What then doesSocratesthink iswrong with a bottom-up theory of knowledge? Hisrefutation of the Dream theory is long and complex, and I shall here try to sketch only its main outlines, since its details do not bear directly on the main contentionsof thisbook.247
Socrates' critique focuses on the Dream theory's requirement of cognitive asymmetry, according to which the kind of account which yields knowledge is built up from starting points which themselves are simply given, and not known.
The word for ‘complex’ (syllabē) means ‘syllable’ aswell, just asthe word for element (stoicheion) also means ‘letter’, making it entirely natural that Socratestakesashisexample of a complex the first syllable of his own name, ‘SO’. The dilemma about thissyllable, articulated by Socratesat 203c4–6, sets the main agenda:
OK, then. Do we say that [1] the complex is both the elements, and, if there are more than two, that it is all the elements? Or that [2] it is one single form that has come into being when they were combined?
Thisdilemma offersusa choice between what we can conveniently call [1] reduction and [2] emergence.
On [1], the complex just is itselements, that is, the ‘sum’ or conjunction of them, variously referred to in the ensuing discussion—see especially 204b7–e13—as ‘all’ (singular or plural), and as
247 Cf. fuller and highly illuminating discussions—though with different conclusions from mine—in Burnyeat (1990: 134–209), Harte (2002: 32–47).
their ‘number’. On this reductionist view, when you have listed the ultimate elements of something you have finished saying what it itself is. (The fact that the letters constituting a syllable must be arranged in a certain order is never noted or exploited by Socrates in this discussion, and should probably be judged irrelevant to it.)
On [2], the elementsare what went into the complex in the first place, but they have now been superseded by something new that has emerged. At 203e2–5 thisisdescribed assomething that hasbeen produced from the combination of the elementsbut isdifferent from them. Socrates' description of this second option suggests the modern terminology of ‘emergence’, often applied to the emergence of life from structures of inanimate components.
[1] impliesa collection of distinct elements, which, however viewed, enumerated, or arranged (cf. 204b10–c3), is the same set. An example might be a book collection: wherever my individual books are at a given time—on the shelf, on my desk, lent to friends, mislaid—they still remain jointly the same book collection. Socrates' own examplesat 204b10–d12 seem likewise to be things plausibly regarded as identical to the sum of their parts, however distributed: (a) the number 6, simply counted out, is the very same thing as
; (b) a given quantity of length or area isidentical to the number of unitsit consists of; (c) an army isthe same thing asitsown number. The non-arithmetical example (c) may seem the hardest to grasp, but I take the point to be that an army, like a book collection, is something that retains its identity so long as all its members continue to exist, however they may be distributed. Whether the individual soldiers of the army are in battle, on home leave, or in marching formation, it remains one and the same army, so long as they continue to constitute it.
[2], by contrast, makes the elements mere ingredients, no longer actively present in the resultant complex. An easy example would be cake. The flour, eggs, and milk that were a cake's original ingredients are no longer its parts; instead something altogether new has superseded them, namely cake. The parts of the cake are not flour, eggs, etc.: they are slices, crumbs, etc. of cake. This, presumably, is the main reason why in the argument that follows Socrates will take it that, on the assumption of [2], a complex does not have parts. A cake does of course have parts in so far as slices, crumbs, etc. are parts, but in the sense relevant to the Dream theory it doesnot, because the parts of cake are still just cake. Hence there is nothing
that you could know about the whole that you did not also know about the parts. The ‘parts’ or ‘elements’
postulated by the Dream theory were not of this kind, but were supposed to be epistemologically independent of the complex.
On the basis of the distinction between [1] and [2], Socrates' argument moves as follows.
203c7–e1. Assuming [1], the complex just is the elements, so anyone who knows the complex ipso facto knows the elements. For example, if ‘SO’ is the same thing as S and O, anyone who knows the syllable must know the letters S and O. This would, however, be enough to demolish the cognitive asymmetry on which the Dream theory is founded.
203e2–204e10. Assuming [2], on the other hand, the complex does not consist of parts, because what consists of partsisthe sum of those parts, which would bring usback to [1]. Apparently the only way to avoid thisisto deny that the ‘whole’ is the same thing as the sum of parts, so that the whole does not, as the sum does, consist of parts.
204e11–205a7. But parts must be partsof a whole. Denying that sumsare wholesisno way out, because both
‘whole’ and ‘sum’ are definable as what you have so long as nothing is missing.
205a8–d3. So if, ason [1], the complex isthe same asitselements, both are equally knowable; if, ason [2], the complex isnot the same asitselements, the complex hasno parts, and hence is unknowable. Either way, the Dream theory cannot survive.
205d4–e8. The dilemma restated.
This refutation has been the subject of intense scrutiny and criticism, and it is not my purpose to review the disputes about it. I shall limit myself to saying why I think it fails, mainly in order to argue that Plato is unlikely to have been aware of the fallacy.
Early on, at 203c7–e1, Socrates argues against the reductionist thesis on the grounds that, if the complex is identical with the elements, you could not know the complex without knowing the elements. This is a move of great interest, with an illuminating analogue in much more recent debatesabout consciousness. There isa natural temptation for those who deny the identity of mental with neurophysiological states to point out that one could in principle know all about some subject's brain state yet not know at all what it is like to be that subject, i.e. know that subject's state of
consciousness. Thisparty thusarguesagainst the identity of something with what constitutesit on the ground that, were the two identical, to know that which constitutes it would be ipso facto to know the thing constituted by it. Socrates in the Theaetetus makes the reverse inference: if something were identical with its constituents, to know the thing would be ipso facto to know the constituents.
Both typesof argument may invite the objection that in intentional contextssuch asthose introduced by ‘know’ the usual rules about substitution of identical terms have to be suspended (the so-called fallacies of ‘referential opacity’).248 For example, water ishydrogen plusoxygen. From thiswe can infer that when Plato drank water he wasdrinking hydrogen plusoxygen. But from the fact that Plato knew that he wasdrinking water we cannot infer that he knew that that he wasdrinking hydrogen plusoxygen.
But this kind of fallacy is easily overlooked. There are numerous instances of it in Plato, including a number in the Theaetetus itself.249It seems to me overwhelmingly probable that Plato regards his argument as a successful objection to any thesis according to which knowledge of a thing can be derived from its analysis into things which are themselves not known.250
A weightier objection might appear to be that Socrates' disjunction between [1] and [2] was not exhaustive. Why did he not consider the following third option?
[3] A complex isthe sum of itselementsplus some formal component—arrangement, structure, function, or the like.
Thisadditional component would correspond, more or less, to the ‘form’ which Aristotle combines with matter to generate substances. It would then be possible to say that it is in virtue of knowledge of its form that we can come to know the entire complex. It is very likely that Plato's own inclinations would point in the same direction, at least to the extent of making form the primary object of knowledge,
248 Cf. Brandt and Kim (1967, esp. 534–7).
249 See above, p. 22, and p. 131 n. 18, and Williams (1972). Celebrated arguments in Plato which the same fallacy might well be diagnosed as underlying include Gorg.
467c5–468e5 and Phd. 74c1–5.
250 To this extent, the reading I propose is in tune with Gail Fine's ascription to Plato of the principle ‘Knowledge must be based on knowledge’ (or, asa variant on this, the
‘interrelation model’ of knowledge); see Fine (1979a ), and further discussion in Annas (1982), Nehamas (1984), Bostock (1988: 243–50). However, asI shall make clear below, I depart from her reading of thisinterrelation ascircular, in favour of a hierarchical interpretation which may very well leave at least one item to be known in an altogether underivative way.
although he would probably regard the ‘form’ in question as a metaphysically separated one. So why does the idea not surface here?
My first answer will of course be that the Socrates of the Theaetetus lacks the metaphysical insights that Plato's seasoned readers are expected to possess. But it is more directly pertinent to the context to point out that, on a hylomorphic account of thiskind, the Dream theory would have collapsed anyway. For either the formal component isto be counted asone of the elements, in which case there isone of the elementswhich cannot be plausibly described as unknowable; or the formal component is not one of the elements, in which case enumeration of a thing's elements was not after all sufficient for knowing it.251 The entire Dream theory depended on restricting the elements to primitive components given in perception alone. Hence the dilemma between [1] and [2] arose from the materialist spirit of Dream theory, and the exhaustiveness of the disjunction was justified in context.
At 206a1–c2 Socrates broaches his own conclusion. Our own experience of learning some system, such as the alphabet or music, confirms that knowledge of the elements (letters, notes) is both essential and in fact prior to knowledge of the complexes (syllables, harmonies) which they constitute. Knowledge of elements is ‘more self-evident and more important’ (206b7–8) than knowledge of complexes. He does not (as he is regularly reported) say here that elementsare actually ‘more knowable’ than complexes, and indeed at 205b2–3 he hasconcluded that elementsand complexesare ‘equally knowable’. He seems to mean rather that they are more directly or underivatively knowable, in accordance with a familiar use of the adjective translated self-evident (enargēs).252
If it isthe whole–part identity that makescomplex and elementsequally knowable, how can it allow the elementsto be more directly knowable than the complex? Mustn't learning the complex be the very same act as learning the elements?
Presumably not, because to know the complex is identical with knowing every element, whereas
251 Cf. Aristotle, Met. H 3, 1043b 4–13.
252 Cf. Rep. 544b4, where the same comparative, ἐναϱγέστϱον, refersback to the principle that a city'scharacter is‘easier to learn’ (368e8) and ‘easier to see’ (434d8) than a soul's, so that (545b5–c5) the former should serve as the reference point for getting to understand the latter. In the Theaetetus itself, note especially 179c6, where Theaetetus' definition ‘Knowledge isperception’ isequated with the thesisthat perceptionsand perceptual judgementsare ‘self-evident (ἐναϱγεῖς) and cases of knowledge’. Cognitive primacy, or (in the comparative) priority, seems to be the dominant notion.
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).