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

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

Sign Relations, Triadic Relations, Relation Theory • Discussion 11
• https://inquiryintoinquiry.com/2023/09/12/sign-relations-triadic-relations-relation-theory-discussion-11/

Re: Michael Shapiro • Redefining Arbitrariness in Language
• https://languagelore.net/
• https://languagelore.net/2023/04/03/redefi-ning-arbitrariness-in-language/

<QUOTE MS:>
The matter of arbitrariness in language is primarily associated with the work of the Swiss linguist, Ferdinand de Saussure (1857–1913), whose book of lectures, Cours de linguistique Générale, is widely recognized to have laid the foundations of European structural linguistics in the twentieth century. One of Saussure's most quoted positions points out that the meaning of words is arbitrary, in that, for instance, the word “arbre” in French and its equivalent “tree” in English have nothing to do “naturally” with the object they signify. Any other sequence of sounds could in theory designate the same object. These are just the words French and English happen to have inherited from their history.
</QUOTE>

My Comment —

I prefer to think of the word “arbitrary” as reminding us how every aspect of a sign's functioning is relative to an arbiter, a judge, an interpreter. That brings semiology more into harmony with Peirce's semiotics — if only Saussure had realized how it embeds all dyadic sign relations within the fold of triadic sign relations!

#Peirce #Semiotics #Saussure #Semiology #Symbols #Symbolism
#SignRelation #TriadicRelation #RelationTheory #Arbitrarity

Survey of Relation Theory
• https://inquiryintoinquiry.com/2023/07/26/survey-of-relation-theory-7/

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 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 )
• 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/

Information‑Theoretic Perspective (Escape from Nominalism)

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

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
#RelationComposition #RelationConstruction #RelationReduction

Inquiry Into Inquiry • Discussion 6
• https://inquiryintoinquiry.com/2023/04/30/inquiry-into-inquiry-discussion-6/

Re: Nicole Rust
• https://mathstodon.xyz/@NicoleCRust@neuromatch.social/110197230713039748

❝Computations or Processes —
How do you think about the building blocks of the brain?❞

I keep coming back to this thread about levels, along with others on the related issue of paradigms, as those have long been major questions for me. I am trying to clarify my current understanding for a blog post. It will start out a bit like this —

A certain amount of “level” language is natural in the sciences but “level” metaphors come with hidden assumptions about higher and lower places in hierarchies which don't always fit the case at hand. In complex cases what look at first like parallel strata may in time be better comprehended as intersecting domains or mutually recursive and entangled orders of being. When that happens we can guard against misleading imagery by speaking of domains or realms instead of levels.

To be continued …

#Peirce #Logic #LogicalGraphs #DifferentialLogic #CactusLanguage
#Inquiry #InquiryDrivenSystem #InquiryIntoInquiry #NeuralNetwork
#Semiotics #RelationTheory #SignRelation #TriadicRelation #Model
#ObjectiveReality #MathematicalStructure #SymbolicRepresentation

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