when using the words in the technical sense,[25] he fails to offer us a clear picture of how he understands each type of abstraction. Despite the scarce fruit borne by these commentaries, there are other resources at our disposal beyond those works bearing Ammonius’ name. As we mentioned above, there also exist two commentaries under the name of Philoponus which, as the manuscript titles suggest, are the “notes by Philoponus from the classes of Ammonius with some personal observations”.[26] These commentaries offer an exegesis of the two Aristotelian source texts for the models of abstraction themselves, and scholars are largely in agreement that the content of the texts we have before us (though variously estranged) does indeed ultimately derive from Ammonius’ original lectures.[27] With this in mind, it seems reasonable to venture that these commentaries do in fact offer some evidence of the views of Ammonius.[28]

If we are to begin with Philoponus’ commentary on De anima 431b12-17,[29] we find ourselves happily confronted by a substantial exegesis of this crucial passage. Philoponus first states that abstract objects, specifically the mathematical ones, are members of “the fourth species of indivisible things”.[30] According to Philoponus, Aristotle calls these objects ‘abstract’ “because intellect itself separates things which are not separate from matter, and abstracting them, so to speak, from the subject, understands them as they are themselves”.[31] In this way we are able to understand hollowness, the triangle, the circle, and other mathematical objects which have their being in matter. This definition of mathematical abstraction seems fairly straightforward and shows no trace of a conflation with inductive abstraction. We thus turn our attention to the commentary of ‘Philoponus’ on Posterior analytics 100a1-9,[32] which de Libera offers as the key passage of section II.19.[33] In commenting this passage, ‘Philoponus’ offers an illustration drawn from his name-sake’s own experience as a physician :

I saw countless times that hellebore carries away the humour, and many such precepts have been imprinted on my imagination, and from these many memories could be gathered up together. And from many memories there came to be within me experience and knowledge that hellebore has the power to carry the humour away. When there comes to a stand and is fixed and stabilized in my soul this knowledge that hellebore is like this and is not otherwise, it assembles the universal, for example, ‘all hellebore purifies’ which universal is a principle of demonstration.[34]

Again this illustration offers no indication of a conflation or a confusion of the two types of abstraction. If these two passages are indicative of Ammonius’ original teachings concerning the two modes of abstraction, it would seem then that the Alexandrian did in fact clearly distinguish between the two modes of abstraction.

In spite of this oversight, de Libera’s assertion holds good with regard to the passage at In Porphyrii Isagogen 41, 15-20, which conforms neither to the model of geometrical abstraction nor to the model of inductive abstraction alone. It indeed seems to contain aspects of both models. It recalls inductive abstraction insofar as Ammonius makes it clear that the viewer observes several waxen tablets and compares several impressions. As we saw above in the example of the hellebore, the central aspect of inductive abstraction is the perception of multiple instances of the same thing from which a universal may be assembled. On the other hand, it also strongly recalls geometrical abstraction insofar as the impressions are in wax and must be mentally separated from the wax in order to conceive of them ‘as they are themselves’. It is only by separating the impression from the wax (just as we separate hollowness from the snub nose) that we can see that it is not an innate property of the wax and was in fact created by an external object, i.e. a single seal. The image of the wax impression seems therefore to imply the central aspects of both types of abstraction (assembly and separation). The same seems to hold concerning the production of the universal posterior to the many of humanity, for as Ammonius points out,[35] it is a parallel case.

We are left to conclude from this investigation that Ammonius may have recognized three possible forms of abstraction, that is to say geometrical, inductive and a conflation of the two. This should hardly come as a surprise, however, given the variety of things which can be abstracted by the human mind. A mathematical object, such as a triangle, clearly requires geometrical abstraction, while demonstrative knowledge, such as ‘gold conducts electricity’ requires inductive abstraction. The acquisition of the vast majority of things which populate our mind, however, such as the forms of everything from ‘tree’ to ‘human’, requires a combination of both modes of abstraction. Such an explanation, in typical Neoplatonic fashion, simultaneously preserves the original Aristotelian distinctions, while offering an explanation for the acquisition of all types of universals posterior to the many.

III. A note on the translation

The following translation is based on the text edited by Busse, which, as the editor points out, has come down to us in what is hardly a pristine state. The choppy and repetitious Greek in which the In Porphyrii Isagogen is written quickly betrays its origin as the transcription of a series of lectures, perhaps left unrevised by the lecturer himself. The narrator often darts between subjects with little or no warning and on more than one occasion offers us a sentence that seems entirely out of place. It is indeed a far cry from the eloquent pen we find on display in Ammonius’ commentary on the De interpretatione. The copyists also seem to have added liberally to the original transcript, leaving us with a dubious prolegomenon and several manuscripts replete with what Busse takes to be later additions.[36] Indeed, certain manuscripts suggest the section of commentary at hand contains just such an additional passage, beginning at line 15. I agree with Busse’s decision to omit this substantial passage (about ten lines), though not because of any suspected Christian content so much as for the fact that it amounts to little more than an inconsequential laundry list of incorporeal and corporeal things.

I have departed from Busse’s text in the following instances :

40, 1 : replace ὑφίσταται with ὑφίστανται utrobique (EFMVp).
40, 2 : for συμπ. (D) read συμπαύονται rather than συμπαύεται (E).
41, 1 : omit τί δέ ἐστι ‘περὶ τὰ ὑφεστῶτα’ (E).
42, 19-20 : replace χωριστά ἐστιν with χωριστά εἰσι τῆς ὕλης (p).

In each case I have done so for the simple reason that the sentence is otherwise grammatically incoherent. Words which do not appear in the original Greek, but are either grammatically implied or logically necessary for the English reader, are supplied in square brackets.

The philological failings of the text aside, it remains clear to even the most inattentive reader that these are indeed the thoughts of the man who, at the admission of even the most hostile of critics, “made the greatest contribution of all commentators who ever lived”.[37]

Ammonius, In Porphyrii Isagogen (ed. A. Busse), 39, 9-42, 26
  “For example concerning both genera and species…”

Porphyry promised to compose a concise lesson, [in] a clear style (39, 10) and to abstain from deeper inquiry. And so, lest someone say, that there was not some deep inquiry concerning these [things], the philosopher wishes to prove this very [thing] to us on this account, [i.e.] that while there was some deeper inquiry concerning these [things], he neglected [it] on purpose. But also in order that what is written might become clear, as we might say.

While there subsist those [universals] among beings, there also exist those [universals] in bare (15) thoughts such as the centaur and the goat-stag, [which] while they subsist to whosoever has conceived [them], they do not subsist for those not having conceived [them], but with the cessation of a thought, they cease [to exist] together with it. For the centaur does not exist in reality, but having beheld a horse and a man we fashion anew the compound in thought which [is] the centaur. And again in the same way while nature made the goat and the stag, fashioning anew according to themselves we made the compound in thought which [is] the goat-stag (40, 5), and in this it has being. Antisthenes therefore said the genera and the species to be in bare thoughts, saying that “while I see the horse, I do not see equinity” and again “while I see the human, I do not see humanity”. That man said these [statements] concerning a living being in a single sense perception and not a possible being in reason [in order] to refer to his own greater discovery. And so it is for the subsisting [things], some corporeal (10) and others incorporeal.

But on the whole some of the ancients said these [things] to be and others not to be. And of those saying them to be, some said them to be bodies, others incorporeal. And while those saying them to be bodies all remained of the same opinion, amongst those saying them to be incorporeal, since [the lot] of incorporeal [things], as it is divided, some subsisting according to themselves such as an angel and a God, others subsisting in other (15) [things] such as whiteness and the geometrical figures, some said these to subsist according to themselves, others said them to subsist in perceptible [things]. But again since the incorporeals subsist in perceptible [things] either throughout the whole as the whiteness is in white lead or according to appearance as a spherical figure, of those saying them to subsist in perceptible [things], some said these to be throughout the whole, others (20) according to appearance. But again others said these [universals] to subsist about the subsisting [things], as, for instance, both place (for this embraces the sensible) and time.

And so, since there are so many choices concerning being and not being it is said that he was able to inquire concerning both genera and species whether they are or whether they depend on bare thoughts alone. For thus Antisthenes (41, 5) suspected. And discovering that they subsist, he could investigate anew, whether they are corporeal or incorporeal. For they became the headings of each section of the division. But discovering anew, for example, [that they are] incorporeal he could investigate if the undivided part is material and in the many or [exists] before these things and is separated [from matter].

(10) But so that what is written may be clear, we will go through the argument by means of an illustration. For neither do they simply and at random call some [things] bodies themselves and others incorporeals, but with a certain logic, nor do they contradict one another ; for each [of them] says reasonable things. Accordingly, consider a signet ring having a certain figure in relief, for example, of Achilles, and many available wax tablets, and the signet ring has made an (15) impression upon all wax tablets. But later, someone coming and beholding the wax tablets, having established that all [the impressions] are from one figure in relief, now has within himself the impression which is the figure in relief in his reasoning faculty. Therefore the seal on the signet ring is said to be prior to the many, but in the wax tablets it is in the many, and in the reasoning faculty of the impression taker it is posterior to the many and (20) posterior in order of being.

Now consider this in the case of genera and species. For the demiurge has all the paradigms of all [things] before himself, as for example when making a human, he has the form of human before himself, in reference to which he makes, looking away from all others. But if someone should object, saying that the ideas are not in the demiurge, let him understand this, that the demiurge fabricates either knowing (25) those [things] fabricated by him or not knowing [them]. But if he does not know [them], he would not be their fabricator. For who would make unknowingly something which he intends to make ? For as nature does not have the ability produces irrationally, nature produces from whatever source not knowingly attending to that being produced. But if he makes something according to a logical state of mind, he doubtless knew altogether that being produced. Therefore if the god does not make [in a manner] worse than befits a man, he knew that (42, 5) being produced by himself. But if he knew that which he makes, it is clearly evident, that there are forms in the demiurge. But the form is in the demiurge just as the relief is in signet-ring, and this form is called prior to the many and [is] separate from matter. But the form of human is even in humans separately in each, as the figures in relief in the wax tablets, and such [forms] are said to be in the many (10) and inseparable from matter. And beholding humans severally, since all have the same form of human, just as someone later coming upon and beholding the wax tablets, we will receive an impression of this in our reasoning faculty, and this is called posterior to the many or after the many and posterior in order of being.

But such [forms] of bodies, while they are separate (for they subsist not in the body, but (15) in the soul), are not simply separate. For Plato is unable to explain these [forms] themselves, which he supposes to be the [forms] prior the many. For he does not simply wish these [forms] to be the thoughts of the demiurge, but altogether intellectual beings, towards which the demiurge looks as to archetypal images to make them thus.

And so it is said that this [question] was to enquire as to whether (20) [genera and species] are incorporeal beings separate from matter as those [forms] with the demiurge, or inseparable as those [forms] in the many, or with the sensible things, that is, those [forms] posterior to the many. But he [Porphyry] declines to speak concerning all these [things]. But one must see that concerning these Aristotle and Plato seem to disagree. For while Aristotle says these [forms] to be inseparable from matter, Plato says them to be separate. But either the philosophers disagree with one another, (25) or not (for I suppose Aristotle to pronounce as a physicist concerning these [things]), but it is presently not the right time to reflect [on this].