The Search for Certainty

Marcus Giaquinto tells the story of one of the great intellectual adventures of the modern era -- the attempt to find firm foundations for mathematics. From the late nineteenth century to the present day, this project has stimulated some of the most original and influential work in logic and philosophy.

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The nineteenth century saw a movement to make higher mathematics rigorous.
This seemed to be on the brink of success when it was thrown into confusion
by the discovery of the class paradoxes. That initiated a period of intense
research into the foundations of mathematics, and with it the birth of
mathematical logic and a new, sharper debate in the philosophy of
mathematics.
The Search for Certainty examines this foundational endeavour from the
discovery of the paradoxes to the present. Focusing on Russell's logicist
programme and Hilbert's finitist programme, Giaquinto investigates how
successful they were and how successful they could be. These questions are
set in the context of a clear, non-technical exposition and assessment of
the most important discoveries in mathematical logic, above all Gödel's
underivability theorems.
More than six decades after those discoveries, Giaquinto asks what our
present perspective should be on the question of certainty in mathematics.
Taking recent developments into account, he gives reasons for a
surprisingly positive response.