To: Gordon F.
From: Geoffrey Klempner
Subject: The road to analytic philosophy
Date: 27 December 2007 13:46
Thank you for your email of 17 December with your essay towards the Associate Award, 'The Road to Analytic Philosophy' Part 1.
Of course you are right that the attempt to make mathematical proofs more rigorous and plug the 'gaps' which call for intuition or imagistic thinking, had a very significant impact on the career of analytic philosophy in the 20th century.
To cite one obvious example, Russell's logicist program in the philosophy of mathematics linked closely to his conception of the nature of philosophy as logical analysis, inspired in large part by Frege's 'Die Grundlagen Der Arithmetik'. From the 'Begriffschrift' onwards, Frege saw his task as primarily to make mathematical reasoning more rigorous, and in this respect his work is complemented by mathematicians such as Peano and Hilbert.
Rudolph Carnap is probably the greatest exponent of the conception of philosophical analysis as the task of constructing a formal system. E.g. his book 'The Logical Structure of the World' (the 'Aufbau').
One of the most important upshots of Carnap's approach was his recognition of the difference between 'internal' and 'external' questions, questions which one seeks an answer within the system (e.g. how to prove Pythagoras' theorem) and questions which are external to the system (e.g. which system of geometry describes the actual physical world).
An analytic philosopher who has followed Carnap's footsteps in distinguishing between questions which are answered within a framework and questions which involve the choice of framework is Stephan Korner ('Categorial Frameworks' and 'Metaphysics: its Structure and Function').
There are in fact multiple points of influence on analytic philosophy. Even the later Wittgenstein, who strongly repudiated the conception of philosophy as systematic analysis and theory construction, often speaks, in the 'Philosophical Investigations' of the influence (almost always pernicious) of imagistic thinking in our attempt to puzzle out the logic of our language. (E.g. 'It was a picture that held us captive' Philosophical Investigations para 115 -- Wittgenstein is talking about how he himself was held captive by a certain 'picture' of the nature of language.)
My main concern (as always) is to steer you towards writing an essay or essays which will be suitable as submissions for the Associate Award. At over 4000 words, the present essay is already considerably longer than the target length of 2000-2500, and you have hardly started on talking about philosophy. This is all history of mathematics.
I think that an essay on the influence of mathematics on analytic philosophy would be acceptable. However, you first need to sharpen the question you are asking. Philosophy is not the same as history of ideas. You are not just explaining how this thought followed from that, but rather concerned with justification, and the clash between different conceptions of the nature of philosophy, and in particular the nature of philosophy as analysis.
I would suggest that Carnap is a major figure here. If you have not looked at much by this philosopher before, you could start with the magnificent volume dedicated to Carnap, 'The Philosophy of Rudolf Carnap' (Library of Living Philosophers, Volume XI), edited by Paul A. Schilpp (1963). Any good university library should have a copy.
While the Vienna Circle is perhaps the greatest milestone in the history of analytic philosophy, the philosophies of Russell and the later Wittgenstein each deviate in a very marked way from the work of the other members of the Vienna Circle. Then you have the American pragmatic tradition which synthesized with the analytic tradition in the work of W.V.O. Quine and subsequent philosophers.
There are so many directions. You need to find a single thread that you can follow -- perhaps picking on a single philosopher whose work is strongly influenced by mathematics, like Carnap, or Reichenbach in the USA, or Russell. And then there is the strange case of A.N. Whitehead. How could a philosopher who collaborated with Russell on Principia Mathematica end up producing a work ('Process and Reality') which is so far off the main track of analytic philosophy (to the extent that philosophy departments in the US identify themselves as 'process philosophers' or 'analytic philosophers')?
At any rate, what you have written here suggests very strongly a connection with Carnap's work, and I therefore think that this is the philosopher who it would be most fruitful to look at.
All the best,