The Role of Mathematics and Intellectual History in (my) Philosophy

Philosophers tend to think other philosophers are doing bad work and resent their success. I find this tendency most pronounced among mid-to-late stage grad students -- people who are good enough to see the flaws in what's published and aptly feel entitled to critique it as a full fledged member of the community. But who have not yet had the gruelling experience of repeatedly trying to better and realising that you can't, that in fact your work is just fodder for the next batch of sharp eyed youngsters hungry to prove themselves. So it goes, so it goes.

One consequence of this is that we all have to get used to justifying our own choice of method or approach to topics. There's always someone out there who thinks its just obvious that you have approached your question in totally the wrong manner, and any non-muddle-head would clearly see that you ought to have... well it just so happens they have a draft manuscript they could share if you are interested. One gets used to fielding thinly veiled versions of this critique from one's condescending peers, faux deferential versions of it from grad students seething with rage, and absurdly aggressive blustering versions of it from philosophers over the age of 55. Again, so it goes.

For me people tend to focus on the use of mathematical arguments or models. Philosophers in general are very strange about formalism. There are clearly many who rather wish they could have succeeded in a real science and hope to use philosophy as a place to show off skills they don't have to rubes who don't know better. Here you tend to find a strange deference to arguments made with symbolism, and much use of variables v in circumstances c where they are probably inapt i.  On the flip side there is a strand of humanist ressentiment against maths, which may have some respectable intellectual roots but in the main is just the losing side of the The Two Culture wars resenting a diminished status. Alas, it is true, a classics degree no longer secures one a minor sinecure in the Raj. Yet somehow I find myself unsympathetic.

For my part I retain the rather dull, unfashionable, maybe even refuted (though I hope not), view that mathematics is ultimately just a way of talking. A language among others. There are ultimately not many questions about writing one's arguments in a formal mode or making of one's thought experiments mathematical models that would not also be questions about the decision to write a paper in French or Twi or English. There are questions of accessibility to intended audience, of whether the vocabulary is rich enough for this phenomenon, and so relatedly how precise one can be in one's descriptions if one speaks in this manner, and so on.

I think in general the trade off for mathematically phrased arguments in philosophy is that it has an impoverished vocabulary and lowers accessibility, but on the flip side it allows one to be very precise and so rule out certain kind of errors (say that of inferring from an implicature as if it was semantically entailed), or at least make them less likely. I don't always get this right. For instance, in my own estimation since I never followed it up with anything the use of formalism in On Fraud was not worth the trade off. The same argument could have been made in prose with the same degree of plausibility, but with considerably greater audience and accessibility. But other times I think it is correct, for instance in Vindicating Methodological Triangulation or Jury Theorems for Peer Review I would not have trusted the somewhat counter-intuitive conclusions without the assurance provided by the theorems. And finally sometimes I opt to drop the formalism from the argument even if it has informed the reasoning; as I think was the right choice here, e.g. All this to say that: using mathematics in philosophy has never really appeared fraught to me, it is a relatively low stakes practical decision that I have sometimes made well, sometimes poorly -- and never with much consequence. The fact that it is what people focus on as methodologically interesting in my work seems to me a pity.

Instead I think it far more challenging to say why it is that I make such frequent use of intellectual history. The paper linked above Vindicating Methodological Triangulation is, for instance, simultaneously an interpretation of Du Bois' method in sociology and an argument for mixed method research. The paper On Fraud draws one of its arguments from the book Objectivity discussed below. Some of my work is dedicated to exegesis, and I will appeal to the claims made in those pieces when making my own positive arguments in later works. I have blogged before about something like a heuristic of discovery in philosophy that makes heavy use of intellectual history, and defended on here something I called "moderate historicism" for interpreting thinkers' works. This, it seems to me, is far more substantial and controversial a commitment of mine, yet in my experience people do not find it anywhere near so noteworthy or disagreeable.

To that end I tried to do a quick survey of some (not all!) of the intellectual histories I have benefited from, and tried to say how I think I have done so. I am going to leave out works which focus on particular figures - even though some of these are among my favourite works of intellectual history. Instead I will just draw from three thematic areas I have often read around in:

One genre I have made much use of are scientific conceptual genealogies. As mentioned, for instance, I quoted from Daston and Gallison's Objectivity in my published work.  The particular use made of it there was to show how in different social conditions, when a behaviour was viewed as acceptable which we now view to be shameful, people could openly admit to behaving in a way that I predicted they would. What was useful to me, then, was learning how changing standards of evaluation changed scientists' behaviour in response. I have also often appealed to Latour and Woolger's Laboratory Life, as having some wonderful reflections on scientists consciously seeking to influence the standards of evaluation to their own gain. Hasok Chang's Inventing Temperature and Dutilh-Novaes' The Dialogical Roots of Deduction have been illuminating to me on broadly similar grounds. (Likewise histories of the social sciences like Porter's The Rise of Statistical Thinking or Hacking The Taming of Chance.) As the social arrangements scientists are subject to change, and their technical capacities increase, different modes of arguing and different means of testing become available and seem more or less tempting. For me as a social epistemologist this is all fascinating as source material, both for inspiring ideas and testing guesses I have against this data. 

At a somewhat deeper level Fleck on syphilis is a good lesson in what kind of social conditions have to be in place for certain kind of ideas to be had or given uptake at all -- this then feeds directly into arguments about what we can or cannot expect science to do for us even in the best case. So one thing, then, I gain from intellectual history, is learning what seem to be the practically necessary requirements for certain kinds of ideas and concepts to be developed and spread, and how it is that scientists respond to different modes of evaluation becoming available to them. 

A second area where I have drawn much from intellectual history is in the study of slavery and race. Even more so than in the study of the sciences this area requires first order historical knowledge of material and social goings on in the past. Just to get the basics of what sort of thing slavery was, how it is related to race and other modes of social organisation, you should be reading works of history and contemporary social theory. This certainly includes some conceptual genealogies of a somewhat similar sort to the scientific type. For instance I very much loved and learned much from Smith's Nature, Human Nature, and Human Difference. Along with Sala-Molins' more caustic and polemical Dark Side of the Light one sees here how the intelligentsia were involved, often entirely complicit and even where not no doubt failing in their duties, in the emergence and stabilisation of concepts that would very largely be used for evil. Garnsey's altogether more dry Ideas of Slavery from Aristotle to Augustine is fascinating for seeing how simultaneously the human heart so persistently rebelled against slavery and yet also so infrequently struck upon universal manumission and abolition as the solution. Some of my previously quoted exegetical work was studying how the logical empiricists tried to resist racialisation, and I have drawn from the above traditions in non-exegetical published work too. These works no doubt also have a salutary moral effect. In reading some of them I was at times reminded me of those passages in Arendt wherein she condemns those who tried to reason with the Nazis on their amoral terms. What appeared to people as hard nosed realism in trying to compromise with the presumedly stone-hearted Hitlerites was actually useful to Nazi bureaucrats in allowing them to evade, even to themselves, the moral reality of what they were doing. All this is useful as a moral instruction, reminding one what locally apparently reasonable compromises will look like with hindsight. 

Intellectual history here is not so much an enriching source of data and instruction as a prerequisite to know what I am talking about. Or, at least, so it seems to me. I must admit that people seem to not only get by but be capable of doing work in the field of philosophy of race without this sort of background. I suspect then what we are really seeing here is intellectual history as a means of masking a deficiency of mine -- I am not a keen sociological observer myself, nor do I have a background in some pertinent science like anthropology or genetics. I have no strong social intuitions, wouldn't trust them if I did, and have no alternate source of information. My only way into this topic is through history and social theory.

Third and finally I have made use of intellectual histories when trying to think about alternative political forms. In two opposite sort of ways! Busia's The Position of the Chief in the Modern Political System of Ashanti documents the pre conquest Ashanti political arrangement and shows what effects British imperialism had upon it. It is fascinating as a detailed account of how a distributed direct democratic system actually worked. It thus provides substance to Wiredu on non party democracy. However Busia comes with his own biases, and the section on Fante literature in Jackson's The African Novel of Ideas provides a good counter-balance to his somewhat idealised picture of pre-colonial polities by showing you what non-Ashanti intelligentsia hoped to achieve. To me these paired well with my readings on the emergence of radical democratic ideas in Britain, such as Hill's classic The World Turned Upside Down or Rees' more recent The Leveller Revolution (on which see also). I tried to read some primary sources here like transcripts of the Putney Debates, Winstanley's Law of Freedom, and Coppe's truly marvellous Fiery Flying Rolles. These all in their own way give substance to things like James' Every Cook Can Govern. Even with blinkers off and acknowledging the huge huge flaws of the fanatical and slave-trading groups described above, these still give me hope. Genuine democracy, conflict riven as it inevitably is, can be made to work. And once you've got it, even just for a bit, it generates its own culture and hence a lasting support base. These works give me not just ideas but hope, faith. 

In contrast to that I have also been interested in the history of technocracies, especially focussed on Confucian government. The key text here has been Kühn's The Age of Confucian Rule: The Song Transformation of China. Here we get to see a period in which highly centralised technocrat bureaucracy was the main form of government. And interestingly enough it also has much to be said in its favour! One here gets the impression of technocratic government arising as an expression of genuinely widely shared cultural values and in opposition to arbitrary government by hereditary warlords. Kiri Paramore's Japanese Confucianism: A Cultural History, Nosco's (ed.) Confucianism and Tokugawa Culture give a similarly positive impression of Japanese Confucianism, leading to its eventual suppression by the fascist regime. Relatedly, the intellectual history of the early 20th century Confucian inspired anarchist movement and actual first order anti-imperialist text in Monster of the 20th Century (along with Chōmin's delightful drunkard's discourse) also helps convey this. (I think to modern sensibilities the White Peak story in Ugetsu is liable to convey a positive image of Mengzi, against what I would guess was the author's intent -- there suppressing the Mengzi is justified on the grounds that it might encourage uprisings against bad rulers!) Contrast this with  Deutchler's nightmarish The Confucian Transformation of Korea for a vision of what Confucianism looks like when it is a top-down elite-driven programme, and maybe sprinkle in the healthy cynicism of AJP Taylor's The Trouble Makers or Luxemburg's sharp analysis of vanguardism, and one is brought back down to earth. Still, even if only under certain cultural conditions, to my own democratic sensibilities it was remarkable that this could ever work at all.

So where then does this leave me? Intellectual histories have played a part in giving me faith in my ideals but also challenging my sense of what is possible. They provide data regarding the behaviour of scientists and inquirers under different evaluative regimes, and illuminate what kind of social or technical conditions are pre-requisites for certain sorts of inquiry to bear fruit. They upbraid me with stern moral lessons while also forming just a humdrum pre-requisite for me to even have anything at all. Modest as my career has been, I could not have done even this little I have done without them.

Now it is tempting to generalise from my own case. To worry that philosophy done without this sort of information runs the risk of being morally lax, devoid of content or connection with the real world, or based upon inaccurate guesses where not -- baseless in its faiths and parochial in its sense of possibility. But I am not sure that is right. Instead I think it better to say: everyone needs something that is, for them, playing the role of grounding one's modal reasoning. We philosophers are very concerned with what is possible, with counter-factuals, with what could or should or would be. Somehow or another you need to  be able to reason about these things in a way that is neither ignorant of what is possible yet not so speculative as to be mere guesswork. For me it is intellectual history that has provided this basis, grounded my sense of the possible in the actual-but-different. I do not think it needs to be intellectual history for everyone, but everyone needs something to play this role.

My current reading


  1. Perhaps tangential, but this helped me see something with regards to a conversation I was having a couple days ago about philosophical genealogies, and how I often find the sort of potted (and often deeply parochial) genealogies many philosophers rely on in making arguments very frustrating. (This conversation was specifically about the disenchantment narrative.) Wasn't sure where I felt the line is between when genealogies are helpful or unhelpful, but now I think it definitely has to do with the difference between a meticulous examination of what was going on vs. looser, typically motivated narratives.

  2. Thank you, for both the argument for historical reading and the reading list.


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