  Thus Peirce maintained the position asserted by Boole that mathematics could be used to analyse logic, not the vice versa relationship between the two disciplines that Gottlob Frege was about to put forward for arithmetic, and which Bertrand Russell was optimistically to claim for all mathematics during the 1900s. Curiously, the third draft of the lithograph contains this contrary stance in “Mathematics, as here defined, belongs to every enquiry; it is even a portion of deductive logic, to the laws of which it is rigidly subject”; but by completion he had changed his mind. Peirce's son Charles claimed to have influenced his father in forming his definitive position, and fiercely upheld it himself; thereby he helped to forge a wide division between the algebraic logic which he was developing from the early 1870s with his father, Boole and de Morgan as chief formative influences, and the logicism (as it became called later) of Frege and Russell and also the ‘mathematical logic’ of Giuseppe Peano and his school in Turin (Grattan-Guinness 1988). 