Granted that truth is valuable we must recognize that certifiable truth is hard to come by, for example in the natural and social sciences. This paper examines the case of mathematics. As a result of the work of Gödel and Tarski we know that truth does not equate with proof. This has been used by Lucas and Penrose to argue that human minds can do things which digital computers can't, viz to know the truth of unprovable arithmetical statements. The argument (...) is given a simple formulation in the context of sorites (Robinson) arithmetic, avoiding the complexities of formulating the Gödel sentence. The pros and cons of the argument are considered in relation to the conception of mathematical truth. (shrink)

In this paper, we demonstrate (1) how harnessing stochasticity can be the basis of creative agency; (2) that such harnessing can resolve the apparent conflict between reductionist (micro-level) accounts of behaviour and behaviour as the outcome of rational and value-driven (macro-level) decisions; (3) how neurophysiological processes can instantiate such behaviour; (4) The processes involved depend on three features of living organisms: (a) they are necessarily open systems; (b) micro-level systems therefore nest within higher-level systems; (c) causal interactions must occur across (...) all the boundaries between the levels of organization. The higher levels constrain the dynamics of lower levels. The experimental evidence and theoretical arguments are shown to be consistent with previous research on the neuronal mechanisms of conscious choice, and with the interconnected multi-level processes by which organisms harness stochasticity, whether conscious or unconscious. (shrink)

Three recent ‘state of the art’ Frankfurt cases are responded to: Widerker’s Brain-Malfunction-W case and Pereboom’s Tax Evasion cases (2 & 3). These cases are intended by their authors to resurrect the neo-Frankfurt project of overturning the Principle of Alternative Possibilities (PAP) in the teeth of the widespread acceptance of some combination of the WKG (Widerker-Kane-Ginet) dilemma, the Flicker of Freedom strategy and the revised PAP response (‘Principle of Alternative Blame’, ‘Principle of Alternative Expectations’). The three neo-Frankfurt cases of Pereboom (...) and Widerker shown to be insufficient for their intended purpose. Of central importance to any account of responsibility is that this applies at the level of the Right and not the Good. Arguments of Carlos Moya are expanded and augmented by considerations from Chisholm, Lucas, Dummett and Lockie (2003) to show that a number of severe problems remain for anyone attempting to resurrect the Frankfurt project. (shrink)

The alleged proof of the non-mechanical, or non-computational, character of the human mind based on Gödel’s incompleteness theorem is revisited. Its history is reviewed. The proof, also known as the Lucas argument and the Penrose argument, is refuted. It is claimed, following Gödel himself and other leading logicians, that antimechanism is not implied by Gödel’s theorems alone. The present paper sets out this refutation in its strongest form, demonstrating general theorems implying the inconsistency of Lucas’s arithmetic and the semantic inadequacy (...) of Penrose’s arithmetic. On the other hand, the limitations to our capacity for mechanizing or programming the mind are also indicated, together with two other corollaries of Gödel’s theorems: that we cannot prove that we are consistent, and that we cannot fully describe our notion of a natural number. (shrink)

A sourcebook/textbook on the problem of free will and determinism. Contains a history of the free will problem, a taxonomy of current free will positions, the standard argument against free will, the physics, biology, and neuroscience of free will, the most plausible and practical solution of the problem, and reviews of the work of the leading determinist Ted Honderich, the leading libertarian Robert Kane, the well-known compatibilist Daniel Dennett, and the determinism-agnostic Alfred Mele.

Mechanism is the thesis that men can be considered as machines, that there is no essential difference between minds and machines.John Lucas has argued that it is a consequence of Gödel's theorem that mechanism is false. Men cannot be considered as machines, because the intellectual capacities of men are superior to that of any machine. Lucas claims that we can do something that no machine can do-namely to produce as true the Gödel-formula of any given machine. But no machine can (...) prove its own Gödel-formula. (shrink)

This is a survey of recent work on God and human freedom. A version of the "basic" argument for the incompatibility of God's omniscience and human freedom is presented. Various possible responses are developed and discussed.