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.

Elements

• Relation Theory

Relational Concepts

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)
• 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)
• Reviews • (1)

• Triadic Relations • Preamble
• Examples • Mathematics • Semiotics

• Triadic Relations • (1) • (2) • (3)
• Discussions • (1) • (2) • (3)

Peirce’s 1870 “Logic of Relatives”

• Overview
• Preliminaries
• Selection 1 • Use of the Letters
• Selection 2 • Numbers Corresponding to Letters
• Selection 3 • The Signs of Inclusion, Equality, Etc.
• Selection 4 • The Signs for Addition
• Selection 5 • The Signs for Multiplication
• Selection 6 • The Signs for Multiplication (cont.)
  • Comment 6.1 • Sets as Sums
• Selection 7 • The Signs for Multiplication (cont.)
  • Comment 7.1 • Proto-Graphical Syntax
• Selection 8 • The Signs for Multiplication (cont.)
  • Comment 8.1
  • Comment 8.2
  • Comment 8.3
  • Comment 8.4
  • Comment 8.5
  • Comment 8.6
• Selection 9 • The Signs for Multiplication (cont.)
  • Comment 9.1
  • Comment 9.2
  • Comment 9.3
  • Comment 9.4
  • Comment 9.5
  • Comment 9.6
  • Comment 9.7
• Selection 10 • The Signs for Multiplication (cont.)
  • Comment 10.1
  • Comment 10.2
  • Comment 10.3
  • Comment 10.4
  • Comment 10.5
  • Comment 10.6
  • Comment 10.7
  • Comment 10.8
  • Comment 10.9
  • Comment 10.10
  • Comment 10.11
  • Comment 10.12
• Selection 11 • The Signs for Multiplication (concl.)
  • Comment 11.1
  • Comment 11.2
  • Comment 11.3
  • Comment 11.4
  • Comment 11.5
  • Comment 11.6
  • Comment 11.7
  • Comment 11.8
  • Comment 11.9
  • Comment 11.10
  • Comment 11.11
  • Comment 11.12
  • Comment 11.13
  • Comment 11.14
  • Comment 11.15
  • Comment 11.16
  • Comment 11.17
  • Comment 11.18
  • Comment 11.19
  • Comment 11.20
  • Comment 11.21
  • Comment 11.22
  • Comment 11.23
  • Comment 11.24
• Selection 12 • The Sign of Involution
• Comment 12.1
• Comment 12.2
• Comment 12.3
• Comment 12.4
• Comment 12.5
• Intermezzo
• Comments • (1) • (2) • (3)
• Discussions • (1) • (2) • (3) • (4) • (5)

Peirce’s 1880 “Algebra of Logic” Chapter 3

• Preliminaries
• Selections • (1) • (2) • (3) • (4) • (5) • (6) • (7) • (8)
• Comments • (7.1) • (7.2) • (7.3) • (7.4) • (7.5)

Resources

• Peirce’s 1870 Logic of Relatives

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