 Secondly, Frege quite rightly and insistently distinguishes on the one hand the ‘game’—arithmetic, set theory, topology or whatever—treated simply as a mathematical object in its own right, a formal system, and, on the another, the theory of the game. ‘Let us remember that the theory of the game must be distinguished from the game itself’ (§107, p. 203). Thus in the ‘game’ of trigonometry we might derive