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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?

Book cover for Susanne Langer's Introduction to Symbolic Logic

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, e.g. between Platonism and finitism.

The book that got me interested in logic - a gentle introduction to the subject by Susanne Langer. As a teenager I stumbled on it in the old Bookmasters store (long gone) at 57th and 7th in Manhattan - a place where I spent many lonely hours browsing, searching for wholeness.

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.

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