Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

January 27, 2007

Peering Through the Veil

Posted by David Corfield

Twice in recent days I have confronted the possibility of experiencing a kind of alienation due to interviews. First, my co-author Darian Leader and I were interviewed by the New Scientist about our book Why Do People Get Ill?. A day or two later we got to see a draft of what was to be selected for publication. Space limitations have meant that statements attributed to one of us are composites of things said by either of us. I don’t think it matters much in terms of the information carried in the interview, but it feels strange to have sentences you never uttered marked as originating from you.

No such chopping in that other recent interview, the one Urs and John gave to Bruce Bartlett about this blog. Even hesitation and laughter have been carefully marked. Here the potential alienation arises from the possibility of being spoken about in a way which clashes with one’s self-image. Of course nothing like this happened, but I would like to take the opportunity to say something about John’s comment about me that when

he’s talking about the philosophy of mathematics, he’s very concerned about the sociology of mathematics, and how people interact, and how you can do mathematics well.

Now ‘sociology’ has a number of uses. On the one hand, it can be taken as a non-normative discipline which seeks to understand and describe how societies operate. Although there may be some or other philosophical stance operating behind the scenes, this activity would seem not to be philosophical as it stands. On the other hand, ‘sociology’ as applied to the study of science and mathematics, as in the ‘sociology of scientific knowledge’, tends to come with a strong dose of social constructivism, and a wish to unmask the resources and techniques of the powerful to represent the way things are. In this context the study of ‘norms’ is largely to understand how the powerful wield certain standards to maintain their position of prominence. We had a discussion about that stance starting back here.

But, as John points out, I want to know “how you can do mathematics well”, and I take this to include the a study of the way the mathematical community operates. So I am interested in description and normitivity, an exercise R. G. Collingwood would have called criteriological. Let me re-quote MacIntyre on the tasks of philosophy:

…philosophy needs to be conceived as having at least a fourfold subject matter and a fourfold task. There is first of all that which has to be learned empirically: the rules and standards, concepts, judgments, and modes of argumentative justification, actually embodied in or presupposed by the modes of activity which constitute the life of the social order in which one is participating. Secondly, there are the dominant ways of understanding or misunderstanding those activities and the relevant rules and standards, concepts, judgments, and modes of argumentative justification. Thirdly, there is the relationship between these two in respect of how far the second is an adequate, and how far an inadequate and distorting representation of the first. And finally there is that of which a philosopher must give an account, if she or he is to vindicate the claim to have been able to transcend whatever limitations may have been imposed by her or his historical and social circumstances, at least to a sufficient extent to represent truly the first three and so to show not just how things appear to be from this or that historical and social point of view, but how things are.

Clearly this is meant to include ordinary political social orders, which it must be said are more chaotic in terms of its “rules and standards, concepts, judgments, and modes of argumentative justification” than a society such as that formed by mathematicians. But is there room for complacency here? I would say “No”, certainly not if Alexandre Borovik is even only half right when he writes about Mathematics in Crisis due to its failure to bring on the next generation. Well, perhaps this is not mathematics’ fault, you may say, internally we’re still doing fine, and externally what can one do in the current materialist culture? But is there not the faintest chance that what we on this blog perceive as lacking in mathematical communication, which we try to counteract by our discussions, is in some way connected with a failure to communicate outside the community to recruit the young? In the UK, for example, did academics allow private examination boards to gain control of the syllabuses of our teenagers in silence. (See the analysis of a typical examination question by Borovik in his Mathematical Abilities and Mathematical Skills.) Had there been a livelier ongoing discussion of the nature of mathematics, one which might have be heard outside of mathematics, could this have happened?

Perhaps mathematicians can lay some of the blame at the feet of philosophers. Philosophical representations of mathematics might be expected to play their role both internally to mathematics, as well as in its external relationships. Concerning the internal state of mathematics, certainly there have been voices - such as Lakatos’s - calling for a much greater openness, but there have not been many. Greek mathematicians were better served. Besides analyses of reasoning within the community, external considerations were also deemed important. Indeed Plato writes in The Republic Book VII:

After plane geometry, I said, we proceeded at once to solids in revolution, instead of taking solids in themselves; whereas after the second dimension the third, which is concerned with cubes and dimensions of depth, ought to have followed.

That is true, Socrates; but so little seems to be known as yet about these subjects.

Why, yes, I said, and for two reasons: –in the first place, no government patronises them; this leads to a want of energy in the pursuit of them, and they are difficult; in the second place, students cannot learn them unless they have a director. But then a director can hardly be found, and even if he could, as matters now stand, the students, who are very conceited, would not attend to him. That, however, would be otherwise if the whole State became the director of these studies and gave honour to them; then disciples would want to come, and there would be continuous and earnest search, and discoveries would be made; since even now, disregarded as they are by the world, and maimed of their fair proportions, and although none of their votaries can tell the use of them, still these studies force their way by their natural charm, and very likely, if they had the help of the State, they would some day emerge into light.

Think just how far we’ve come from our philosophical origins. Do the 856 pages of the The Oxford Handbook of Philosophy of Mathematics and Logic give even a hint that we should expect a quest for knowledge, such as mathematics, to have a political dimension? How many of these pages concern the lived experience of doing mathematics? Let’s recall MacIntyre’s warning:

Philosophers do in fact become irrelevant to others not only by making their utterances inaccessible, but also by losing sight of the often complex and indirect connections between their own specialized, detailed and piecemeal enquiries and those larger questions which give point and purpose to the philosophical enterprise, which rescue it from being no more than a set of intellectually engaging puzzles.

One philosophy/theology blog I very much enjoy is the always interesting Siris. This post pointed me to a discussion by Mary Midgley of the stance of her fellow moral philosopher Iris Murdoch. This extract begins with Midgley quoting Murdoch from The Sovereignty of Good:

We are anxiety-ridden animals. Our minds are continually active, fabricating an anxious, self-pre-occupied, often falsifying veil which partially conceals the world.

What chiefly pierces that veil is a sharp, direct perception of things which are no part of our own being. For instance:

I am looking out of my window in an anxious and resentful state of mind, oblivious of my surroundings, brooding perhaps on some damage done to my prestige. Then suddenly I observe a hovering kestrel. In a moment everything is altered. The brooding self with its hurt vanity has disappeared. There is nothing now but kestrel. And when I return to thinking of the other matter it seems less important … (page 84)

The veil, however, is persistent and terribly hard to detect. In every age it subtly provides new, unnoticed ways of evading reality. Detecting those new forms is a prime business of philosophy, but of course philosophers often find it no easier than other people.

To return to our health book, for which I have set up what I intend to be a fairly casual blog, Darian and I have tried to penetrate the veil formed by the way illness is represented by medical researchers and medical practitioners, and by the pharmaceutical industry. But what difference is there between veil-detection and the sociologists’ unmasking? It’s simply the belief that there is an objective notion of goodness as applicable to the way we conduct our affairs. Certainly, value judgement terms can be wielded merely to bolster positions of power, but then they are being applied incorrectly.

Posted at January 27, 2007 10:17 AM UTC

TrackBack URL for this Entry:

15 Comments & 0 Trackbacks

Re: Peering Through the Veil

It would have been much better if you were able to be at that interview and speak for yourself, David. The instant I read my description of your interests, I started regretting its lack of subtlety — in particular the word ‘sociology’, with all its connotations. I’m glad you’re setting things straight.

Interviews are a funny business. In particular, there’s a big difference between what people are willing to put up with in spoken conversation, and what they’re willing to read. You say that ‘even hesitation and laughter have been carefully marked’ in this version of our interview. That’s true. But in fact, the original transcript was been edited to turn lots of hesitant, ungrammatical sentences into something readable. For example, this awkward mess:

John: Umm… and so I’ve had… in addition to all those things, being a moderator took a lot of work. So I mean, the discussing physics is fun, but there’s all sorts of other stuff that’s not so fun, like being an administrator, and, and when my wife moved to the same side of the country as me, I had less time than I did before, and I started getting more grad students, and being able to talk about things to them, and that seemed more productive than talking to people who didn’t really do anything with the information…

was polished to:

In addition to all those things, being a moderator took a lot of work. Discussing physics is fun, but there’s all sorts of other stuff that’s not so fun, like being an administrator. And when my wife moved to the same side of the country as me, I had less time than I did before, and I started getting more grad students, and being able to talk about things to them, and that seemed more productive than talking to people who didn’t really do anything with the information…

From doing this, we learned that every written interview is actually a work of art cunningly made to preserve the feel of live conversation, but with the awkwardness of actual speech carefully smoothed out.

I just got interviewed by the UC Riverside paper. It mainly about the crackpot index, which is fine — except they took the item:

5 points for each mention of “Einstien”, “Hawkins” or “Feynmann”.

and wrote it as

5 points for each mention of “Einstein”, “Hawkins” or “Feynmann”.

thereby ruining the joke.

Oh well! The good thing about this kind of screwup is that nobody really cares much except the person being interviewed.

Posted by: John Baez on January 27, 2007 6:11 PM | Permalink | Reply to this

Re: Peering Through the Veil

Yes, real speech is generally a huge mess compared to the way it’s represented. I once took an interest in approaches to psychology that looked very closely at what is being done when one speaks. Instead of the baloney of ‘measuring’ a person’s ‘attitudes’ through questionnaires, when you let them speak about a topic, say immigration, you see what a huge amount of work is being done. From the perspective that an individual at a given time has a fixed attitude, what this speech displays is flagrant contradiction. Small wonder they prefer people to tick boxes from 1 to 5.

If, however, you think about what people are doing with speech, in terms of things like self-presentation, you realise that they’re generally being very clever. Even those pauses are doing some work.

Posted by: David Corfield on January 28, 2007 8:27 AM | Permalink | Reply to this

Re: Peering Through the Veil

they took the item:

5 points for each mention of “Einstien”, “Hawkins” or “Feynmann”.

and wrote it as

5 points for each mention of “Einstein”, “Hawkins” or “Feynmann”.

thereby ruining the joke.

I see that The Highlander's spellchecker knows how to spell ‘Einstein’, but not ‘Hawking’ or ‘Feynman’.

This isn't the first time that people have thus misread the index, is it? Perhaps you should add ‘[sic]’ to the published version.

Posted by: Toby Bartels on January 29, 2007 1:53 AM | Permalink | Reply to this

Re: Peering Through the Veil

Toby wrote:

This isn’t the first time that people have thus misread the index, is it?

No — and that’s the reason I included item 20:

20. 20 points for emailing me and complaining about the crackpot index. (E.g., saying that it “suppresses original thinkers” or saying that I misspelled “Einstein” in item 8.)

where of course item 8 was:

8. 5 points for each mention of “Einstien”, “Hawkins” or “Feynmann”.

I now have a lot of fun replying to people who complain that I mispelled “Einstein” in item 8 — I just say “you just racked up some crackpot points on item 20”, and get sheepish emails in return.

The really infuriating thing is that in the Highlander interview, I was explaining precisely this whole business… but they miscopied item 8 as

8. 5 points for each mention of “Einstein”, “Hawkins” or “Feynmann”.

thereby making everything I said completely incomprehensible!

I was going to write a letter to the editor but I decided it was a losing battle: they’d probably correct my deliberate misspelling again, and make me seem even more like a bizarre jerk.

Oh, and by the way — I told them I work on “higher categories and physics”, and they wrote “higher categories of physics”. So, I also look like a snob who doesn’t deign to ponder the lower categories of physics.

(I mean, it might be true — but I wouldn’t come out and say it!)

The only reason I can still walk around campus without feeling the need to put a paper bag over my head is that every article in the Highlander is marred by at least one absurd typo or grammatical error. Wasn’t this where you found the wonderful headline:

SAT Scores a Poor Predictor of College Grades

      Consciousness Is More Important

? It was a typo for “conscientiousness”.

Anyway, so David isn’t the only one who has “experienced a kind of alienation” in his interviews.

Posted by: John Baez on January 30, 2007 3:21 AM | Permalink | Reply to this

Re: Peering Through the Veil

I know people who were interviewed by the MIT Tech and couldn’t understand the sentences attributed to them when they read the interview printed in the paper. Sometimes, two phrases fifteen minutes apart in a conversation get put together without so much as a comma in between, never mind an ellipsis.

Voo Doo, the school’s humor magazine (“MIT’s only intentionally humorous campus publication”) generally holds itself to a higher standard, which is easier to do when all of your quotes are made up anyway.

That “Consciousness Is More Important” headline is very, ah, Leary-esque. In fact, I can see a great Voo Doo article coming out of that…

Posted by: Blake Stacey on January 30, 2007 7:44 PM | Permalink | Reply to this

Re: Peering Through the Veil

Wasn’t this [The Highlander] where you found the wonderful headline: […] ?


Posted by: Toby Bartels on January 31, 2007 7:50 PM | Permalink | Reply to this

Re: Peering Through the Veil

The real purpose of questionnaires is feeding the insatiable hunger of the regression machine.

David, I’m curious why you shy away from the chracterization of your work as “sociology”. Does having your work tagged as sociology make it harder for it to get listened to by your fellow philosophers?

Posted by: Walt on January 28, 2007 6:56 PM | Permalink | Reply to this

Re: Peering Through the Veil

To the extent that sociology is value neutral then it’s just not philosophy. Of course it’s results could be used by philosophy. If sociologists tell us that in societies run according to principles X, A will occur, while where principles Y hold sway, B will occur, and if we have argued that A pertains more closely to the good life than B, then their findings are useful.

But look closely enough and you often find strong value judgements underlying the work of sociologists, economists, and psychologists. Many famous experiments in social psychology have originated from the experimenter’s deploring some event, e.g., Milgram and the obedience experiments after the obedience of those carrying out the commands of the Nazis, the bystander apathy experiments after the Kitty Genovese murder.

Value judgements in these examples were openly discussed by the experimenters, which is not always the case. But even when this is so, the ‘problem’ is generally located with the individual, reflecting a more subtle, unarticulated philosophical attitude.

To provide the antithesis of the currently fragmented human sciences, think of Aristotle’s psychology, ethics, economics, and politics integrated into a theory of the good life.

Posted by: David Corfield on January 29, 2007 8:33 AM | Permalink | Reply to this

Re: Peering Through the Veil

So is Kuhn’s The Structure of Scientific Revolutions sociology, or philosophy?

Posted by: Walt on January 31, 2007 5:19 PM | Permalink | Reply to this

Re: Peering Through the Veil

I’d call it philosophy. Kuhn writes in The Essential Tension, page xv:

the early models of the sort of history that has so influenced me and my historical colleagues is the product of a post-Kantian European tradition which I and my philosophical colleagues continue to find opaque. Increasingly, I suspect that anyone who believes history may have a deep philosophical import will have to learn to bridge the longstanding divide between the Continental and English-language philosophical traditions.

So Kuhn is attracted by anti-empiricist historians, such as Alexandre Koyré, as well as more sociological historians, such as Ludwig Fleck, but has only the resources of the Anglophone version of logical positivism and logical empiricism to guide him.

You can see the relationship between Kuhn and Carnap clearly. For Carnap all questions are posed within a specific linguistic framework. You shouldn’t ask questions about entities within a framework from outside. But then how to decide between two frameworks? Sometimes it possible to form a larger framework which contains them both. Otherwise, you are left with merely pragmatic considerations, which are never decisive.

Posted by: David Corfield on February 5, 2007 1:33 PM | Permalink | Reply to this

Re: Peering Through the Veil

[The following is somewhat off-topic but in keeping with one of the themes of this post, namely, sustaining the engagement of philosophical investigation with the “larger questions which give point and purpose to the philosophical enterprise”.]

Have you (David) been paying much attention to the area of computer science associated with the term formal ontology, and the kinds of issues that come into play in it? The field is of course derived in part from old themes in philosophy, and the study of knowledge representation in AI and computer science generally. This paper is a sample of writing in the field, dealing with specific questions of great practical significance in contemporary health informatics. Also see the Buffalo Ontology Site.

In addition, it seems to me that there are strong connections between formal ontology (and knowledge representation) and a theme of Barry Mazur’s paper When is one thing equal to some other thing?:

3  Objects versus structure

Mathematics thrives on going to extremes whenever it can. Since the “compromise” we sketched above has “mathematical objects determined by the network of relationships they enjoy with all the other objects of their species,” perhaps we can go to extremes within this compromise, by taking the following further step. Subjugate the role of the mathematical object to the role of its network of relationships—or, a further extreme—simply replace the mathematical object by this network.

This may seem like an impossible balancing act. But one of the elegant–and surprising—accomplishments of category theory is that it performs this act, and does it with ease.

Posted by: Chris Weed on January 31, 2007 5:52 AM | Permalink | Reply to this

Re: Peering Through the Veil

So do the Buffalo group use any category theory? It seems like the obvious (for us) thing to do. In fact it’s already being done in some sense by Mike Johnson and Robert Rosebrugh, as I mention in this post and the first comment.

Posted by: David Corfield on January 31, 2007 8:03 AM | Permalink | Reply to this

Re: Peering Through the Veil

I don’t know. The theory of ontologies as understood in computer science evidently has strong connections with the theory of types in programming languages, and I believe the latter has been one of the prime motivations for the introduction of category theory into theoretical computer science, so it would seem to make sense.

Posted by: Chris Weed on January 31, 2007 4:24 PM | Permalink | Reply to this

Re: Peering Through the Veil

If the Buffalo group doesn’t use category theory, that would be a real pity. Bill Lawvere and Steve Schanuel are both top-notch category theorists at Buffalo, and Lawvere has written on computer science.

Posted by: John Baez on January 31, 2007 9:40 PM | Permalink | Reply to this

Re: Peering Through the Veil

The edition of New Scientist which features our interview is out. Also we’re in today’s Independent. (“Every doctor in the country should read it.”) Last Saturday we were in The Times, and on Monday in the Yorkshire Post.

Posted by: David Corfield on February 16, 2007 8:19 AM | Permalink | Reply to this

Post a New Comment