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Lecture 2 (15th July 1948)

The argument starts off from an account of Zeno's criticism of the doctrine that things are “a many”. Zeno contended this leads to contradictory results and incidentally remarks that he was trying to give the partisans of the many as good as they give - the point being that they had tried to show that Eleaticism led to absurdities - he in his turn was showing that Pythagoreanism led to just as great absurdities. It is a general feature of Rationalist criticism to dub views self-contradictory or self-refuting as against which the true view would be held to be self-establishing, ie., you get a division between the certain and the absurd taking the place of the empirical division between true and false and you'll notice that in the somewhat obscure and partially confused account that Socrates gives of method in the Phaedo the same points are made; i.e., the question is raised whether hypotheses do or do not lead to contradictory consequences (contradict one another); i.e., rationalistic refutation as against the empirical refutation which consists of showing that an hypothesis has consequences that contradict fact or what is assessed as fact by the persons arguing independently of the hypothesis and not as a consequence of it - which of course is the actual way in which Socrates proceeds in the dialogues and which is the account of the Socratic method presented by Burnet in Thales to Plato. It does not really establish Eleaticism if Zeno shows absurdities in the doctrine of multiplicity - just to set one group of arguments against another. The criticism is not complete until the unsoundness of one set of arguments has been shown and of course if we reject the notion of absurdity it would mean showing one of the conflicting hypotheses false because it has false consequences and that is connected again with the view that in fact both Pythagoreanism (Socraticism) and Eleaticism are false and untenable because they are both doctrines of ultimates and the real outcome is that there are no ultimates, either one or many - that there are only empirical or historical things, i.e., no irreducible or absolute realities - no “things-in-themselves” or no limits and hence it is suggested that that is really what Gorgias shows in supporting his thesis “There are none”, namely, no ultimate reality as contrasted with empirical reality though again that doesn't commit us to the sophistic conclusion that empirical reality is mind-dependent - that is only to treat mind as an absolute in the objectionable way.

One way in which the point could be put is if you formulate a notion by combining incompatible elements. For example where XeY:


then XYaZ

XeZ (argument depends on XiY)


then XYeZ

Unit: (indivisible magnitude) an incompatible … [?]

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It is perfectly easy to show many units coalesce into one but can criticise the One in the same way.

Now the particular arguments of Zeno on the many that is mentioned here is that “if things are many they must be both like and unlike”. What does this mean? If we are going to treat that as involving a contradiction then we have to be clear what is meant by “like” and “unlike”. In ordinary discussion we find no difficulty in saying that two things are both like and unlike - namely in the sense they have some characters in common and another character(s) in which they differ.

(1) AaX


(2) AaY


The point rather is that like and unlike are incomplete expressions. We should say A and B are alike in being X but are unlike in the fact that only one of them is Y. The general statement A is like B ennumeration of the term (A or B) without any predicate yet having been applied to it. However, Zeno's argument has more force than this - it is directed against the Pythagorean units each of which was just one or has unity as its whole character so that we couldn't distinguish one unit from another - would have to say that they were alike in all respects. On the other hand, if there are two of them we must be able to show some difference between them - they must be unlike if we are to say this is unit X and this is unit Y. Trouble is caused then because it isn't a question of respects in which things can resemble and differ from another but of total natures, of what a thing just is, and of course we get the same difficulty with any rationalistic theory. In Thales, e.g., if two things both just water - water the true substance or constitution then you can't find any difference between one and the other - in other words what we may call “substatialism” is a form of rationalism and is open to the general objections to rationalism. Now, it is partly to escape such difficulties that the later Pythagoreans and Socrates following them made the division between empirical and rational - that later Pythagoreans replaced the doctrine that things are numbers with the doctrine that things are like (approach) numbers - that what is just one or just six stands above experience (history) and things are to be described according as they approach one or other of these standards and Socrates adds to those mathematical standards (including the just equal) such standards as the just beautiful - aesthetic and moral standards - and thus we get the doctrine of forms - a doctrine which separates the empirical or historical from the unhistorial or absolute but in the same way as there is a difficulty (impossibility) of distinguisihing and relating what a thing absoutely and essentially is and what it relatively or accidentally is so there is the difficulty (impossibility) of distinguisihg or relating the two different realms - the realm of the historical

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and the realm of the unhistorical (becoming and being) - it is that difficulty that Socrates is vainly trying overcome in the Phaedo with the doctrine of participation and its that attempt that is now being shown up in Parmenides. What is being shown is that you don't reduce your difficulties by formulating those two realms. Empirically speaking there is no difficulty in saying A and B both like and unlike when we mean in different respects. It would be impossible to say things like and unlike in the same respect but this point is obscured by Socrates when he argues that things could not partake of one another because if we are dealing with the same respect there would be the same opposition whether we are concerned with particular examples, A and B, or with general possibilities, a question of comparability or otherwise of general characteristics. No difference in either case and if it is a question of different respects, i.e., likeness in respect of X no opposition to likeness in respect of Y and in fact the two cases are not distinct at all but both can be understood only empirically.

N.B. Socrates difficulties in Phaedo with relations in general (smaller and greater).