Dr Benjamin Marschall talks about language and mathematics in our latest Q&A with new Junior Research Fellows.
How did you become interested in philosophy?
I came to philosophy through political theory: like many people I was a sort-of teenage Marxist at school who borrowed the Communist Manifesto from the local library. I concluded that philosophy is needed to understand the world properly and hence decided to study it at university, not knowing anything about what that entails specifically. After a detour through working as a computer programmer I eventually pursued this plan, but what gripped me were not the classes on political philosophy. Instead, I was fascinated by more abstract and foundational issues in logic, metaphysics, and the philosophy of language.
In various ways nearly all my work since then has revolved around the question of how we should conceive of the relationship between language and the world. An example: sentences have structure, they consist of names, predicates, quantifiers, and so on. Should we assume that there are also worldly entities, such as facts, that correspond to sentences and mirror their structure? Or is this a confused way of thinking, caused by mistaking features of representations with features of reality?
Your thesis is on Rudolf Carnap’s philosophy of mathematics, please tell us more.
Carnap was one of the members of the so-called Vienna Circle, a group of philosophers, mathematicians, and scientists that were active in the 1920s and 1930s. Roughly put their aim was to make philosophy a less obscure and more scientifically tractable enterprise by relying on formal and empirical methods rather than pure speculation. In one famously polemical paper on Heidegger, Carnap for instance describes metaphysical philosophers as musicians without musical ability!
I had not actually planned to work on Carnap when I came to Cambridge for my PhD. During my first year I got seriously interested in the history of analytic philosophy though – not very surprising, given that many of the founding figures such as Bertrand Russell and Ludwig Wittgenstein were active here, indeed often as Fellows of Trinity. What I found especially striking about Carnap was that his work continues to be contentious. Dismissive attitudes towards the Vienna Circle are widespread, and their approach is often portrayed as being based on implausible and outdated assumptions. Historians of philosophy, on the other hand, have argued that Carnap’s position is much more subtle and attractive than is commonly supposed. So I wanted to find out for myself who is right.
What questions does the philosophy of mathematics consider?
One fundamental question concerns what we are even doing when using mathematical language. If I say “there is a planet between Mars and Saturn” I talk about the physical world by describing the relations between objects in space and time. What about “there is a prime number between 5 and 11” though? On the face of it I am also describing how certain objects relate to each other, but it seems that numbers are abstract objects – ie they are not to be found in space and time. Many philosophers have thought that the abstractness of mathematical objects raises some very difficult questions, such as how we can have any knowledge about them. For this reason some think that we need to re-interpret what mathematicians are doing in order to avoid a commitment to abstract objects.
Carnap’s own position on this matter is quite unique, which makes it difficult to sum up. He effectively thought that the philosophical worries about abstract objects I alluded to are misguided, and that we should just get on with using mathematics. This sounds rather anti-philosophical, and Carnap’s approach is indeed radical and iconoclastic. In my research I have tried to assess whether the position is internally coherent, or whether there are some philosophical issues even Carnap must face rather than dismiss. I have argued that the latter is the case, but I nevertheless sympathise with the general contention that many debates in the philosophy of mathematics are not particularly fruitful.
What do you plan to work on at Trinity?
While working on my PhD I came across the philosopher Susan Stebbing, who was influential in the British philosophical scene in the 1930s and also the first woman to become a professor of philosophy in the UK. Her work had been largely forgotten since her early death in 1943, and only recently some scholars have begun to seriously study her again. Stebbing went to Girton and was influenced by Cambridge philosophers, in particular GE Moore – another Fellow of Trinity – but was also unusually well-informed about the Vienna Circle, and for instance invited Carnap for a series of lectures to London. I think that Stebbing’s views on philosophical methodology deserve more attention than they have received so far, and plan to study how her position developed over time. Since archival material by Stebbing and related figures is based in Cambridge and London, Trinity is a great place for this project, and I am very excited to join the College.
You can read more on Dr Marschall’s website.