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Thursday, April 13, 2006

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."

"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.


dennis said...


Your comment raises three things in my mind:
1) whether philosophy of mathematics should be thoroughly informed by advanced mathematics 2) philosophical approaches to advanced mathematics. (One would expect there could be many such approaches, including extensions of traditional ones.)
3) concern with the political-moral dimension.

On the first point, you are undoubtedly right in recommending a turn to “real” mathematics. I suspect that philosophy basically has missed the mathematics and the mathematical experience of a good number of decades. If this, indeed, is the situation, then philosophy is not in a good position to judge what is, or is not, a worthy contribution to philosophy of “real” mathematics.

To continue on a similar point: One response (perhaps the dominate one within philosophy) to your book contends that you do not successfully develop or raise substantial philosophical issues. Bays, e.g., writes:

I don’t think Corfield is particularly successful at generating serious philosophy out of reflection on core mathematics. At many points, he seems to simply assume that pieces of cutting-edge mathematics (or mathematical history) will have philosophical payoffs, and he then substitutes a (admittedly, very nice) description of this mathematics for actual discussion of the purported payoffs. (Timothy Bays, )

I suspect that Bays demands too much of pioneers, like yourself, who endeavour to shift the centre of focus toward “real” mathematics. If we want philosophy that addresses modern mathematical experience and modern mathematics (in a way, e.g., that cognitive philosophy of Fodor, Dennett, Searle, and so forth addresses cognitive science), the way to start, it seems to me, is not to demand immediate, evident payoffs (which is not to say that your book is deficient in this regard). The way to start may be to attract mathematicians to philosophy based on the theoretical concerns informing mathematics and to take seriously these concerns (including learning the relevant mathematics, for those who can). For myself, I found a number of discussions in your book quite philosophically stimulating. The discussion, e.g., of tension between seeing groups as basic varieties and seeing groupoids as a basic varieties raises issues, for me, such as how the mathematical world is fundamentally sliced up, whether there is one way to slice it up, and whether the slicing up in some fundamental way relates to how the empirical world is sliced up.

(I recently reread Bays review of your book. Has the review been rewritten? It does not seem as critical of your book as, I recall, it once was.)

Regarding the second point, I appreciate your interest in MacIntyre. Engaging and elaborating a philosophy more directly mathematical might be another option. Husserl’s, it seems to me, is one to consider. (I liked Richard Tieszen’s recent book on Husserl, *Phenomenology, Logic, and the Philosophy of Mathematics*, Cambridge University Press, 2005.) Husserl developed a vast repertoire and at one time seriously engaged some leading mathematicians.

Finally, regarding the third point, to me mathematicization of vast fields of human endeavour comes primarily to mind. This may be bringing us to the brink of disaster. See, e.g., John Ikerd, (2005). *Sustainable Capitalism: a matter of common sense.* Bloomfield, CT, Karmanian Press. Ikerd, a former conservative agricultural economist who now writes in somewhat of a Marxist vein, paints a picture of negative outcomes of the mathematicization of economics of the early 20th century and beyond. (Ikerd also maintains an interesting webpage,


April 14, 2006 5:31 PM  
Anonymous said...

Have you read the book Kierkegaard After MacIntyre?

Continental philosophy (represented by Kierkegaard) meets Analytic philosophy (represented by MacIntyre) makes for good reading

April 15, 2006 2:49 PM  
Anonymous said...

I think that I mostly agree with you.

But scientific theories also have political implications, e.g. The theory of evolution or genetics.

The theories can still be studied without regarding theese implications. (Eventhough the motivation for studing might stem from political or moral concern. And undersanding of theese motivies are, from a historical point of view very important).

Somehow I feel that the thought that one can examine a subject from a totaly disconnected rational perspective is a central element of what philosophy is. (What I mean is a kind of "ethics is science the of moral" point of view.)

It seems that you long for a broder humanistic study of mathematics, that includes a historical perspective on the subject. This seems also to include some "purely" philosophical questions like what is the role of history (or a genealogy in Focault's and Nietzsches sense) for understanding.

April 16, 2006 11:04 AM  
david said...


Following your points:

1) I'm fairly sure Bays' review hasn't been rewritten. I have always read it as largely negative with a grudging admission that I'm right to say that philosophers ought to look at what mathematicians have done over the past few decades.

I'm not sure I'd call it the dominant response tout court. Among analytic philosophers of mathematics, yes. But philosophers of science are generally much more sympathetic. But then this is probably because, even if they didn't expect to find it so, very similar issues concern me in the book to their own, such as the 'slicing up' you mention.

2) I must try Tieszen's book. I have tried to get to grips with Husserl with little success. I know Rota, whose writings I admire, was a passionate Husserlian, but I don't understand him when he writes about Husserl.

I imagine that this is a common occurrence, but with some philosophers I enjoy everything they write. Collingwood and MacIntyre are two such philosophers for me. Something like a 'historical rationalism' is the common denominator, a position which drew me to Lakatos many years ago.

3) If Ikerd is against mathematicization of the economic-political sphere, I couldn't be in closer agreement. The inappropriate use of formal calculi is simply dangerous. But hasn't a fair part of analytic philosophy, certainly that part termed 'philosophical logic' been just this? I have always seen logic as a facet of mathematics, and so an attempt, say, to model knowledge by some variety of modal logic (does Kx imply KKx, where K is 'knows that', etc.) is applied mathematics, and should be judged as such. Fine for modelling in some small part of computer science maybe, but nothing much to do with a theory of knowledge in its deepest sense. Mathematicized economics and logic-based analytic philosophy have much in common, a sign of the hidden political dimension of the apparent depoliticization of philosophy.

April 17, 2006 7:23 PM  
david said...

Anonymous 1,

Thanks for this reference. It wouldn't surprise me if Kierkegaard scholars could show that MacIntyre had got their man wrong. I rather suspect that his representation of pre-Enlightenment Scotland is not always accurate either. But then his project is monumentally large, and would need a large team of co-workers to carry it out properly.

April 17, 2006 7:26 PM  
david said...

Anonymous 2,

One thing I'm driving at is a point MacIntyre takes from Aristotle that rational enquiry aims at the discovery of the proper hierarchical arrangement of categories of the relevant entities. Any proposed hierarchy is hypothetical and may need to be overturned. It seems clear that the natural sciences work this way. I've been trying to develop a similar thesis for mathematics. What MacIntyre wanted to revive was that the idea ethics could be such an enquiry.

April 17, 2006 7:50 PM  
Kenny said...

I don't think that analytic philosophers are all as attached to such sharp divides within their department as you seem to suggest. Although there certainly is a large amount of compartmentalization, it seems that philosophers in all areas are expected to pay at least some attention to the core concerns of mind, language, epistemology, and metaphysics, which are relevant for work in all areas fairly directly. Areas like logic, the philosophy of science and mathematics, and ethics bear a slightly more tangential relation, but they are often seen to have direct impacts - for instance, the role of logic in explaining language, the role of ethics in explaining the normativity of epistemic concepts, and the role of science in its connection to all philosophical endeavors. It's true that the political implications of much work is downplayed, but I think this is mainly out of a sort of modesty, that the relevancy of a position in the philosophy of mind for political action is quite remote and will not clearly guide action in one way or another.

April 17, 2006 9:49 PM  
david said...


Thanks for forcing me to be more precise. I think what worries MacIntyre about contemporary philosophy is how it doesn't realise how thoroughly infused it is with the thought patterns of modern Western society.

I'll talk about this in my next post, but to give a glimpse of this here, when you discuss an APA discussion of relativism on your blog, we hear about whether things taste nice, or are funny, or whether you'll go shopping tomorrow. When MacIntyre discusses relativism, we're thrown back to Ireland in 1700 to consider someone able to live in the Irish community at St. Columba's oak-grove, or in the English plantation at Londonderry. Although these are two names for the same place, they function in very different systems of thought. E.g., the Irish have no concept of the individual property rights being forced on them by the English, while the English have little idea of what St. Columba could mean to the Irish.

April 18, 2006 10:07 AM  
Anonymous said...

Less formally, I've blogged about "What are mathematical entities and how do we come to know about them?" at:


on the thread: Excerpt from GENE515

This partly answers a question asked of me when I was 21 years old, by my doctoral thesis advisor Oliver G. Selfridge. When I say "Man" I am echoing and older text, and not excluding Woman.

Excerpt from GENE515

What is Man, that he may know Number? What is Number that it may be known by Man?

-- Professor Jonathan Vos Post

April 18, 2006 3:44 PM  

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