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(1848–1925) German mathematician, logician and philosopher. One of the earliest writings of Frege that is of interest to contemporary philosophers is the 1879 monograph, Begriffsschrift or Concept-script. The work introduced second-order logic and new notation, a fragment of which was the first notation adequate to express first-order logic as we know it. Frege envisioned Begriffsschrift as the first part of a project designed to define the real numbers from purely logical concepts and to show, by proving basic truths of arithmetic from definitions and logical laws, that all mathematics, with the exception of Euclidean geometry, was ultimately a branch of logic. This project was initially described in a philosophical monograph, Foundations of Arithmetic published in 1884 and its details were to have been carried out in a later, mathematical work, Basic Laws of Arithmetic. Basic Laws was to be published in three parts: a part which sets out the basic laws of logic, a part in which the positive integers are defined and the basic laws of arithmetic are proved, and a part in which the real numbers are defined and the foundations laid for assimilating analysis to logic. Volume I of Basic Laws, which contained Part I of the project and the beginning of Part II, was published in 1893. But when the second volume, published in 1903, was n press, Frege received a now-famous letter in which ... log in or subscribe to read full text