The Possibility of Physical Hypercomputation

Hypercomputation is "the study of computation beyond that defined by the Turing machine, and is also known as super-Turing, non-standard or non-recursive computation." This is a relatively new multidisciplinary area and remains something of a speculative backwater. However, many research ideas here fit rather naturally into my general areas of philosophical research: in particular, relations between the foundations of mathematics/logic and physics, and my work on theories of truth, and more recently philosophy of mind and psychology. The broad structure of my talk will be:

(1) To discuss what the implications of hypercomputation might be: implications for the foundations/philosophy of mathematics, and connections with some philosophical ideas about the Church-Turing Thesis, "supertasks", and other oddities.

(2) To discuss whether it makes sense to suppose that hypercomputational processes could be physically realized.