08 September 2005

You Can't Get There from Here

Quine said on a variety of occasions (I heard him say it once myself) that he always regretted that he hadn't studied more medieval philosophy of logic. Perhaps it was his friendship with Geach which had led him to think this.

This seems to be a true counterfactual: He wouldn't have been helped in this regard by the new Oxford Handbook of Philosophy of Mathematics and Logic--at least if the review in NDPR is accurate (see it here). According to the reviewer, J.C. Beall, the history covered by the handbook begins with Mill and Kant, entirely neglecting ancient and medieval logic. Here is Beall's summary:

Section One: Historical Background

Lisa Shabel. 'Apriority and Application: Philosophy of Mathematics in the Modern Period'. This essay discusses Kant's relevant views, and the views of his predecessors.

John Skorupski. 'Later Empiricism and Logical Positivism'. This essay lays out the influence of later empiricism on the target fields, and discusses the impact and ideas of John Stuart Mill and the logical positivists.

Juliet Floyd. 'Wittgenstein on Philosophy of Logic and Mathematics'. Like the other chapters in this section and their target figures, Floyd's essay nicely sketches the content and history of Wittgenstein's thought, as well as the ongoing impact that surfaces in different interpretations -- for example, inconsistency approaches to truth, and so on.

What explains the omission of about 2200 years of philosophy of logic? Not having the book, I can only conjecture. Perhaps the editor thinks that ancient and medieval logic have already been covered elsewhere. True, but then the philosophy of recent mathematics and logic, too, have been covered elsewhere. Isn't the point of a handbook to have it all in one source? Or maybe the Handbook takes itself to cover only 'mathematical logic' and its philosophy. Fine: but then the book misses entirely the question of the 'two logics', surely an important part of the philosophy of logic .

Beall writes:

If I were introducing someone to 'core, analytic philosophy', I would send them to the philosophy of mathematics and logic -- or, at least, I would like to, if a suitably accessible guide were available. As it turns out, there is now such a guide: Shapiro's Handbook does the trick.

Good enough, but then call it the Handbook of Analytic Philosophy of Logic and Mathematics. One must concede, of course, that the analytic movement is most important in this area. But if only that contribution is to be covered, make that condition explicit.