Panmere

This is the error that infects the formalist theory of fractions and of negative and complex numbers. It is made a postulate that the familiar rules of calculations shall still hold, where possible, for the newly-introduced numbers, and from this their general properties and relations are deduced. If no contradiction is anywhere encountered, the introduction of the new numbers is held to be justified, as though it were impossible for a contradiction still to be lurking somewhere nevertheless, and as though freedom from contradiction amounted straight away to existence.
— Gottlob Frege , The Foundations of Arithmetic