Thursday, December 20, 2012

Parmenides as monist, nature of logical constants

To: Chris M.
From: Geoffrey Klempner
Subject: Parmenides as monist, nature of logical constants
Date: 16th January 2009 12:52

Dear Christian,

Thank you for your email of 3 January, with your unseen timed essay in response to the University of London Plato and the Presocratics question, 'In what sense was Parmenides a monist?', and your email of 11. January, with your unseen timed essay in response to the UoL Logic question, 'What does it mean to say that an expression is a logical constant?'

Parmenides

This is an excellent essay, which covers just about every angle that I can think of.

Your distinction at the beginning -- between the sense of the question, 'Was Parmenides a monist, and if so what kind?' and 'Assuming Parmenides was a monist, what kind of monist was he?' -- looks a bit hair-splitting to me. Whenever you come across a question which asks, 'In what sense was philosopher A an XYZ-ist?' you can always read this as saying, 'In what sense, if any, was philosopher A an XYZ-ist?'

However, there is an important distinction to be made which does affect the way one answers this question. What do we mean when we talk about 'monism' or 'dualism' or 'pluralism' in the context of metaphysics? This would be a good way to start, because it lays the foundations for the things you say afterwards, including your assessment of the views of Curd and Palmer.

Monism is often taken to refer to a view in ontology: that there ultimately exists only one kind of entity. Another term for materialism -- the view held very widely today -- is material monism. However, another metaphysical view which cuts across the distinctions between material monism, dualism etc. would be the objective idealist theory that the real is the Absolute -- in other words, the denial of the reality of relations, a view which you find in Hegel or Bradley. The first form of monism holds that every thing is ultimately the same kind of substance, while he second form of monism holds that ultimately there are no separate 'things'.

In these terms Anaximenes might be described as a material monist who was also a pluralist. Parmenides can be plausibly interpreted (as you note) as offering a kind of radical critique of the project undertaken by his predecessors. So it would not be stretching a point too far to ask how, from an ontological point of view, Parmenides view of the connection between the Way of Truth and the Way of Appearances differs from Milesian philosophy.

Here, you seem to make the interesting suggestion that Parmenides, in effect, takes the whole structure of Milesian physics and adds a third level. The Way of Appearance comprehends both the physical arche (light and night) and the phenomena which are explained in terms of that arche. The Way of Truth offers a metaphysical arche, undifferentiated Being, which in a sense 'trumps' the physical explanation.

You also suggest that Plato's theory of the world of forms and the world of appearances represents a possible realization of what Parmenides might have been struggling to express. The problem with this view is, first, that Plato is clearly not a monist but a two-world dualist. Secondly, the world of forms is not 'one' in any meaningful sense. It is true that the form of the Good occupies a unique position at the top of the hierarchy of forms. But there are still many forms, not one form, and there is no suggestion that this plurality is itself ultimately 'unreal'.

We are left with the remaining puzzle of finding a meaningful place for appearances, if, as Parmenides explicitly says, nothing that can be said about them is true. Taken at face value, this is a 'radical ontological monism' which completely disconnects from the beliefs of 'mortals' offering no foundation, no explanation, just an unresolved paradox.

Logical constants

In this excellent essay, after looking at the existing alternatives you offer an explanation of your own which I find intriguing.

We are to 'imagine a being that has a superior capacity to think and process information'. An example you could have quoted is the Dustin Hoffman film, 'Rain Man' (1988) where the autist-savant played by Hoffman is able to instantly 'count' the matches dropped on the floor, numbering over a hundred. In fact, I have read reports of experiments with normal infants who have been taught to subitize surprisingly large numbers of objects.

This suggestion deserves to be investigated further. The first question one needs to ask is the question posed by Michael Dummett in his British Academy lecture, 'The Justification of Deduction'. Why do we need logic at all? Dummett gives the example of a 'proof' that it is possible to walk across every bridge over a river, crossing each bridge once only. Looking at a map of the city with the bridges marked in, you might say, a person of superior intellectual ability (an autist-savant or perhaps one of the infants who has been put through the requisite training) would simply 'see' what others would need to laboriously work out.

What does that mean, exactly? The knowledge of the layout of the city, represented by the map is, and is not, exhausted by what one can say about the structure of the map itself. It also includes all the things one can deduce such as whether or not it is necessary to cross a bridge in order to get from A to B, or the minimum number of left turns that you need to take. To say that an autist-savant would simply 'see' this still leaves the question how one represents this knowledge.

I have chosen the example of a map, in order to avoid the question of the relativity of different forms of language. A map is a map. In Wittgenstein's sense, the pictorial form of a physical map is not 'logical form'. It's pictorial form is peculiar to maps (different, e.g. from a drawing or painting from nature) in that it ignores perspective. Some maps -- like the London Tube map -- are not drawn to scale. Aliens who had vastly superior intellectual powers, and whose language (logical form) reflected this ability would still have a use for physical maps. Even if an alien could instantly 'see' the answer to our questions about the bridges or left turns, there still needs to be a way, in principle, to represent this implicit knowledge.

You can probably see what I am working up to: even if superior beings don't need logic, because they instantly see the conclusion of logical inferences which we would make laboriously by following logical rules, nevertheless *what* they see is something that it must be possible, in principle, to express. The logical structure of inferences is there, even if they do not consciously run though it, even if their language contains concepts which imply a recognitional capacity that human beings could never possess.

You can run the same argument over the simple arithmetical sum, two plus two equals four. It is a thing of wonder to beginning students of mathematics that one can 'prove' that two plus two equals four by applying Peano's axioms. The claim is that the arithmetical truth in question is more perspicuously represented by the laborious proof because it includes an explanation of what 'number' is -- the repeated application of the successor function.

A similar claim could be made concerning the logical constants. They are required for a 'perspicuous' representation of human knowledge, even in cases where in fact (pragmatically) their use can be dispensed with.

Which brings us back to the question of how one identifies the logical constants. Perhaps it does not take us right back to the beginning, because the theory-laden term 'perspicuous representation' has been introduced. But that just begs a larger question.

All the best,

Geoffrey