### Brandom's Analytic Pragmatism

Robert Brandom (Pittsburgh) has been giving the John Locke Lectures in Oxford over the past few weeks, and has made available the texts of all six lectures. His position is neither one of those rare philosophies with which I find myself instantly admiring every part, nor is it one of those all too common ones which feel quite foreign. As such it should be good for me to think hard about what he's trying to do.

Here he is characterising the pragmatism of the later Wittgenstein:

Brandom's way is to cut back towards analytic philosophy:

Now, rather than restrict ourselves to features of all discursive practices, I take it as important to look at specific privileged discursive practices, one of which many would agree is mathematics. So, I am interested in features of mathematics shared with the natural sciences, and other disciplined forms of enquiry, which may not be found in every discursive practice. But it seems to me that Brandom offers a way of accounting for my sense that analytic philosophy of mathematics is far too narrow by encouraging us to consider the full relevance of normative vocabulary to a practicing mathematician. It struck me reading these lectures that where most philosophers of mathematics want to stop is with the treatment of assertions of, and inferences between, mathematical propositions, things like 2 + 2 = 4. Where I have spent much of my philosophical time, however, has been on mathematical value judgements. In Brandom's language I could put it thus: one could not count as engaging in the autonomous discursive practice that is research mathematics, or such a practice that contains research mathematics, while not making value judgements about the organisation of concepts or predictions about how one's subfield will proceed.

Let's consider this by treating a piece of exposition selected for no special reason - Claus Michael Ringel's Some Remarks Concerning Tilting Modules and Tilted Algebras. Origin. Relevance. Future. Now, I can honestly say I know nothing about tilted modules or algebras. I know what a module is, and I know what an algebra is, but I have no clue what 'tilted' means here. Let us proceed then together in ignorance. Consider these assertions:

To return to Ringel, we also find the language of modality, "...and it may well be, that in future...". Later in the article, he says:

Here he is characterising the pragmatism of the later Wittgenstein:

At every stage, what practical extensions of a given practice are possible for the practitioners can turn on features of their embodiment, lives, environment, and history that are contingent and wholly particular to them. And which of those developments actually took place, and in what order, can turn on any obscure fact. The reason vocabulary-kinds resist specification by rules, principles, definitions, or meanings expressed in other vocabularies is that they are the current time-slices of processes of development of practices that have this character-and that is why the collection of uses that is the cumulative and collective result of such developments-by-practical-projection is a motley. If that is right, then any codification or theoretical systematization of the uses of those vocabulary-kinds by associating with them meanings, specifiable in other vocabularies, which determine which uses are correct will, if at all successful, be successful only contingently, locally, and temporarily. Semantics on this view is an inherently Procrustean enterprise, which can proceed only by theoretically privileging some aspects of the use of a vocabulary that are not at all practically privileged, and spawning philosophical puzzlement about the intelligibility of the rest. On this conception, the classical project of analysis is a disease that rests on a fundamental and perennial kind of misunderstanding-one that can be removed or ameliorated only by heeding the advice to replace concern withPhrased like this, you can see why Wittgenstein has been taken to heart by a certain strand of social epistemology, such as that maintained by David Bloor or Martin Kusch.meaningby concern withuse. The recommended philosophical attitude to discursive practice is accordingly descriptive particularism, theoretical quietism, and semantic pessimism. (lecture 2)

Brandom's way is to cut back towards analytic philosophy:

I want to show how pragmatism can be turned from a pessimistic, even nihilistic, counsel of theoretical despair into a definite, substantive, progressive and promising program in the philosophy of language: indeed, how it can be understood as simply the latest phase of the analytic project. (lecture 2)But to do so it must take on board the pragmatist concern of what one is doing when one uses a vocabulary. However, had we look closely enough, we should have already known that analytic philosophy knew this:

supplementing the traditional philosophical analytical concern with relations between the meanings expressed by different kinds of vocabulary by worrying also about the relations between those meanings and the use of those vocabularies in virtue of which they express those meanings-as I recommended in my first lecture-is not so much extending the classical project of analysis as it is unpacking it, to reveal a pragmatic structure that turns out already to have been implicit in the semantic project all along.Now, engaging in any 'autonomous discursive practice' (i.e., using a vocabulary such that one need use no other), necessarily involves the activities of asserting and inferring. The task Brandom sets himself is to relate the logical, normative, modal, and intentional vocabularies to the practices and abilities necessary or sufficient to engage in such discursive activity. Perhaps the quickest way to point out the difference between his programme and what might be called 'orthodox' analytic philosophy is his treatment of modality. All talk of truth-makers is absent, so there's no recourse to possible worlds: I could have been unwell today. Some truth-maker must make this true. The truth-maker is some possible world in which I am unwell. Instead, modality is treated in terms of incompatibility of assertion. I am inconsistent if I assert "it is impossible for copper to melt at below 0 degrees centigrade" while also saying that my pipes will melt this winter when it freezes.

Now, rather than restrict ourselves to features of all discursive practices, I take it as important to look at specific privileged discursive practices, one of which many would agree is mathematics. So, I am interested in features of mathematics shared with the natural sciences, and other disciplined forms of enquiry, which may not be found in every discursive practice. But it seems to me that Brandom offers a way of accounting for my sense that analytic philosophy of mathematics is far too narrow by encouraging us to consider the full relevance of normative vocabulary to a practicing mathematician. It struck me reading these lectures that where most philosophers of mathematics want to stop is with the treatment of assertions of, and inferences between, mathematical propositions, things like 2 + 2 = 4. Where I have spent much of my philosophical time, however, has been on mathematical value judgements. In Brandom's language I could put it thus: one could not count as engaging in the autonomous discursive practice that is research mathematics, or such a practice that contains research mathematics, while not making value judgements about the organisation of concepts or predictions about how one's subfield will proceed.

Let's consider this by treating a piece of exposition selected for no special reason - Claus Michael Ringel's Some Remarks Concerning Tilting Modules and Tilted Algebras. Origin. Relevance. Future. Now, I can honestly say I know nothing about tilted modules or algebras. I know what a module is, and I know what an algebra is, but I have no clue what 'tilted' means here. Let us proceed then together in ignorance. Consider these assertions:

...at the time the Handbook was conceived, there was a common understanding that the tilted algebras (as the core of tilting theory) were understood well and that this part of the theory had reached a sort of final shape. But in the meantime this has turned out to be wrong: the tilted algebras have to be seen as factor algebras of the so called cluster tilted algebras, and it may well be, that in future the cluster tilted algebras and the cluster categories will topple the tilted algebras. The impetus for introducing and studying cluster tilted algebras came from outside, in a completely unexpected way. (p. 26, my emphasis)What does that normative 'have to be seen as' mean? Something like: anyone sufficiently well-informed about the practice must see tilted algebras in this way, at pain otherwise of being charged with blindness, inconsistency, irresponsibility, or worse. It's a question of getting the concepts right. Here again is Brandom:

Where enough TOTE (test-operate-test-exit) cycles of this sort have been engaged in to produce a relatively stable discursive practice, objective facts about what actually follows from and is incompatible with what will have been incorporated in the material inferences and incompatibilities that articulate the concepts expressed by the vocabulary deployed according to the practical norms implicit in that practice. This essentially holistic process involves getting on to how things objectively are not just by making true claims, but also by acknowledging the right concepts. (lecture 6)The idea of TOTE cycles is to provide a basic form of "practical involvement with objects exhibited by a sentient creature dealing skillfully with its world". With this pragmatist outlook we get away from the image of a language hoping to hook onto the world, and see instead world and word emerging as two poles of a practice.

To return to Ringel, we also find the language of modality, "...and it may well be, that in future...". Later in the article, he says:

It should be noted that some of the strange phenomena of tilted algebras disappear when passing to cluster tilted algebras. (p. 32)So phenomena can be strange. They don't fall into lawlike patterns.

The cluster tilting theory has produced a lot of surprising results - it even answered some question which one did not dare to ask. (p. 32)So, one would not have been counted irresponsible had one not asked these questions, until now.

Again we find this blending of intentional, modal and normative vocabularies. Perhaps Brandom's onto something with his "objective pragmatism" which...we have exhibited the cluster tilted algebras without reference to cluster categories, in order to show the elementary nature of these concepts. But a genuine understanding of cluster tilted algebras...is not possible in this way. (p. 37)

sees those features of discursive practice that are made explicit by modal vocabulary and those that are made explicit by normative vocabulary as complementary, as each in principle fully intelligible only in terms of its relation to the other. Its understanding is, as the slogan that forms the title of this lecture has it, that discursive intentionality is a pragmatically mediated semantic relation, that essentially involves both what one is doing in saying something, and what is said about how it is with what one is thereby talking about. (lecture 6)With some space for Hegel (lectures 5&6) and a whiff of category theory (mentioned once) in his diagrammatic representations of vocabularies and practices, this is an extremely interesting programme.

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