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Parmenides' case against plurality


To: Scott B.
From: Geoffrey Klempner
Subject: Parmenides' case against plurality
Date: 17th October 2008

Dear Scott,

Thank you for your email of 8 October, with your University of London essay taken from the Greek Philosophy: Presocratics and Plato paper, in response to the question, 'Critically assess Parmenides' denial of plurality.'

Parmenides case against plurality is important because the atomists Leucippus and Democritus put forward a view of reality which ostensibly respects Parmenides' strictures concerning what it is to 'be'. Each indestructible 'atom' is an instantiation of Parmenidean being, a Parmenidean 'one'.

The exam question is quite specific: what it asks you to do is look at the argument which Parmenides targets at the hypothesis of plurality. However, what you have done is attempt a complete exposition of Parmenides' arguments. Although you mention his argument against the possibility of a vacuum, the only time the rejection of plurality as such gets mentioned is in your penultimate sentence, 'He also denied the idea of plurality and the common sense belief that there are many things.'

In an examination, you will lose marks for this. I can't stress enough the importance of answering the question, and organizing the structure of your essay for this purpose alone. So far as the content of your essay is concerned, you give a reasonably good account of Parmenides' arguments. (I am glad to see that you have found my notes on Parmenides useful!)

What does Parmenides say about plurality? Here is the relevant fragment authored by Simplicius, quoted in Kirk, Raven and Schofield 'The Presocratic Philosophers' p. 250:

'Nor is it divided, since it all exists alike; nor is it more here and less there, which would prevent it from holding together, but it is all full of being. So it is all continuous: for what is draws near to what is.' (Fr. 8, 22-5).

Some of the fragments are less than clear, but this is a precise, carefully formulated attack on plurality which attempts to demolish all the possible ways in which plurality might be constituted.

First, 'all exists alike', so reality cannot be 'divided'. So you can't have a volume of quality F next to a volume of quality G, because there can't be different qualities.

Next, 'nor is there more here and less there.' You might think, OK, I accept that there is only one quality F, but maybe (as in Anaximenes' air) the quality F-ness can be more or less dense, in which case this would suffice for drawing distinctions between different parts of reality and thus give rise to plurality.

Finally, there can be nothing to prevent reality from 'holding together'. Arguably, there is room for different interpretations of Anaximenes' view of condensation and rarefaction. Putting aside our modern knowledge of physics, the notion of differences in density does not logically entail the idea of a vacuum, in which component parts would be more or less widely dispersed. This only follows if we accept the hypothesis of separated parts as an explanation for differences in density.

However, it is reasonable to speculate that the evidence from this fragment is that Parmenides does hold that differences of density can only be explained by a vacuum. The point to note, however, is that his argument does not depend on this. Differences of density alone would be cases of 'what is not' because the area where the quality of F-ness is less dense, is 'not as dense' as the area where the quality of F-ness is more dense, whether this entails a vacuum or not.

How would one go about attacking this argument? That's what the examiner is interested in. Obviously, you have to say something about the background assumptions working here, the case which Parmenides makes for 'it is'. However, the meat of the essay is in the investigation of the particular conclusions concerning plurality which Parmenides draws from the assertion 'it is'.

Is reality spatially extended? It seems it must be, if one can talk of it being 'like a ball well-rounded on every side'. However, it follows logically from the hypothesis that A is spatially extended that there are different locations within A. The fact that we can't identify different parts doesn't entail that we cannot even speak of parts. At least, there is room for debate here over what constitutes a 'part'. Parmenides would argue that we have no coherent notion of a part of reality in the absence of an actual distinguishing feature.

Or perhaps Parmenides' talk of 'well-rounded' reality is merely intended as metaphorical. To say that reality is an object of thought, and indeed the only possible object of thought, is not to claim that reality is thought. So reality is neither, as such, 'spatial' or 'mental'. Like all the other terms Parmenides casts away, these are just concepts which we use in differentiating our 'reality'.

This suggests a different tack: that, actually, Parmenides does have a strong case for the view that *There is only one reality.* This view is implied by the idea that truth is objective rather than subjective, absolute rather than relative. Every statement we make is measured against 'reality'. If there could be more than one reality then nothing would be 'true' or 'false' as such, but only relative to one of several possible 'realities'.

I'm not saying that this relatively anodyne reading of Parmenides is necessarily correct. Parmenides is uncompromising in his rejection of the beliefs of 'two-headed mortals'. This seems hard to square with the idea that you can have your everyday mundane plurality and yet also claim that 'reality is one'.

I hope that you will get a better idea from this of the kind of essay you need to write in order to satisfy the examiner. A major part of learning to philosophize consists in learning to identify arguments and assess their validity. The Presocratics present a superb subject matter to develop and practice your skills on.

All the best,