Differential Logic • 1
• https://inquiryintoinquiry.com/2024/10/30/differential-logic-1-a/
Introduction —
Differential logic is the component of logic whose object is
the description of variation — focusing on the aspects of change,
difference, distribution, and diversity — in universes of discourse
subject to logical description. A definition that broad naturally
incorporates any study of variation by way of mathematical models,
but differential logic is especially charged with the qualitative
aspects of variation pervading or preceding quantitative models.
To the extent a logical inquiry makes use of a formal system, its
differential component governs the use of a “differential logical
calculus”, that is, a formal system with the expressive capacity
to describe change and diversity in logical universes of discourse.
Simple examples of differential logical calculi are furnished by
“differential propositional calculi”. A differential propositional
calculus is a propositional calculus extended by a set of terms for
describing aspects of change and difference, for example, processes
taking place in a universe of discourse or transformations mapping
a source universe to a target universe. Such a calculus augments
ordinary propositional calculus in the same way the differential
calculus of Leibniz and Newton augments the analytic geometry of
Descartes.
Resources —
Survey of Differential Logic
• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/
Regards,
Jon
cc: https://www.academia.edu/community/lJX2qa
cc: https://www.researchgate.net/post/Differential_Logic_The_Logic_of_Change_an…
Interesting question.
John
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There may be a cosmic speed limit on how fast anything can grow
Alan Turing's theories about computation seem to have a startling consequence, placing hard limits on how fast or slow any physical process in the universe can grow
https://www.newscientist.com/article/2454024-there-may-be-a-cosmic-speed-li…
A newly proposed cosmic speed limit may constrain how fast anything in the universe can grow. Its existence follows from Alan Turing’s pioneering work on theoretical computer science, which opens the intriguing possibility that the structure of the universe is fundamentally linked to the nature of computation.
Cosmic limits aren’t a new idea. While studying the relationship between space and time, Albert Einstein showed that nothing in the universe can exceed the speed of light, as part of his special theory of relativity. Now, Toby Ord at the University of Oxford is proposing a new physical limit based on computation.
“I had the seed of this idea more than 20 years ago,” he says. “It would apply to any quantity you can directly measure, including mass, charge, energy, etc., and even more subtle things like the time intervals between a sequence of events.” . . .
