Not only must the mathematician understand the meanings of the constant symbols introduced and defined in the science, but also his intelligent assent is required to be given to certain axioms (or primarily fundamental propositions) expressed in terms of these symbols; and his intelligence must be further exercised in following the demonstrative procedure by which derivative formulae are progressively inferred. He discovers, not only the comparatively unimportant fact that the conclusions are true provided that the originally premised axioms are true, but also the more important fact that the conclusions follow demonstratively from a judicious combination of these axioms and t/zese alone — none other being required. The account of symbolism and allied topics in Part II includes references to pro cesses of thought and thus is largely psychological in this respect differing from the accounts given by professedly formal logicians.