Differential Logic • The Logic of Change and Difference
• https://inquiryintoinquiry.com/2023/08/22/differential-logic-%ce%b1/

Differential logic is the logic of variation — the logic of change and difference.

Differential logic is the component of logic whose object is the description of variation, for example, the aspects of change, difference, distribution, and diversity, in universes of discourse subject to qualitative logical description. In its formalization, differential logic treats the principles governing the use of a “differential logical calculus”, in other words, a formal system with the expressive capacity to describe change and diversity in logical universes of discourse.

A simple case of a differential logical calculus is furnished by a differential propositional calculus. This augments ordinary propositional calculus in the same way the differential calculus of Leibniz and Newton augments the analytic geometry of Descartes.

Resources —

Differential Logic
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview
• Part 1 ( https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1 )
• Part 2 ( https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2 )
• Part 3 ( https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3 )

Differential Propositional Calculus
• https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Overview
• Part 1 ( https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1 )
• Part 2 ( https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2 )

Differential Logic and Dynamic Systems
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview
• Part 1 ( https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1 )
• Part 2 ( https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_2 )
• Part 3 ( https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3 )
• Part 4 ( https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_4 )
• Part 5 ( https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_5 )

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DiscreteDynamicalSystems
#Leibniz #BooleanFunctions #BooleanDifferenceCalculus #QualitativeDynamics
#DifferentialPropositions #MinimalNegationOperators #NeuralNetworkSystems

Survey of Abduction, Deduction, Induction, Analogy, Inquiry • 3
• https://inquiryintoinquiry.com/2023/04/02/survey-of-abduction-deduction-induction-analogy-inquiry-3/

This is a Survey of blog and wiki posts on three elementary forms of inference, as recognized by a logical tradition extending from Aristotle through Charles S. Peirce. Particular attention is paid to the way these inferential rudiments combine to form the more complex patterns of analogy and inquiry.

Blog Dialogs —

• Abduction, Deduction, Induction, Analogy, Inquiry
1. https://inquiryintoinquiry.com/2012/08/16/abduction-deduction-induction-analogy-inquiry-1/
2. https://inquiryintoinquiry.com/2012/11/21/abduction-deduction-induction-analogy-inquiry-2/
3. https://inquiryintoinquiry.com/2016/02/17/abduction-deduction-induction-analogy-inquiry-3/
•••
29. https://inquiryintoinquiry.com/2020/03/15/abduction-deduction-induction-analogy-inquiry-29/
30. https://inquiryintoinquiry.com/2020/12/15/abduction-deduction-induction-analogy-inquiry-30/
31. https://inquiryintoinquiry.com/2022/10/14/abduction-deduction-induction-analogy-inquiry-31/

Blog Series —

Functional Logic • Inquiry and Analogy
• https://inquiryintoinquiry.com/2023/06/20/functional-logic-inquiry-and-analogy-preliminaries-2/
1. https://inquiryintoinquiry.com/2023/06/21/functional-logic-inquiry-and-analogy-1-2/
2. https://inquiryintoinquiry.com/2023/06/22/functional-logic-inquiry-and-analogy-2-2/
3. https://inquiryintoinquiry.com/2023/06/23/functional-logic-inquiry-and-analogy-3-2/
•••
19. https://inquiryintoinquiry.com/2023/07/17/functional-logic-inquiry-and-analogy-19-2/
20. https://inquiryintoinquiry.com/2023/07/18/functional-logic-inquiry-and-analogy-20-2/
21. https://inquiryintoinquiry.com/2023/07/19/functional-logic-inquiry-and-analogy-21-2/
Discussion
• https://inquiryintoinquiry.com/2023/07/06/functional-logic-inquiry-and-analogy-discussion-1/

OEIS Wiki —

Functional Logic • Inquiry and Analogy
• https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Inquiry_and_Analogy

Prospects for Inquiry Driven Systems
• https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems

Introduction to Inquiry Driven Systems
• https://oeis.org/wiki/Introduction_to_Inquiry_Driven_Systems

Information = Comprehension × Extension
• https://oeis.org/wiki/Information_%3D_Comprehension_%C3%97_Extension

Inquiry Driven Systems • Inquiry Into Inquiry
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Overview

#Peirce #Logic #Abduction #Deduction #Induction #Analogy #Inquiry
#FunctionalLogic #DifferentialLogic #DynamicsOfInquiry #Semiotics
#InquiryDrivenSystem #InformationEqualsComprehensionTimesExtension

Survey of Definition and Determination • 2
• https://inquiryintoinquiry.com/2023/04/06/survey-of-definition-and-determination-2/

In the early 1990s, “in the middle of life's journey” as the saying goes, I returned to grad school in a systems engineering program with the idea of taking a more systems-theoretic approach to my development of Peircean themes, from signs and scientific inquiry to logic and information theory.

Two of the first questions calling for fresh examination were the closely related concepts of definition and determination, not only as Peirce used them in his logic and semiotics but as researchers in areas as diverse as computer science, cybernetics, physics, and systems sciences were finding themselves forced to reconsider the concepts in later years. That led me to collect a sample of texts where Peirce and a few other writers discuss the issues of definition and determination. There are copies of those selections at the following sites.

Collection Of Source Materials
• https://oeis.org/wiki/User:Jon_Awbrey/EXCERPTS

Excerpts on Definition
• https://oeis.org/wiki/User:Jon_Awbrey/EXCERPTS#Definition

Excerpts on Determination
• https://oeis.org/wiki/User:Jon_Awbrey/EXCERPTS#Determination

What follows is a Survey of blog and wiki posts on Definition and Determination, with a focus on the part they play in Peirce's interlinked theories of signs, information, and inquiry. In classical logical traditions the concepts of definition and determination are closely related and their bond acquires all the more force when we view the overarching concept of constraint from an information-theoretic point of view, as Peirce did beginning in the 1860s.

#Peirce #Logic #Definition #Determination #DifferentialLogic
#Inference #Information #Inquiry #Semiotics #SignRelations
#AI #Cybernetics #IntelligentSystems #InquiryDrivenSystems

Logic Syllabus • 5
• https://inquiryintoinquiry.com/logic-syllabus/

Related Articles
• https://oeis.org/wiki/Logic_Syllabus#Related_articles

Cactus Language • https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview
Futures Of Logical Graphs • https://oeis.org/wiki/Futures_Of_Logical_Graphs
Differential Propositional Calculus • https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Overview
Differential Logic • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview
Differential Logic and Dynamic Systems • https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview
Propositions As Types Analogy • https://oeis.org/wiki/Propositions_As_Types_Analogy
Propositional Equation Reasoning Systems • https://oeis.org/wiki/Propositional_Equation_Reasoning_Systems
Prospects for Inquiry Driven Systems • https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems
Introduction to Inquiry Driven Systems • https://oeis.org/wiki/Introduction_to_Inquiry_Driven_Systems
Inquiry Driven Systems • Inquiry Into Inquiry • https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Overview

#Logic #LogicSyllabus #CactusLanguage #LogicalGraphs #DifferentialLogic
#DifferentialPropositionalCalculus #DifferentialLogicAndDynamicSystems
#PropositionsAsTypesAnalogy #PropositionalEquationReasoningSystems
#Inquiry #InquiryDrivenSystems #InquiryIntoInquiry #DynamicalSystems

Logic Syllabus • 5
• https://inquiryintoinquiry.com/logic-syllabus/

Related Articles
• https://oeis.org/wiki/Logic_Syllabus#Related_articles

Cactus Language • https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview
Futures Of Logical Graphs • https://oeis.org/wiki/Futures_Of_Logical_Graphs
Differential Propositional Calculus • https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Overview
Differential Logic • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview
Differential Logic and Dynamic Systems • https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview
Propositions As Types Analogy • https://oeis.org/wiki/Propositions_As_Types_Analogy
Propositional Equation Reasoning Systems • https://oeis.org/wiki/Propositional_Equation_Reasoning_Systems
Prospects for Inquiry Driven Systems • https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems
Introduction to Inquiry Driven Systems • https://oeis.org/wiki/Introduction_to_Inquiry_Driven_Systems
Inquiry Driven Systems • Inquiry Into Inquiry • https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Overview

#Logic #LogicSyllabus #CactusLanguage #LogicalGraphs #DifferentialLogic
#DifferentialPropositionalCalculus #DifferentialLogicAndDynamicSystems
#PropositionsAsTypesAnalogy #PropositionalEquationReasoningSystems
#Inquiry #InquiryDrivenSystems #InquiryIntoInquiry #DynamicalSystems

Logic Syllabus • 3
• https://inquiryintoinquiry.com/logic-syllabus/

Logical Concepts
• https://oeis.org/wiki/Logic_Syllabus#Logical_concepts

Ampheck • https://oeis.org/wiki/Ampheck
Boolean Domain • https://oeis.org/wiki/Boolean_domain
Boolean Function • https://oeis.org/wiki/Boolean_function
Boolean-Valued Function • https://oeis.org/wiki/Boolean-valued_function
Differential Logic • https://oeis.org/wiki/Differential_logic
Logical Graph • https://oeis.org/wiki/Logical_Graphs
Minimal Negation Operator • https://oeis.org/wiki/Minimal_negation_operator
Multigrade Operator • https://oeis.org/wiki/Multigrade_operator
Parametric Operator • https://oeis.org/wiki/Parametric_operator
Peirce's Law • https://oeis.org/wiki/Peirce%27s_law
Propositional Calculus • https://oeis.org/wiki/Propositional_calculus
Sole Sufficient Operator • https://oeis.org/wiki/Sole_sufficient_operator
Truth Table • https://oeis.org/wiki/Truth_table
Universe of Discourse • https://oeis.org/wiki/Universe_of_discourse
Zeroth Order Logic • https://oeis.org/wiki/Zeroth_order_logic

#Logic #LogicSyllabus #Ampheck #BooleanDomain #BooleanFunction #BooleanValuedFunction
#DifferentialLogic #LogicalGraph #MinimalNegationOperator #MultigradeOperator
#ParametricOperator #PeircesLaw #PropositionalCalculus #SoleSufficientOperator
#TruthTable #UniverseOfDiscourse #ZerothOrderLogic

@NicoleCRust @knutson_brain

Here's the beginning of a prospective blog series I started … this topic interacts strongly with a host of others I've been struggling to articulate over the years …

Inquiry Into Inquiry • Discussion 6
• https://inquiryintoinquiry.com/2023/04/30/inquiry-into-inquiry-discussion-6/

Re: Nicole Rust
• https://mathstodon.xyz/@NicoleCRust@neuromatch.social/110197230713039748

❝Computations or Processes —
How do you think about the building blocks of the brain?❞

I keep coming back to this thread about levels, along with others on the related issue of paradigms, as those have long been major questions for me. I am trying to clarify my current understanding for a blog post. It will start out a bit like this —

A certain amount of “level” language is natural in the sciences but “level” metaphors come with hidden assumptions about higher and lower places in hierarchies which don't always fit the case at hand. In complex cases what look at first like parallel strata may in time be better comprehended as intersecting domains or mutually recursive and entangled orders of being. When that happens we can guard against misleading imagery by speaking of domains or realms instead of levels.

To be continued …

#Peirce #Logic #LogicalGraphs #DifferentialLogic #CactusLanguage
#Inquiry #InquiryDrivenSystem #InquiryIntoInquiry #NeuralNetwork
#Semiotics #RelationTheory #SignRelation #TriadicRelation #Model
#ObjectiveReality #MathematicalStructure #SymbolicRepresentation

Inquiry Into Inquiry • Discussion 6
• https://inquiryintoinquiry.com/2023/04/30/inquiry-into-inquiry-discussion-6/

Re: Nicole Rust
• https://mathstodon.xyz/@NicoleCRust@neuromatch.social/110197230713039748

❝Computations or Processes — How do you think about the building blocks of the brain?❞

I keep coming back to this thread about levels, along with others on the related issue of paradigms, as those have long been major questions for me. I am trying to clarify my current understanding for a blog post. It will start out a bit like this —

A certain amount of “level” language is natural in the sciences but “level” metaphors come with hidden assumptions about higher and lower places in hierarchies which don't always fit the case at hand. In complex cases what look at first like parallel strata may in time be better comprehended as intersecting domains or mutually recursive and entangled orders of being. When that happens we can guard against misleading imagery by speaking of domains or realms instead of levels.

To be continued …

#Peirce #Logic #LogicalGraphs #DifferentialLogic #CactusLanguage
#Inquiry #InquiryDrivenSystem #InquiryIntoInquiry #NeuralNetwork
#Semiotics #RelationTheory #SignRelation #TriadicRelation #Model
#ObjectiveReality #MathematicalStructure #SymbolicRepresentation

Survey of Differential Logic • 5
• https://inquiryintoinquiry.com/2023/04/25/survey-of-differential-logic-5/

This is a Survey of work in progress on Differential Logic, resources under development toward a more systematic treatment.

Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description. A definition as broad as that 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 treats the use of a differential logical
calculus — a formal system with the expressive capacity to describe change and diversity in logical universes of discourse.

Please follow the above link for the full set of resources.
Articles and blog series on the core ideas are linked below.

Differential Propositional Calculus
• https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Overview
1 https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1
2 https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2
• https://inquiryintoinquiry.com/2020/02/16/differential-propositional-calculus-overview/

Differential Logic
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview
1 https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1
2 https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2
3 https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3
• https://inquiryintoinquiry.com/2020/03/20/differential-logic-overview/

Differential Logic and Dynamic Systems
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview
1 https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1
2 https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_2
3 https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3
4 https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_4
5 https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_5
• https://inquiryintoinquiry.com/2023/03/04/differential-logic-and-dynamic-systems-overview-2/

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DynamicSystems
#BooleanFunctions #BooleanDifferenceCalculus #QualitativePhysics
#CactusCalculus #MinimalNegationOperators #NeuralNetworkSystems

Differential Logic and Dynamic Systems • Overview 2
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview

The work pursued here is coordinated with a parallel application focusing on #NeuralNetworkSystems but the dependencies are arranged to make the present article the main and the more self-contained work, to serve as a conceptual frame and a technical background for the network project.

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DynamicSystems
#BooleanFunctions #BooleanDifferenceCalculus #QualitativeChange

Differential Logic and Dynamic Systems • Overview
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview

❝Stand and unfold yourself.❞

— Hamlet • Francisco • 1.1.2

This article develops a differential extension of propositional calculus and applies it to analyzing the temporal evolution of systems whose states are described in qualitative logical terms.

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DynamicSystems
#BooleanFunctions #BooleanDifferenceCalculus #QualitativeChange

Differential Logic and Dynamic Systems • Overview
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview

❝Stand and unfold yourself.❞

— Hamlet • Francisco • 1.1.2

This article develops a differential extension of propositional calculus and applies it to analyzing the temporal evolution of systems whose states are described in qualitative logical terms.

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DynamicSystems
#BooleanFunctions #BooleanDifferenceCalculus #QualitativeChange

Differential Logic and Dynamic Systems • Overview
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview

❝Stand and unfold yourself.❞

— Hamlet • Francisco • 1.1.2

This article develops a differential extension of propositional calculus and applies it to analyzing the temporal evolution of systems whose states are described in qualitative logical terms.

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DynamicSystems
#BooleanFunctions #BooleanDifferenceCalculus #QualitativeChange

Differential Logic and Dynamic Systems • Overview 4
• https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

Logic-based systems have tended to be static in character, largely because we have lacked a proper logical analogue of differential calculus. The work laid out in this series of posts is intended to address that lack.

#Logic #DifferentialLogic #DiscreteDynamicalSystems
#LogicalTransformations #TransformationsOfDiscourse
#IntelligentSystems #InquiryDrivenSystems #Semiotics

Differential Logic and Dynamic Systems • Overview 3
• https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

Symbolic models use logical methods to describe systems and their agents in qualitative terms, deriving logical consequences of a system’s description or an agent’s state of information.

#Logic #DifferentialLogic #DiscreteDynamicalSystems
#LogicalTransformations #TransformationsOfDiscourse
#IntelligentSystems #InquiryDrivenSystems #Semiotics

Differential Logic and Dynamic Systems • Overview 2
• https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

Dynamic models take their cue from physics, using quantitative measures and differential equations to model the evolution of a system’s state through time.

#Logic #DifferentialLogic #DiscreteDynamicalSystems
#LogicalTransformations #TransformationsOfDiscourse
#IntelligentSystems #InquiryDrivenSystems #Semiotics

Differential Logic and Dynamic Systems • Overview 1
• https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

In modeling intelligent systems, whether we are trying to understand a natural system or engineer an artificial system, there has long been a tension or trade-off between dynamic paradigms and symbolic paradigms.

#Logic #DifferentialLogic #DiscreteDynamicalSystems
#LogicalTransformations #TransformationsOfDiscourse
#IntelligentSystems #InquiryDrivenSystems #Semiotics

The Phantom of the Operators • η
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3#The_Phantom_of_the_Operators_:_.CE.B7

❝I was wondering what the reason could be, when I myself raised my head and everything within me seemed drawn towards the Unseen, which was playing the most perfect music!❞

— Gaston #Leroux • “The Phantom of the Opera”

#DifferentialLogic #DynamicSystems
#DifferentialLogicAndDynamicSystems

#AThoughtForOurTimes

Differential Logic and Dynamic Systems • Propositional_Transformations
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3#Propositional_Transformations

❝If only the word “artificial” were associated with the idea of “art”, or expert skill gained through voluntary apprenticeship (instead of suggesting the factitious and unreal), we might say that “logical” refers to artificial thought.❞

— John Dewey • “How We Think”

#Peirce #Logic #DifferentialLogic #InquiryDrivenSystems
#Dewey #ArtificialThought #PropositionalTransformation

RK's remark prompts a few thoughts on my part —

That strikes me as a problem in cross-paradigm communication — an interaction among communities or traditions of interpretation using different analogies to comprehend object situations which may or may not be compatible.

Whether it's #Dialectic in #Aristotle's or #Hegel's sense the logic of shifting paradigms is the #Logic of #Abduction.

#Peirce #Analogy #Paradigm #Anomaly #ParadigmChange
#Commensurability #Incommensurability #DifferentialLogic