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Название: A Subject With No Object: Strategies for Nominalistic Interpretation of Mathematics
Авторы: Burgess J., Rosen G.
Аннотация:
'A preface is not, in my book, an introduction.' So a prominent philo- sopher of mathematics once wrote. To judge from his practice, he took
the function of an introduction to be to begin the exposition of his
subject, and that of a preface to place it in its intellectual context. We will
follow his example.
For all its wealth of results, and for all the power of its applications,
mathematics as of about 1800 dealt with only a handful of mathematical
structures, all closely connected with the models of time and space used
in classical physics: the natural, rational, real, and complex number sys-
tems; the Euclidean spaces of dimensions one, two, and three. Indeed,
mathematics was widely held to deal directly with the structure of physical
space and time, and to provide an example of pure thought arriving at
su bstantive information about the natural world. The central question in
philosophy of mathematics at that period was how this could be possible.
All that changed completely during the nineteenth century with the intro-
duction of more and more novel mathematical structures, beginning with
the first non-Euclidean spaces.