The Department of Mathematics
Phone: (646) 312-4127
Location: VC 6-222
I received a B.A. and M.A. from Cambridge University, and a Ph.D. from Manchester University in 1977. After spells in Paris and Princeton, I joined Baruch College as a professor in 1982. My research area is Mathematical Logic, and the philosophical background to my research has been the question: What is the relationship between language and reality? (assuming there is such a thing as reality). I have studied this question in the technical context of the formal "language" of arithmetic, and the "reality" of the structure of the natural numbers (0,1,2,3, etc.) that arithmetic purports to describe. In fact, no reasonable language can capture this reality exactly and uniquely: there are always "non-standard" structures that do the job too. These are the models of arithmetic.
More recently I have explored more general ways to erode the distinction between language ("the dress of thought" -- Dr. Johnson) and the thought it dresses, in a philosophical study of logical principles for reasoning about natural objects, as opposed to the abstract objects of mathematics. You can read about this in my article, Steps towards a logic of natural objects. Questions about natural objects and feasibility led to my current investigations into finite sets, and the pictures on my website. I explore the same general questions in poetry, song, and music, in the person of my alter ego, T. G. Vanini.