Iain Cameron's Diary
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2005-10-09 - 11:33 a.m.
I have finished the book about Einstein and Godel. The author, Yourgrau, believes that Godel’s work has been unjustly marginalised and this book is part of a wider campaign to bring it the attention it deserves. Part of the problem is the physicists desire to steer clear of absurdity and (so he suggests) philosophers’ desire to stick to analytic issues. I think the last point is overstated. For me he makes a good argument that the incompleteness proof shows that when people do maths and logic they are using something more than mechanical rules – something which he chooses to call intuition. The novel step is the proposed method of examining intuition – Y thinks the answer is phenomenology – an area I need to look into more. As far as I can work out this is a kind of disciplined reflection on one’s own mental processes – something that it is essential to any kind of sustained creative work.
The other interesting thing about Yourgrau is the way that he brings the Weils into the story. He keeps quoting Simone Weil and it seems her brother was a mathematician who hung out with some of the Princetown crew. Its uncanny the way that Princetown attracted the most original thinkers from across Europe.
Vita has won the school art prize which is being presented on Monday and so I am going to stay at home here in Guildford that day. Steve has sent me some very interesting consumer research on what school children don’t like about science which I will get stuck into. I am wondering about getting the Donovan autobio.
I picked up Anthony Kenny’s Penguin book on Wittgenstein and read through the chapter on the start of his rejection of his first philosophy (the Tractatus). I had forgotten how excited the world had got about truth tables which are introduced in the Tractatus. These are simple structures defining logical words like “and” – X and Y is true if and only if both X and Y are true and false otherwise. It seems the excitement arose because it was a new way of explaining logic – in some sense more profound than the deductive system. In a deductive system you only know if a proposition is true by seeing if you can derive it from the axioms. But with the Tractatus method of truth tables there is an alternative more direct procedure.
One way of thinking about the Tractatus is that it is an attempt to explain what the world must be like if logic is going to work reliably. But it’s the logic which includes the method of truth tables.
Yourgrau complains that the Tractatus was a further incentive to positivism and that this philosophy was hostile to the true implications of Godel’s incompleteness theorem. This is only partly true in my view – and by the time that Godel made that discovery Wittgenstein was changing his view.
I was struck, reading Kenny, by the way that Wittgenstein tackled Russells Paradox in the Tractatus. He suggests that the paradox dissolves if you are disciplined about your use of symbols – and that does seem to me to be true – that looks a lot like one up to a purely formal philosophy of logic.
Yourgrau suggests that there is another way of avoiding the paradox – that arises directly from Russell’s way of creating sets – take everything that’s in the universe and determine whether it’s a member of the set or not. Unfortunately the set that you are creating seems to be one of the things in the universe – and that leads directly to contradiction. Yourgrau refers to another procedure for establishing a set which I need to get my head round.
The next step has to be to read the record of Wittgenstein’s seminar on the foundation of mathematics at Trinity where Turing is a member of the class. It seems to me that there may be more continuity between the two phases of his philosophy than is sometimes thought – this isn’t at all an original point. But the thought in the back of my mind is whether the continuity has something to do with a phenomenological method.