#analogy — Public Fediverse posts

Objects, Models, Theories • 1
• https://inquiryintoinquiry.com/2026/09/10/objects-models-theories-1-a/

Happy Birthday, Charles Sanders Peirce❢ — September 10, 1839

I return once more to a recurring subject.

Re: Artem Kaznatcheev • Three Types of Mathematical Models
• https://egtheory.wordpress.com/2013/09/08/mathematical-models/

In speaking of models one tends to find denizens of different disciplines talking at cross purposes to one another. Logicians use the word to describe what may be distinguished as “logical models”, saying a model is whatever satisfies a theory — anything a theory holds true of — and that is the sense used in the logical subject of “model theory”.

Almost everyone else uses the word to describe what may be called “analogical models”, analogues being things holding enough properties in common with other things that learning about Thing 2 (the analogue system) can teach us about Thing 1 (the object system).

It is actually quite easy to integrate those two senses of the word “model” into a coherent picture of the whole situation, namely, the triadic relationship among objects, analogues, and theories. We'll get into that further as the discussion proceeds.

Resources —

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

Survey of Abduction, Deduction, Induction, Analogy, Inquiry
• https://inquiryintoinquiry.com/2025/05/01/survey-of-abduction-deduction-induction-analogy-inquiry-5/

cc: https://www.academia.edu/community/VDDKwZ
cc: https://www.researchgate.net/post/Objects_Models_Theories

#Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
#Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
#Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations

Objects, Models, Theories • 1
• https://inquiryintoinquiry.com/2026/09/10/objects-models-theories-1-a/

Happy Birthday, Charles Sanders Peirce❢ — September 10, 1839

I return once more to a recurring subject.

Re: Artem Kaznatcheev • Three Types of Mathematical Models
• https://egtheory.wordpress.com/2013/09/08/mathematical-models/

In speaking of models one tends to find denizens of different disciplines talking at cross purposes to one another. Logicians use the word to describe what may be distinguished as “logical models”, saying a model is whatever satisfies a theory — anything a theory holds true of — and that is the sense used in the logical subject of “model theory”.

Almost everyone else uses the word to describe what may be called “analogical models”, analogues being things holding enough properties in common with other things that learning about Thing 2 (the analogue system) can teach us about Thing 1 (the object system).

It is actually quite easy to integrate those two senses of the word “model” into a coherent picture of the whole situation, namely, the triadic relationship among objects, analogues, and theories. We'll get into that further as the discussion proceeds.

Resources —

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

Survey of Abduction, Deduction, Induction, Analogy, Inquiry
• https://inquiryintoinquiry.com/2025/05/01/survey-of-abduction-deduction-induction-analogy-inquiry-5/

cc: https://www.academia.edu/community/VDDKwZ
cc: https://www.researchgate.net/post/Objects_Models_Theories

#Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
#Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
#Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations

Objects, Models, Theories • 1
• https://inquiryintoinquiry.com/2026/09/10/objects-models-theories-1-a/

Happy Birthday, Charles Sanders Peirce❢ — September 10, 1839

I return once more to a recurring subject.

Re: Artem Kaznatcheev • Three Types of Mathematical Models
• https://egtheory.wordpress.com/2013/09/08/mathematical-models/

In speaking of models one tends to find denizens of different disciplines talking at cross purposes to one another. Logicians use the word to describe what may be distinguished as “logical models”, saying a model is whatever satisfies a theory — anything a theory holds true of — and that is the sense used in the logical subject of “model theory”.

Almost everyone else uses the word to describe what may be called “analogical models”, analogues being things holding enough properties in common with other things that learning about Thing 2 (the analogue system) can teach us about Thing 1 (the object system).

It is actually quite easy to integrate those two senses of the word “model” into a coherent picture of the whole situation, namely, the triadic relationship among objects, analogues, and theories. We'll get into that further as the discussion proceeds.

Resources —

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

Survey of Abduction, Deduction, Induction, Analogy, Inquiry
• https://inquiryintoinquiry.com/2025/05/01/survey-of-abduction-deduction-induction-analogy-inquiry-5/

cc: https://www.academia.edu/community/VDDKwZ
cc: https://www.researchgate.net/post/Objects_Models_Theories

#Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
#Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
#Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations

Objects, Models, Theories • 1
• https://inquiryintoinquiry.com/2026/09/10/objects-models-theories-1-a/

Happy Birthday, Charles Sanders Peirce❢ — September 10, 1839

I return once more to a recurring subject.

Re: Artem Kaznatcheev • Three Types of Mathematical Models
• https://egtheory.wordpress.com/2013/09/08/mathematical-models/

In speaking of models one tends to find denizens of different disciplines talking at cross purposes to one another. Logicians use the word to describe what may be distinguished as “logical models”, saying a model is whatever satisfies a theory — anything a theory holds true of — and that is the sense used in the logical subject of “model theory”.

Almost everyone else uses the word to describe what may be called “analogical models”, analogues being things holding enough properties in common with other things that learning about Thing 2 (the analogue system) can teach us about Thing 1 (the object system).

It is actually quite easy to integrate those two senses of the word “model” into a coherent picture of the whole situation, namely, the triadic relationship among objects, analogues, and theories. We'll get into that further as the discussion proceeds.

Resources —

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

Survey of Abduction, Deduction, Induction, Analogy, Inquiry
• https://inquiryintoinquiry.com/2025/05/01/survey-of-abduction-deduction-induction-analogy-inquiry-5/

cc: https://www.academia.edu/community/VDDKwZ
cc: https://www.researchgate.net/post/Objects_Models_Theories

#Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
#Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
#Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations

Objects, Models, Theories • 1
• https://inquiryintoinquiry.com/2026/09/10/objects-models-theories-1-a/

Happy Birthday, Charles Sanders Peirce❢ — September 10, 1839

I return once more to a recurring subject.

Re: Artem Kaznatcheev • Three Types of Mathematical Models
• https://egtheory.wordpress.com/2013/09/08/mathematical-models/

In speaking of models one tends to find denizens of different disciplines talking at cross purposes to one another. Logicians use the word to describe what may be distinguished as “logical models”, saying a model is whatever satisfies a theory — anything a theory holds true of — and that is the sense used in the logical subject of “model theory”.

Almost everyone else uses the word to describe what may be called “analogical models”, analogues being things holding enough properties in common with other things that learning about Thing 2 (the analogue system) can teach us about Thing 1 (the object system).

It is actually quite easy to integrate those two senses of the word “model” into a coherent picture of the whole situation, namely, the triadic relationship among objects, analogues, and theories. We'll get into that further as the discussion proceeds.

Resources —

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

Survey of Abduction, Deduction, Induction, Analogy, Inquiry
• https://inquiryintoinquiry.com/2025/05/01/survey-of-abduction-deduction-induction-analogy-inquiry-5/

cc: https://www.academia.edu/community/VDDKwZ
cc: https://www.researchgate.net/post/Objects_Models_Theories

#Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
#Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
#Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations

Douglas Hofstadter: Analogy as the Core of Cognition [video]

https://www.youtube.com/watch?v=n8m7lFQ3njk

Comments: https://news.ycombinator.com/item?id=49587121

#HackerNews #DouglasHofstadter #Analogy #Cognition #Video #AIResearch #CognitiveScience

Douglas Hofstadter: Analogy as the Core of Cognition [video]

https://www.youtube.com/watch?v=n8m7lFQ3njk

Comments: https://news.ycombinator.com/item?id=49587121

#HackerNews #DouglasHofstadter #Analogy #Cognition #Video #AIResearch #CognitiveScience

Douglas Hofstadter: Analogy as the Core of Cognition [video]

https://www.youtube.com/watch?v=n8m7lFQ3njk

Comments: https://news.ycombinator.com/item?id=49587121

#HackerNews #DouglasHofstadter #Analogy #Cognition #Video #AIResearch #CognitiveScience

Douglas Hofstadter: Analogy as the Core of Cognition [video]

https://www.youtube.com/watch?v=n8m7lFQ3njk

Comments: https://news.ycombinator.com/item?id=49587121

#HackerNews #DouglasHofstadter #Analogy #Cognition #Video #AIResearch #CognitiveScience

Douglas Hofstadter: Analogy as the Core of Cognition [video]

https://www.youtube.com/watch?v=n8m7lFQ3njk

Comments: https://news.ycombinator.com/item?id=49587121

#HackerNews #DouglasHofstadter #Analogy #Cognition #Video #AIResearch #CognitiveScience

Mechanical Logic Gates With Amplification https://hackaday.com/2024/09/20/mechanical-logic-gates-with-amplification/ #digitallogic #electronics #leverlogic #mechanical #amplifier #logicgate #teaching #Science #analogy #capstan #analog #pulley

Mechanical Logic Gates With Amplification - One of the hardest things about studying electricity, and by extension electronics... - https://hackaday.com/2024/09/20/mechanical-logic-gates-with-amplification/ #digitallogic #electronics #leverlogic #mechanical #amplifier #logicgate #teaching #science #analogy #capstan #analog #pulley

Functional Logic • Inquiry and Analogy • 5

Inquiry and Analogy • Aristotle’s “Paradigm” • Reasoning by Analogy

Aristotle examines the subject of analogical inference or “reasoning by example” under the heading of the Greek word παραδειγμα, from which comes the English word paradigm.  In its original sense the word suggests a kind of “side‑show”, or a parallel comparison of cases.

We have an Example (παραδειγμα, or analogy) when the major extreme is shown to be applicable to the middle term by means of a term similar to the third.  It must be known both that the middle applies to the third term and that the first applies to the term similar to the third.

E.g., let A be “bad”, B “to make war on neighbors”, C “Athens against Thebes”, and D “Thebes against Phocis”.  Then if we require to prove that war against Thebes is bad, we must be satisfied that war against neighbors is bad.  Evidence of this can be drawn from similar examples, e.g., that war by Thebes against Phocis is bad.  Then since war against neighbors is bad, and war against Thebes is against neighbors, it is evident that war against Thebes is bad.

Aristotle, “Prior Analytics” 2.24, Hugh Tredennick (trans.)

Figure 6 shows the logical relationships involved in Aristotle’s example of analogy.

Resources

• Logic Syllabus
• Boolean Function
• Boolean-Valued Function
• Logical Conjunction
• Minimal Negation Operator
• Functional Logic • Part 1 • Part 2 • Part 3
• Cactus Language • Part 1 • Part 2 • Part 3 • References • Document History

cc: FB | Peirce Matters • Laws of Form • Mathstodon • Ontolog • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

#Abduction #Analogy #Argument #Aristotle #CSPeirce #Constraint #Deduction #Determination #DiagrammaticReasoning #Diagrams #DifferentialLogic #FunctionalLogic #Hypothesis #Indication #Induction #Inference #Information #Inquiry #Logic #LogicOfScience #Mathematics #PragmaticSemioticInformation #ProbableReasoning #PropositionalCalculus #Propositions #Reasoning #Retroduction #Semiotics #SignRelations #Syllogism #TriadicRelations #Visualization