{"id":5670,"date":"2021-10-25T11:25:07","date_gmt":"2021-10-25T09:25:07","guid":{"rendered":"http:\/\/icar.cnrs.fr\/dicoplantin\/?p=5670"},"modified":"2025-08-12T10:46:01","modified_gmt":"2025-08-12T08:46:01","slug":"syllogism-e","status":"publish","type":"post","link":"https:\/\/icar.cnrs.fr\/dicoplantin\/syllogism-e\/","title":{"rendered":"Syllogism"},"content":{"rendered":"

SYLLOGISM<\/strong><\/span><\/h1>\n

In the Aristotelian world, the theory of the syllogism encompasses all reasoning, whether in science, dialectic or rhetoric<\/strong>. In science, that is, in logic, the syllogism is defined as<\/p>\n

an argument in which, certain things being laid down, something other than these necessarily comes about through them (Aristotle, Top<\/em>., I, 1).<\/p>\n

The classical syllogism is a discourse consisting of three propositions<\/a>, where \u201ccertain things being established\u201d are the premises<\/strong> of the syllogism, and \u201csomething other than these necessarily follows from them\u201d is the conclusion<\/strong>.<\/p>\n

Syllogistic inference involves two premises<\/span>, while immediate inference<\/strong> is based upon one premise<\/span>, see proposition<\/a>.<\/p>\n

The logic of the analyzed propositions concerns the conditions of validity of the syllogism. A valid<\/em> syllogism<\/strong> is one such that, if its premises are true<\/em>, its conclusion is necessarily true<\/em>. The premises of a syllogism cannot be true and its conclusion false.
\nThe conclusion of a syllogism need not be a necessary <\/em>truth, it’s a truth that necessarily<\/em> follows from the premises<\/em>.<\/p>\n

In Aristotle’s words, the syllogism, is a \u201cdemonstration<\/strong>\u201d,<\/p>\n

when the premises from which the reasoning starts are true and primary, or are such that our knowledge of them has originally come through premises which are primary and true\u201d (ibid.<\/em>).<\/span><\/p>\n

1. Terms of the Syllogism<\/span><\/h1>\n

The syllogism articulates three terms, the major<\/em> term T<\/strong>, the minor<\/em> term t<\/strong> and the middle<\/em> term M<\/strong>:<\/p>\n

\u2014\u00a0The major<\/em><\/span> term T <\/strong>is the predicate<\/em> of the conclusion.
\nThe premise containing the great term T<\/strong> is called the major premise<\/em>.<\/p>\n

\u2014\u00a0The minor<\/em><\/span> term t<\/strong> is the subject<\/em> of the conclusion.
\nThe premise containing the minor term t<\/strong> is called the minor premise<\/em>.<\/p>\n

\u2014\u00a0The middle<\/em><\/span> term M <\/strong>connects the major and the minor terms, and consequently disappears in the conclusion, which is of the form <\u00a0t<\/strong> is T<\/strong>\u00a0>.<\/p>\n

2. Figures of the Syllogism<\/span><\/h2>\n

The form of the syllogism varies according to the position (subject or predicate) of the middle term in the major and minor premises. There are 4 possibilities, which form the 4 figures<\/em><\/strong> of the syllogism, see figures<\/a>. For example, a syllogism in which the middle term is subject in the major premise and predicate in the minor premise is a syllogism of the first figure<\/strong>:<\/p>\n

Major Premise\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 M\u00a0–\u00a0T<\/strong> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 man-reasonable<\/span>
\nMinor Premise\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 t\u00a0–\u00a0M<\/strong> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 horse-man<\/span>
\nConclusion \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0 t\u00a0–\u00a0T<\/strong> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 horse-reasonable<\/span><\/p>\n

3. Modes of Syllogism<\/span><\/h2>\n

– The mode<\/em> of the syllogism depends on the quantity<\/em><\/strong> of the three propositions that make up the syllogism. A proposition can be universal<\/em> or particular<\/em>, affirmative<\/em> or negative<\/em>, giving a total of four<\/em> possibilities.
\n– Each of these four possibilities for the major premise can be combined with a minor premise, that also admits four possibilities, to give a conclusion that also admits four possibilities, for a total of 4 x 4 x 4 = 64 forms<\/strong>.
\n– Moreover, each of these forms admits the 4 figures<\/strong>, making a total of 256 modes<\/em>. Some of these modes are valid, others are not.<\/p>\n

For example, the first figure<\/em> of the syllogism corresponds to the case where, a universal conclusion is derived from two universal premises.<\/span> This deduction corresponds to the valid mode:<\/p>\n

Major Premise<\/em> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 All humans are rational
\nMinor Premise<\/em> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 All Greeks are human beings
\nConclusion<\/em> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 All Greeks are rational<\/p>\n

This mode is known as Barbara<\/em>, where the three occurrences of the vowel a<\/strong> mark that the major, minor and conclusion are universal, see proposition<\/a>.<\/p>\n

4. Example: The conclusive modes of the first figure<\/span><\/h2>\n

Syllogistic reasoning is clearly expressed in the language of set theory.
\n\u2014 Two (non-empty) sets are disjoint if their intersection is empty; they have no elements in common.
\n\u2014 Two sets intersect if they have some elements in common.
\n\u2014 One set is contained in the other if all the elements of the first set also belong to the second set.<\/p>\n

In the following, M<\/strong> will be read as \u201cset M<\/strong>\u201d, similarly for P<\/strong> and S<\/strong>. The first figure of the syllogism admits four conclusive modes.<\/p>\n

A – A – A syllogism<\/h3>\n

A<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 every M<\/strong> is P<\/strong>
\nA<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 all S<\/strong> are M<\/strong>
\nA<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 hence<\/em> all S<\/strong> are P.<\/strong><\/p>\n

A – I – I syllogism<\/h3>\n

A<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 every M<\/strong> is P
\n<\/strong>I<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 some S<\/strong> are M
\n<\/strong>I<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 hence<\/em> some S<\/strong> are P<\/strong><\/p>\n

E – A – E syllogism<\/h3>\n

E<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 no M<\/strong> is P
\n<\/strong>A<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 all S<\/strong> are M
\n<\/strong>E<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 therefore<\/em> no S<\/strong> is P<\/strong><\/p>\n

E – I – O syllogism<\/h3>\n

E<\/strong> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 no M<\/strong> is P
\n<\/strong>I <\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 some S<\/strong> is M
\n<\/strong>O<\/strong> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 therefore<\/em> some S<\/strong> is not P<\/strong><\/p>\n

These basic forms of reasoning are used in classification, \u00a73<\/a>, Syllogistic reasoning about natural taxonomies.<\/p>\n

5. Evaluation of syllogisms <\/span><\/h1>\n

See <\/span>Paralogisms<\/span><\/span><\/a><\/span><\/p>\n

6. Syllogisms with premise(s) having a concrete subject<\/span><\/h1>\n

The above definitions correspond to the traditional (Aristotelian) categorical syllogism, using quantified variables.
\nThe word syllogism<\/em> is also used to refer to a form of reasoning in which a premise has a concrete<\/em> subject<\/em>. A concrete subject is a subject that refers to a unique single individual, by means of various expressions such as this<\/em>, this being<\/em>, Peter<\/em>, the N who<\/em>.<\/p>\n

Syllogisms that instantiate a universal proposition are examples of such syllogisms. These assign to an individual the properties of the class to which it belongs:<\/p>\n\n\n\n\n\n
the x<\/strong>-s are B <\/strong><\/td>\n\u00a0human beings have a right to respect<\/td>\n<\/tr>\n
this is an x<\/strong><\/td>\nthis man is a human being<\/td>\n<\/tr>\n
this is B<\/strong><\/td>\nthis man deserves respect<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The following type of reasoning is based on two concrete propositions. It can also be called, rather metaphorically, \u201csyllogistic\u201d. It disproves universal propositions like as \u201call swans are white<\/em>\u201d, see proof by fact.<\/a><\/p>\n

This is a swan \u00a0\u00a0\u00a0\u00a0 the proposition refers to a concrete individual
\n<\/em>This is black \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 the proposition attaches a property to the same individual
\n<\/em>Applied to the same subject, \u201cto be black\u201d and \u201cto be white\u201d are opposite<\/a><\/em> predicates
\n<\/em>Therefore the claim \u201call the swans are white<\/em>\u201d is false.<\/span><\/p>\n

7. Syllogistic Forms<\/span><\/span><\/h1>\n

A polysyllogism, <\/strong>is \u00ab\u00a0a series of syllogisms connected in such a way that the conclusion of one serves as a premise for the next.\u00a0\u00bb (Chenique 1975, p. 255). The polysyllogism is also called a logical <\/strong>sorite<\/strong>.<\/a>
\nThe term sorite<\/em> can also applies to an abbreviated polysyllogism<\/strong><\/em> \u201cin which the conclusion of each syllogism is not expressed, except in the last one\u201d (Chenique 1975, pp. 256-257).<\/p>\n

In the polysyllogism stricto sensu, the rules of syllogism apply at each step; the previous conclusion enters as a premise in the following one, and a new premise is introduced, that allows the reasoning to continue. The transmission of the truth is flawless, from the first argument to the final conclusion.<\/p>\n

A chain of propositions whose syntactic form and mode of linking more or less imitate those of a syllogism may also be called a syllogism, with more or less justification; see expression; linked argument; epicheirema<\/a><\/p>\n

The famous syllogism \u201cEverything rare is expensive, a cheap horse is a rare thing, so a cheap horse is expensive<\/em>\u201d is based on two contradictory premises, so it is natural that its conclusion is absurd.<\/p>\n","protected":false},"excerpt":{"rendered":"

SYLLOGISM In the Aristotelian world, the theory of the syllogism encompasses all reasoning, whether in science, dialectic or rhetoric. In science, that is, in logic, the syllogism is defined as an argument in which, certain things being laid down, something other than these necessarily comes about through them (Aristotle, Top., I, 1). The classical syllogism […]<\/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-5670","post","type-post","status-publish","format-standard","hentry","category-non-classe"],"_links":{"self":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/5670","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=5670"}],"version-history":[{"count":16,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/5670\/revisions"}],"predecessor-version":[{"id":14672,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/5670\/revisions\/14672"}],"wp:attachment":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/media?parent=5670"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/categories?post=5670"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/tags?post=5670"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}