The programme requires Forms to be posited as objects of scientific knowledge. They provide the sciences with a subject-matter about which their statements are made, and of which these statements hold true. 'The true' is not clearly distinguishable in Greek from 'the real', nor 'that which is the case' from 'that which exists'. See previous note and on 66b 1— c5. The requirement that what is known must 'be true' thus gives rise to the view that the objects of knowledge must be 'realities' or 'existents'. And, since the truths attained in mathematics and dialectic are timeless or eternal, the 'realities' are credited with this feature as well. The Forms thus serve as timeless realities discovered in mathematics and dialectic. Their existence is a necessary condition for there being scientific knowledge at all.
For certain mathematical concepts, such as squareness, circularity, and equality, the Forms are treated as ideal exemplars of properties that are never perfectly embodied in physical objects. No piece of wood is perfectly square, no stone is perfectly circular, no two sticks are exactly equal. The perfect Square or Circle, or
Absolute Equality, may thus be thought of as a standard, to which objects in the sensible world approximate but of which they fall short. The Form serves as a paradigm for such properties. Indeed 'paradigm' derives from a word Plato sometimes uses for Forms in this role. It connotes an individual used as a pattern, sample, or model for a given property, to determine whether or how far other individuals possess it. Just as the length or weight of a thing is determined by appealing, ultimately, to the standard metre or pound, so—according to the Theory—there is an implicit appeal to the Form F when an individual is judged to be F.
This idea is fairly naturally extended to concepts of value. No man or society is perfectly just or good. Yet to say that individuals fall short of perfect justice or goodness is to suggest that these ideals exist independently of any particular man or society, and may be more or less closely approached by them. Moreover, since the ascription of these properties is often uncertain or controversial, the Form is supposed, once again, to provide a paradigm or measure against which individuals can be assessed. In the Republic Plato portrays the perfectly just man and society with this express purpose.
There is, however, a crucial difference between Platonic paradigms and the standards used in weighing or measuring physical objects. The standard metre is itself a sensible item, whereas a Form is not. It is an important feature of the Theory that no sensible item can provide an ultimate standard against which others may be measured. Sensible Fs are inherently defective, and must therefore fail to be 'really' F. Only a non-sensible F can be properly so called. The Form cannot be identified with any of its sensible instances. The various grounds for this claim will be discussed below. See on 74b7— c6.
(c) The Forms posited in the Phaedo are mainly those for the quantitative and value concepts studied in mathematics and dialectic. But the Theory has a further dimension: it offers a general account of predication and naming. Forms are the designata of common adjectives and nouns predicated of individual subjects. Thus at 102b2 (cf.78e2, 102cl0, 103b7) it will be said that things called 'large', 'small' and 'beautiful' are 'named after' the relevant Forms. The prime bearer of the name kF' is the Form F. It is the one thing common to each of the many Fs, the single feature F-ness shared by its many instances, the meaning of their common name. In this capacity, it functions as what later came to be called a 'universal'.
In the Republic (596a) Forms are said to be posited for each plurality of things 'to which we apply the same name'. This formula is so broad that it has sometimes been doubted whether Plato would seriously have posited Forms for every item it covers. Forms for artificial objects, for example, seldom appear. Such Forms as Shuttle (Cratylus 389b), Bed, and Table {Republic 596b) are introduced only for special purposes, and may have played no part in the Theory in its original form. Yet, clearly, a far wider range of Forms is demanded by a theory of 'universals' than by the concerns of mathematics and dialectic. This implication is faced in the Parmenides (130c—d), where misgivings are expressed over extending the Theory to such classes as Hair, Mud, and Dirt.
It should be noted that the 'universal' role of Forms is distinct from their scientific and paradigmatic roles. Immense difficulty is incurred if these roles are conflated by treating all Forms alike as postulates of a single, comprehensive 'theory'. Some of the resulting problems will be considered further below. See on 74d4—8 and 102a 10—d4.
(3) The Theory of Forms and the belief in immortality were called by F. M. Cornford the 'twin pillars' of Platonic philosophy. But the metaphor misrepresents the logical relationship between them. For the doctrine of immortality is logically dependent upon the Theory. All of the major arguments except the first are based upon it. This dependence is made explicit at 76e—77a, 92d—e and 100b. The Theory is clearly fundamental.
It is, however, nowhere defended, but is simply accepted without argument by all parties (65d6, 74b 1, 78d8-9, 92d6-e2, 100cl-2, 102al0—bl). Its status is well described in Simmias' words at 85c8— dclass="underline" it is 'the best and least refutable of human doctrines'. These words, though they do not, as uttered by Simmias, refer to the Theory, are so closely echoed by Socrates later that they may be taken to express his own position. Cf.99c6—100a8 and see on 84d4— 85dl0. The Theory is 'the theory he judges to be strongest', adopted provisionally and for the sake of argument. It offers the most plausible solution he can find to the problems outlined above.
Socrates will urge that the validation of a first principle should not be mixed up with the testing of its consequences (lOlel—3). Similarly, criticism of arguments based upon the Theory should be distinguished from criticism of the Theory itself. The arguments for immortality must remain inconclusive without a defence of the Theory, as Socrates recognizes at 107b4—6. But the Theory is, in this dialogue, subordinated to the discussion of immortality and cannot be further investigated here.
A lucid exposition of the Theory of Forms is given in G. Ryle's article 'Plato', in the Encyclopaedia of Philosophy, ed. P. Edwards (New York, 1967) vi. 320-4.
66b 1— c5. For the text and translation at 66b4 see note 10. The words translated 'that, we say, is truth' (66b7) mean, more literally, 'we say the true to be that', the referent of 'that' being 'what we desire'. Cf.67bl. 'The true' combines a neuter singular adjective with the definite article, not to designate an individual Form, but to characterize the Form world in general. Many other adjectives are so used. Cf., e.g., 79d2, 80bl-2, 81a5, 83e2, 84a8. 'The A' in such passages does not mean 'the Form A' but 'that (domain) which is A', where 'A' is an attribute of Forms as such—'pure', 'divine', 'immortal' and the like.
The adjective translated 'true' can also mean 'real', as well as 'genuine' or 'truthful'. It has an attributive use, in which 'true T means 'genuine X or 'X properly so called'—e.g. 'true goodness' (69b3). Plato commonly uses 'the truly X" in this sense—e.g. 'genuine philosophers' (64b9), Note also that 'true' or 'real' admits of degrees—cf., e.g., 65el—2, 83c7. See note 8, and on 83b2—3.
'True' has generally been used, and 'truth' for the abstract noun. But 'real' has seemed necessary at 81b4,83b3,83c7, and 83d6. Like the verb 'to be' (see on 65c2—4), 'the true' embraces that which exists as well as that which is the case. Since the Platonic Form world is 'the real', and knowledge of it affords 'the truth', the two senses of the word naturally converge in references to it. 'Truth' in this sense is perhaps meant at 65b9, 66a6, 66d7, 67b 1, and 99e6. Sometimes the meaning seems more general, as at 91cl—2, 102b9, and 115al. At 65b2 'truth' approaches 'veracity', and at 89d6 'true' approaches 'truthful'. See also on 89dl-4 and 90b4-91c5.