Differential Propositional Calculus • 15
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https://inquiryintoinquiry.com/2023/12/04/differential-propositional-calcul…
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
•
https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part…
Differential Extension of Propositional Calculus
•
https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part…
Regards,
Jon
cc:
https://www.academia.edu/community/l7pvk5