{"id":5391,"date":"2021-10-23T11:45:43","date_gmt":"2021-10-23T09:45:43","guid":{"rendered":"http:\/\/icar.cnrs.fr\/dicoplantin\/?p=5391"},"modified":"2025-05-12T18:34:39","modified_gmt":"2025-05-12T16:34:39","slug":"relation-e","status":"publish","type":"post","link":"https:\/\/icar.cnrs.fr\/dicoplantin\/relation-e\/","title":{"rendered":"Relation"},"content":{"rendered":"

RELATIONS<\/span><\/h1>\n

A relation is a two-place predicate R<\/strong> that associates two objects, a<\/strong> and b. <\/strong>This is denoted by \u201caR<\/strong>b\u201d. Relations are characterized by three general properties, symmetry<\/em>, transitivity<\/em>, and reflexivity<\/em>:<\/p>\n

– Symmetry, or reciprocity<\/em>: The same relationship holds between a<\/strong> and b<\/strong> and b <\/strong>and a<\/strong>.
\n– Reflexivity<\/em>: The relationship connects an object to itself.
\n– Transitivity<\/em>: The relationship connecting a<\/strong> to b<\/strong> and b<\/strong> to c<\/strong> also connects a<\/strong> to c<\/strong>.<\/p>\n

1. Symmetry, or reciprocity<\/span><\/h1>\n

A relation is symmetric <\/span><\/em>or reciprocal<\/em><\/a> if it relates both a<\/strong> to b<\/strong> and b<\/strong> to a<\/strong>.
\nIn other words, both \u201caRb<\/strong>\u201d and \u201cbRa<\/strong>\u201d hold.<\/span>
\nIf a<\/strong> loves b<\/strong>, b<\/strong> does not necessarily love a<\/strong>: a love relationship is not symmetrical.
\n\u201cMeeting<\/em>\u201d is a symmetric relationship. The following argument is no more or less logical than any other, but it would be a valid point in a detective novel. It can only be rejected by accusing Peter of lying.<\/p>\n

If Peter confessed to meeting Paul at the bar, then we must assume that Paul met Peter. Paul cannot deny the obvious.<\/p>\n

2. Reflexivity<\/span><\/h1>\n

A reflexive<\/em> relation relates a being to itself. It is noted \u201caRa<\/strong>\u201d.<\/span>
\n\u201c\u2014 Being contemporary of \u2014<\/em>\u201d is a reflexive relationship: a<\/strong> is his own strict contemporary.
\nFor the average person, the causal relationship is not reflexive. Only God is causa sui<\/em>, his own cause.<\/p>\n

The reflexive relation can be used ad hominem<\/em><\/a>. For example, the principle \u201ccharity begins at home<\/em>\u201d for example forces the reflexivity of the relationship \u201ca<\/strong> makes charity to b<\/strong>\u201d. Nevertheless, the love of others can be used to encourage self-care:<\/p>\n

If you love all humanity, then you should try to love yourself as well!<\/span><\/p>\n

A counselor’s competence can be challenged by inviting them to make a reflexive use of their talents:<\/p>\n

Doctor, heal thyself!<\/span><\/p>\n

Such replies correspond to the ad hominem<\/em> variety, setting up practices against words.<\/p>\n

3. Transitivity<\/span><\/h1>\n

A relation is transitive if, when it connects a<\/strong> to b<\/strong> and b<\/strong> to c<\/strong>, then it also connects a<\/strong> to c<\/strong>.<\/span>
\nIn other words, \u201caRb<\/strong> and bRc<\/strong>\u201d implies that \u201caRc<\/strong>\u201d.<\/p>\n

However if a<\/strong> loves b<\/strong>, and if b<\/strong> loves c<\/strong>, then a<\/strong> does not necessarily love c.<\/strong> Thus a relationship of love is not transitive.
\nThe relation \u201cbeing the father of <\/em>\u201d is not transitive, but \u201cbeing an ancestor of<\/em>\u201d is transitive. If a<\/strong> is an ancestor of b<\/strong> and if b<\/strong> is an ancestor of c<\/strong>, then a<\/strong> is an ancestor of c<\/strong>.<\/p>\n

These inferences based on the transitivity of a predicate apply whenever at least three objects are positioned on a graduated scale.<\/p>\n

If a<\/strong> is bigger, older, richer … than b
\n<\/strong>and b<\/strong> larger, older, richer … than c<\/strong>,<\/span>
\nThen a is bigger, older, richer … than c<\/strong>.<\/span><\/p>\n

These inferences are part of the unnoticed evidence exploited by everyday reasoning and argument. They are sometimes considered to be \u201cquasi-logical\u201d, see quasi-logic<\/a>; but being\u00a0sound and valid<\/em> does not preclude being an argument<\/em>.<\/p>\n

4. Conversion<\/span><\/h1>\n

S. Conversion<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

RELATIONS A relation is a two-place predicate R that associates two objects, a and b. This is denoted by \u201caRb\u201d. Relations are characterized by three general properties, symmetry, transitivity, and reflexivity: – Symmetry, or reciprocity: The same relationship holds between a and b and b and a. – Reflexivity: The relationship connects an object to […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-5391","post","type-post","status-publish","format-standard","hentry","category-non-classe"],"_links":{"self":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/5391","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/comments?post=5391"}],"version-history":[{"count":15,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/5391\/revisions"}],"predecessor-version":[{"id":14278,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/5391\/revisions\/14278"}],"wp:attachment":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/media?parent=5391"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/categories?post=5391"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/tags?post=5391"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}