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Euclid's Heritage. Is Space Three-Dimensional? (Hardcover, 1993 ed.)
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Euclid's Heritage. Is Space Three-Dimensional? (Hardcover, 1993 ed.)
Series: The Western Ontario Series in Philosophy of Science, 52
Expected to ship within 10 - 15 working days
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The three spatial characteristics of length, height and depth are
used in the same unreflective way by laymen, technicians and
scientists alike to describe the forms, positions and measure of
bodies and hollow bodies. But how do we know that the space we live
in has just these three dimensions? The question has occupied
philosophers and scientists since antiquity. The answers proposed
have become ever more presumptuous and have increasingly lost sight
of everyday intuitions and have sacrificed explanatory power. In
Euclid's Heritage Janich shows that all explanations of
three-dimensionality hinge on an unreflective geometrical language
which seems to accept the lack of an alternative for the three
sorts of entities -- points, lines and planes -- that bound the
three extended entities -- lines, planes and solids. This is a
Euclidean heritage in a dual sense: Euclid himself adopted a
geometrical language from the art of figure drawing, and left a
tradition of doing geometry as planimetry and of doing stereometry
by rotating plane figures. The systematic approach offered here
starts out from operational definitions of the spatial forms --
plane, straight edge and perpendicularity -- and proofs that only
three planes can intersect pairwise orthogonally. This is the
constructive solution in the frame theory of action, providing an
unequivocal characterisation of spatial relations in the physical
world. The traditional order of geometric concepts turns out to be
the most important obstacle to the methodical ordering of everyday
scientific concepts.
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