We’re talking about J. Anthony Lucas’s classic argument that Gödel’s Second Incompleteness Theorem rules out man-machine equivalence. This is an argument that Penrose revived and popularized in the 1990s. This fallacious argument is a thoroughly dead horse. But I’ll give it another beating here. Do note that the Lucas-Penrose argument is a completely distinct issue from PenroseHameroff speculation that the brain can act as a coherent quantum computer. It’s to Penrose’s credit that he’s associated with multiple controversial ideas!

This paper addresses the question whether the past couple of decades of formal research in belief revision offers evidence of a new psychologism in logic. In the first part I examine five potential arguments in favour of this thesis and find them all wanting. In the second part of the paper I argue that belief revision research has climbed up a hierarchy of models for the change of doxastic states that appear to be clearly normative at the bottom, but are (...) more amenable to an empirical-descriptive interpretation on higher levels. I conclude that this observation might offer a foothold for the thesis that there is a new psychologism in logic. (shrink)

It is argued, by use of specific examples, that mathematical understanding is something which cannot be modelled in terms of entirely computational procedures. Our conception of a natural number (a non-negative integer: 0, 1, 2, 3,…) is something which goes beyond any formulation in terms of computational rules. Our ability to perceive the properties of natural numbers depends upon our awareness, and represents just one of the many ways in which awareness provides an essential ingredient to our ability to understand. (...) There is no bar to the quality of understanding being the result of natural selection, but only so long as the physical laws contain a non-computational ingredient. (shrink)

My primary aim in this chapter is to explain in what the traditional mind–body problem consists, what its possible solutions are, and what obstacles lie in the way of a resolution. The discussion will develop in two phases. The first phase, sections 1.2–1.4, will be concerned to get clearer about the import of our initial question as a precondition of developing an account of possible responses to it. The second phase, sections 1.5–1.6, explains how a problem arises in our attempts (...) to answer the question we have characterized, and surveys the various solutions that can be and have been offered. More specifically, sections 1.2–1.4 are concerned with how to understand the basic elements of our initial question – how we should identify the mental, on the one hand, and the physical, on the other – and with what sorts of relations between them we are concerned. Section 1.2 identifies and explains the two traditional marks of the mental, consciousness and intentionality, and discusses how they are related. Section 1.3 gives an account of how we should understand ‘physical’ in our initial question so as not to foreclose any of the traditional positions on the mind–body problem. Section 1.4 then addresses the third element in our initial question, mapping out the basic sorts of relations that may hold between mental and physical phenomena, and identifying some for special attention. Sections 1.5–1.6 are concerned with explaining the source of the difficulty in answering our initial question, and the kinds of solutions that have been offered to it. Section 1.5 explains why our initial question gives rise to a problem, and gives a precise form to the mind–body problem, which is presented as a set of four propositions, each of which, when presented independently, seems compelling, but which are jointly inconsistent. Section 1.6 classifies responses to the mind–body problem on the basis of which of the propositions in our inconsistent set they reject, and provides a brief overview of the main varieties in each category, together with some of the difficulties that arise for each. Section 1.7 is a brief conclusion about the source of our difficulties in understanding the place of mind in the natural world. (shrink)

The philosophy of information (PI) is a new area of research with its own field of investigation and methodology. This article, based on the Herbert A. Simon Lecture of Computing and Philosophy I gave at Carnegie Mellon University in 2001, analyses the eighteen principal open problems in PI. Section 1 introduces the analysis by outlining Herbert Simon's approach to PI. Section 2 discusses some methodological considerations about what counts as a good philosophical problem. The discussion centers on Hilbert's famous analysis (...) of the central problems in mathematics. The rest of the article is devoted to the eighteen problems. These are organized into five sections: problems in the analysis of the concept of information, in semantics, in the study of intelligence, in the relation between information and nature, and in the investigation of values. (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)

Recent studies of Wittgenstein's later writing have made clear that they stand as a defence of two main ideas: that scepticism about the possibility of interpersonal discussions about our subjective feelings is misplaced and, as a seemingly startling corollary; that a mind state account of most 'mental activities' is incoherent. This leads to a great emphasis on skills and practices which, a fortiori, are definable only relationally, by reference to targets. In this paper I try to show that the 'computer' (...) analogue for the mind f ails on both of Wittgenstein's dimensions. There are no physiognomic language games in the computer centre, while the 'target' aspect of skill and practice concepts ties them in to a wholly human world. (shrink)

Though my ultimate concern is with issues in epistemology and metaphysics, let me phrase the central question I will pursue in terms evocative of philosophy of religion: What are the implications of our logic-in particular, of Cantor and G6del-for the possibility of omniscience?

The Research Assessment Exercise was introduced in 1986 by Thatcher, and was continued by Blair. So it has now been running for 21 years. During this time, the rules governing the RAE have changed considerably, and the interval between successive RAEs has also varied. These changes are not of great importance as far as the argument of this paper is concerned. We will concentrate on the main features of the RAE which can be summarised as follows.

Computational and information-theoretic research in philosophy has become increasingly fertile and pervasive, giving rise to a wealth of interesting results. In consequence, a new and vitally important field has emerged, the philosophy of information (PI). This essay is the first attempt to analyse the nature of PI systematically. PI is defined as the philosophical field concerned with the critical investigation of the conceptual nature and basic principles of information, including its dynamics, utilisation, and sciences, and the elaboration and application of (...) information-theoretic and computational methodologies to philosophical problems. I argue that PI is a mature discipline for three reasons: it represents an autonomous field of research; it provides an innovative approach to both traditional and new philosophical topics; and it can stand beside other branches of philosophy, offering a systematic treatment of the conceptual foundations of the world of information and the information society. (shrink)

This paper outlines and discusses the relative merits and problems of two current interpretations of Philosophy of Information (PI), the metaphysical approach and the analytical approach. The paper argues that both approaches complement one another, being normative and mutually compatible.

This article is by design a response to Alastair M. Taylor's "For Philosophers and Scientists: A General Systems Paradigm." That work is an advance over stage theories. But its focus on modernization tacitly accepts marginalization. Its focus on an undifferentiated evolving human species disregards intra- and intersocietal conflicts. Its uncritical talk of societal energy shifts obscures the reality of conquest and exploitation. If general systems theory is to be truly objective, it should take into account world-around system imbalance and the (...) relevance of Newton's Third Law. (Publisher omitted title of this article and used only its subtitle.). (shrink)

John Haugeland's Mind design and Mind design II are organized around the idea that the fundamental idea of cognitive science is that, “intelligent beings are semantic engines — in other words, automatic formal systems with interpretations under which they consistently make sense”. The goal of artificial intelligence research, or the problem of “mind design” as Haugeland calls it, is to develop computers that are in fact semantic engines. This paper canvasses the changes in artificial intelligence research reflected in the different (...) selections of essays found in each volume. While Mind design II is a worthy successor to Mind design, there are some notable developments in artificial intelligence which suggest that seemingly intelligent behavior need not be guided by semantic engines at all. (shrink)

This chapter reviews some interesting research trends in the philosophy of information (PI). First, PI is defined; then, a series of open problems in PI on which philosophers are currently working is considered. The conclusion highlights the innovative character of this new area of research.

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)

Gödel's two incompleteness theorems are among the most important results in modern logic, and have deep implications for various issues. They concern the limits of provability in formal axiomatic theories. The first incompleteness theorem states that in any consistent formal system F within which a certain amount of arithmetic can be carried out, there are statements of the language of F which can neither be proved nor disproved in F. According to the second incompleteness theorem, such a formal system cannot (...) prove that the system itself is consistent (assuming it is indeed consistent). These results have had a great impact on the philosophy of mathematics and logic. There have been attempts to apply the results also in other areas of philosophy such as the philosophy of mind, but these attempted applications are more controversial. The present entry surveys the two incompleteness theorems and various issues surrounding them. (shrink)