Philosophy and politics

The difficulties faced by philosophers of mathematics of my persuasion stem, I think, from our reluctance to fit in with the dominant analytic tradition, while not being readily classifiable in that catch-all category ‘continental philosophy’. If mathematics assisted at the birth of analytic philosophy, the latter now grown up doesn’t look favourably upon anyone thinking about mathematics in terms other than its own. Consider the questions analytic philosophy asks of mathematics today: If we use mathematics in our science, are we committed to the existence of mathematical entities? What are mathematical entities and how do we come to know about them? Are the natural numbers anything more than a structure? What is a structure? Like-minded colleagues and I are not happy to place ourselves in a framework that would take these to be the primary questions to ask of the discipline Harvard mathematician Barry Mazur calls "mankind’s longest conversation". Where perhaps we have most grievously failed is in properly articulating a shared philosophical stance which would require the study of what we take to be more important matters, rather relying too heavily on what we imagine to be obvious, that mathematical thought through the ages should be our central concern.

Recently I have turned to the writings of Alasdair MacIntyre to help with this articulation. Here I have selected three quotations:

It thus turns out that, just as the achievements of the natural sciences are in the end to be judged in terms of achievements of the history of those sciences, so the achievements of philosophy are in the end to be judged in terms of the achievements of the history of philosophy. The history of philosophy is on this view that part of philosophy which is sovereign over the rest of the discipline. This is a conclusion which will seem paradoxical to some and unwelcome to many. But it has at least one merit: it is not original. Vico, Hegel and Collingwood all at various points come very close to theses remarkably, and indeed not at all by coincidence, similar. (The relationship of philosophy to its past, 47)

(MacIntyre acknowledge the possibility that such a history will have to tell of centuries long reversals in the fortunes of a tradition of enquiry.)

Greek thought, like Greek practice, understands morals-and-politics as a unified object of enquiry; modern moral theory distinguishes itself both from political philosophy and even more sharply from political science. So the academic division of labour allows us to pretend that our pupils can understand Aristotle’s Ethics without reading the Politics and vice versa. Greek moral thought make central to its concerns issue of the nature of human psychology which are as alien to characteristically modern moral philosophy as are some of its central issues, the fact/value distinction and the relationship of morality to utility, for example, to Plato and Aristotle. (The relationship of philosophy to its past, 38-39)

…philosophy, like all other institutionalized human activities, is a milieu of conflict. And the conflicts of philosophy stand in a number of often complex and often indirect relationships to a variety of other conflicts. The complexity, the indirectness and the variety all help to conceal from us that even the more abstract and technical issues of our discipline – issues concerning naming, reference, truth and translatability – may on occasion be as crucial in their political or social implications as are theories of the social contract or of natural right. The former no less than the latter have implications for the nature and limitations of rationality in the arenas of political society. All philosophy, one way or another, is political philosophy. (Relativism, Power and Philosophy, 12-13)

MacIntyre is certainly no marginal figure in Anglo-American philosophy. Indeed, the last of these quotations comes from a lecture delivered during his presidency of the American Philosophical Association. But while these quotations hint at an integrated philosophy which is political to its core, it is very unlikely that you will hear his name outside ethics classes. For instance, I very much doubt students electing for lectures in the philosophy of science will hear of ‘Epistemological Crises, Dramatic Narratives and the Philosophy of Science’ (excerpt from a soon to be published collection of essays). Such transgressions of boundaries are not encouraged. Despite the ructions mentioned here, the dominant post-Quinean analytic tradition is generally happy to cede some departmental space to allow ‘Continent Philosophy’ to be taught. Although many ‘continental’ philosophers have, like MacIntyre, had very different conceptions of what philosophy should be like, generally a more closely integrated and political discipline, such courses tend to be self-contained, and don’t spill over to challenge analytic philosophy’s tidy way of treating ethics, aesthetics, metaphysics, mind, language, knowledge, etc. as largely disjoint subjects. ‘Continental’ approaches to science are generally limited to certain kind of history of science programme, which enjoy exposing the ebb and flow of power in scientific communities.

Commentators (this book and this book) have noted how peculiarly apolitical analytic philosophy in the second half of the 20th century has been. If we think of the activism of the Vienna Circle, this clearly stands in need of explanation. Whether McCarthyism is responsible, or an increasing desire to make philosophy a professional academic discipline with a standard set of problem areas, what is beyond dispute is that contemporary philosophy of mathematics has become an insular affair without a whiff of politics associated to it. So, were we to adopt a MacIntyrean stance, clearly much would have to change. My understanding of his ideas suggests that epistemology and metaphysics would have to be treated very differently. Instead of the epistemology of the individual - ‘How do I know that 2 + 2 = 4 ?’, it would develop an account of rational traditions of mathematical enquiry – ‘Why was the mathematical community justified in adopting, and making precise, Riemann’s conception of a manifold?’. Instead of a timeless metaphysics - ‘What is a number?’, it would question the underlying presuppositions of the discipline - ‘Are there tensions between the conceptions of space of a Connes and a Grothendieck?’. Its gift to other branches of philosophy would be a clearer understanding of what participation in a form of rational enquiry involves, and of what it means for theoretical and practical advances to be rationally justified.

And this gives us a clue as to how the philosophy of mathematics may be related to politics and ethics. While the political role of Plato’s theory of Forms was apparent to Popper, and while Plato managed to discuss mathematics in a political/ethical context in the Republic, can we, who surely do not recommend that our future rulers learn mathematics for a decade, do likewise? Well, what if we consider our lives to be formed of a series of interlocking practices, including the very important ones of maintaining a thriving family and community? Then we might learn from a practice with the pedigree of mathematics – mankind’s longest conversation – about the necessity of certain intellectual and moral virtues. Saying so, we must not remain blind to its faults. While I think it is fair to say that mathematics is flourishing at present, this is not because of a complete absence of institutional irrationality. Its most obvious failing is that exposition is not justly rewarded. Lakatos realised this in the 1960s, and so have mathematicians such as Rota and Thurston more recently. This is troubling. If the mathematical community cannot conduct its affairs both rationally and justly, it seems unlikely that other communities will fare better. In the bluntest terms, unless irrationality and injustice are remediable, can we imagine that humankind will be able to learn to govern itself well enough to avert ecological catastrophe?

To end on an encouraging note, read the Wednesday, February 15 entry of this blog to see that the spirit of Plato lives on: "Using the word job in a pure math course is nothing but mortifying."

References:
"The Relationship of Philosophy to its Past," in Philosophy in History, Richard Rorty, J.B. Schneewind and Quentin Skinner, eds. (Cambridge: Cambridge University Press, 1984) pp. 31-48.

"Relativism, Power and Philosophy," in Proceedings and Addresses of the American Philosophical Association (Newark, Delaware: APA, 1985) pp. 5-22. Reprinted in After Philosophy: End or Transformation, Kenneth Baynes, James Bohman and Thomas McCarthy, eds. (Cambridge: MIT Press, 1987) pp. 385-411. Available on JSTOR.