This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without (...) providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. (shrink)

The reason Descartes cites for invoking the demon argument in addition to the dream argument is that the demon argument is intended to broaden the scope of Descartes’ scepticism, to subsume additional beliefs under it. I present an additional, unfamiliar reason. There is, I argue, an important difference between the two sceptical arguments. It pertains not to their scope, but to their “depth”, to the kind of scepticism they are capable of inducing.

Pragmatist responses to radical skepticism do not receive much attention in contemporary analytic epistemology. This observation is my motivation for undertaking a search for a coherent pragmatist reply to radical doubt, one that can compete, in terms of clarity and sophistication, with the currently most popular approaches, such as contextualism and relevant alternatives theory. As my point of departure I take the texts of C. S. Peirce and William James. The Jamesian response is seen to consist in the application of (...) a wager argument to the skeptical issue in analogy with Pascal's wager. The Peircean strategy, on the other hand, is to attempt a direct rejection of one of the skeptic's main premises: that we do not know we are not deceived. I argue that while the Jamesian attempt is ultimately incoherent, Peirce's argument contains the core of a detailed and characteristically "pragmatic" rebuttal of skepticism, one that deserves to be taken seriously in the contemporary debate. (shrink)

A number of recent philosophers, including Michael Williams, Barry Stroud and Donald Davidson, have argued that scepticism about the external world stems from the foundationalist assumption that sensory experience supplies the data for our beliefs about the world. In order to assess this thesis, I offer abrief characterisation of the logical form of sceptical arguments. I suggest that sceptical arguments rely on the idea that many of our beliefs about the world are ‘underdetermined’ by the evidence on which they are (...) based. Drawing on this characterisation of scepticism, I argue that Williams, Stroud andDavidson are right to see the foundationalist assumption as essential to the sceptic’s argument, but wrong to think that scepticism is inevitable once that assumption is in place. By pursuing an analogy with some recent debates in the philosophy of science, I try to locate the additional assumptions which the sceptic must make, in order to derive her conclusion. (shrink)

A shift from a metaphysical framework of substance to one of process enables an integrated account of the emergence of normative phenomena. I show how substance assumptions block genuine ontological emergence, especially the emergence of normativity, and how a process framework permits a thermodynamic-based account of normative emergence. The focus is on two foundational forms of normativity, that of normative function and of representation as emergent in a particular kind of function. This process model of representation, called interactivism, compels changes (...) in many related domains. The discussion ends with brief attention to three domains in which changes are induced by the representational model: perception, learning, and language. (shrink)