The burning philosophical question that followed me throughout my philosophical education, and ultimately drove me to do a PhD in philosophy is the following: What role does mathematics play in our scientific theories? It appears to be an indispensable one. Just as talk of electrons and black holes is indispensable to our theorising about the world, so talk of numbers and functions appears to be. Some philosophers have argued that the indispensability of mathematics to science means that scientific evidence for the existence of unobservable physical objects (e.g. electrons and black holes) is equally evidence for the existence of mathematical objects (e.g. numbers and functions). This is the indispensability argument for mathematical platonism. Under the dedicated supervision of Dr. David Liggins and Prof. Chis Daly, I explored the prospects of a recently developed means of blocking this argument. The idea is to motivate the claim that mathematics is indispensable only for expressive purposes: it allows us to say things about physical objects that would otherwise be extremely difficult or even impossible to say. In contrast, talk of electrons and black holes plays an explanatory role: it allows us to identify the things in the world that are responsible for observable phenomena. In the first half of my thesis, I argued that we ought to adopt this view, and that this allows us rationally to believe in the unobservable physical posits of science while rejecting the existence of mathematical objects. In the second half, I attempted to motivate the claim that this is in fact how ordinary speakers already use mathematical language.
I feel extremely lucky to have done my PhD at Manchester. My thesis crossed the boundaries of philosophy of science and mathematics and the philosophy of language. For this reason, I benefitted greatly from the range of expertise at Manchester. I learnt a lot by attending reading groups on philosophy of linguistics, philosophy of mind, and metaphysics. The regular research seminars exposed me to a wide range of philosophical topics outside of my area, while also giving me the opportunity to present my own work to members of staff and other post-graduate students. The intellectual environment at Manchester is stimulating. There were also opportunities to develop skills that have turned out to be essential to my career, such as undergraduate teaching, and the organising of research events. I also received a lot of excellent advice and much-needed encouragement when I came to the end of my PhD and began to think about applying for jobs in philosophy. I am extremely grateful to everyone at Manchester for my time there. It is an excellent place to do post-graduate research.
After graduating in September 2015, I began a year of temporary lecturing at the University of Leeds from January to December 2016, lecturing in the philosophy of religion and metaphysics, and leading tutorials on all kinds of topics. In January 2017, I began a three-year British Academy post-doctoral fellowship at the University of Leeds. I am currently trying to develop an account of how mathematics features in science that is informed by the history of mathematical and scientific theory development.