Foundations of Mathematics | Systems Community of Inquiry

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

Blog Series

Notes On Categories • (1)
Precursors Of Category Theory • (1) • (2) • (3) • (4) • (5) • (6)

Discussions • (1) • (2) • (3)

Categories à la Peirce

C.S. Peirce • A Guess at the Riddle

Peirce’s Categories • (1) • (2) • (3) • (4) • (5) • (6) • (7) • (8) • (9) • (10) • (11) • (12) • (13) • (14) • (15) • (16) • (17) • (18) • (19) • (20) • (21)

C.S. Peirce and Category Theory • (1) • (2) • (3) • (4) • (5) • (6) • (7) • (8)

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

#abstraction, #ackermann, #analogy, #aristotle, #c-s-peirce, #carnap, #category-theory, #foundations-of-mathematics, #hilbert, #hypostatic-abstraction, #kant, #logic, #mathematics, #propositions-as-types-analogy, #relation-theory, #saunders-mac-lane, #semiotics, #type-theory, #universals

In the present Survey of blog and wiki resources for 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.

Elements

Relation Theory

Relational Concepts

Relation Composition	Relation Construction	Relation Reduction
Relative Term	Sign Relation	Triadic Relation
Logic of Relatives	Hypostatic Abstraction	Continuous Predicate

Illustrations

Six Ways of Looking at a Triadic Relation ⌬ 1

Information‑Theoretic Perspective

Mathematical Demonstration and the Doctrine of Individuals • (1) • (2)

Blog Series

Logic of Relatives

Relation Theory • (1) • (2) • (3) • (4) • (5) • (6)

Discussions • (1) • (2) • (3) • (4) • (5)

Relations & Their Relatives • (1) • (2) • (3) • (4)

Comments • (1) • (2) • (3)
Discussions • (1) • (2) • (3) • (4) • (5) • (6) • (7) • (8) • (9) • (10) • (11) • (12) • (13) • (14) • (15) • (16) • (17) • (18) • (19) • (20) • (21) • (22) • (23) • (24) • (25)