Hypercomputation: Philosophical issues (Q1434379)

The term hypercomputation refers to the computation of functions or numbers which are uncomputable by a universal Turing machine. In this paper the author surveys several models of hypercomputation resulting from acceleration, asynchronous coupling and environmental interaction of standard Turing machines. He also considers hypercomputation based on ``random'' input and the measurement of observables. Well-known epistemic and physical objections to the possibility of hypercomputation are discussed. They concern the identification and verification of the presence of a non-recursive source and the very realizability of such a source under various finiteness conditions. The author attempts to rebut these ``a priori'' qualms. Accordingly, he asserts that the possibility of hypercomputation is a downright empirical question. The author then defends the relevance of Turing's conception of an oracle machine for the hypercomputation debate. Finally the paper contains a brief but informed exegesis of Turing's writings on the notion of machine, the scope of computability, and their relation to mind and learning.