Bryn Mawr Classical Review

Reviewed by Lloyd Gerson, University of Toronto (lloyd.gerson@utoronto.ca)

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Plato in his Parmenides has Parmenides himself reject rather emphatically the ingenuous suggestion of the young Socrates that Forms are concepts (noēmata) in souls (132B3-C11). But neither in this dialogue nor anywhere else does Plato say clearly what exactly he thinks concepts actually are. And yet some presumed account of concepts and concept formation is clearly just offstage in numerous places. For example, in Timaeus the Demiurge looks to the 'Living Animal' and fashions a cosmos according to it out of the pre-cosmic receptacle of becoming (30C2-31A1). One naturally surmises that the Demiurge is intended to provide a 'conceptualizing link' between Forms and their sensible images. How are we to understand the thoughts in the intellect of the Demiurge? Or again, Socrates is famously dedicated to attaining true logoi of Forms and relentlessly skewers his interlocutors both for their inability to express such logoi and for their willingness to make momentous moral decisions without them. Presumably, these logoi are or include concepts. What, after all, would an accurate or true concept of a Form amount to whether this is expressed in ordinary Attic Greek or in some rather more exotic 'mentalese'? Consider the various accounts of recollection we find in the dialogues. Should we not expect that some sort of theory of concepts will be deployed to explain the process of recollecting the innate knowledge in us? Finally, the so-called method of collection and division found in Phaedrus, Sophist, and Statesman seems to at least involve something like what we typically call 'conceptual analysis'. But how exactly are these putative concepts related to eternal Forms? This list of issues crying out for clarification could easily be greatly extended. The more one thinks about it, the more one is inclined to the view that a theory of concepts and of concept formation should have been thematized explicitly by Plato. But, alas, it is apparently not so.

Christoph Helmig in this learned, original, and wide-ranging work, sets out to survey and analyze the contributions of the entire ancient Platonic tradition to the formulation of a theory of concepts and of concept formation. In the first chapter (13-37), he attempts to answer the question 'what is a concept in ancient Greek philosophy generally?' The question is not obviously answerable, for as Helmig notes, the various terms that are most frequently used for what we sometimes translate by the single English word 'concept'—ennoia, logos, noēma, katholou—are not obviously synonymous. Helmig argues, though, that these terms are sufficiently alike in their meaning that general criteria for their use can be set forth covering them all (16-23). These are: (1) concepts are (fairly) stable mental entities; (2) concepts are universal and shareable; (3) concepts must link up with reality; (4) concepts can be incomplete and possess more idiosyncratic than objective features; (5) there are degrees of the mastery of concepts, measurable by their proximity to the grasp of essences; (6) concept formation is susceptible to error; (7) concepts can be classified according to their origin (whether empirical or innate) but also according to their content and function. Focusing just on the first criterion, one can see, as does Helmig, the looming complexities within complexities facing the exegete and the philosopher. What, after all, is a mental entity, especially for a Platonist? Is it individuated by its content? But if that is the case, how does it differ from the extramental entity that is a Form? If, on the other hand, it is individuated by its having a relational property to a subject, for example, as an intentional object, then how is the concept's shareability accounted for? Is it by there being an identical content, which, once again, would need to be distinguished from the Form? These puzzles are really only the tip of the iceberg, and then when one adds the remaining criteria, things go from bad to worse. As I say, Helmig is very much aware of these puzzles. In the remainder of the book, he assembles almost all the central texts from Plato to Proclus relevant to his theme, trying to interpret them in a way that leads to a coherent picture. In my view, he does not completely succeed primarily because there is not a coherent picture to be found. I will return to this point toward the end of this review.

The second chapter (39-86) is devoted to Plato, specifically those passages in Parmenides, Meno, Phaedo, Phaedrus, Timaeus, Theaetetus, and Sophist wherein Plato seems to be assuming an account of concepts and concept formation in his arguments about knowledge (epistēmē), belief (doxa, recollection, and language. Somewhat surprisingly, Republic is barely touched on and Cratylus is not mentioned at all. The main conclusion that emerges from this chapter is that for Plato the process or activity of concept attainment is always to be understood in relation to eternal Forms and to the innate knowledge of these. Thus, concepts come from—ek would be the correct Greek word here—the pathos in the soul that is the knowledge of Forms. They are always images of the content of each Form, although the different ways in which words and concepts are images is never clearly stated. Nor is there a clear distinction between images and symbols. The primacy of innatism for Plato does not, of course, preclude what we would naturally call concept formation from empirical experience. But this innatism provides the authoritative justification for criticism of empirically derived concepts, whatever these may be.

The third chapter (87-140), titled 'Aristotle's Reaction to Plato' is aimed at setting forth what Helmig takes to be the fundamental differences between Aristotle and Plato in the matter of concept formation and the acquisition of knowledge. Helmig focuses on Posterior Analytics II 19 and the account of induction and then, somewhat more surprisingly, on Aristotle's account of mathematical abstraction. He argues that the key to understanding Aristotle's view of concepts is his rejection of innatism. Indeed, insofar as empirical concept formation is concerned, this would seem to be obviously true, though one wonders if it could have possibly been otherwise for Plato. And yet, as Helmig mentions only in passing (34), later Aristotelian commentators, both Peripatetic and Platonist, thought that this could hardly be the whole story, given what Aristotle says about the active intellect in De Anima III 5 and elsewhere. If the active intellect, when separated from the embodied person 'is what it is', that is, manifests its true nature by, presumably, thinking all that is thinkable, then it is not at all absurd to insist that there is a sort of innatism underlying our capacity for empirical concept formation, much as Plato himself was interpreted to hold. As much can be said for Helmig's lucid discussion of mathematical abstraction, where the central issue is how 'perfect' mathematical figures and numbers can be abstracted from natural bodies. Helmig's view is that for Aristotle, mathematicals inhere in bodies without qualification (107). But he adds, 'it is undecided whether or not mathematicals are perfectly instantiated (his emphasis).' I am not quite sure I understand what imperfect instantiation would be in this case, but if it is imperfect in any sense, then the same considerations that led Aristotle to posit an active intellect would seem to come into play in the transition from sense-perception to mathematical conceptualization.

The fourth chapter (141-204) addresses three 'case studies' in the later tradition's reflection on Plato and Aristotle on concepts. The three cases are Alcinous, Alexander of Aphrodisias and Porphyry (treated as one on the topic of universals), and Plotinus. Alcinous, in his Didaskalikos produced the only extent handbook of Platonic philosophy in the period known as Middle Platonism. In chapter four, he tries to summarize his understanding of Plato's epistemology. The criterion of truth for sensibles is called doxastic logos, evidently a gloss on Sophist 263E-264A (not mentioned by Helmig) where doxa that arises from sense-perception is distinguished from doxa that arises from thought alone. As Helmig interprets Alcinous, doxastic logos is available to us owing to our innate knowledge. I find this interpretation persuasive in that it serves as a sort of systematization of the insight offered by Plato in the so-called recollection argument in Phaedo to the effect that our ability to judge (i.e., have doxa of) sensibles is dependent on our prior knowledge of Forms. The section on Alexander and Porphyry is full of interest but, alas, too brief, given the cascading confusions introduced the substantializing of the Greek adverb katholou and it apparent use as a synonym for concept. For this move invites us to think of Forms as universals as opposed to what I take to be the more accurate historical approach according to which Forms can be considered universally in thinking, but can also be particularized in individuals since Forms are in themselves neither universals nor particulars. The section on Plotinus is also too brief, as indicated by Helmig's treatment of Plotinus merely as 'Wegbereiter' of Syrianus and Proclus. Although Helmig has some useful things to say about recollection and its role in the formation of empirical concepts, there is almost no discussion of the extensive treatment of memory in Ennead IV 3, 24 - IV 4, 12, a treatise in itself, highly relevant, I would think, to Helmig's theme.

The fifth chapter is really an introduction to the sixth and seventh chapters, by far the longest section of the book (ch.5, 205-221; chs. 6-7, 223-333) on Syrianus, the teacher of Proclus, and on Proclus himself. The principal thesis advanced in these chapters is that Syrianus, followed by Proclus, have a theory of concept formation that is 'a systematization and elaboration of Plato's theory of recollection (208)'. On this theory, the acquisition of universal concepts through sense experience is not exactly rejected but definitely made subordinate to the reflection in the intellect or in some cases projection of innate Forms. What is especially interesting and original in the later Neoplatonic accounts of Platonic epistemology is the apparent shift—perhaps beginning in Iamblichus—from the Platonic insistence that epistēmē and doxa have distinct or discontinuous objects to the view that it is possible to have both modes of cognition of Forms, though it is not clear that these philosophers took it to be possible to have both modes of cognition of sensibles. Helmig's two chapters on Proclus serve as the first detailed study of doxa in Proclus and in other Neoplatonists, although Helmig generously acknowledges many previous studies of particular texts and problems. I cannot here in a limited space do justice to the detailed analysis Helmig provides of Proclus' account of the stages of concept formation, especially on how error arises and the delicate problem of how we acquire concepts of things of which there are no Forms. A brief concluding chapter argues that at least in the matter of concept formation, the Neoplatonic assumption of the harmony of Plato and Aristotle is to be resisted.

This book serves to open numerous channels for debate and further research. It is particularly successful in demonstrating the fruitfulness of the study of later Greek philosophy for better understanding both Plato and Aristotle. I would be pleased to have Helmig and Proclus persuade me that they have not just misunderstood Plato in supposing that it is possible to have doxa of Forms. From Alcinous to Proclus (and, I would add, even before the one and after the other), there is a wealth of material discussing in a way that is both sympathetic and critical the problems any careful reader of Plato will encounter. It is books like this one that are, in my opinion, revitalizing the study of the major works of the canon of ancient philosophy.