 Secondly, Hilbert and Frege differ importantly over the connection between truth and consistency. Taking a theory to be axiomatized by a set of multiply-interpretable sentences, Hilbert’s view is that the consistency of such a set suffices for the existence of the (or a) collection of mathematical entities mentioned in the theory. The consistency, for example, of a theory of complex numbers is all that’s needed to justify the mathematical practice of reasoning in terms of such numbers. For Frege on the other hand, consistency can never guarantee existence. His preferred example to make this point is that the consistency (in Hilbert’s sense) of the trio of sentences 