Jon Awbrey<p>Peirce's 1885 “Algebra of Logic” • Selection 1.1<br />• <a href="https://inquiryintoinquiry.com/2024/03/24/peirces-1885-algebra-of-logic-selection-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/03</span><span class="invisible">/24/peirces-1885-algebra-of-logic-selection-1/</span></a></p><p>❝On the Algebra of Logic❞<br />❝A Contribution to the Philosophy of Notation❞</p><p>❝§1. Three Kinds Of Signs❞</p><p>❝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.</p><p>❝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”.]</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicOfRelatives" class="mention hashtag" rel="tag">#<span>LogicOfRelatives</span></a> <a href="https://mathstodon.xyz/tags/RelationTheory" class="mention hashtag" rel="tag">#<span>RelationTheory</span></a> <a href="https://mathstodon.xyz/tags/RelativeTerm" class="mention hashtag" rel="tag">#<span>RelativeTerm</span></a> <br /><a href="https://mathstodon.xyz/tags/MonadicRelation" class="mention hashtag" rel="tag">#<span>MonadicRelation</span></a> <a href="https://mathstodon.xyz/tags/DyadicRelation" class="mention hashtag" rel="tag">#<span>DyadicRelation</span></a> <a href="https://mathstodon.xyz/tags/TriadicRelation" class="mention hashtag" rel="tag">#<span>TriadicRelation</span></a> <a href="https://mathstodon.xyz/tags/SignRelation" class="mention hashtag" rel="tag">#<span>SignRelation</span></a> <br /><a href="https://mathstodon.xyz/tags/AlgebraOfLogic" class="mention hashtag" rel="tag">#<span>AlgebraOfLogic</span></a> <a href="https://mathstodon.xyz/tags/PredicateCalculus" class="mention hashtag" rel="tag">#<span>PredicateCalculus</span></a> <a href="https://mathstodon.xyz/tags/Quantification" class="mention hashtag" rel="tag">#<span>Quantification</span></a> <a href="https://mathstodon.xyz/tags/Semiotics" class="mention hashtag" rel="tag">#<span>Semiotics</span></a> <br /><a href="https://mathstodon.xyz/tags/RelationComposition" class="mention hashtag" rel="tag">#<span>RelationComposition</span></a> <a href="https://mathstodon.xyz/tags/RelationConstruction" class="mention hashtag" rel="tag">#<span>RelationConstruction</span></a> <a href="https://mathstodon.xyz/tags/RelationReduction" class="mention hashtag" rel="tag">#<span>RelationReduction</span></a></p>
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#RelationComposition
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Jon Awbrey<p>Survey of Relation Theory<br />• <a href="https://inquiryintoinquiry.com/2024/03/23/survey-of-relation-theory-8/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/03</span><span class="invisible">/23/survey-of-relation-theory-8/</span></a></p><p>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.</p><p>Please follow the above link for the full set of resources.<br />A few basic articles are linked below.</p><p>Relation Theory<br />• <a href="https://oeis.org/wiki/Relation_theory" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Relation_theory</span><span class="invisible"></span></a></p><p>Relation Composition<br />• <a href="https://oeis.org/wiki/Relation_composition" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Relation_composi</span><span class="invisible">tion</span></a></p><p>Relation Construction<br />• <a href="https://oeis.org/wiki/Relation_construction" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Relation_constru</span><span class="invisible">ction</span></a></p><p>Relation Reduction<br />• <a href="https://oeis.org/wiki/Relation_reduction" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Relation_reducti</span><span class="invisible">on</span></a></p><p>Relative Term<br />• <a href="https://oeis.org/wiki/Relative_term" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Relative_term</span><span class="invisible"></span></a></p><p>Sign Relation<br />• <a href="https://oeis.org/wiki/Sign_relation" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Sign_relation</span><span class="invisible"></span></a></p><p>Triadic Relation<br />• <a href="https://oeis.org/wiki/Triadic_relation" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Triadic_relation</span><span class="invisible"></span></a></p><p>Six Ways of Looking at a Triadic Relation ⌬ 1<br />• <a href="https://inquiryintoinquiry.com/2015/02/04/six-ways-of-looking-at-a-triadic-relation-%E2%8C%AC-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2015/02</span><span class="invisible">/04/six-ways-of-looking-at-a-triadic-relation-%E2%8C%AC-1/</span></a></p><p>Mathematical Demonstration and the Doctrine of Individuals<br />• <a href="https://inquiryintoinquiry.com/2023/05/16/mathematical-demonstration-and-the-doctrine-of-individuals-1-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/05</span><span class="invisible">/16/mathematical-demonstration-and-the-doctrine-of-individuals-1-a/</span></a><br />• <a href="https://inquiryintoinquiry.com/2023/05/16/mathematical-demonstration-and-the-doctrine-of-individuals-2-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/05</span><span class="invisible">/16/mathematical-demonstration-and-the-doctrine-of-individuals-2-a/</span></a></p><p>Peirce's 1870 “Logic of Relatives” —<br />• <a href="https://inquiryintoinquiry.com/2019/09/24/peirces-1870-logic-of-relatives-overview/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2019/09</span><span class="invisible">/24/peirces-1870-logic-of-relatives-overview/</span></a><br />• <a href="https://inquiryintoinquiry.com/2014/01/27/peirces-1870-logic-of-relatives-preliminaries/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2014/01</span><span class="invisible">/27/peirces-1870-logic-of-relatives-preliminaries/</span></a></p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicOfRelatives" class="mention hashtag" rel="tag">#<span>LogicOfRelatives</span></a> <a href="https://mathstodon.xyz/tags/RelationTheory" class="mention hashtag" rel="tag">#<span>RelationTheory</span></a> <a href="https://mathstodon.xyz/tags/RelativeTerm" class="mention hashtag" rel="tag">#<span>RelativeTerm</span></a> <br /><a href="https://mathstodon.xyz/tags/MonadicRelation" class="mention hashtag" rel="tag">#<span>MonadicRelation</span></a> <a href="https://mathstodon.xyz/tags/DyadicRelation" class="mention hashtag" rel="tag">#<span>DyadicRelation</span></a> <a href="https://mathstodon.xyz/tags/TriadicRelation" class="mention hashtag" rel="tag">#<span>TriadicRelation</span></a> <a href="https://mathstodon.xyz/tags/SignRelation" class="mention hashtag" rel="tag">#<span>SignRelation</span></a> <br /><a href="https://mathstodon.xyz/tags/PredicateCalculus" class="mention hashtag" rel="tag">#<span>PredicateCalculus</span></a> <a href="https://mathstodon.xyz/tags/ContinuousPredicate" class="mention hashtag" rel="tag">#<span>ContinuousPredicate</span></a> <a href="https://mathstodon.xyz/tags/HypostaticAbstraction" class="mention hashtag" rel="tag">#<span>HypostaticAbstraction</span></a> <br /><a href="https://mathstodon.xyz/tags/RelationComposition" class="mention hashtag" rel="tag">#<span>RelationComposition</span></a> <a href="https://mathstodon.xyz/tags/RelationConstruction" class="mention hashtag" rel="tag">#<span>RelationConstruction</span></a> <a href="https://mathstodon.xyz/tags/RelationReduction" class="mention hashtag" rel="tag">#<span>RelationReduction</span></a></p>
Jon Awbrey<p>Survey of Relation Theory<br />• <a href="https://inquiryintoinquiry.com/2023/07/26/survey-of-relation-theory-7/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/07</span><span class="invisible">/26/survey-of-relation-theory-7/</span></a></p><p>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.</p><p>Please follow the above link for the full set of resources.<br />A few basic articles are linked below.</p><p>Elements —<br />• Relation Theory ( <a href="https://oeis.org/wiki/Relation_theory" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Relation_theory</span><span class="invisible"></span></a> )</p><p>Relational Concepts —<br />• Relation Composition ( <a href="https://oeis.org/wiki/Relation_composition" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Relation_composi</span><span class="invisible">tion</span></a> )<br />• Relation Construction ( <a href="https://oeis.org/wiki/Relation_construction" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Relation_constru</span><span class="invisible">ction</span></a> )<br />• Relation Reduction ( <a href="https://oeis.org/wiki/Relation_reduction" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Relation_reducti</span><span class="invisible">on</span></a> )<br />• Relative Term ( <a href="https://oeis.org/wiki/Relative_term" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Relative_term</span><span class="invisible"></span></a> )<br />• Sign Relation ( <a href="https://oeis.org/wiki/Sign_relation" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Sign_relation</span><span class="invisible"></span></a> )<br />• Triadic Relation ( <a href="https://oeis.org/wiki/Triadic_relation" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Triadic_relation</span><span class="invisible"></span></a> )<br />• Logic of Relatives ( <a href="https://oeis.org/wiki/Logic_of_relatives" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Logic_of_relativ</span><span class="invisible">es</span></a> )<br />• Hypostatic Abstraction ( <a href="https://oeis.org/wiki/Hypostatic_abstraction" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Hypostatic_abstr</span><span class="invisible">action</span></a> )<br />• Continuous Predicate ( <a href="https://oeis.org/wiki/Continuous_predicate" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Continuous_predi</span><span class="invisible">cate</span></a> )</p><p>Illustrations —</p><p>Six Ways of Looking at a Triadic Relation ⌬ 1<br />• <a href="https://inquiryintoinquiry.com/2015/02/04/six-ways-of-looking-at-a-triadic-relation-%E2%8C%AC-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2015/02</span><span class="invisible">/04/six-ways-of-looking-at-a-triadic-relation-%E2%8C%AC-1/</span></a></p><p>Information‑Theoretic Perspective (Escape from Nominalism)</p><p>• Mathematical Demonstration and the Doctrine of Individuals<br />• <a href="https://inquiryintoinquiry.com/2023/05/16/mathematical-demonstration-and-the-doctrine-of-individuals-1-2/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/05</span><span class="invisible">/16/mathematical-demonstration-and-the-doctrine-of-individuals-1-2/</span></a><br />• <a href="https://inquiryintoinquiry.com/2023/05/16/mathematical-demonstration-and-the-doctrine-of-individuals-2-2/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/05</span><span class="invisible">/16/mathematical-demonstration-and-the-doctrine-of-individuals-2-2/</span></a></p><p>Peirce's 1870 “Logic of Relatives” —</p><p>Overview<br />• <a href="https://inquiryintoinquiry.com/2019/09/24/peirces-1870-logic-of-relatives-overview/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2019/09</span><span class="invisible">/24/peirces-1870-logic-of-relatives-overview/</span></a></p><p>Preliminaries<br />• <a href="https://inquiryintoinquiry.com/2014/01/27/peirces-1870-logic-of-relatives-preliminaries/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2014/01</span><span class="invisible">/27/peirces-1870-logic-of-relatives-preliminaries/</span></a> </p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicOfRelatives" class="mention hashtag" rel="tag">#<span>LogicOfRelatives</span></a> <a href="https://mathstodon.xyz/tags/RelationTheory" class="mention hashtag" rel="tag">#<span>RelationTheory</span></a> <a href="https://mathstodon.xyz/tags/RelativeTerm" class="mention hashtag" rel="tag">#<span>RelativeTerm</span></a><br /><a href="https://mathstodon.xyz/tags/MonadicRelation" class="mention hashtag" rel="tag">#<span>MonadicRelation</span></a> <a href="https://mathstodon.xyz/tags/DyadicRelation" class="mention hashtag" rel="tag">#<span>DyadicRelation</span></a> <a href="https://mathstodon.xyz/tags/TriadicRelation" class="mention hashtag" rel="tag">#<span>TriadicRelation</span></a> <a href="https://mathstodon.xyz/tags/SignRelation" class="mention hashtag" rel="tag">#<span>SignRelation</span></a><br /><a href="https://mathstodon.xyz/tags/RelationComposition" class="mention hashtag" rel="tag">#<span>RelationComposition</span></a> <a href="https://mathstodon.xyz/tags/RelationConstruction" class="mention hashtag" rel="tag">#<span>RelationConstruction</span></a> <a href="https://mathstodon.xyz/tags/RelationReduction" class="mention hashtag" rel="tag">#<span>RelationReduction</span></a></p>
Jon Awbrey<p>Logic Syllabus • 4<br />• <a href="https://inquiryintoinquiry.com/logic-syllabus/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/logic-s</span><span class="invisible">yllabus/</span></a></p><p>Relational Concepts<br />• <a href="https://oeis.org/wiki/Logic_Syllabus#Relational_concepts" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Logic_Syllabus#R</span><span class="invisible">elational_concepts</span></a></p><p>Continuous Predicate • <a href="https://oeis.org/wiki/Continuous_predicate" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Continuous_predi</span><span class="invisible">cate</span></a><br />Hypostatic Abstraction • <a href="https://oeis.org/wiki/Hypostatic_abstraction" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Hypostatic_abstr</span><span class="invisible">action</span></a><br />Logic of Relatives • <a href="https://oeis.org/wiki/Logic_of_relatives" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Logic_of_relativ</span><span class="invisible">es</span></a><br />Logical Matrix • <a href="https://oeis.org/wiki/Logical_matrix" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Logical_matrix</span><span class="invisible"></span></a><br />Relation • <a href="https://oeis.org/wiki/Relation" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Relation</span><span class="invisible"></span></a><br />Relation Composition • <a href="https://oeis.org/wiki/Relation_composition" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Relation_composi</span><span class="invisible">tion</span></a><br />Relation Construction • <a href="https://oeis.org/wiki/Relation_construction" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Relation_constru</span><span class="invisible">ction</span></a><br />Relation Reduction • <a href="https://oeis.org/wiki/Relation_reduction" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Relation_reducti</span><span class="invisible">on</span></a><br />Relation Theory • <a href="https://oeis.org/wiki/Relation_theory" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Relation_theory</span><span class="invisible"></span></a><br />Relative Term • <a href="https://oeis.org/wiki/Relative_term" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Relative_term</span><span class="invisible"></span></a><br />Sign Relation • <a href="https://oeis.org/wiki/Sign_relation" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Sign_relation</span><span class="invisible"></span></a><br />Triadic Relation • <a href="https://oeis.org/wiki/Triadic_relation" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Triadic_relation</span><span class="invisible"></span></a></p><p><a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicSyllabus" class="mention hashtag" rel="tag">#<span>LogicSyllabus</span></a> <a href="https://mathstodon.xyz/tags/ContinuousPredicate" class="mention hashtag" rel="tag">#<span>ContinuousPredicate</span></a> <a href="https://mathstodon.xyz/tags/HypostaticAbstraction" class="mention hashtag" rel="tag">#<span>HypostaticAbstraction</span></a> <a href="https://mathstodon.xyz/tags/LogicOfRelatives" class="mention hashtag" rel="tag">#<span>LogicOfRelatives</span></a><br /><a href="https://mathstodon.xyz/tags/LogicalMatrix" class="mention hashtag" rel="tag">#<span>LogicalMatrix</span></a> <a href="https://mathstodon.xyz/tags/Relation" class="mention hashtag" rel="tag">#<span>Relation</span></a> <a href="https://mathstodon.xyz/tags/RelationComposition" class="mention hashtag" rel="tag">#<span>RelationComposition</span></a> <a href="https://mathstodon.xyz/tags/RelationConstruction" class="mention hashtag" rel="tag">#<span>RelationConstruction</span></a> <a href="https://mathstodon.xyz/tags/RelationReduction" class="mention hashtag" rel="tag">#<span>RelationReduction</span></a><br /><a href="https://mathstodon.xyz/tags/RelationTheory" class="mention hashtag" rel="tag">#<span>RelationTheory</span></a> <a href="https://mathstodon.xyz/tags/RelativeTerm" class="mention hashtag" rel="tag">#<span>RelativeTerm</span></a> <a href="https://mathstodon.xyz/tags/SignRelation" class="mention hashtag" rel="tag">#<span>SignRelation</span></a> <a href="https://mathstodon.xyz/tags/TriadicRelation" class="mention hashtag" rel="tag">#<span>TriadicRelation</span></a></p>
Jon Awbrey<p>Survey of Relation Theory <br />• <a href="https://inquiryintoinquiry.com/2023/04/01/survey-of-relation-theory-6/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/04</span><span class="invisible">/01/survey-of-relation-theory-6/</span></a></p><p>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.</p><p>Please follow the above link for the full set of resources.<br />A few basic articles are linked below.</p><p>Elements —<br />• Relation Theory ( <a href="https://oeis.org/wiki/Relation_theory" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Relation_theory</span><span class="invisible"></span></a> )</p><p>Relational Concepts —<br />• Relation Construction ( <a href="https://oeis.org/wiki/Relation_construction" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Relation_constru</span><span class="invisible">ction</span></a> )<br />• Relation Composition ( <a href="https://oeis.org/wiki/Relation_composition" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Relation_composi</span><span class="invisible">tion</span></a> )<br />• Relation Reduction ( <a href="https://oeis.org/wiki/Relation_reduction" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Relation_reducti</span><span class="invisible">on</span></a> )<br />• Relative Term ( <a href="https://oeis.org/wiki/Relative_term" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Relative_term</span><span class="invisible"></span></a> )<br />• Sign Relation ( <a href="https://oeis.org/wiki/Sign_relation" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Sign_relation</span><span class="invisible"></span></a> )<br />• Triadic Relation ( <a href="https://oeis.org/wiki/Triadic_relation" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Triadic_relation</span><span class="invisible"></span></a> )<br />• Logic of Relatives ( <a href="https://oeis.org/wiki/Logic_of_relatives" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Logic_of_relativ</span><span class="invisible">es</span></a> )<br />• Hypostatic Abstraction ( <a href="https://oeis.org/wiki/Hypostatic_abstraction" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Hypostatic_abstr</span><span class="invisible">action</span></a> )<br />• Continuous Predicate ( <a href="https://oeis.org/wiki/Continuous_predicate" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Continuous_predi</span><span class="invisible">cate</span></a> )</p><p>Illustrations —</p><p>Six Ways of Looking at a Triadic Relation ⌬ 1<br />• <a href="https://inquiryintoinquiry.com/2015/02/04/six-ways-of-looking-at-a-triadic-relation-%E2%8C%AC-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2015/02</span><span class="invisible">/04/six-ways-of-looking-at-a-triadic-relation-%E2%8C%AC-1/</span></a></p><p>Peirce's 1870 “Logic of Relatives” —</p><p>Overview<br />• <a href="https://inquiryintoinquiry.com/2019/09/24/peirces-1870-logic-of-relatives-overview/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2019/09</span><span class="invisible">/24/peirces-1870-logic-of-relatives-overview/</span></a></p><p>Preliminaries<br />• <a href="https://inquiryintoinquiry.com/2014/01/27/peirces-1870-logic-of-relatives-preliminaries/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2014/01</span><span class="invisible">/27/peirces-1870-logic-of-relatives-preliminaries/</span></a></p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicOfRelatives" class="mention hashtag" rel="tag">#<span>LogicOfRelatives</span></a> <a href="https://mathstodon.xyz/tags/RelationTheory" class="mention hashtag" rel="tag">#<span>RelationTheory</span></a> <a href="https://mathstodon.xyz/tags/RelativeTerm" class="mention hashtag" rel="tag">#<span>RelativeTerm</span></a><br /><a href="https://mathstodon.xyz/tags/MonadicRelation" class="mention hashtag" rel="tag">#<span>MonadicRelation</span></a> <a href="https://mathstodon.xyz/tags/DyadicRelation" class="mention hashtag" rel="tag">#<span>DyadicRelation</span></a> <a href="https://mathstodon.xyz/tags/TriadicRelation" class="mention hashtag" rel="tag">#<span>TriadicRelation</span></a> <a href="https://mathstodon.xyz/tags/SignRelation" class="mention hashtag" rel="tag">#<span>SignRelation</span></a><br /><a href="https://mathstodon.xyz/tags/PredicateCalculus" class="mention hashtag" rel="tag">#<span>PredicateCalculus</span></a> <a href="https://mathstodon.xyz/tags/ContinuousPredicate" class="mention hashtag" rel="tag">#<span>ContinuousPredicate</span></a> <a href="https://mathstodon.xyz/tags/HypostaticAbstraction" class="mention hashtag" rel="tag">#<span>HypostaticAbstraction</span></a><br /><a href="https://mathstodon.xyz/tags/RelationComposition" class="mention hashtag" rel="tag">#<span>RelationComposition</span></a> <a href="https://mathstodon.xyz/tags/RelationConstruction" class="mention hashtag" rel="tag">#<span>RelationConstruction</span></a> <a href="https://mathstodon.xyz/tags/RelationReduction" class="mention hashtag" rel="tag">#<span>RelationReduction</span></a></p>
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