As he is showing me out from New College, Timothy Williamson tells me he is aware that he might come over to some people as an “arrogant prick”. It would be understandable for someone in his position to be a little conceited, even if not disgracefully phallic, for in the mainstream British, analytic tradition, Williamson is without doubt the pre-eminent philosopher of his generation. I have often asked academics who the stars are among British philosophers for whom free bus travel is not an imminent prospect or present reality, and Williamson is the only person who is regularly and reliably name-checked.

In print, Williamson certainly seems to lack no self-confidence, but in person there is no trace of haughtiness. When he answers my questions, his voice sounds almost hesitant, and there are frequent pauses between clauses and even single words. Yet when I later transcribe our conversation, I find, unusually for an interviewee, that almost all his sentences are perfectly formed, as are the thoughts they express. It is not clear whether the manner of the spoken words or the matter of their written equivalents gives a more accurate impression of the mind that produced them.

Since 2000, Williamson has been Wykeham Professor in Logic at Oxford University, a post previously held by AJ Ayer, Michael Dummett and David Wiggins. But although he stands at the pinnacle of his profession, he is all but invisible to anyone outside it. That is because he works in the analytical stream of philosophy, which has become celebrated or derided, depending on your point of view, for its technicality and inaccessibility. For those not steeped in it, if the specialised lexicon doesn’t lose you, then its generous use of formal symbolic logic will. But for Williamson, such ways of writing and thinking are second nature.

“I find that, for me, translating what somebody says in English into symbols when it’s some kind of complex statement, tends to make it clearer what they’re saying,” he tells me in his New College room, which looks as if it hasn’t been redecorated for about thirty years. “Many other people go the other way: they like to translate from symbols into English to understand what the symbols are saying.”

When Williamson explains why this is so, it is the rest of the world that suddenly sounds deviant.

“If you take a mathematical equation, if you try to write it out in words you get something that’s virtually unintelligible. Another analogy would be with maps. A map gives you a much more perspicuous representation of how things are laid out than some sort of verbal description of them does. Formulas are a bit like logical maps, they just make it very clear what the logical relations are.

“I don’t think that formalisation is a panacea or all philosophy should proceed by formalising,” he adds later. “There’s plenty of good philosophy that’s written in ordinary prose and in many cases it would not benefit from being formalised.” Nor does he think that being comfortable with such methods is a prerequisite for being a good philosopher. “I don’t think all philosophers have to be well versed in formal methods. Philosophy benefits from having a wide variety of people with a wide variety of skills. Some very intelligent people have a kind of symbol blindness, and they get blocked with mathematics and they get blocked in pretty much the same way with logic.”

Nevertheless, Williamson clearly does think that we ignore or reject the rigorous use of logic at our peril, whether or not logic is our primary interest.

“To give one example, a lot of the contemporary discussion of the question of the relation between the world and our knowledge of the world, which is a central philosophical issue by anyone’s standards, is informed by a logical result which essentially seems to show that there are truths about the world which can’t be known, a proof first devised by the logician Alonso Church. That’s a little formal result which doesn’t necessarily carry its metaphysical moral on its face, but if you don’t know about it you’re ignorant of an extremely important constraint on theorising about that absolutely central philosophical question.”

Williamson is a robust defender of the analytic method against those who see it as lacking “relevance”. “It seems to me that people shouldn’t spend too much time worrying about whether what they’re doing is significant. It’s better that they worry about whether what they’re saying is true.”

In any case, what can look like dry technicality is, by his lights, simply a commendably rigorous way of approaching the same questions that philosophers have always found important.

“The kinds of questions that have led analytic philosophers to work in all the specialised areas that they work in, do go back to the same sort of questions that Plato, Aristotle and other great philosophers of the past were working on. But I think that what people have to realise is that if you ask an exciting question, and then you make a serious effort to find out what the answer to it is, you just can’t expect that every step on the way will be equally exciting. The point of rigour is actually to enable one’s mistakes to be as easily spotted as possible, so that they can be corrected. It seems to me that people who don’t care about rigour are really treating the question that they’re supposed to be answering unseriously, because they’re not doing their best to give them the right answers.”

For those who still doubt the value of such work, Williamson has plenty of evidence that “there are very clear connections even between what seem like the most abstract and driest areas of philosophy and the most practical applications.” For instance, “The concept of a computer emerged from problems in theoretical logic which at the time seemed to have no practical application, but thinking about those abstract problems in logic led Turing to essentially define what a computer was and even to give an abstract specification of how to build one, even though no computers were in existence; and we all know how big a role computers play in our lives.”

Even modal logic, which examines the logic of possibility and necessity, has benefits beyond the philosophy seminar room.

“It’s been reinterpreted in epistemic terms and that’s turned out to be of extreme importance in economics, for example. Theoretical economists need to understand the idea of common knowledge because the predictions about how economic agents will act in various situations depends on what features of their situation are common knowledge and which ones are just private information. Modal logic turned out to be exactly the right framework for understanding that sort of issue.

“Another development of modal logic was something called dynamic logic which has been used to important effect in computer programming, in particular in devising methods for checking programmes to make sure that they don’t behave in ways that they are not supped to behave. Of course, those are not the applications that philosophers originally developed these tools for, but it turned out, as is very often the case in science, that ideas that are developed for their own sake turn out to have completely unexpected and highly practical applications.”

Williamson has an even more surprising example of unforeseen practical applications which is closer to home. “Recently I had an email from a missionary in Africa who said that he’d found the chapter on assertion in Knowledge and its Limits very useful in thinking about how to understand dialogues between people communicating across a religious divide. I’m not religious, so it’s not that I’m particularly keen on the idea of my work being used to spread Christianity or anything like that. But that’s an example of a practical application which hadn’t remotely occurred to me. That it should have some connection with missionary work was a bolt from the blue.”

Williamson has a confidence in what he is doing which not all his colleagues share. Simon Glendinning, for example, has talked about the way in which analytical philosophy conceives of its “continental” cousin as sloppy and obscurantist. This he calls “the false personification by self-styled analytic philosophy of a possibility which is internal to and which threatens all philosophising, that is the possibility of being empty, the possibility of sophistry.”

When I ask Williamson if he ever feels any anxiety that what he’s doing might be empty, he answers with a swift and emphatic “no”.

“A lot of the work that I do is at the logical end of the subject where there’s no more danger of emptiness than there is in mathematics. There are some people who think mathematics is empty, but I think that’s a somewhat ridiculous view. But I think even at the much less formal end of the subject, it’s really neurotic in many cases to worry about whether what people are saying is just completely empty. It’s as meaningful as any other theoretical discourse. Of course, it’s true that it’s easier to stray into bullshit in formal philosophy than it is in natural science, and so I think one does have to be monitoring oneself and others to make sure that one isn’t descending into bullshit. It’s an occupational hazard but it’s hopelessly exaggerated to think that means that it might turn out that philosophy is by its nature always empty.”

Even if it is not strictly empty, might the branch of philosophy where he has ended up turn out to be a cul-de-sac?

“Well, yes, it’s a possibility that we’ll descend into barbarism, and evolutionary biologists could worry that fundamentalist religion will take over and their research won’t be pursued and will just be replaced by creationism, but that doesn’t mean that they should be worrying about whether what they’re doing is worthless.”

That answer is revealing because it suggests that the only way Williamson can imagine that analytical philosophy could be a cul-de-sac is if other people go off in the wrong direction. This implies a great deal of confidence that this is the right direction for philosophy.

“I’m confident that the overall direction is right,” he agrees. “I mean, of course in every discipline, some lines of enquiry turn out not to be very fruitful. So of course, it could be that some of the lines of enquiry that I’m engaged on just turn out not to lead anywhere very interesting. I don’t think so, but it’s not crazy to wonder about that. But to think that the whole pursuit of philosophy by rigorous argument is radically misconceived, that really strikes me as a neurotic doubt.”

Williamson thinks that the idea that philosophy could be thus misconceived “partly depends on misconceptions about philosophy that represent it as being much more different from other sorts of discourse than it really is.”

This relates to one of the core arguments of The Philosophy of Philosophy, which is that, despite its technicality, philosophy is continuous with various other areas of human thought. For instance, it is continuous with natural science but not a department of it.

“Natural science is a fairly specific set of enquiries which are characterised by the prominent use of experiment and observation and although I don’t think those methods are totally irrelevant to philosophy, I think they have a much smaller role in philosophy than they do in physics. Part of what I was doing in the book was trying to explain how the armchair methods of philosophy, just sitting and thinking, can be a perfectly valid way of thinking about questions which really are questions about the world and not simply our words or concepts. What I was arguing was not that observation and experiment is in principle irrelevant to philosophy, and I think sometimes it really is relevant. But just as with mathematics, there are quite objective forms of enquiry that don’t centre on those methods of enquiry and it seems to me that a lot of philosophy is in a similar position to that.”

And the natural sciences also have those elements as well, in certain corners.

“Absolutely. I think that actually people tend to underestimate how important armchair thinking is in a subject like physics. It’s not just in isolated corners. A lot of physicists spend most of their time just doing mathematics.”

More generally, the kind of thinking that goes on philosophy is continuous with other forms of thinking.

“One of the distinctive methods of armchair philosophy is doing thought experiments. Of course, it’s not only philosophy that does thought experiments. Galileo and Einstein did them too. But it is something very noticeable about a lot of contemporary analytic philosophy that a great deal of the argument proceeds by thought experiments and what I was arguing in the book was that there is nothing magical going on there. All that’s happening is that we’re talking about what would be the case if such and such a scenario were realised. In doing that we’re using the same kind of cognitive skills, broadly speaking, as we use when we’re talking about what would have happened if Hitler hadn’t invaded the Soviet Union or whatever. They’re not radically different sorts of activity. What’s happening is that philosophy is taking those quite ordinary forms of thought and then just using them in a more disciplined and systemic way, but without transforming them into something radically different. And that’s an important reason for not taking very seriously the idea that philosophy might turn out to be empty, because it’s hard to see how philosophy could turn out to be empty, given that it’s essentially using these commonsensical forms of thinking, without all the rest of our thinking turning out to be to be empty too.”

It may seem odd that Williamson has a conception of philosophy which sees it as being so continuous with other aspects of life and thinking, while at the same time it is capable of producing journals and papers that at least at first sight seem so very different and utterly alien to it. Is that just because the steps in between are not evident?

“Yes. Maybe it’s clearer if one thinks about some natural science, chemistry or whatever. Most people couldn’t make head or tail of an article published in a journal of theoretical chemistry, but nevertheless it’s pretty clear that natural sciences have developed through a series of refinements from quite ordinary observation and thinking about the world. I think what one has to learn from that is that those processes of refinement and imposing various kinds of intellectual discipline on ordinary thinking can transform it to the point where, at first glance, it seems to be unrecognisably different. You have to understand more deeply what’s going on to see that the differences are still only on a continuum.”

The job of making this continuum evident to the wider world is one he considers to be important.

“I don’t think philosophers have a duty to explain every step of their own work to a wider public, any more than people working in any other specialised area do. But I do think it’s extremely important that lines of communication should be kept open, so that it’s possible for people to find out something about what philosophers are doing, in the same sort of way that people can find out what scientists are doing by reading books of popular science at various levels of difficulty. Sometimes those books are written by scientists or philosophers, sometimes by people who are also at the forefront of research, like Stephen Hawking. But sometimes they are written by people who I guess see their primary role as communicating philosophy to a wider public.

“There need to be intermediate stages, as it were, of popularising ideas and drawing out their more practical implications and so on. I’m not using the word ‘popularisation’ in any negative sense at all. It seems to me that’s an essential part of the overall intellectual economy. It’s just that I don’t think it has to be the same people who are producing the specialised research who are also explaining its bearing to a wider public. Sometimes they’re good at doing that, and that’s fine, but other people who are doing excellent research may be either too busy doing it or too untalented at communicating very accessibly to be the right people to give an idea to others of what they’ve come up with.”

What philosophers themselves need to get better at is not communication, but philosophy. Williamson ends The Philosophy of Philosophy with a self-confessed headmasterly injunction that philosophers must do better. In what ways?

“In every way,” says, laughing. “The argument I was making there was not that there’s some kind of radical transformation of philosophy that is available to us now so that we can suddenly turn ourselves into creatures who never make mistakes or anything like that. It’s much more that there’s a lot of variation across the philosophical community in various kinds of philosophical skill, in argument and in evaluating thought experiments, and so on, and those skills are not a matter of magic, they’re not totally mysterious, they’re ones that people can be trained in and some philosophical training is better than other philosophical training. So what I was trying to encourage people to do is to become more aware of methodological standards and of the ways in which all sorts of aspects of our work can be cleaned up and done a bit better. That’s not something that’s going to make an overnight difference. But I think something that happens in natural science is that relatively small differences in how skilfully people carry out experiments can in the long run make quite a big difference to the reliability of theorising, because the data is better and so it can discriminate more finely and more reliably between different theories. I think that kind of change of degree, not of kind, in what we’re doing can make philosophy significantly better than it is now. Those are changes that have gradually been happening over the past century but in a very patchy way. I just think we should take that process further and be a bit more systematic and self-conscious about it.”

Further reading
The Philosophy of Philosophy (Blackwell, 2007)
Knowledge and Its Limits (Oxford University Press, 2000)
Vagueness (Routledge, 1994)

A longer version of this interview appears in issue 45 of The Philosophers’ Magazine.