Abstract:

It is commonly agreed that the well-known Lucas–Penrose arguments and even Penrose's `new argument' in [Penrose, R. (1994): Shadows of the Mind, Oxford University Press] are inconclusive. It is, perhaps, less clear exactly why at least the latter is inconclusive. This note continues the discussion in [Lindström, P. (2001): Penrose's new argument, J. Philos. Logic 30, 241–250; Shapiro, S.(2003): Mechanism, truth, and Penrose's new argument, J. Philos. Logic 32, 19–42] and elsewhere of this question.

Keywords: knowability (in mathematics); Lucas–Penrose thesis

Document Type: Research article

DOI: 10.1007/s10992-005-9014-7

Affiliations: 1: Email: per.lindstrom@mbox334.swipnet.se