#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 • 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 -
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
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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
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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
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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
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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
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🧠⚙️ #Brain vs. #Computer – Why the #Analogy Falls Short
Is the human brain really just a biological supercomputer? A metaphor that, upon closer inspection, falls short by a wide margin!
📺 https://youtu.be/1ouxs6P3Enc
📎 https://philosophies.de/index.php/2022/11/20/das-verkoerperte-bewusstsein/
#Zoomposium #ThomasFuchs #BrainVsComputer #Embodiment #Consciousness #PhilosophyOfMind #Phenomenology #Neuroconstructivism #CognitiveSciences #ArtificialIntelligence #MachineConsciousness #EmbodiedConsciousness #Anthropology #MindAndBrain
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🧠 #Brain vs. #Computer💻: Why this #analogy is misleading 🚫
We tend to view the brain as complex #hardware and #consciousness as #software.
📺 https://youtu.be/1ouxs6P3Enc
📎https://philosophies.de/index.php/2022/11/20/das-verkoerperte-bewusstsein/
#Zoomposium #BrainVsComputer #Consciousness #ArtificialConsciousness #ThomasFuchs #Neurophilosophy #Embodiment #Enactivism #PhilosophyOfMind #AI #Digitalization #HardProblemOfConsciousness #Zoomposium #BeingHuman #Phenomenology
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Survey of Precursors Of Category Theory • 6
• https://inquiryintoinquiry.com/2025/05/05/survey-of-precursors-of-category-theory-6/A few years ago I began a sketch on the “Precursors of Category Theory”, tracing the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice. A Survey of resources on the topic is given below, still very rough and incomplete, but perhaps a few will find it of use.
Background —
Precursors Of Category Theory
• https://oeis.org/wiki/Precursors_Of_Category_TheoryPropositions As Types Analogy
• https://oeis.org/wiki/Propositions_As_Types_AnalogyBlog Series —
Notes On Categories
• https://inquiryintoinquiry.com/2013/02/22/notes-on-categories-1/Precursors Of Category Theory
1. https://inquiryintoinquiry.com/2024/05/25/precursors-of-category-theory-1-a/
2. https://inquiryintoinquiry.com/2024/05/26/precursors-of-category-theory-2-a/
3. https://inquiryintoinquiry.com/2024/05/27/precursors-of-category-theory-3-a/
4. https://inquiryintoinquiry.com/2024/05/28/precursors-of-category-theory-4-a/
5. https://inquiryintoinquiry.com/2024/05/29/precursors-of-category-theory-5-a/
6. https://inquiryintoinquiry.com/2024/05/30/precursors-of-category-theory-6-a/Precursors Of Category Theory • Discussion
1. https://inquiryintoinquiry.com/2020/09/13/precursors-of-category-theory-discussion-1/
2. https://inquiryintoinquiry.com/2020/09/21/precursors-of-category-theory-discussion-2/
3. https://inquiryintoinquiry.com/2020/09/25/precursors-of-category-theory-discussion-3/Categories à la Peirce —
C.S. Peirce • A Guess at the Riddle
• https://inquiryintoinquiry.com/2012/03/21/c-s-peirce-a-guess-at-the-riddle/Peirce's Categories
1. https://inquiryintoinquiry.com/2015/10/30/peirces-categories-1/
2. https://inquiryintoinquiry.com/2015/10/31/peirces-categories-2/
3. https://inquiryintoinquiry.com/2015/11/04/peirces-categories-3/
•••
19. https://inquiryintoinquiry.com/2020/05/13/peirces-categories-19/
20. https://inquiryintoinquiry.com/2020/05/14/peirces-categories-20/
21. https://inquiryintoinquiry.com/2020/06/25/peirces-categories-21/C.S. Peirce and Category Theory
1. https://inquiryintoinquiry.com/2021/06/23/c-s-peirce-and-category-theory-1/
2. https://inquiryintoinquiry.com/2021/06/24/c-s-peirce-and-category-theory-2/
3. https://inquiryintoinquiry.com/2021/06/27/c-s-peirce-and-category-theory-3/
4. https://inquiryintoinquiry.com/2021/06/28/c-s-peirce-and-category-theory-4/
5. https://inquiryintoinquiry.com/2021/06/29/c-s-peirce-and-category-theory-5/
6. https://inquiryintoinquiry.com/2021/06/30/c-s-peirce-and-category-theory-6/
7. https://inquiryintoinquiry.com/2021/07/01/c-s-peirce-and-category-theory-7/
8. https://inquiryintoinquiry.com/2021/07/02/c-s-peirce-and-category-theory-8/#Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
#Abstraction #Analogy #CategoryTheory #FunctionalLogic #RelationTheory
#PrecursorsOfCategoryTheory #PropositionsAsTypes #Semiotics #TypeTheory -
Interpreter and Interpretant • Selection 10.2
• https://inquiryintoinquiry.com/2025/02/11/interpreter-and-interpretant-selection-10-a/
• https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lhyet3gfzk2cIn logical terms, the analogy of experience proceeds by inducing a Rule about the validity of a current knowledge base and then by deducing a Fact, the applicability of that knowledge base to a current experience.
Step 1 is Inductive, abstracting a Rule from a Case and a Fact.
• Case : E_past ⇒ E_poss, Chosen events fairly sample Collective events.
• Fact : E_past ⇒ K_pres, Chosen events support the Knowledge regime.
────────────────────────────────────────────────
• Rule : E_poss ⇒ K_pres, Collective events support the Knowledge regime.Step 2 is Deductive, admitting a Case to a Rule and arriving at a Fact.
• Case : E_pres ⇒ E_poss, Current events fairly sample Collective events.
• Rule : E_poss ⇒ K_pres, Collective events support the Knowledge regime.
────────────────────────────────────────────────
• Fact : E_pres ⇒ K_pres, Current events support the Knowledge regime.References —
Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.
• https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052
• https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_InquiryDewey, J. (1910), How We Think, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY.
• https://www.gutenberg.org/files/37423/37423-h/37423-h.htmResources —
Survey of Abduction, Deduction, Induction, Analogy, Inquiry
• https://inquiryintoinquiry.com/2024/02/27/survey-of-abduction-deduction-induction-analogy-inquiry-4/Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2024/01/26/survey-of-semiotics-semiosis-sign-relations-5/#Peirce #Logic #Semiotics #Semiosis #SignRelations
#JohnDewey #Interpreter #Interpretant #Pragmatism
#Abduction #Deduction #Induction #Analogy #Inquiry -
Interpreter and Interpretant • Selection 10.1
• https://inquiryintoinquiry.com/2025/02/11/interpreter-and-interpretant-selection-10-a/
• https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lhyet3gfzk2cTransfer —
Returning to the scene of Dewey's “Sign of Rain” example, let's continue examining how the transfer of knowledge through the analogy of experience works in that case.
By way of a recap, we began by considering a fragment K_pres of the reasoner's knowledge base which is logically equivalent to a conjunction of two rules.
• K_pres ⇔ (B ⇒ A) ∧ (B ⇒ D).
K_pres may be thought of as a piece of knowledge or item of information allowing for the possibility of certain conditions, expressed in the form of a logical constraint on the present universe of discourse.
Next we found it convenient to express all logical statements in terms of their models, that is, in terms of the primitive circumstances or elements of experience over which they hold true.
• Let E_past be the chosen set of experiences, or the circumstances in mind under “past experience”.
• Let E_poss be the collective set of experiences, or the prospective total of possible circumstances.
• Let E_pres be the current experience, or the circumstances immediately present to the reasoner.
If we think of the knowledge base K_pres as referring to the “regime of experience” over which it is valid, then the sets of models involved in the analogy may be ordered according to the relationships of set inclusion or logical implication existing among them.
Figure 4 shows the subsumption relations involved in the analogy of experience.
Figure 4. Analogy of Experience
• https://inquiryintoinquiry.files.wordpress.com/2025/02/analogy-of-experience.png#Peirce #Logic #Semiotics #Semiosis #SignRelations
#JohnDewey #Interpreter #Interpretant #Pragmatism
#Abduction #Deduction #Induction #Analogy #Inquiry -
Interpreter and Interpretant • Selection 9.2
• https://inquiryintoinquiry.com/2025/01/27/interpreter-and-interpretant-selection-9-a/Transfer —
In logical terms, the analogy of experience proceeds by inducing a Rule about the validity of a current knowledge base and then by deducing a Fact, the applicability of that knowledge base to a current experience.
Step 1 is Inductive, abstracting a Rule from a Case and a Fact.
• Case : E_past ⇒ E_poss, Chosen events fairly sample Collective events.
• Fact : E_past ⇒ K_pres, Chosen events support the Knowledge regime.
────────────────────────────────────────────────
• Rule : E_poss ⇒ K_pres, Collective events support the Knowledge regime.Step 2 is Deductive, admitting a Case to a Rule and arriving at a Fact.
• Case : E_pres ⇒ E_poss, Current events fairly sample Collective events.
• Rule : E_poss ⇒ K_pres, Collective events support the Knowledge regime.
────────────────────────────────────────────────
• Fact : E_pres ⇒ K_pres, Current events support the Knowledge regime.References —
Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.
• https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052
• https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_InquiryDewey, J. (1910), How We Think, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY.
• https://www.gutenberg.org/files/37423/37423-h/37423-h.htmResources —
Survey of Abduction, Deduction, Induction, Analogy, Inquiry
• https://inquiryintoinquiry.com/2024/02/27/survey-of-abduction-deduction-induction-analogy-inquiry-4/Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2024/01/26/survey-of-semiotics-semiosis-sign-relations-5/#Peirce #Logic #Semiotics #Semiosis #SignRelations
#JohnDewey #Interpreter #Interpretant #Pragmatism
#Abduction #Deduction #Induction #Analogy #Inquiry -
Interpreter and Interpretant • Selection 9.1
• https://inquiryintoinquiry.com/2025/01/27/interpreter-and-interpretant-selection-9-a/Transfer —
Let's examine how the transfer of knowledge through the analogy of experience works in the case of Dewey's “Sign of Rain” example.
For concreteness, consider a fragment K_pres of the reasoner's knowledge base which is logically equivalent to a conjunction of two rules.
• K_pres ⇔ (B ⇒ A) ∧ (B ⇒ D).
K_pres may be thought of as a piece of knowledge or item of information allowing for the possibility of certain conditions, expressed in the form of a logical constraint on the present universe of discourse.
It is convenient to have the option of expressing all logical statements in terms of their models, that is, in terms of the primitive circumstances or elements of experience over which they hold true.
• Let E_past be the chosen set of experiences, or the circumstances in mind under “past experience”.
• Let E_poss be the collective set of experiences, or the prospective total of possible circumstances.
• Let E_pres be the current experience, or the circumstances immediately present to the reasoner.
If we think of the knowledge base K_pres as referring to the “regime of experience” over which it is valid, then the sets of models involved in the analogy may be ordered according to the relationships of set inclusion or logical implication existing among them.
#Peirce #Logic #Semiotics #Semiosis #SignRelations
#JohnDewey #Interpreter #Interpretant #Pragmatism
#Abduction #Deduction #Induction #Analogy #Inquiry -
Interpreter and Interpretant • Selection 8
• https://inquiryintoinquiry.com/2025/01/24/interpreter-and-interpretant-selection-8-a/Transfer —
What exactly gives the acquisition of a knowledge base its distinctively inductive character? It is evidently the “analogy of experience” involved in applying what we've learned in the past to what confronts us in the present.
Whenever we find ourselves approaching a problem with the thought, “If past experience is any guide …” we can be sure the analogy of experience has come into play. We are seeking to find analogies between past experience as a totality and present experience as a point of application.
From a statistical point of view what we mean is this — “If past experience is a fair sample of possible experience then knowledge gained from past experience may usefully apply to present experience”. It is that mechanism which allows a knowledge base to be carried across gulfs of experience which remain indifferent to the effective contents of its rules.
Next we'll examine how the transfer of knowledge through the analogy of experience works out in the case of Dewey's “Sign of Rain” example.
References —
Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.
• https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052
• https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_InquiryDewey, J. (1910), How We Think, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY.
• https://www.gutenberg.org/files/37423/37423-h/37423-h.htm#Peirce #Logic #Semiotics #Semiosis #SignRelations
#JohnDewey #Interpreter #Interpretant #Pragmatism
#Abduction #Deduction #Induction #Analogy #Inquiry -
Precursors Of Category Theory • 3
• https://inquiryintoinquiry.com/2024/05/27/precursors-of-category-theory-3-a/❝Act only according to that maxim by which you can at the same time will that it should become a universal law.❞
— Immanuel Kant (1785)
C.S. Peirce • “On a New List of Categories” (1867)
❝§1. This paper is based upon the theory already established, that the function of conceptions is to reduce the manifold of sensuous impressions to unity, and that the validity of a conception consists in the impossibility of reducing the content of consciousness to unity without the introduction of it.❞ (CP 1.545).
❝§2. This theory gives rise to a conception of gradation among those conceptions which are universal. For one such conception may unite the manifold of sense and yet another may be required to unite the conception and the manifold to which it is applied; and so on.❞ (CP 1.546).
Cued by Kant's idea regarding the function of concepts in general, Peirce locates his categories on the highest levels of abstraction able to provide a meaningful measure of traction in practice. Whether successive grades of conceptions converge to an absolute unity or not is a question to be pursued as inquiry progresses and need not be answered in order to begin.
Resources —
Precursors Of Category Theory
• https://oeis.org/wiki/Precursors_Of_Category_TheoryPropositions As Types Analogy
• https://oeis.org/wiki/Propositions_As_Types_AnalogySurvey of Precursors Of Category Theory
• https://inquiryintoinquiry.com/2024/05/24/survey-of-precursors-of-category-theory-5/#Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
#Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
#FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
#CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals -
Precursors Of Category Theory • 2.3
• https://inquiryintoinquiry.com/2024/05/26/precursors-of-category-theory-2-a/In the logic of Aristotle categories are adjuncts to reasoning whose function is to resolve ambiguities and thus to prepare equivocal signs, otherwise recalcitrant to being ruled by logic, for the application of logical laws. The example of ζωον illustrates the fact that we don't need categories to “make” generalizations so much as to “control” generalizations, to reign in abstractions and analogies which have been stretched too far.
References —
• Aristotle, “The Categories”, Harold P. Cooke (trans.), pp. 1–109 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.
• Karpeles, Eric (2008), Paintings in Proust, Thames and Hudson, London, UK.
Resources —
Precursors Of Category Theory
• https://oeis.org/wiki/Precursors_Of_Category_TheoryPropositions As Types Analogy
• https://oeis.org/wiki/Propositions_As_Types_AnalogySurvey of Precursors Of Category Theory
• https://inquiryintoinquiry.com/2024/05/24/survey-of-precursors-of-category-theory-5/#Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
#Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
#FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
#CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals -
Precursors Of Category Theory • 2.2
• https://inquiryintoinquiry.com/2024/05/26/precursors-of-category-theory-2-a/Aristotle —
❝Things are equivocally named, when they have the name only in common, the definition (or statement of essence) corresponding with the name being different. For instance, while a man and a portrait can properly both be called animals (ζωον), these are equivocally named. For they have the name only in common, the definitions (or statements of essence) corresponding with the name being different. For if you are asked to define what the being an animal means in the case of the man and the portrait, you give in either case a definition appropriate to that case alone.
❝Things are univocally named, when not only they bear the same name but the name means the same in each case — has the same definition corresponding. Thus a man and an ox are called animals. The name is the same in both cases; so also the statement of essence. For if you are asked what is meant by their both of them being called animals, you give that particular name in both cases the same definition.❞ (Aristotle, Categories, 1.1a1–12).
Translator's Note. ❝Ζωον in Greek had two meanings, that is to say, living creature, and, secondly, a figure or image in painting, embroidery, sculpture. We have no ambiguous noun. However, we use the word ‘living’ of portraits to mean ‘true to life’.❞
#Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
#Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
#FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
#CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals -
Precursors Of Category Theory • 2.1
• https://inquiryintoinquiry.com/2024/05/26/precursors-of-category-theory-2-a/❝Thanks to art, instead of seeing one world only, our own, we see that world multiply itself and we have at our disposal as many worlds as there are original artists …❞
— Marcel Proust
When it comes to looking for the continuities of the category concept across different systems and systematizers, we don't expect to find their kinship in the names or numbers of categories, since those are legion and their divisions deployed on widely different planes of abstraction, but in their common function.
#Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
#Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
#FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
#CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals -
Precursors Of Category Theory • 1
• https://inquiryintoinquiry.com/2024/05/25/precursors-of-category-theory-1-a/A few years ago I began a sketch on the “Precursors of Category Theory”, tracing the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice. My notes on the project are still very rough and incomplete but I find myself returning to them from time to time.
Preamble —
❝Now the discovery of ideas as general as these is chiefly the willingness to make a brash or speculative abstraction, in this case supported by the pleasure of purloining words from the philosophers: “Category” from Aristotle and Kant, “Functor” from Carnap (“Logische Syntax der Sprache”), and “natural transformation” from then current informal parlance.❞
— Saunders Mac Lane • “Categories for the Working Mathematician”
Resources —
Precursors Of Category Theory
• https://oeis.org/wiki/Precursors_Of_Category_TheoryPropositions As Types Analogy
• https://oeis.org/wiki/Propositions_As_Types_AnalogySurvey of Precursors Of Category Theory
• https://inquiryintoinquiry.com/2025/05/05/survey-of-precursors-of-category-theory-6/#Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
#Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
#FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
#CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals -
Survey of Precursors Of Category Theory • 5
• https://inquiryintoinquiry.com/2024/05/24/survey-of-precursors-of-category-theory-5/A few years ago I began a sketch on the “Precursors of Category Theory”, tracing the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice. A Survey of resources on the topic is given below, still very rough and incomplete, but perhaps a few will find it of use.
Background —
Precursors Of Category Theory
• https://oeis.org/wiki/Precursors_Of_Category_TheoryPropositions As Types Analogy
• https://oeis.org/wiki/Propositions_As_Types_AnalogyBlog Series —
Notes On Categories
• https://inquiryintoinquiry.com/2013/02/22/notes-on-categories-1/Precursors Of Category Theory
1. https://inquiryintoinquiry.com/2013/12/20/precursors-of-category-theory-1/
2. https://inquiryintoinquiry.com/2013/12/30/precursors-of-category-theory-2/
3. https://inquiryintoinquiry.com/2014/01/03/precursors-of-category-theory-3/Precursors Of Category Theory • Discussion
1. https://inquiryintoinquiry.com/2020/09/13/precursors-of-category-theory-discussion-1/
2. https://inquiryintoinquiry.com/2020/09/21/precursors-of-category-theory-discussion-2/
3. https://inquiryintoinquiry.com/2020/09/25/precursors-of-category-theory-discussion-3/Categories à la Peirce —
C.S. Peirce • A Guess at the Riddle
• https://inquiryintoinquiry.com/2012/03/21/c-s-peirce-a-guess-at-the-riddle/Peirce's Categories
1. https://inquiryintoinquiry.com/2015/10/30/peirces-categories-1/
2. https://inquiryintoinquiry.com/2015/10/31/peirces-categories-2/
3. https://inquiryintoinquiry.com/2015/11/04/peirces-categories-3/
•••
19. https://inquiryintoinquiry.com/2020/05/13/peirces-categories-19/
20. https://inquiryintoinquiry.com/2020/05/14/peirces-categories-20/
21. https://inquiryintoinquiry.com/2020/06/25/peirces-categories-21/C.S. Peirce and Category Theory
1. https://inquiryintoinquiry.com/2021/06/23/c-s-peirce-and-category-theory-1/
2. https://inquiryintoinquiry.com/2021/06/24/c-s-peirce-and-category-theory-2/
3. https://inquiryintoinquiry.com/2021/06/27/c-s-peirce-and-category-theory-3/
4. https://inquiryintoinquiry.com/2021/06/28/c-s-peirce-and-category-theory-4/
5. https://inquiryintoinquiry.com/2021/06/29/c-s-peirce-and-category-theory-5/
6. https://inquiryintoinquiry.com/2021/06/30/c-s-peirce-and-category-theory-6/
7. https://inquiryintoinquiry.com/2021/07/01/c-s-peirce-and-category-theory-7/
8. https://inquiryintoinquiry.com/2021/07/02/c-s-peirce-and-category-theory-8/#Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
#Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
#FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
#CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals -
As the guinea pig of time meets the the celery stick of destiny I find my Sunday is in its final hours and the light of myopic wandering becomes the unlit path to the fumbling key in the lock of impermanence.
May your Sunday be / is / was a calming experience. #Sunday #analogy #analogies #what? -
Survey of Precursors Of Category Theory • 4
• http://inquiryintoinquiry.com/2023/08/01/survey-of-precursors-of-category-theory-4/A few years ago I began a sketch on the “Precursors of Category Theory”, tracing the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice. A Survey of resources on the topic is given below, still very rough and incomplete, but perhaps a few will find it of use.
Background —
Precursors Of Category Theory
• https://oeis.org/wiki/Precursors_Of_Category_TheoryPropositions As Types Analogy
• https://oeis.org/wiki/Propositions_As_Types_AnalogyBlog Series —
Notes On Categories
• https://inquiryintoinquiry.com/2013/02/22/notes-on-categories-1/Precursors Of Category Theory
1. https://inquiryintoinquiry.com/2013/12/20/precursors-of-category-theory-1/
2. https://inquiryintoinquiry.com/2013/12/30/precursors-of-category-theory-2/
3. https://inquiryintoinquiry.com/2014/01/03/precursors-of-category-theory-3/Precursors Of Category Theory • Discussion
1. https://inquiryintoinquiry.com/2020/09/13/precursors-of-category-theory-discussion-1/
2. https://inquiryintoinquiry.com/2020/09/21/precursors-of-category-theory-discussion-2/
3. https://inquiryintoinquiry.com/2020/09/25/precursors-of-category-theory-discussion-3/Categories à la Peirce —
C.S. Peirce • A Guess at the Riddle
• https://inquiryintoinquiry.com/2012/03/21/c-s-peirce-a-guess-at-the-riddle/Peirce's Categories
1. https://inquiryintoinquiry.com/2015/10/30/peirces-categories-1/
2. https://inquiryintoinquiry.com/2015/10/31/peirces-categories-2/
3. https://inquiryintoinquiry.com/2015/11/04/peirces-categories-3/
•••
19. https://inquiryintoinquiry.com/2020/05/13/peirces-categories-19/
20. https://inquiryintoinquiry.com/2020/05/14/peirces-categories-20/
21. https://inquiryintoinquiry.com/2020/06/25/peirces-categories-21/#Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
#Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
#FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
#CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals