#monadicrelation — Public Fediverse posts on home.social

Jon Awbrey @[email protected] · 2024-03-25 · 13:00 UTC

Peirce's 1885 “Algebra of Logic” • Selection 1.1
• https://inquiryintoinquiry.com/2024/03/24/peirces-1885-algebra-of-logic-selection-1/

❝On the Algebra of Logic❞
❝A Contribution to the Philosophy of Notation❞

❝§1. Three Kinds Of Signs❞

❝Any character or proposition either concerns one subject, two subjects, or a plurality of subjects. For example, one particle has mass, two particles attract one another, a particle revolves about the line joining two others. A fact concerning two subjects is a dual character or relation; but a relation which is a mere combination of two independent facts concerning the two subjects may be called “degenerate”, just as two lines are called a degenerate conic. In like manner a plural character or conjoint relation is to be called degenerate if it is a mere compound of dual characters.

❝A sign is in a conjoint relation to the thing denoted and to the mind. If this triple relation is not of a degenerate species, the sign is related to its object only in consequence of a mental association, and depends upon a habit. Such signs are always abstract and general, because habits are general rules to which the organism has become subjected. They are, for the most part, conventional or arbitrary. They include all general words, the main body of speech, and any mode of conveying a judgment. For the sake of brevity I will call them “tokens”.❞ [Note. Peirce more frequently calls these “symbols”.]

#Peirce #Logic #LogicOfRelatives #RelationTheory #RelativeTerm
#MonadicRelation #DyadicRelation #TriadicRelation #SignRelation
#AlgebraOfLogic #PredicateCalculus #Quantification #Semiotics
#RelationComposition #RelationConstruction #RelationReduction

#relationreduction #relationconstruction #relationcomposition #semiotics #quantification #predicatecalculus

Jon Awbrey @[email protected] · 2024-03-23 · 18:15 UTC

Survey of Relation Theory
• https://inquiryintoinquiry.com/2024/03/23/survey-of-relation-theory-8/

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.

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

Relation Theory
• https://oeis.org/wiki/Relation_theory

Relation Composition
• https://oeis.org/wiki/Relation_composition

Relation Construction
• https://oeis.org/wiki/Relation_construction

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

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/

Mathematical Demonstration and the Doctrine of Individuals
• https://inquiryintoinquiry.com/2023/05/16/mathematical-demonstration-and-the-doctrine-of-individuals-1-a/
• https://inquiryintoinquiry.com/2023/05/16/mathematical-demonstration-and-the-doctrine-of-individuals-2-a/

Peirce's 1870 “Logic of Relatives” —
• https://inquiryintoinquiry.com/2019/09/24/peirces-1870-logic-of-relatives-overview/
• 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

#relationreduction #relationconstruction #relationcomposition #hypostaticabstraction #continuouspredicate #predicatecalculus

Jon Awbrey @[email protected] · 2023-04-16 · 17:00 UTC

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 )