ONT Re: Differential Logic
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DLOG. Note D12
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| 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, [Wil, 249]
A 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 some later
stage. I am trying to develop a "differential theory of qualitative equations"
that parallels the application of differential geometry to dynamic systems. The
idea of a tangent vector is key to this 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 these constructions that can be discovered
within the realm of propositional calculus, so long as they serve to fill out the
general theme.
Jon Awbrey
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