Williamson’s Philosophy of Philosophy

PhilPhilI’ve been trying to make my way through Tim Williamson’s The Philosophy of Philosophy, for the second time. I read it as PhD student and, I suspect, thought I was getting more out of it than I was in fact. Now I think I’m seeing a bit more.

Williamson wants to explain what he takes to be the true nature and methodology of philosophy. One of his central aims is to dispute what he calls “philosophical exceptionalism” – the view that philosophy seeks to do something fundamentally different from what other sciences do.

One prominent version of philosophical exceptionalism (one that I find attractive) is the notion that philosophy primarily studies our concepts, whereas the other sciences study the things in the world that make up the objects of our (non-reflexive) concepts. Williamson attacks this notion. Philosophy, he insists, also studies the world outside of thought. It is interested in our concepts only because the kinds of questions it asks about the world require a lot of conceptual reflection to answer. It is really just an especially thinky sort of natural science.

That’s much too big for me to comment on in a blog. But one little thing I noticed was Williamson’s attack on Dummett:

Dummett claimed … that the traditional questions of metaphysics [can be answered] by the analysis of thought and language. For example, in order to determine whether there are numbers, one must determine whether number words such as “7” function semantically like proper names in the context of sentences uttered in mathematical discourse. But what is it so to function? Although devil words such as “Satan” appear to function semantically like proper names in the context of sentences uttered in devil-worshipping discourse, one should not jump to the conclusion that there are devils. (20)

This is a strangely superficial misconstrual of Dummett’s claim. Dummett did not claim that working out how number terms function semantically in mathematical discourse is sufficient to answering the question of whether numbers exist. He claimed only that it is necessary, and that it is the most philosophy can do to help with answering that question.

If, for instance, quantifiers in mathematical discourse function semantically in a way that suggests a verificationist interpretation, then it is not unreasonable to conclude that mathematical objects exist simply by being constructed by mathematicians following certain procedures. We could then easily know whether certain mathematical objects exist by observing that mathematicians are in fact carrying out the relevant constructions. This latter, however, is not a job for which the philosopher is especially well suited. It can be done just as well if not better by a mathematician or even a sociologist of mathematics.

If, on the other hand, quantifiers in mathematical discourse function classically, then mathematical objects cannot be taken to exist merely by being constructed. It will be a tougher job to work out whether or not they exist. Again, there is no argument that the philosopher should have any particular aptitude for this task. If numbers are abstract objects revealed through mathematical intuition, then discovering them is the job of whoever possesses the relevant powers of intuition, as is the job of convincing the rest of us to trust reports of such intuitions. There is no reason to think philosophers should be particularly up to this job, and the same applies on other theories of what mathematical objects might be.

Just the same applies with devils. The semantic functioning (or, with less needless technicality, the use) of a term like “Satan” can reveal to us whether it aims to refer to a thing and, if so, to a thing of some particular sort. René Girard argues that when Christ called Satan a scandal he was making something closer to an identity statement than a predication. Alfred North Whitehead’s contribution to a Cambridge Apostles debate on the existence of the devil was: “he is the homogenous”. Whitehead clearly intended, not to stipulate “devil” as meaning “homogenous”, but rather to help us to remember, in case we had forgotten, the deep link already present in our collective understanding between devilishness and homogeneity; we need only think of Blake’s Dark Satanic Mills and industrial mass production. At least part of both Whitehead’s and Girard’s point is that we can’t talk meaningfully about Satan without recognising that “Satan” is at least as much the name for a type of thing, or for a flattening and nauseating relation among things, as it is the name for a thing.

All this is philosophy; the names of the devil are being tested for their range of use. Philosophy is in the business of knowing what should count as catching the devil – at least for an Apostle or a Cambridge Apostle. The hunt itself is never the business of philosophy, but without it we are condemned to sniffing out herrings.

What Williamson attacks is a parody of Dummett’s position, based on the absurd claim that we can settle questions about what exists merely by examining how language works. No sensible person, least of all Dummett, is suggesting that. What Dummett stresses is only how valuable the examination of language can be for pursuing questions about what exists. We search through the inventory of nature for a thing we have named in language; all hope of picking the thing out of the inventory vanishes if we fail to know how language works to name it.

The latter contribution – philosophy’s contribution, on Dummett’s reckoning – can make a very large portion of the whole project. An examination of language cannot tell us whether or not there are sets. But it makes an astonishing contribution. We might have thought that “set” can just mean whatever we group together as such. But Russell’s paradox shows that this can’t be right: we can come up with a way of specifying a set that makes sense within the most naïve set theory, yet the set specified cannot exist on pain of contradiction. So sets must be something other than what we specify as such within naïve set theory, or else they are nothing at all. Well, are there sets, then, and what are they if so? To the extent that answering that is just seeking to know what we mean by “set” – at least what we can sensibly mean by it – then it remains the job of philosophy. But when a set theory is up and running and includes a procedure for determining which putative sets exist then applying the procedure is no longer really philosophy. The philosopher can turn set theorist, or she can retreat from the problem as outside her remit.

It is clear enough why Williamson doesn’t like this vision of philosophy. He doesn’t want to retreat from making substantive existence claims. He notes, with some pride, “the revival of metaphysical theorizing, realist in spirit … associated with Saul Kripke, David Lewis, Kit Fine, Peter van Inwagen, David Armstrong, and many others” (19). I’m sceptical about that revival and even more sceptical of the claim that it should be part of philosophy, or indeed of any specialised subject.

Take, for example, the relation of grounding that has interested many recent metaphysicians. A good deal of philosophical writing on it consists of working out the semantic functioning of terms expressing grounding relations. Fine, for instance, determines that claims involving grounding must adhere to certain schemata, e.g. (where ‘A’ and ‘B’ stand for facts and ‘<‘ stands for a ‘strong’ grounding relation and ‘≤’ stands for a ‘weak’ grounding relation):

A<B // A≤B.

What do we know when we know that grounding claims must adhere to such a schema? We know by its lights that something has gone wrong if we find ourselves asserting that A<B ∧ ¬(A≤B). But is it wrong because the world is such that facts cannot be grounded thusly, or is it wrong because that is not the right way to specify grounding relations? More generally, is there more to the existence of grounding relations than their having been specified according to the right procedures? Simply working out the semantics doesn’t tell us the answer. If we were to find something in the logic of grounding akin to Russell’s paradox, something that showed us that grounding relations couldn’t be just what we specify them as (within… naïve grounding theory??), then that would tell us part of the answer. But I am not aware that anything like that has been 128px-Set_theory_icon_svgfound.

Fine, of course, says that grounding relations are independent of what we specify. But so far he has not shown this; he has only shown how we do and do not talk about grounding. If we know about objective grounding relations, how do we know about them? Is it by some special metaphysical intuition? Does the philosopher have particularly strong powers of metaphysical intuition? If so, then why should she be bothering to work out how we talk about grounding? She should be intuiting how facts really are grounded and then telling us, so that we can adjust our grounding talk accordingly. But why should we believe that the philosopher has particularly strong powers of metaphysical intuition? If she doesn’t – if we can all intuit grounding relations and other metaphysical facts as readily as she can – then whatever her special business is, it is not metaphysical knowledge. Designing formal systems that track our metaphysical knowledge may help us towards getting more of it. But such systems do not amount to metaphysical knowledge on their own.

So philosophers who do the sort of metaphysics celebrated by Williamson seem to be in a bind. The claim to have special metaphysical knowledge is hard to credit and anyway doesn’t square with the practice of modern metaphysicians, which consists largely of trying to find generation principles rendering a set of sentences that, when appropriately translated into natural language, contains the largest possible number of sensible-sounding statements and the smallest possible number of silly-sounding statements. The contrasting claim, that metaphysical knowledge is evenly distributed throughout the population, undermines the notion of having metaphysics itself as a specialised science, though a parasitic science of working out how best to express metaphysical knowledge may certainly be specialised.

There is a way out of the bind. The metaphysician can claim that metaphysical claims are not justified by bare intuition, but rather through a kind of abductive inference, to the effect that the best explanation for the metaphysical portion of our language being semantically structured in this way points to some isomorphic metaphysical structure in reality beyond language. That is quite an abduction. By what power is it supposed that substantial forms in nature are inflown into the material of language? If some sort of evolutionary psychology is invoked here, I protest that evolutionary psychology is at best geared to explain how the use of language preserves the representation of alleles in the gene pool. In no way is it even geared to explaining how language could absorb forms from the world outside of itself. If metaphysicians are abducing that from the structure of language then their inference is not to the best explanation but to an extravagant and rather bad one, however serviceable it might be to their professional self-image.

Personally, I’d rather think what Dummett thinks: that philosophy is about uncovering and clarifying our concepts. It is not about working out what the (rest of the) world is like. But I might be missing Williamson’s point.


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