I shall attempt in this chapter to open up another mode of understanding Bach within his historical context. This involves comparing his attitude to music with the metaphysical theories of certain rationalist philosophers of the Baroque era. Much of what I propose here is certainly conjectural: there is no question of a direct line of influence, or even that Bach was necessarily conscious of these parallels. I intend rather to show that Bach's musical thinking and that of the metaphysicians might depend on a similar historical world-view and, more importantly, that Bach's musical mind is equal to the greatest intellects of the age, even though he had no academic pretensions himself.

Gottfried Leibniz (1646–1716) and particularly his pupil Christian Wolff (1679–1754) are certainly very close to Bach historically; indeed Leibniz's name has occurred intermittently in Bach criticism and research, particularly in the decades leading up to 1950. Bach was closely associated with a follower of Leibniz and Wolff, Lorenz Mizler, who published Leibniz's famous dictum concerning music in the second issue of his Musikalische Bibliothek: 'Music is the hidden arithmetical exercise of a mind unconscious that it is calculating.' But the metaphysics and personality of an older, consistently shunned figure, Benedict de (or Baruch) Spinoza (1632–77), may be even closer to Bach's creative personality, although – for religious reasons – this was something that Bach could not possibly have acknowledged consciously.