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Pythagoras: numbers and reality


To: Leonidas M.
From: Geoffrey Klempner
Subject: Pythagoras: numbers and reality
Date: 12 March 2002 15:57

Dear Leonidas,

I do apologize for keeping you waiting so long for my reply to your notes on unit 14 of the Ancient Philosophy program (11 February) and your second essay, on Pythagoras (9 February). If you've followed my Glass House notebook and the Philosophy Pathways newsletter you will know that these last four weeks have been a traumatic time for me. This is in fact the second day of what is going to be a long haul: catching up on a month's backlog of letter writing.

I'll start with the essay:

'Just as Thales said everything is made of water, so the Pythagoreans said that everything is made of numbers.' - is that a fair assessment of the Pythagorean theory? Were they proved right?

In unit 6, I do not give much credence to the idea that things 'are' numbers, emphasizing instead the doctrine of Philolaus (echoed in the 'Critique of Pure Reason' where Kant discusses 'intensive and extensive magnitudes') that everything that exists can be analysed into 'unlimited' and 'limiter'. In your essay, you make a creditable effort to show how the idea that the fundamental elements of things literally 'are' numbers is not so mad as it sounds - by tracing the connection noticed by Guthrie with the primitive belief that 'there is a natural affiliation between the object and a part of the object, or the picture or even the name of it'.

A classic illustration of this is the voodoo doll, which you stick pins in, in order to cause injury or death to your enemy, which the doll, in some sense, 'is' and does not merely represent.

We are not talking about rational inference here, but rather 'theory' in the sense of explaining something unknown by analogy with, or using as a metaphor something known. In this case, what is 'known' is something that we would call a primitive superstition. Yet it doesn't take such a great effort to get into the mind-set where the idea of affinities makes sense. - This is something I admit that I completely missed.

From the opposite side, historically - from contemporary physics - it appears that physicists are now talking about explaining matter/energy in terms of something yet more fundamental, which is not a million miles away from Pythagorean 'laws of harmony'. Only certain sets of possible laws, it now seems, obey the mathematical requirements for laws that are truly universal, equally true from all points of view, at all places and times. And these laws are held to be sufficient in themselves for the generation of matter. (I have heard such an enterprise described as 'experimental metaphysics'.) A nineteenth century physicist would surely regard such ideas as the wildest fantasy, certainly as far out as the Pythagorean theory.

Unit 14

Let's look at your four alternatives, A-D.

A. 'Any human can formulate his own theory about the ultimate nature of things...and there is no way to choose which theory is valid.' - This would be consistent with what Karl Popper says about scientific theories being conjectures which the experimenter seeks to refute. The fact that a scientific theory has passed every test we have been able to devise does not show that it is true. Truth, as correspondence with what is objectively out there, can never be known. However, although Popper agrees that 'any human being' can formulate a theory', it doesn't follow that any theory is as *good* or as *useful* as any other theory.

B. 'Human beings can not surpass their sensory even if things exist beyond and independently of human perception, we can not find a Truth accounting for their existence.' - This looks like a formulation of Kant's distinction between phenomena and noumena. Sensory perception, according to Kant, gives 'things' in 'space' (there could be no perception at all if data could not be organized into a framework involving space or something analogous to space). But 'things' in 'space' are not *things in themselves*. Of that, we can have no knowledge.

C. 'There is no such thing as truth...'. - This I have difficulty with, or, rather what you go on to say as the two alternatives: idealism (to exist is to be or be perceived), or naive realism (things are exactly as they appear). Berkeley, according to Kant, falls into the fallacy of thinking that how things are in themselves (i.e. in God's mind) can be conceived in terms of concepts that apply to the human, finite case. So there are our perceptions and God's perceptions. According to either Kant or Berkeley, however, there *is* truth, namely, how things are in metaphysical reality. The second of your two alternatives seems pretty crazy. (I remember our daughter when she was small remarked that the sun followed her when she walked along. 'Suppose that someone is walking in the opposite direction?' I asked her, 'Does the sun follow them too?' 'Yes, she replied, without any sense of inconsistency.)

D. 'The real nature of things can be conceived through sensory perception and not through reasoning alone.' - That will do as a statement of empiricism.

- One alternative that you have missed is what I describe as 'anti-realism' in unit 14, which seems to be a rather better candidate to the ones you give for a theory that says, 'There is no such thing as Truth.'

The question left unresolved by all these alternatives - all these 'isms' - is whether Protagoras is posing a problem that we should be worried about ('knowledge is not possible because man is the measure'), or proposing a solution ('knowledge is not possible according to the traditional view, but it is possible according to my view that man is the measure'). My feeling, for what it is worth, is that Protagoras is talking about metaphysics and also about ethics, conceived as part of metaphysics. His statement is an attack on metaphysics, and simultaneously a defence of 'down to earth' knowledge.

All the best,