Frege's writings on mathematics are best known for the claim that numbers are classes of equinumerous concepts in his Grundlagen Der Arithmetik, his derivation of the Peano Axioms of arithmetic in the Grundgesetze Der Arithmetik, and the inconsistency of his formal logical system. In the last few decades, philosophers have noted that his derivation can be reconstructed using consistent principles, particularly Hume's Principle: that two classes have the same number if a bijection can be drawn between them. However, little attention is paid to his theory of the real numbers: that they are ratios of magnitudes, where magnitudes are relations of objects meeting certain formal criteria. I shall recount in detail the historical and logical context of Frege's explication of the reals and argue that, adapted to neologicist needs, it provides a suitable definition of the real numbers, and that reflection on the status of ratios suggests that what makes particular abstraction principles true or false is their role in a practical enterprise requiring the objects introduced by that principle
"},{"label":"Degree","value":["Bachelor of Arts with Departmental Honors"]},{"label":"Author-supplied Keywords","value":["Real numbers","Frege","Neologicism"]},{"label":"Administrative Note","value":"Drupal Node ID: 24193