Mathematics and the Image of Reason

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. It is this perception of mathematics that the author wishes to dispel because it hides the role of mathematics in science and thereby contributes to the misconception of scientific rationality in particular, and the character of reason in general. Reason comes to be set in opposition to imagination, is at odds with creative thought, and is discarded as irrelevant to the postmodern, post-structuralist age. Analysing the logicism of the three key figures in the philosophy of mathematics – Frege, Russell and Hilbert – Mary Tiles demonstrates that mathematics and mathematically informed reasoning are in fact far from irrelevant to the power structures of a technological culture.