{"id":5364,"date":"2021-10-23T10:13:54","date_gmt":"2021-10-23T08:13:54","guid":{"rendered":"http:\/\/icar.cnrs.fr\/dicoplantin\/?p=5364"},"modified":"2025-05-11T14:42:05","modified_gmt":"2025-05-11T12:42:05","slug":"proportion-and-proportionality-e","status":"publish","type":"post","link":"https:\/\/icar.cnrs.fr\/dicoplantin\/proportion-and-proportionality-e\/","title":{"rendered":"Proportion and Proportionality"},"content":{"rendered":"

The argument of PROPORTION <\/span><\/h1>\n

1. Argument based on proportion<\/strong><\/span><\/p>\n

1.1 Proportion
\n<\/span><\/h3>\n

A relation<\/em><\/strong> is a stable association between two things:<\/p>\n

shell : fish <\/span>
\nglove : hand <\/span>
\nleader : group<\/span>
\nold age : life<\/span><\/p>\n

There is a relation of proportionality<\/strong> between two pairs of things if these two pairs are connected by the same or a similar relation in their respective fields.
\nA proportion<\/em><\/strong> [1] is an equality (an equivalence) between relations<\/em>; it implies at least four terms.<\/p>\n\n\n\n\n
Domain A<\/strong><\/td>\nDomain B<\/strong><\/td>\nSAME RELATION<\/strong><\/td>\n<\/tr>\n
shell : fish
\nglove : hand
\nleader : group
\nold age : life<\/td>\n		feather : bird
\nshoe : foot
\ncaptain : ship
\nevening : day<\/td>\n		A<\/strong> covers the body of<\/em> B<\/strong>
\nA protects<\/em> B
\nA guides B<\/em>
\nA is the last moment of B<\/em><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The relationship A<\/strong> between shell and fish, is identical (similar) to the relationship B<\/strong> between feather and bird.<\/em>
\nShells are to fish what feathers are to birds<\/em>.<\/span><\/p>\n

In arithmetic<\/strong> a proportion is a relationship between two numbers. 3\/6, 1\/2, 50\/100, etc. express the same proportion.
\nThe equality of proportion corresponds to a first degree equation, with one unknown. This equation corresponds to the \u00ab\u00a0rule of three\u00a0\u00bb: a\/b = x\/c, from which ac = bx and x = ac\/b – Three eggs cost \u20ac1.20, how much do four eggs cost?<\/em><\/p>\n

In geometry<\/strong>, we talk about similarity of shape. Two similar figures have the same shape but different sizes. Two similar triangles have the same angles and proportional sides.<\/p>\n

1.2 P<\/strong>roportional a<\/strong>rgument<\/strong><\/span><\/h3>\n

This argument uses the analogy of proportion through mechanisms of parallelism:<\/p>\n

(Since) a ship needs a pilot, every group needs a leader!<\/em><\/span>
\nPilot: Ship = X : Group: <\/span>
\nWho is the pilot in a group?<\/em> \u2014 The leader!<\/em><\/span><\/p>\n

The process of understanding is the same in the case of mathematics as it is in argumentation. The reasoning that mathematically extracts the value of \u2018x\u2019 from the arithmetic proportion is the same as the argument that extracts the necessity of a leader for a group from the analogy between a ship\u2019s crew and a group of people.<\/p>\n

1.3 Metaphor and analogy of proportion<\/span> <\/span><\/h2>\n

In the Poetics<\/em>, Aristotle defines metaphor as the application to a thing of a name foreign to it, by a shift from genus to species, from species to genus, from species to genus, or according to a relation of analogy. (Trans. Magnien, p. 139). The \u00ab\u00a0relation of analogy\u00a0\u00bb is defined using examples of proportional metaphors<\/a>:<\/p>\n

A cup has the same relation to Dionysus as a shield has to Ares. So we would say that the cup is \u00ab\u00a0the shield of Dionysus<\/span>\u00a0\u00bb and that the shield is \u00ab\u00a0the cup of Ares<\/span>. <\/span>
\nOr again, old age has the same relation to life as the evening has to the day, so that we can say that the evening is \u00ab\u00a0the old age of the day<\/span>\u00a0\u00bb and old age […] is \u00ab\u00a0the evening of life<\/span>\u00a0\u00bb or \u00ab\u00a0the twilight of life\u00a0\u00bb. (Id., p. 140)<\/span><\/p>\n

1.4 Destruction of the Proportional Analogy<\/strong><\/span><\/h3>\n

The basic form \u00ab\u00a0An A<\/strong> without a B<\/strong> is like an X<\/strong> without a Y<\/strong><\/em>\u00a0\u00bb can be used to destroy the argument based on this proportional analogy:<\/p>\n

L1 – A group without a leader is like a ship without a pilot.<\/em><\/span>
\nL2 – Yes, and a woman without a man is like a fish without a bicycle (a feminist slogan).<\/em><\/span><\/p>\n

2. Proportionate measure<\/strong> <\/span><\/h2>\n

The idea of proportionate measure has two Latin names:
\n– Argument ad modum<\/em>, from modus<\/em> \u00ab\u00a0measure\u00a0\u00bb
\n– Arg. ad temperentiam, from temperentia, \u00ab\u00a0just measure, just proportion\u00a0\u00bb.<\/p>\n

The argument of proportionate measure justifies a rule by affirming that it is reasonable, balanced, and modifiable according to the evolution of its object.<\/span>
\nThis argument assumes that there is a graduated scale of the severity of the riots (domain A) and a corresponding graduated scale of the severity of the repression (domain B), depending on the severity of the riots. The idea of proportion corresponds to the covariance on these two scales.<\/p>\n

The more\/less the demonstration \u00ab\u00a0endangers the security of the state, the citizens, their property…\u00a0\u00bb.<\/span>
\nThe more\/less repression is to be expected.<\/span><\/p>\n

A judicial system that is not proportional<\/span> would apply the same punishment to all offenders.
\nA judicial system that is not proportionate<\/span> would not take into account the circumstances of the criminal act.<\/p>\n

The argument of proportionality is invoked a contrario in the recurring press release:<\/p>\n

The association,( the union, the government…) condemns the disproportionate use of force.<\/em><\/span><\/p>\n

<\/h3>\n

Flexing one’s muscles means announcing severe repression and, by applying the law of proportionality, proclaiming the strength of the enemy.
\nConsider a situation of unrest described as the work of a few isolated troublemakers. According to the principle of proportionate repression, it is expected that ordinary repressive measures will suffice: a relatively harmless demonstration: light repression.
\nHowever, the authorities decided to organize a large military show to \u00ab\u00a0impress the enemy\u00a0\u00bb and \u00ab\u00a0reassure the population\u00a0\u00bb.<\/p>\n

The argument of proportionate action allows for a calculation that defeats this psychological strategy:<\/p>\n

Far from diminishing the enemy, the show of force made him appear larger.
\nPierre Miquel, La guerre d’Alg\u00e9rie<\/em>, 1993[2]\n

The conclusion is based on the topos: \u00ab\u00a0You don’t fire a cannon at flies<\/em>\u00ab\u00a0; if we were really dealing with a few isolated hotheads, we wouldn’t be positioning tanks in front of official buildings. So this is a real popular uprising.
\nThis paradox<\/a> can be found in the case of a strong refutation of a position declared to be weak.<\/p>\n

The proportionate measure is a form of argument about the just measure, which can also be defined as the middle measure.<\/p>\n

\n[1] Latin proportio<\/em>, \u00ab\u00a0proportion; analogy\u00a0\u00bb. The. Latin word translates the Greek analogia<\/em> [\u1f00\u03bd\u03b1\u03bb\u03bf\u03b3\u03af\u03b1] \u00ab\u00a01. Mathematical proportion 2. Correspondence, analogy\u00a0\u00bb (Bailly \u1f00\u03bd\u03b1\u03bb\u03bf\u03b3\u03af\u03b1)<\/p>\n[2] Paris, Fayard, p. 190.<\/p>\n","protected":false},"excerpt":{"rendered":"

The argument of PROPORTION 1. Argument based on proportion 1.1 Proportion A relation is a stable association between two things: shell : fish glove : hand leader : group old age : life There is a relation of proportionality between two pairs of things if these two pairs are connected by the same or a […]<\/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-5364","post","type-post","status-publish","format-standard","hentry","category-non-classe"],"_links":{"self":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/5364","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=5364"}],"version-history":[{"count":13,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/5364\/revisions"}],"predecessor-version":[{"id":14243,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/5364\/revisions\/14243"}],"wp:attachment":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/media?parent=5364"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/categories?post=5364"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/tags?post=5364"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}