Cf: Differential Logic • Overview
At:
http://inquiryintoinquiry.com/2020/03/20/differential-logic-%e2%80%a2-overview/
All,
The previous series of posts on Differential Propositional Calculus
( https://inquiryintoinquiry.com/?s=Differential+Propositional+Calculus )
brought us to the threshold of the subject without quite stepping over,
but I wanted to lay out the necessary ingredients in the most concrete,
intuitive, and visual way possible before taking up the abstract forms.
One of my readers on Facebook told me "venn diagrams are obsolete" and
of course we all know they become unwieldy as our universes of discourse
expand beyond four or five dimensions. Indeed, one of the first lessons
I learned when I set about implementing CSP's graphs and GSB's forms on the
computer was that 2-dimensional representations of logic are a death trap
in numerous conceptual and computational ways. Still, venn diagrams do us
good service in visualizing the relationships among extensional, functional,
and intensional aspects of logic. A facility with those relationships is
critical to the computational applications and statistical generalizations
of logic commonly used in mathematical and empirical practice.
At any rate, intrepid readers will have amped up their visual imaginations
well enough at this point to pick their way through the cactus patch ahead.
The link above or the transcript below outlines my last, best introduction
to Differential Logic, which I'll be working to improve as I serialize it
to my blog.
Part 1 ( https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1 )
Introduction (
https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Introduction )
Cactus Language for Propositional Logic (
https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Cactus_Language_for_Propositional_Logic )
Differential Expansions of Propositions (
https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Differential_Expansions_of_Propositions )
Bird's Eye View (
https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Bird.27s_Eye_View )
Worm's Eye View (
https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Worm.27s_Eye_View )
Part 2 ( https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2 )
Propositional Forms on Two Variables (
https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2#Propositional_Forms_on_Two_Variables )
Transforms Expanded over Differential Features (
https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2#Transforms_Expanded_over_Differential_Features )
Transforms Expanded over Ordinary Features (
https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2#Transforms_Expanded_over_Ordinary_Features )
Operational Representation (
https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2#Operational_Representation
)
Part 3 ( https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3 )
Development • Field Picture (
https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Development_.E2.80.A2_Field_Picture )
Proposition and Tacit Extension (
https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Proposition_and_Tacit_Extension )
Enlargement and Difference Maps (
https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Enlargement_and_Difference_Maps )
Tangent and Remainder Maps (
https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Tangent_and_Remainder_Maps
)
Least Action Operators (
https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Least_Action_Operators
)
Goal-Oriented Systems (
https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Goal-Oriented_Systems
)
Further Reading (
https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Further_Reading )
Document History (
https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Document_History )
Regards,
Jon
inquiry into inquiry: https://inquiryintoinquiry.com/
academia: https://independent.academia.edu/JonAwbrey
oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey
facebook page: https://www.facebook.com/JonnyCache
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