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_Theory

Propositions As Types Analogy
• https://oeis.org/wiki/Propositions_As_Types_Analogy

Blog 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

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

#FunctionalLogic • #Inquiry and #Analogy

Richard Kunstwadl comments —
• https://www.academia.edu/s/2970b92e1f?source=work#comment_1302356

“Would you agree if we reflect a schema, in the way operational handling is done in the form, we build a dialectics through the way we transfer knowledge!? And that this correlation of dialectics and transfer is traditionally done by analogy!”

#Peirce #Information #Anomaly #Paradigm
#Logic #Abduction #Deduction #Induction

#FunctionalLogic • #Inquiry and #Analogy
• https://www.academia.edu/s/2970b92e1f?source=mathstodon

This report discusses C.S. #Peirce's treatment of analogy, placing it in relation to his overall theory of inquiry. We begin by introducing three basic types of reasoning Peirce adopted from classical logic. In Peirce's analysis both inquiry and analogy are complex programs of logical inference which develop through stages of these three types, although normally in different orders.

#Logic #Abduction #Deduction #Induction

#FunctionalLogic • #Inquiry and #Analogy
• https://www.academia.edu/s/2970b92e1f

This report discusses C.S. #Peirce's treatment of analogy, placing it in relation to his overall theory of inquiry. We begin by introducing three basic types of reasoning Peirce adopted from classical logic. In Peirce's analysis both inquiry and analogy are complex programs of logical Inference which develop through stages of these three types, although normally in different orders.

#Logic #Abduction #Deduction #Induction