#analogy — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #analogy, aggregated by home.social.
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Objects, Models, Theories • 2
• https://inquiryintoinquiry.com/2026/09/12/objects-models-theories-2-a/Re: Gödel's Lost Letter • The Graph Of Math
• https://rjlipton.com/2013/11/15/the-graph-of-math/GLL:
❝Kurt Gödel is said to have been a latecomer to appreciating the power of Model Theory. He was of course the greatest architect of Proof Theory, which stands in contrast to Model Theory. Model Theory concerns itself with what could be true, while Proof Theory deals with what can be proved. The latter sounds more definite, but they are supplementary: a statement is capable of being true somewhere precisely when its negation cannot be proved. The question is, where is that somewhere? And when?❞What — if anything — is the common sense that connects the different senses of the word “model”, as it has been used over the years in logic, mathematics, and the special sciences? It's a problem I've been running into for several decades now and I think I can trace the roots of it going back as far as Aristotle’s treatment of analogy.
Resources —
Functional Logic • Inquiry and Analogy
• https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Inquiry_and_AnalogySurvey of Abduction, Deduction, Induction, Analogy, Inquiry
• https://inquiryintoinquiry.com/2025/05/01/survey-of-abduction-deduction-induction-analogy-inquiry-5/#Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
#Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
#Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations -
Objects, Models, Theories • 2
• https://inquiryintoinquiry.com/2026/09/12/objects-models-theories-2-a/Re: Gödel's Lost Letter • The Graph Of Math
• https://rjlipton.com/2013/11/15/the-graph-of-math/GLL:
❝Kurt Gödel is said to have been a latecomer to appreciating the power of Model Theory. He was of course the greatest architect of Proof Theory, which stands in contrast to Model Theory. Model Theory concerns itself with what could be true, while Proof Theory deals with what can be proved. The latter sounds more definite, but they are supplementary: a statement is capable of being true somewhere precisely when its negation cannot be proved. The question is, where is that somewhere? And when?❞What — if anything — is the common sense that connects the different senses of the word “model”, as it has been used over the years in logic, mathematics, and the special sciences? It's a problem I've been running into for several decades now and I think I can trace the roots of it going back as far as Aristotle’s treatment of analogy.
Resources —
Functional Logic • Inquiry and Analogy
• https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Inquiry_and_AnalogySurvey of Abduction, Deduction, Induction, Analogy, Inquiry
• https://inquiryintoinquiry.com/2025/05/01/survey-of-abduction-deduction-induction-analogy-inquiry-5/#Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
#Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
#Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations -
Objects, Models, Theories • 2
• https://inquiryintoinquiry.com/2026/09/12/objects-models-theories-2-a/Re: Gödel's Lost Letter • The Graph Of Math
• https://rjlipton.com/2013/11/15/the-graph-of-math/GLL:
❝Kurt Gödel is said to have been a latecomer to appreciating the power of Model Theory. He was of course the greatest architect of Proof Theory, which stands in contrast to Model Theory. Model Theory concerns itself with what could be true, while Proof Theory deals with what can be proved. The latter sounds more definite, but they are supplementary: a statement is capable of being true somewhere precisely when its negation cannot be proved. The question is, where is that somewhere? And when?❞What — if anything — is the common sense that connects the different senses of the word “model”, as it has been used over the years in logic, mathematics, and the special sciences? It's a problem I've been running into for several decades now and I think I can trace the roots of it going back as far as Aristotle’s treatment of analogy.
Resources —
Functional Logic • Inquiry and Analogy
• https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Inquiry_and_AnalogySurvey of Abduction, Deduction, Induction, Analogy, Inquiry
• https://inquiryintoinquiry.com/2025/05/01/survey-of-abduction-deduction-induction-analogy-inquiry-5/#Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
#Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
#Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations -
Objects, Models, Theories • 2
• https://inquiryintoinquiry.com/2026/09/12/objects-models-theories-2-a/Re: Gödel's Lost Letter • The Graph Of Math
• https://rjlipton.com/2013/11/15/the-graph-of-math/GLL:
❝Kurt Gödel is said to have been a latecomer to appreciating the power of Model Theory. He was of course the greatest architect of Proof Theory, which stands in contrast to Model Theory. Model Theory concerns itself with what could be true, while Proof Theory deals with what can be proved. The latter sounds more definite, but they are supplementary: a statement is capable of being true somewhere precisely when its negation cannot be proved. The question is, where is that somewhere? And when?❞What — if anything — is the common sense that connects the different senses of the word “model”, as it has been used over the years in logic, mathematics, and the special sciences? It's a problem I've been running into for several decades now and I think I can trace the roots of it going back as far as Aristotle’s treatment of analogy.
Resources —
Functional Logic • Inquiry and Analogy
• https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Inquiry_and_AnalogySurvey of Abduction, Deduction, Induction, Analogy, Inquiry
• https://inquiryintoinquiry.com/2025/05/01/survey-of-abduction-deduction-induction-analogy-inquiry-5/#Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
#Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
#Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations -
Objects, Models, Theories • 2
• https://inquiryintoinquiry.com/2026/09/12/objects-models-theories-2-a/Re: Gödel's Lost Letter • The Graph Of Math
• https://rjlipton.com/2013/11/15/the-graph-of-math/GLL:
❝Kurt Gödel is said to have been a latecomer to appreciating the power of Model Theory. He was of course the greatest architect of Proof Theory, which stands in contrast to Model Theory. Model Theory concerns itself with what could be true, while Proof Theory deals with what can be proved. The latter sounds more definite, but they are supplementary: a statement is capable of being true somewhere precisely when its negation cannot be proved. The question is, where is that somewhere? And when?❞What — if anything — is the common sense that connects the different senses of the word “model”, as it has been used over the years in logic, mathematics, and the special sciences? It's a problem I've been running into for several decades now and I think I can trace the roots of it going back as far as Aristotle’s treatment of analogy.
Resources —
Functional Logic • Inquiry and Analogy
• https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Inquiry_and_AnalogySurvey of Abduction, Deduction, Induction, Analogy, Inquiry
• https://inquiryintoinquiry.com/2025/05/01/survey-of-abduction-deduction-induction-analogy-inquiry-5/#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_AnalogySurvey 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_AnalogySurvey 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_AnalogySurvey 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_AnalogySurvey 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_AnalogySurvey 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 -
Propositions As Types Analogy • 1
• https://inquiryintoinquiry.com/2013/01/29/propositions-as-types-analogy-1/One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.
Proof Hint ∶ Proof ∶ Proposition
∷
Untyped Term ∶ Typed Term ∶ Typeor
Proof Hint ∶ Untyped Term
∷
Proof ∶ Typed Term
∷
Proposition ∶ TypeSee my working notes on the Propositions As Types Analogy —
• https://oeis.org/wiki/Propositions_As_Types_Analogy#Mathematics #CategoryTheory #ProofTheory #TypeTheory
#Logic #Analogy #Isomorphism #PropositionalCalculus
#CombinatorCalculus #CombinatoryLogic #LambdaCalculus
#Peirce #LogicalGraphs #GraphTheory #RelationTheory