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

Logic Syllabus • 4
• https://inquiryintoinquiry.com/logic-syllabus/

Relational Concepts
• https://oeis.org/wiki/Logic_Syllabus#Relational_concepts

Continuous Predicate • https://oeis.org/wiki/Continuous_predicate
Hypostatic Abstraction • https://oeis.org/wiki/Hypostatic_abstraction
Logic of Relatives • https://oeis.org/wiki/Logic_of_relatives
Logical Matrix • https://oeis.org/wiki/Logical_matrix
Relation • https://oeis.org/wiki/Relation
Relation Composition • https://oeis.org/wiki/Relation_composition
Relation Construction • https://oeis.org/wiki/Relation_construction
Relation Reduction • https://oeis.org/wiki/Relation_reduction
Relation Theory • https://oeis.org/wiki/Relation_theory
Relative Term • https://oeis.org/wiki/Relative_term
Sign Relation • https://oeis.org/wiki/Sign_relation
Triadic Relation • https://oeis.org/wiki/Triadic_relation

#Logic #LogicSyllabus #ContinuousPredicate #HypostaticAbstraction #LogicOfRelatives
#LogicalMatrix #Relation #RelationComposition #RelationConstruction #RelationReduction
#RelationTheory #RelativeTerm #SignRelation #TriadicRelation

Survey of Relation Theory
• https://inquiryintoinquiry.com/2023/04/01/survey-of-relation-theory-6/

In this Survey of blog and wiki posts on Relation Theory, relations are viewed from the perspective of combinatorics, in other words, as a topic in discrete mathematics, with special attention to finite structures and concrete set-theoretic constructions, many of which arise quite naturally in applications. This approach to relation theory is distinct from, though closely related to, its study from the perspectives of abstract algebra on the one hand and formal logic on the other.

Please follow the above link for the full set of resources.
A few basic articles are linked below.

Elements —
• Relation Theory ( https://oeis.org/wiki/Relation_theory )

Relational Concepts —
• Relation Construction ( https://oeis.org/wiki/Relation_construction )
• Relation Composition ( https://oeis.org/wiki/Relation_composition )
• Relation Reduction ( https://oeis.org/wiki/Relation_reduction )
• Relative Term ( https://oeis.org/wiki/Relative_term )
• Sign Relation ( https://oeis.org/wiki/Sign_relation )
• Triadic Relation ( https://oeis.org/wiki/Triadic_relation )
• Logic of Relatives ( https://oeis.org/wiki/Logic_of_relatives )
• Hypostatic Abstraction ( https://oeis.org/wiki/Hypostatic_abstraction )
• Continuous Predicate ( https://oeis.org/wiki/Continuous_predicate )

Illustrations —

Six Ways of Looking at a Triadic Relation ⌬ 1
• https://inquiryintoinquiry.com/2015/02/04/six-ways-of-looking-at-a-triadic-relation-%E2%8C%AC-1/

Peirce's 1870 “Logic of Relatives” —

Overview
• https://inquiryintoinquiry.com/2019/09/24/peirces-1870-logic-of-relatives-overview/

Preliminaries
• https://inquiryintoinquiry.com/2014/01/27/peirces-1870-logic-of-relatives-preliminaries/

#Peirce #Logic #LogicOfRelatives #RelationTheory #RelativeTerm
#MonadicRelation #DyadicRelation #TriadicRelation #SignRelation
#PredicateCalculus #ContinuousPredicate #HypostaticAbstraction
#RelationComposition #RelationConstruction #RelationReduction