{"id":5318,"date":"2021-10-22T18:51:24","date_gmt":"2021-10-22T16:51:24","guid":{"rendered":"http:\/\/icar.cnrs.fr\/dicoplantin\/?p=5318"},"modified":"2025-05-09T16:02:12","modified_gmt":"2025-05-09T14:02:12","slug":"5318-2","status":"publish","type":"post","link":"https:\/\/icar.cnrs.fr\/dicoplantin\/5318-2\/","title":{"rendered":"Paralogism"},"content":{"rendered":"

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

In classical Aristotelian logic, a paralogism is defined as an invalid syllogism<\/a>. These paralogisms of deduction are \u201carguments of traditional syllogistic form which break one or another of a well-known set of rules\u201d (Hamblin 1970, p. 44).<\/p>\n

1. Syllogism Rules
\n<\/span><\/h2>\n

Traditional logic has established the following rules for identifying and eliminating invalid syllogisms.
\nThe following syllogisms respect all the rules of the syllogism; they are valid.<\/p>\n

A syllogism contains three terms.<\/strong><\/p>\n

Nothing can be deduced from two negative premises,
\n<\/strong><\/p>\n

no M is P<\/span>
\nno S is M<\/span>
\nno conclusion<\/em><\/span><\/p>\n

If one premise is negative, then the conclusion must also be negative.<\/strong><\/p>\n

no M is P \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 the major premise is negative.
\n<\/em>some S are M,<\/span>
\nso<\/em> some S are not P \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 the conclusion is negative<\/em><\/span><\/p>\n

In a valid syllogism, the middle term must be distributed at least once.<\/strong><\/p>\n

no M is P \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 M is distributed (universal).
\n<\/em>all S are M,<\/span>
\nso<\/em> no S is P \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 the conclusion is valid.<\/em><\/span><\/p>\n

If a premise is particular, then the conclusion is particular<\/strong><\/p>\n

no M is P<\/span>
\nsome S are M \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 the minor premise is particular.
\n<\/em>So<\/em>, some S are not P \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>the conclusion is particular<\/span>.<\/em><\/p>\n

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

A paralogism is a syllogism that does not respect one or more of the preceding rules. Of the 256 possible modes of the syllogism, only 19 modes are valid, meaning a syllogism can be fallacious in 237 different ways.
\nWhether it \u201cseems\u201d conclusive or not is irrelevant. The term paralogism<\/em>\u00a0 refers to a miscalculation.<\/p>\n

The main forms of syllogistic paralogisms are as follows. The first form corresponds to the paralogism of homonymy, the others correspond to an inadequate distribution of qualities and quantities.<\/p>\n

(1) Paralogism of four terms.<\/span>
\n(2) Paralogism of two negative premises.<\/span>
\n(3) Paralogism of a positive conclusion drawn from a negative premise.<\/span>
\n(4) Paralogism of the undistributed middle term.<\/span>
\n(5) Paralogism of the universal conclusion from a particular major.<\/span>
\n(6) Paralogism of a universal conclusion drawn from a particular minor.<\/span><\/p>\n

Examples<\/strong><\/em><\/p>\n

\u2014\u00a0The following paralogism consists of four terms<\/strong>:<\/p>\n

Metals are simple bodies.
\n<\/em>Bronze is a metal.
\n<\/em>* Therefore bronze is a simple body.<\/em><\/p>\n

\u2014\u00a0The following paralogism concludes from two negative premises<\/strong>:<\/p>\n

Some B are not C \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 some rich are not arrogant
\n<\/em>No A is B \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 no poet is rich.
\n<\/em>* Therefore<\/em> No A is C\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 *no poet is arrogant<\/em>.<\/p>\n

\u2014\u00a0The following paralogism concludes universally from a particular major premise<\/strong>.<\/p>\n

all A are B \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 all men are mortal
\n<\/em>no C is A \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 no dog is man
\n<\/em>* Therefore<\/em> No C is B \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 * no dog is mortal<\/em>.<\/p>\n

In the major premise, \u201call men are mortal<\/em>\u201d, the major term, mortal<\/em>, is not distributed: this premise says nothing about all mortals, but only about certain mortals, namely, that \u201cthey are men<\/em>\u201d. Yet the conclusion \u201cNo dog is mortal<\/em>\u201d claims something of all mortals: \u201cno mortal is a dog<\/em>\u201d. The major term is distributed in the conclusion and not in the major premise. Thus, the conclusion affirms more than the premise, which is impossible.<\/p>\n

3. Evaluation Using the Rules of the Syllogism<\/span><\/h2>\n

Traditionally, syllogisms are evaluated using a system of rules (\u00a71), in a step-by-step process.<\/p>\n

\u2014\u00a0Check the number of terms, and propositions.
\n\u2014\u00a0Identify the middle term, the major term, and the minor term.
\n\u2014 Determine the quantity and quality of the premises and the conclusion.
\n\u2014\u00a0Identify the distribution of terms.
\n\u2014 Check the organization of the distribution of terms: check that the middle term is distributed at least once. If the major term or the minor term is distributed in the conclusion, ensure that it is also distributed in the premises and so on.<\/p>\n

This cumbersome method is based on the unintuitive notion of the quantity of predicates. It shifts the analyst’s attention from what the syllogism asserts, that is, from the understanding of the structure and articulation of the syllogism, to the fragmented application of a system of rules.While it may develop the ability to apply an algorithm, but it is far from an everyday critical thinking process.<\/p>\n

4. Evaluation with Venn Diagrams<\/span><\/h1>\n

The use of Venn diagrams provides a clearer, more intuitive basis for evaluating syllogisms. Three intersecting circles represent the three sets corresponding to the three terms. The assertion made by each premise is carried to the corresponding circle.
\nIf a premise asserts that a set (consisting of a circle or a portion of a circle) contains no elements, that circle or the portion of a circle is blacked out (striped).<\/p>\n

If a premise asserts that a set (id<\/em>.) contains one or more elements, a cross is placed in the circle or portion of a circle.
\nThus, a part of a circle is either black (i.e., has a cross), or remains white. If it is white, nothing can be said about it.<\/p>\n

Once the data from the premises is plotted on the diagram, the result can be compared with what the conclusion. The diagram shows<\/em> whether the syllogism is or is not valid.<\/p>\n

Consider the following syllogism:<\/strong><\/em><\/p>\n

Some rich people are not arrogant.<\/span>
\nNo poet is rich.<\/span>
\n* No poet is arrogant.<\/span><\/p>\n

The three intersecting circles represent the rich (R), the poets (P) and the arrogant (A), respectively.<\/p>\n

\"\"<\/p>\n

– \u201cSome rich are not arrogant<\/em>\u201d: look at the circle of the rich and the circle of the arrogant; put a cross outside of their intersection: there are some people within this zone.
\n– \u201cNo poet is rich<\/em>\u201d: look at the circles of poets and of the rich people. Blacken their intersection: there is nobody within this zone.
\n– Finally, look at the circles of poets and of arrogant people. The conclusion asserts that the intersection of the circle of poets and the circle of arrogant people is black; but we see that this is not the case; it is partly white.
\nConclusion: This syllogism is a paralogism.<\/p>\n

Consider the syllogism:<\/p>\n

No M<\/strong> is P
\n<\/strong>All S<\/strong> is M
\n<\/strong>Therefore No S<\/strong> is P<\/strong><\/span><\/p>\n

The three intersecting circles represent the set M<\/strong>, S<\/strong> and P<\/strong>.<\/p>\n

\u2014\u00a0\u201cNo M<\/strong> is P<\/strong><\/em>\u201d: the intersection of the circles M<\/strong> and P<\/strong> is black (empty).
\n\u2014\u00a0\u201cEvery S<\/strong> is M<\/strong><\/em>\u201d: the non-intersecting zone of the circles S<\/strong> and P<\/strong> is black (empty).
\n\u2014 Looking at the intersection of the\u00a0 S<\/strong> and P<\/strong> circles, we can see that the intersection is black (empty); this is precisely what the conclusion claims, \u201cNo S<\/strong> is P<\/strong><\/em>\u201d. This syllogism is valid.<\/p>\n

5. Paralogism of the permutation of the <\/span>quantifiers<\/h2>\n

By generalization, the word paralogism<\/em> can refer to any error in applying the rules of formal logic.
\nFor example, the paralogism of quantification is an error committed when the existential quantifier and the universal quantifier are permuted:<\/p>\n

All humans have a father; so they have the same father<\/span><\/p>\n

For every human H<\/strong>, there is a human F<\/strong>, such that F<\/strong> is the father of H
\n<\/strong>* Therefore<\/em> there is a human F<\/strong> such that for every human H<\/strong>, F<\/strong> is the father of H<\/strong>.<\/span><\/p>\n

The following passage may contain such a paralogism:<\/p>\n

And all the geniuses of science, including Copernicus, Kepler, Galileo, Descartes, Leibnitz, Buler, Clarke, Cauchy, speak like [Newton]. They all lived in true worship of the harmony of the worlds and of the all-powerful hand that threw them into space and sustained them.<\/span>
\nAnd this conviction is not based on impulses, like poets. Figures, theorems of geometry give it its necessary basis. And their reasoning is so simple that children would follow it. First, they state that matter is essentially inert. It follows that, if any material element is in motion, it is because another has constrained it; for every motion of matter is necessarily a communicated motion. Thus they assert that if there is an immense motion in the heavens, which in the infinite deserts carries away\u00a0 billions of suns with a weight that crushes the imagination, it is because there is an omnipotent engine.
\n<\/em>Secondly, they state that this movement of the heavens presupposes the solution of the problems of calculation, which have required thirty years of study, etc.
\n<\/em>\u00c9m. Bougaud, [Christianity and the Present Times<\/em>], 1883. [2]<\/span><\/p>\n

\n

[1]<\/a> (My italics).
\n[2]<\/a> Em. Bougaud, Le Christianisme et le temps pr\u00e9sent,<\/em> t. I. Paris: Poussielgue Fr\u00e8res, 5th ed., 1883.<\/p>\n

\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

PARALOGISM In classical Aristotelian logic, a paralogism is defined as an invalid syllogism. These paralogisms of deduction are \u201carguments of traditional syllogistic form which break one or another of a well-known set of rules\u201d (Hamblin 1970, p. 44). 1. Syllogism Rules Traditional logic has established the following rules for identifying and eliminating invalid syllogisms. The […]<\/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-5318","post","type-post","status-publish","format-standard","hentry","category-non-classe"],"_links":{"self":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/5318","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=5318"}],"version-history":[{"count":10,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/5318\/revisions"}],"predecessor-version":[{"id":14216,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/5318\/revisions\/14216"}],"wp:attachment":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/media?parent=5318"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/categories?post=5318"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/tags?post=5318"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

But bronze is not a simple body but an alloy. In the minor premise, bronze is said to be a metal because it resembles an authentic metal such as iron, it can be melted and formed. In the major premise, metal<\/em> is used in its strict sense. However, Metal<\/em> is homonymous, and the syllogism actually has four terms, see ambiguity<\/a>.<\/p>\n