Title and department: Assistant Professor of Philosophy
Hometown: Cambridge, UK
Educational/professional background: As an undergraduate I studied mathematics and philosophy at King’s College London. I was a graduate student, and a postdoc, in philosophy at Oxford. I then taught at Yale and Texas Tech (with a year in between as a research fellow at Glasgow), before coming to UW.
How did you get into your field of research?
My PhD dissertation was on truth and paradox. Broadly speaking, it was concerned with the question: To what extent can we use language to talk about language itself; or analogously, to what extent can we think about thought itself? The issue is that once we allow (say) a language to talk about itself, we run into sentences like “this very sentence is untrue.” This sentence is either true or it isn’t, of course. If it is true, then what it says is the case; but that is that it isn’t true. So it must not be true. But that’s what it says! So it must be true after all.
What this shows is that if we try to describe how a language that talks about itself works, we end up contradicting ourselves. This threatens the very idea that such languages are possible.
I had thought about these questions from a relatively technical perspective as an undergraduate. But when I was invited to think about them in a more philosophical way by a graduate class, I realized that this is what I wanted to write my dissertation on. I was completely taken with this idea that these apparently isolated puzzles (involving “this sentence is not true,” for example) might necessitate fundamental limits on the extent to which we can understand language and thought “from the inside.”
Could you please describe your area of focus?
I am interested in paradoxes like those involving “this sentence is untrue.” But my interest is less in these paradoxes in and of themselves (e.g. is that sentence true or isn’t it?) than in the surprisingly far-reaching light that these shed on a range of philosophical issues. I have already mentioned the prospect that they might induce limits on language and thought. Here is another global issue that they have consequences for. Consider laws of logic such as: If a statement of the form `p and q’ is true, then p must be true too. These seem to be the strictest laws we have: stricter than laws of nature, perhaps even than those of mathematics. In recent work, however, I have argued that a lesson we should draw from the paradoxes is that (almost) all of these laws in fact have exceptions.
What main issue do you address or problem do you seek to solve in your work?
There isn’t a single main issue. But here is one in addition to those I have already mentioned. The striking thing about the paradoxes is that they lead a kind of double life. On the one hand, they threaten to show that certain informal concepts, such as that of truth, are incoherent, at least as we naturally conceive of them. On the other hand, however, essentially the same arguments are used to establish certain fundamental (and straightforwardly legitimate) mathematical results. One of these is Cantor’s theorem, which is standardly taken to show that there are in fact different sizes of infinity. This theorem is a fascinating result. I believe, however, that the standard interpretation of it (i.e. as showing that there is different sizes of infinity) is wrong. This is something that I have argued for, in part, by drawing on the connections between the proof of the theorem and the paradoxes that echo it.
What attracted you to UW-Madison?
It is obviously a first-rate university. But it has a wonderful philosophy department in particular. When I visited I was struck by just how vital an intellectual community it is. Everywhere I turned there were people with robust ideas, and curiosity to spare.
What was your first visit to campus like?
It was during the time of the polar vortex … When I arrived in Madison I couldn’t go out much, but I was still struck by the beauty of the place. Even though the visit was essentially a job interview, my conversations with students and faculty were universally rewarding and enjoyable. By the time I was waiting in the airport for my return flight, it was clear to me just how lucky I would be to have the chance to work here.
What’s one thing you hope students who take a class with you will come away with?
I hope to give students the ability to think about any topic that interests them with clarity, rigor and imagination. An ability to map out the intellectual terrain simply but precisely. And an ability then to see novel, perhaps unexpected, routes through this.
Do you feel your work relates in any way to the Wisconsin Idea? If so, please describe how.
Philosophy is a funny subject. On the one hand, it can get pretty abstract pretty quickly. On the other hand, though, studying it seems to do wonders for one’s ability to think about almost anything — from the very abstract to the far more concrete. I hope that by teaching it (and my teaching is strongly informed by my research), I will give students a skill that will allow them to contribute to really any aspect of life in Wisconsin.
What’s something interesting about your area of expertise you can share that will make us sound smarter at parties?
We all know that there are finite sets (that is, collections of objects) whose members can’t be paired off with one another. For example, if you have a set of six knives, and one of five forks, then however hard you try to pair each knife with a fork, one is going to be left over. You might have thought that this couldn’t happen with infinite sets — infinity is infinity, right? But it turns out that it can. For example, consider, on the one hand, the set of natural numbers (0, 1, 2 etc.) and, on the other, the set of all setsof natural numbers. (This latter set will contain every set whose members are all natural numbers: for example, the set of even numbers, the set of numbers larger than a hundred, etc.) It turns out that, however hard you try, there is no way of pairing off the members of these two sets. You can arrange things so that each number is paired with a distinct set of numbers, but there will always be some set of numbers left over, just like before there was always one knife left over. If the people you’re talking to haven’t yet told you that they need to go and get another drink, you could mention that while this is often taken to show that there are different sizes of infinity, there is more room for interpreting this result than had been appreciated.
What are you looking forward to doing or experiencing in Madison?
I am really looking forward to experiencing, to being part of, the intellectual and cultural life of the university. In the first instance in my department, but also much more broadly. I am looking forward in particular to going to events related to the arts.
Hobbies/other interests:
I am interested in visual art, recently Chinese calligraphy in particular. Also films, electronic music and riding round unfamiliar cities on bikes.