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This is the first critically evaluative study of Gaston Bachelard's philosophy of science to be written in English. Bachelard's professional reputation was based on his philosophy of science, though that aspect of his thought has tended to be neglected by his English-speaking readers. Dr Tiles concentrates here on Bachelard's critique of scientific knowledge. Bachelard emphasised discontinuities in the history of science; in particular he stressed the ways of thinking about and investigating the world to be found in modern science. This, as the author shows, is paralleled by those debates...

A thorough account of the philosophy of mathematics. In a cogent account the author argues against the view that mathematics is solely logic.

A century ago, Georg Cantor demonstrated the possibility of a series of transfinite infinite numbers. His methods, unorthodox for the time, enabled him to derive theorems that established a mathematical reality for a hierarchy of infinities. Cantor's innovation was opposed, and ignored, by the establishment; years later, the value of his work was recognized and appreciated as a landmark in mathematical thought, forming the beginning of set theory and the foundation for most of contemporary mathematics.
As Cantor's sometime collaborator, David Hilbert, remarked, -No one will drive us from...

As science has become increasingly more mathematical and as computers continue to infiltrate life in affluent societies, the philosopher's concern with mathematics has, paradoxically, dwindled. It has come to be tacitly presumed that mathematics is nothing but logic.