A scientific community cannot practice its trade without some set of received beliefs. These beliefs form the foundation of the "educational initiation that prepares and licenses the student for professional practice". The nature of the "rigorous and rigid" preparation helps ensure that the received beliefs are firmly fixed in the student's mind. Scientists take great pains to defend the assumption that scientists know what the world is like...To this end, "normal science" will often suppress novelties which undermine its foundations. Research (...) is therefore not about discovering the unknown, but rather "a strenuous and devoted attempt to force nature into the conceptual boxes supplied by professional education". (shrink)

Thomas S. Kuhn's classic book is now available with a new index.

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

Most sociologists of science have accepted R. K. Merton's view that there is no intrinsic connection between the ideas scientists hold and the way they behave. Merton based his approach on an extended analogy between science and economics. He assumed a division between the scientific "product" governed by an inflexible a-social logic and the processes of scientiftc "production" propelled by "non-logical" social behavior. Kuhn rejects this "divorce of convenience" and argues that "local" traditions which resist rationalization characterize both the theory (...) and practice of science. Politics, law, and religion provide more apt analogies for scientift activity than economics. However, Kuhn's attempt to replace epistemology with sociology in order to retain the notion of progressiveness in science blunts his contribution. His sociological approach would be most fruitful if he adopted "epistemological agnosticism.". (shrink)

I criticize a recent paper by Thomas Tymoczko in which he attributes fundamental philosophical significance and novelty to the lately-published computer-assisted proof of the four color theorem (4CT). Using reasoning precisely analogous to that employed by Tymoczko, I argue that much of traditional mathematical proof must be seen as resting on what Tymoczko must take as being "empirical" evidence. The new proof of the 4CT, with its use of what Tymoczko calls "empirical" evidence is therefore not so novel as he (...) maintains. Finally, without attempting to give a full account of the notion of empirical mathematical evidence, I sketch a view showing how the use of calculation injects an empirical ingredient into proof. (shrink)

In the present article two possible meanings of the term mathematical structure are discussed: a formal and a nonformal one. It is claimed that contemporary mathematics is structural only in the nonformal sense of the term. Bourbaki's definition of structure is presented as one among several attempts to elucidate the meaning of that nonformal idea by developing a formal theory which allegedly accounts for it. It is shown that Bourbaki's concept of structure was, from a mathematical point of view, a (...) superfluous undertaking. This is done by analyzing the role played by the concept, in the first place, within Bourbaki's own mathematical output. Likewise, the interaction between Bourbaki's work and the first stages of category theory is analyzed, on the basis of both published texts and personal documents. (shrink)

The ArgumentRecent studies in the philosophy of mathematics have increasingly stressed the social and historical dimensions of mathematical practice. Although this new emphasis has fathered interesting new perspectives, it has also blurred the distinction between mathematics and other scientific fields. This distinction can be clarified by examining the special interaction of thebodyandimagesof mathematics.Mathematics has an objective, ever-expanding hard core, the growth of which is conditioned by socially and historically determined images of mathematics. Mathematics also has reflexive capacities unlike those of (...) any other exact science. In no other exact science can the standard methodological framework usedwithinthe discipline also be used to study the nature of the discipline itself.Although it has always been present in mathematical research, reflexive thinking has become increasingly central to mathematics over the past century. Many of the images of the discipline have been dictated by the increase in reflexive thinking which has also determined a great portion of the contemporary philosophy and historiography of mathematics. (shrink)