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Propositional reasoning is the ability to draw conclusions on the basis of sentence connectives such as and, if, or, and not. A psychological theory of prepositional reasoning explains the mental operations that underlie this ability. The ANDS (A Natural Deduction System) model, described in the following pages, is one such theory that makes explicit(More)
There is no broadly accepted definition of 'life.' Suggested definitions face problems, often in the form of robust counter-examples. Here we use insights from philosophical investigations into language to argue that defining 'life' currently poses a dilemma analogous to that faced by those hoping to define 'water' before the existence of molecular theory.(More)
I explore the conceptual foundations of Alan Turing's analysis of computability, which still dominates thinking about computability today. I argue that Turing's account represents a last vestige of a famous but unsuccessful program in pure mathematics, viz., Hilbert's formalist program. It is my contention that the plausibility of Turing's account as an(More)
Astrobiologists are aware that extraterrestrial life might differ from known life, and considerable thought has been given to possible signatures associated with weird forms of life on other planets. So far, however, very little attention has been paid to the possibility that our own planet might also host communities of weird life. If life arises readily(More)
Since the mid-twentieth century, the concept of the Turing machine has dominated thought about effective procedures. This paper presents an alternative to Turing's analysis; it unifies, refines, and extends my earlier work on this topic. I show that Turing machines cannot live up to their billing as paragons of effective procedure; at best, they may be said(More)