Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre (...) Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations. (shrink)

Modern empiricism has been conditioned in large part by two dogmas. One is a belief in some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truth which are synthetic, or grounded in fact. The other dogma is reductionism: the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience. Both dogmas, I shall argue, are ill founded. One effect of abandoning them is, as (...) we shall see, a blurring of the supposed boundary between speculative metaphysics and natural science. Another effect is a shift toward pragmatism. (shrink)

This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...

PART ONE I 'Alternative' in 'Alternative logic There are many systems of logic — many-valued systems and modal systems for instance - which are non-standard ...

The present essay is addressed simultaneously to two distinct audiences.

A study in the philosophy of science, proposing a strong form of the doctrine of scientific realism' and developing its implications for issues in the philosophy of mind.

This paper outlines the functional capacities of a novel scheme for cognitive representation and computation, and it explores the possible implementation of this scheme in the massively parallel organization of the empirical brain. The suggestion is that the brain represents reality by means of positions in suitably constitutes phase spaces; and the brain performs computations on these representations by means of coordinate transformations from one phase space to another. This scheme may be implemented in the brain in two distinct forms: (...) (1) as a phase-space sandwich, which may explain certain laminar structures, such as cerebral cortex and the superior colliculus; and (2) as a neural matrix, which may explain other structures, such as the beautifully orthogonal architecture of the cerebellum. (shrink)

The Mind-Body Problem Questions: What is the mind? What is its connection to the body? Most basic division of answers: Dualist and Materialist (or Physicalist) responses.