## Philosopher

My Work in Logic |

My D.Phil. thesis concerned the way we reason about infinite objects in mathematics. I was particularly vexed by the part of mathematics that deals in higher infinities, such as set theory. These higher infinities are *very* abstract. There can be no empirical evidence for them. So how can such mathematics claim the status of a science?

I suggested that when we reason about such objects mathematically, we are really reasoning about finite projections of them. I showed how this resolves some longstanding debates in the foundations of mathematics, such as between **Platonism** and **finitism**. I developed some mathematical evidence to support the theory. I'm still proud of this work. It provides a more rigorous justification for infinitistic mathematics than the commonly accepted but rather facile assertions of Platonism.

More recently, my ideas about reasoning with finite projections motivated my work in **Diagrammatic Theorem Proving**, which I carried out in collaboration with **Dave Barker-Plummer**. This is one way in which my philosophical interests have informed my work in **computers**.