you can get to know the elementsone by one in advance of knowing the complex, and indeed asa meanstowards knowing it. In Socrates' own examples of reading and music, it is scarcely deniable that the learning sequence followed isexactly that.
The ‘elements’ of which Socratessaysall this—alphabetic letters, musical notes—are still very much the kind of perceptible constituents assumed in the Dream theory. Nevertheless, the intuition which his parting shot conveys is highly Platonic in spirit: whatever the items may eventually turn out to be that knowledge is based on, they must themselves not only be known too, but must be more directly, self-evidently, or underivatively known than the items known on the basisof them. The model of knowledge which thishintsat is, I think, Plato'sown. It isnot simply a coherence account of knowledge, based on a complex network of cognitions. It is essentially hierarchical. Some things are known derivatively, thanksto prior and more direct knowledge of other things. Such a hierarchy would, one supposes, have to have an absolute starting point in something known in an altogether underivative way. Such a role is indeed played by the Form of the Good in the Republic, and I see every reason to infer from Socrates' ground for rejecting the Dream theory that Plato still has that same kind of hierarchical metaphysics in mind as the true basis of knowledge.253
Socrateshimself doesnot have Plato'shierarchical metaphysicsin mind. But hisintuitionsabout the order of acquiring knowledge, based on childhood learning experiences which start from something irreducibly primary, already point tellingly in that same direction. If Plato feels able to attribute these intuitions to his master Socrates, the acknowledgement no doubt owes much to Socrates' ubiquitous insistence on the primacy of definition in any investigation (item 4, p. 33 above).
unintentional. Moreover, he adds, it could be refuted in other ways. But what hasbeen refuted? Not the definition of knowledge astrue judgement plusa logos, which Theaetetushasremembered hearing from someone or other: that will continue to be discussed. And not the further equation of logos with an enumeration of elements, for that too will now continue to be considered as a live option, with explicit reference back to its formulation in the Dream theory (207b6).
All that hasbeen refuted, then, isthe cognitive asymmetry of the Dream theory.
At 206c7–8 Socratesundertakesto list three thingsthat Theaetetus' anonymousinformant254may have meant by logos in saying that knowledge is ‘true judgement plusa logos’. One is quickly dismissed as irrelevant: ‘statement’.255Clearly the commonplace ability to articulate one'sjudgementsinto vocal assertionsisnot enough to make them knowledge, he pointsout.
The second possible meaning of logos, however, is to be taken seriously: ‘the ability, when asked what each thing is, to render the answer to one'squestioner by going through the thing'selements’ (206e6–207a1). Socratesexplainsthis with the example of Hesiod's line in the Works and Days (456), ‘A hundred timbershasa wagon.’ A non-expert might be able to list the complex (or ‘syllabic’) partsof a wagon, for example ‘wheels, axle, yoke’, etc. But only someone with knowledge could give a list of its hundred ultimate elements, presumably starting with so many spokes, so many dowels, etc.
What kind of a theory isbeing described, and what isitsorigin? In broaching thisdifficult and too rarely asked question, we can usefully start with the words quoted from Hesiod. It has, to the best of my knowledge, gone unnoticed that the original context isof direct
254 ‘OK then, what in the world doeshe want logos to signify to us? It seems to me that he means one of three things.’ The reference isto the ‘someone’ of 201c7, Theaetetus' informant, and the meaning in question is therefore speaker's meaning. Of the eight translations I have consulted, Valgimigli alone recognizes this. All the others, apart from Levett, adopt formulations which make it sound as if Socrates were stating a fact of lexicography.
255 ‘… making one'sthought evident through the voice with descriptions(̔ϱήματα) and names(ὀνόματα)’ (206d1–2). Here asoften (esp. Crat. 431b3–c1; Sph. 262a1–d7), complete statements are taken to contain both ‘names’ and ‘descriptions’, cast in the role of subject and predicate respectively (cf. p. 126 above). Socrates' point in specifying it here isnot to go back on hisearlier assertion (189e4–190a8) that thought itself even without vocal articulation is already linguistic in form, but to insist that the internal utterance which when externalized makesa vocal ‘statement’ is not just any internal utterance, but one which already contains both a subject and a predicate.
significance for their interpretation. Hesiod's catalogue of farming advice has brought him to the need to possess your own wagon and oxen: you cannot count on being able to borrow them when you need them (453–4). But in order to have your own wagon, you must make sure you have ready the entire kit of parts (457). ‘A man whose wealth is in mere thought talksof constructing a wagon. He isa fool, and does not know: a hundred timbershasa wagon’ (455–6).256 It wassurely the wordswhich I have emphasized that first drew somebody's attention to their immediate sequel as implying a definition of knowledge. For it looksasif the need to be able to recite the inventory of all hundred wagon parts (not, of course, merely to be able to say how many there are) was read by somebody as Hesiod's own recommendation for how to acquire knowledge on the subject of wagons. I have not found any other traces of the interpretation, but Hesiod was widely revered as authoritative (as Heraclitus famously complained),257 and it is conceivable that some Presocratic author had cited the line in support of the thesis that only when we have discovered all of a thing's constituent parts can we be said to know it. There is certainly no reason to assume that Plato himself is responsible for extracting this message from Hesiod, both because, as the ensuing refutation will confirm, he doesnot regard the Hesiodic view (if such it is) as in any way authoritative, and because in the present Theaetetus passage he fails to cite the context which would have brought out the full significance of Hesiod's line. Rather, what we have here is evidence that someone else'sactual theory of knowledge isbeing alluded to: it isnot purely Plato'sown ad hoc construct. If I were forced to guess the source, I would suggest the atomists, Leucippus and Democritus, whom Plato notoriously never once names in his writings. The reason for thinking of atomic constituents will become a little clearer shortly.
A second serious problem, which I have never seen adequately addressed,258let alone solved, is why despite the demise of the Dream theory Socratesin thisway immediately goeson to consider another theory in which a thing's logos isa list of itselements. There are two
256 νήπιος, οὐδὲ τὸ οἶδ̕ ἑκατὸν δέ τε δούϱατ̕ ἀμὰξης.
257 HeraclitusB40, 57, 106 DK.
258 McDowell (1973: 252–3) does at least ask the question, and, if briefly and with little conviction, canvasses one possible answer (his item (1) ). Most other discussion focuses on new points Plato wishes to make in refuting the theory without pausing to ask what the point of the theory itself is meant to be.
main differencesfrom the Dream, each representing in itsown way a philosophical advance.
First, the new theory's examples of ‘elements’, such as the spokes of a wagon-wheel, are functional parts with a definable formal aspect, and therefore are not entirely comparable to what I took, in the Dream theory, to be primitive material components given only in direct sensation. It seems a fair guess that in Plato's eyes ‘elements’ like these would be superior candidates for being ultimate constituents of bodies; and that suspicion is to some extent confirmed towardsthe end of the dialogue, where SocratestreatsTheaetetus' ‘constituents’ asincluding such formal featuresas his own particular snubness, or snub nose (208c5–10).259
Secondly, In keeping with this rescued formal aspect of the elements, the revised theory quietly drops any mention of cognitive asymmetry. It is not entirely clear that this latter can be so simply done, because if knowledge of X depends on a logos which lists X's elements, and if elements do not have elements, we may seem to have little choice but to accept that the elementsby which X isknown are themselvesunknowable—in short, back to cognitive asymmetry.
However, in view of the firm refutation of cognitive asymmetry, combined with the absence of any mention of it here, we must assume Socrates to be leaving open the question how elementsthemselvesare known, rather than condemning them to unknowability. Presumably in this special case of elements themselves they are known in some other way, e.g.
by stating their function in the whole (cf. the previousparagraph). Let uskeep the question asopen asSocratesleaves it. The problem remains: why reiterate the element theory in this new form?
My contention is that only when we have understood the Dream theory correctly can we see the point of the revised element theory. What Socrates has in mind, I suggest, is not this time a Presocratic mode of analysis into primitive elemental stuffs, in the style of Anaxagoras and Empedocles, but the kind of structural element theory that had been pioneered by the early atomists, and that was
259 For the point, see Burnyeat (1990: 140), who takes Theaetetus' snubness to be treated as a constituent. It may alternatively be that by ‘and likewise the other things you consist of’ Socrates means, not purely formal features like snubness of the nose and bulgingness of the eyes, but ‘and so too for your other parts’ (i.e. other than your nose).
But, even if so, the same general point would survive, namely that a thing's constituents are to be understood structurally and formally, not in a narrowly material way.
to be articulated in a more sophisticated form by Plato himself in the Timaeus. Plato'sversion isbased on analysisof stuffs, via geometrically defined particles, into primary triangles (cf. p. 72 above). According to the Timaeus, the things that conventional physics claims to ‘know’ asthe world's‘elements’—earth, water, air, and fire—are in reality not even
‘syllables’ (48b3–c2; syllabai, the same word as I have hitherto translated ‘complexes’, but here used in its alphabetic sense of minimal complexes). They are analysable into particles with the forms of four regular solids, and those solids themselves further analysable into combinations of primary triangles. This already mirrors the revised element theory in the Theaetetus, where the ability to resolve an object only into its complex parts is declared cognitively insufficient (207a9–d2). In the Timaeus even the primary trianglesare not proclaimed asthe ultimate starting pointsof knowledge, but their own underlying principlesare left mysterious: these are known only to god and to a favoured handful of human beings(53d6–7), and to pursue them would require a methodology alien to the current physical investigation (47c2–d1). It is not hard to conjecture from this that the ultimate principles are ones whose understanding requires high-level mathematics, much as, in another domain of inquiry, understanding of the Good no doubt does.260But so far asthe term ‘elements’ isconcerned, in the Timaeus it isthe primary trianglesthat are so designated (54d6, 55a8, 55b4, 57c9, 61a7).261It seems then that, according to Plato's own physics, complex bodies may be analysed exhaustively all the way down to primary triangles, their ultimate ‘elements’, and those elements, while not having ‘elements’, i.e.
constituents, of their own, could in theory be explained and known by appeal to some even more fundamental principles, presumably through some higher-level mathematical analysis.262
The revised element theory in the Theaetetus is so close in spirit to this Timaean physics that I find it hard to doubt that Plato has it, or something very like it, in mind. Unlike the Presocratic-style reductionist Dream theory, the Timaeus' physics resolves compound
260 Cf. Cooper (1977).
261 56b5, where the pyramid isthe ‘element’ of fire, isthe only exception I have been able to find.
262 This assumes that the ultimate analysis of the triangles would locate them in the intelligible realm, rather than treat them as imperfect and unstable particulars. To pursue this idea would involve some complex speculation about Plato's unwritten doctrines on the mathematicals.
bodiesinto ultimate ‘elements’ that may somehow be knowable, and which certainly have a form and a structural function within the whole. Hisspeaker Socrates, to fit the historical retrojection, has to be referring not to the Timaean theory itself but to some unspecified forerunner of it—most probably to Democritean atomism, which resembles the Timaean theory in regarding itsprimary elementsasmore genuinely knowable than the physical compoundsthey constitute.
The question remains, even without cognitive asymmetry, whether such a resolution into elements is the route to knowing the compound bodies. Socrates can see that it is not, and what the Theaetetus sets out to exhibit is why.
Briefly, Socrates' objection to the revised element theory is the following (207d3–208b12). One might succeed in stating the elements of a given complex, but on another occasion misstate those same elements—asoften in fact happens when in spelling you spell a certain syllable right but misspell the same syllable in a different word. Someone who did that could not be said to have ‘known’ the syllable, or complex, even on the first occasion. The point of this criticism is that getting something right on one occasion can guarantee no more than true judgement, and in itself lacks the reliability which characterizes knowledge. It is easy to see that the insight applied here is the thoroughly Socratic one from the Meno (96e1–98b5) that we have already met (pp. 149–50 above): the difference between true judgement and knowledge liesin the latter'sdependability.
When combined with the refutation of the Dream theory, the refutation of the revised element theory will have the effect of explaining two insights underlying the philosophical direction that Socrates chose to take. He not only rejected existing (Anaxagorean-style) reductionist physics as a route to knowledge, but also saw that even an improved physics, along the lines of a reformed atomism, could never, in principle, be the basis of knowledge. We need to keep both of these insights in mind in order to see why Socrates' own search for knowledge abandoned physics altogether, and took instead the path that it did, that of pure dialectic. And if Plato would eventually, in the Timaeus, reinstate physics, that wascertainly not asa meansto knowledge, a cognitive state to which itsmethodology could never aspire (Timaeus 27d5–28a4, 29b3–d3), but asa mode of
investigation condemned to remain in the realm of less or more plausible ‘judgement’ or ‘opinion’ (doxa).