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Philosophia Mathematica 1994 2(1):5-15; doi:10.1093/philmat/2.1.5
© 1994 by Oxford University Press
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© Oxford University Press

Cohesive Toposes and Cantor's 'lauter Einsen'

F. W. LAWVERE*

*Mathematics Department, State University of New York at Buffalo, 106 Diefendorf Hall, Buffalo, N. Y. 14214, U. S. A. (MTHFWL@ubvms.cc.buffalo.edu)

For 20th century mathematicians, the role of Cantor's sets has been that of the ideally featureless canvases on which all needed algebraic and geometrical structures can be painted. (Certain passages in Cantor's writings refer to this role.) Clearly, the resulting contradication, 'the points of such sets are distinc yet indistinguishable', should not lead to inconsistency. Indeed, the productive nature of this dialectic is made explicit by a method fruitful in other parts of mathematics (see 'Adjointness in Foundations', Dialectia 1969). This role of Cantor's theory is compared with the role of Galois theory in algebraic geometry.


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