  Jevons' principles of number reflect his insistence that mathematics should be based on logic, not the other way round. He occupies a somewhat contradictory position in the history of logic, since his formalism was inspired by the works of Boole, who gave mathematics priority over logic. Jevons attempts to define ‘number’ by counting ‘units’ in space or time. When counting coins, every coin should receive a proper name: we should count C′ + C″ + C′′′ + C′′′′ + …  The coins are equal to each other (they all belong to the class C); they are different only because they reside on different points in space. Before counting, we should reduce all identical alternatives; the remaining ‘units’ reside on different points in space and time.  “A unit is any object of thought which can be discriminated from every other object treated as a unit in the same problem” (Jevons 1874: 157). The concept of ‘unit’ encounters some severe difficulties, as noted by Frege. We can only add up Cs that are identical, but they cannot denote different things if the same symbol C is used. Jevons was unable to resolve this contradiction.