Fire over water:
The image of the condition before transition.
Thus the superior man is careful
In the differentiation of things,
So that each finds its place.

— I Ching ䷿ Hexagram 64

Differential Extension of Propositional Calculus

This much preparation is enough to begin introducing my subject, if I excuse myself from giving full arguments for my definitional choices until a later stage.  To express the goal in a turn of phrase, the aim is to develop a differential theory of qualitative equations, one which can parallel the application of differential geometry to dynamical systems.  The idea of a tangent vector is key to the work and a major goal is to find the right logical analogues of tangent spaces, bundles, and functors.  The strategy is taken of looking for the simplest versions of those constructions which can be discovered within the realm of propositional calculus, so long as they serve to fill out the general theme.

Reference

• Wilhelm, R., and Baynes, C.F. (trans.), The I Ching, or Book of Changes,
  Foreword by C.G. Jung, Preface by H. Wilhelm, 3rd edition, Bollingen Series XIX, Princeton University Press, Princeton, NJ, 1967.

Resources

• Differential Logic and Dynamic Systems
• Differential Extension of Propositional Calculus

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