The Prisoners in the Cave

 @SemprePhi drew my attention to the following book review on the 23^rd November:

Phillip Sidney Horky, Plato and Pythagoreanism 2013. Reviewed by Simon Trépanier bmcr.brynmawr.edu/2014/2014-05-1… #brynmawr #philosophy

I responded in four short posts, which I’ve now augmented with further discussion.

@SemprePhi Hi. Thanks for the pointer to Horky's book and the review. Where to start! You cannot rely on Aristotle for accurate information about the Pythagoreans. Huffman has been occupying academic space for thirty years, and won't cross the boundaries. 1/

Note the whole argument is based on the idea that philosophy in Greece is an autocthonous development. Not invented elsewhere. I've shown that Pythagoras derived many of his ideas from Mesopotamia. And that these influences are reflected in Plato. They just don't want to see. 2/

Or they fear to step outside the accepted paradigm for fear of committing heresy, and having to pay for their sin. There is much information about what Pythagoras brought back from the east in Greek writing. But scholars don't know what it is, and why [it] is important. 3/

In order to stay within the acceptable paradigm, or 'episteme', they don't read the full range of sources which are available. Consequently it is difficult to make sense of the sources that they do read. If you read the full range of sources, it is an eye-opener. 4/

Philosophers and Historians are nervous about crossing the boundaries of their subjects, not just because of the risk to their reputations. They are happiest when sense can be made of what they are looking at. That sense isn’t always the sense that things made in antiquity. Modern scholars make fictions, and sit upon the pile they have made.

The philosopher Adrian Moore wrote a history of the infinite in 1990, and presented a series on BBC radio in 2016 on the same subject. Both discuss the problems and issues around the human response to the idea of the infinite. However Moore’s idea of the history of man’s relationship is strangely structured. Writing about the broadcast series I pointed out that:

We  get many clues about the Greek understanding of the infinite and the unlimited from a number of Plato’s dialogues, including The Timaeus, The Sophist, The Republic, The Theaetetus, The Laws, and The Parmenides. In skipping Plato, the first reference to Parmenides and his notion of the universe as simply one and one alone, is as an introduction in the first episode to his pupil Zeno of Elea, and his response to paradox. There is no discussion of Plato’s demolition of Parmenides arguments, no discussion of the Platonic forms, no discussion of the relationship of the forms to the form of the Good, which is another way of talking about what is infinite, and no discussion of what amounts to a different logical modality in the pages of Plato (where he discusses things passing into one another by means of their similitude), which is a way of understanding the relationship of finite things to the infinite.  

What Moore has constructed is a Catholic perspective on the idea of the infinite, since it is viewed from the perspective of Thomas Aquinas and Bishop Anselm. What made sense to those scholars, makes sense to Moore. Plato was largely unavailable to any scholars  of that period (with the exception of some sections of the Timaeus). But to write now about the infinite as if the writings of Plato are unknown to us, or of no importance to our understanding of the human response to the infinite, is difficult to fathom. I summarised part of this first episode of the series as follows:

Essentially Aristotle’s rapprochement, which Moore characterises as an attempt to make the concept of the infinite more palatable to the Greeks, involved dividing the idea of the infinite into two. As already mentioned, one of these was the potential infinite, and the second was the actual infinite. As outlined in the first episode, Zeno’s paradoxes depended on the idea of an infinite divisibility, which seemed to make the idea of any kind of movement impossible, since that would require a universe of infinite complexity. Zeno therefore regarded all forms of movement as illusion. Since in order to travel a certain distance, you would have to travel half the distance to your destination, and then half of the distance remaining, and then half of that, and half of what still remained, and so on. Which would result in an infinite number of steps. Which would be impossible. 

Aristotle’s response was that though the various stages of the journey could be understood in such a way, the stages were not marked, and did not have to be considered in making a journey. The idea of limit is however a crucial point. What Aristotle was saying is that there are two ways of looking at the idea of what a limit is.  Essentially there is limitation which is defined by what a thing is, and there is limitation which is not. In the first case the limit of a thing cannot be transcended without the nature of that thing turning into something else.

The essence of this argument is that there are forms of limit which can be ignored. One of which is the actual infinite: instead we should deal with the potential infinite. The actual infinite, by its nature, is always there. But we cannot deal with it. The potential infinite we can work with, since it is not always there, and spread infinitely through reality. So we can count numbers without ever arriving at infinity, or ever being in danger of arriving there. Moore mentioned that this conception of infinity more or less became an orthodoxy after Aristotle, though not everyone accepted that his argument against actual infinity was solid. Which is something of an understatement. Aristotle’s distinction between the potential infinite and the actual infinite is between what is, in practical terms, something we can treat as finite, and what is actually infinite. 

 

Moore has defined himself as an Aristotelian finitist, meaning that, since (he argues), man cannot deal with the actual infinite, only the potential infinite can make any sense to us. And so, much ancient discussion is swept away, as of very little interest or importance. This is why we cannot easily understand much of the intellectual world of antiquity. Instead we choose to write unflattering fictions about it.

I said that we cannot rely on Aristotle for accurate information on the Pythagoreans. This is not because I regard him as a poor scholar. Both Plato and Aristotle taught in the Academy in Athens. They were both dealing with a body of traditional doctrine (there are many passages where a comparison shows this – their discussion of the importance of the liver, for example). But they had quite different ways of discussing doctrine. Plato gives the reader real information about the subject, but hedges it about with other arguments, and sometimes talks in terms of images and myth (the account of the prisoners in the cave, in the Republic, for example). So his work makes sense to those who already know the doctrine, and intrigues those who don’t. Aristotle on the other hand, seems to have had the job of sifting through students to find those who might have the intelligence to  be able to grasp the essence of the doctrine (when properly instructed). He did this sometimes by constructing complex sophistical arguments which actually contradicted doctrine, and sometimes even rational sense.

Two examples: The first is Aristotle’s Nicomachean Ethics, originally a series of lectures, ends up concluding the gods cannot act in the world, but only contemplate. Imagine the response to that argument in the ancient world! Why did Aristotle argue like this? He was looking for students who could provide critical rational responses to the argument, and who could  see that it did not make any sense in a reality which was (at the time) populated by divinities expected to play a constructive role in the world. The second example is Aristotle’s comments on logical modality (mostly in the Metaphysics), which I’ve discussed elsewhere (in ‘Logical Modality in Classical Athens’). This also contradicts traditional doctrine which underpinned the human relationship with the divine. And not just in Greece. Plato discusses the logical modality which enables contact and engagement with the divine, and other authors do too. We ignore all of this information concerning doctrine, because we prefer the unfathomable shadows on the wall.

However, despite the occasional tricksiness of Aristotle, he tells us something important, which, if we are familiar with relevant texts by other authors, we can figure out. I quote again from my critical review of Adrian Moore’s broadcast History of the Infinite, concerning the arguments of Zeno:.

The idea of limit is however a crucial point. What Aristotle was saying is that there are two ways of looking at the idea of what a limit is.  Essentially there is limitation which is defined by what a thing is, and there is limitation which is not. In the first case the limit of a thing cannot be transcended without the nature of that thing turning into something else.

Aristotle’s discussion references the doctrinal view which is also discussed by Plato. Which is that there is an important connection between the idea of limit and the infinite. The infinite is just another way of specifying what is unlimited, and beyond the physical world. Paradoxically, it is the actual limit of what is, and what can be. This does not represent a retreat from commerce with the actual infinite, but actually tells us how that commerce was supposed to work.

However the physical and finite world is also full of limits. These sometimes function as boundaries, and serve to close off access. Some limits you can choose to pass beyond, and there are others which you cannot pass. And in some cases, because of the nature of the limit, it is the nature of the limit itself which allows commerce with the ultimate limit of everything, which is where the Gods were once understood to have their existence.

This is the most important thing to understand about antiquity, both east and west. For Moore, the actual infinite is simply something which defies our understanding. In antiquity, the actual infinite was something of vital importance, and which we could have commerce with through its earthlly analogues (totalities, completions, limits. etc). Aristotle, in talking about Zeno’s paradox, is referencing the key doctrinal point, which is that reality has a double nature. And that we have (if we are properly informed), a choice about how we respond to that double nature.

In modern times, we no longer have this choice, since the doctrine concerning actual infinity has been mostly lost, and in fact entirely lost to those who function in the modern successors of Plato’s Academy. We are stuck in a world that imagines it must deal with everything in terms of calculable finitudes. Effectively we are, to quote the Mesopotamian king Esarhaddon, “blind and deaf ” for the whole of our lives.

It was not always so.