  The historiography of logic conceives of a Fregean revolution in which modern
mathematical logic (also called symbolic logic) has replaced Aristotelian
logic. The preeminent expositors of this conception are Jean van Heijenoort
(1912-1986) and Donald Angus Gillies. The innovations and characteristics that
comprise mathematical logic and distinguish it from Aristotelian logic,
according to this conception, created ex nihlo by Gottlob Frege (1848-1925) in
his Begriffsschrift of 1879, and with Bertrand Russell (1872-1970) as its chief
This position likewise understands the algebraic logic of Augustus De Morgan
(1806-1871), George Boole (1815-1864), Charles Sanders Peirce (1838-1914), and
Ernst Schr\"oder (1841-1902) as belonging to the Aristotelian tradition. The
"Booleans" are understood, from this vantage point, to merely have rewritten
Aristotelian syllogistic in algebraic guise.
  The most detailed listing and elaboration of Frege's innovations, and the
characteristics that distinguish mathematical logic from Aristotelian logic,
were set forth by van Heijenoort. I consider each of the elements of van
Heijenoort's list and note the extent to which Peirce had also developed each
of these aspects of logic. I also consider the extent to which Peirce and Frege
were aware of, and may have influenced, one another's logical writings.
