The Architecture of Modern Mathematics: Essays in History and Philosophy

The Architecture of Modern Mathematics: Essays in History and Philosophy

The Architecture of Modern Mathematics: Essays in History and Philosophy

The Architecture of Modern Mathematics: Essays in History and Philosophy

Synopsis

This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research and how a number of historical accounts can be deepened by embracing philosophical questions.

Excerpt

J. FERREIRÓS AND J.J. GRAY

The aim of this book of essays is to advance contemporary work in creating stronger links between the history and philosophy of mathematics. It has become clear through several conferences and publications that the present situation at the beginning of the twenty-first century is congenial to this kind of historico-philosophical enterprise. The editors have brought together an important international group of scholars whose contributions focus on the history and philosophy of modern mathematics, roughly from 1800 to 1970.

For most of the twentieth century philosophers of mathematics tended to study their subject from an ahistorical systematic perspective. In the Anglo-American tradition, despite the presence of attractive proposals such as those of Lakatos or Kitcher, historical approaches have remained in the minority. The once powerful German trend of historico-philosophical studies died out, largely as a result of the Nazi period and the Second World War. Philosophers in the Latin traditions (e.g. Cavaillès in France, Gonseth in Switzerland, or De Lorenzo in Spain) have long been groping toward historical perspectives, but here also we lack satisfactory overall pictures and an adequate integration of such proposals with systematic knowledge.

Two complementary developments in recent years have been crucial for the present state of affairs. Within the English-speaking sphere, analytical philosophy has ceased to be regarded as a monolithic, obviously correct approach, and its historical origins have begun to be subjected to careful scrutiny. Through the intermediary of symbolic logic, a core element in that approach, the history of analytical philosophy led into the history of mathematics and its foundations. Recent historians have consciously followed this lead, and our book stresses this connection. Meanwhile, the emergence of a community of professional historians of mathematics led to more sophisticated inquiries into the subject, raising questions about the nature of mathematical knowledge and its origins in mathematical practices.

And yet there are significant problems in researching and writing the history of mathematics that are bringing historians and philosophers together. The history of modern mathematics provides opportunity for realizing that many pivotal mathematical contributions (especially in the period 1870–1930) were not philosophically neutral. Great mathematicians such as Gauss, Riemann, Kronecker, Dedekind, Hilbert, Poincaré, Brouwer or Weyl (to name but a few) have concerned themselves with eminently philosophical questions in the course of their research.

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