Cohesive Toposes and Cantor's 'iaufcer Einsen'

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 contradiction, 'the points of such sets are distinct 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', Dialectics 1969). This role of Cantor's theory is compared with the role of Galois theory in algebraic geometry. at U nirsity of K nt on O cber 7, 2011 philm at.oxfoournals.org D ow nladed fom