Skip to main content
Select Source:

syllogism

syllogism, a mode of argument that forms the core of the body of Western logical thought. Aristotle defined syllogistic logic, and his formulations were thought to be the final word in logic; they underwent only minor revisions in the subsequent 2,200 years. Every syllogism is a sequence of three propositions such that the first two imply the third, the conclusion. There are three basic types of syllogism: hypothetical, disjunctive, and categorical. The hypothetical syllogism, modus ponens, has as its first premise a conditional hypothesis: If p then q; it continues: p, therefore q. The disjunctive syllogism, modus tollens, has as its first premise a statement of alternatives: Either p or q; it continues: not q, therefore p. The categorical syllogism comprises three categorical propositions, which must be statements of the form all x are y,no x is y,some x is y, or some x is not y. A categorical syllogism contains precisely three terms: the major term, which is the predicate of the conclusion; the minor term, the subject of the conclusion; and the middle term, which appears in both premises but not in the conclusion. Thus: All philosophers are men (middle term); all men are mortal; therefore, All philosophers (minor term) are mortal (major term). The premises containing the major and minor terms are named the major and minor premises, respectively. Aristotle noted five basic rules governing the validity of categorical syllogisms: The middle term must be distributed at least once (a term is said to be distributed when it refers to all members of the denoted class, as in all x are y and no x is y); a term distributed in the conclusion must be distributed in the premise in which it occurs; two negative premises imply no valid conclusion; if one premise is negative, then the conclusion must be negative; and two affirmatives imply an affirmative. John Venn, an English logician, in 1880 introduced a device for analyzing categorical syllogisms, known as the Venn diagram. Three overlapping circles are drawn to represent the classes denoted by the three terms. Universal propositions (all x are y, no x is y) are indicated by shading the sections of the circles representing the excluded classes. Particular propositions (some x is y, some x is not y) are indicated by placing some mark, usually an "X," in the section of the circle representing the class whose members are specified. The conclusion may then be read directly from the diagram.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"syllogism." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. 19 Sep. 2018 <http://www.encyclopedia.com>.

"syllogism." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. (September 19, 2018). http://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/syllogism

"syllogism." The Columbia Encyclopedia, 6th ed.. . Retrieved September 19, 2018 from Encyclopedia.com: http://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/syllogism

Learn more about citation styles

Citation styles

Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

Notes:
  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.

syllogism

syl·lo·gism / ˈsiləˌjizəm/ • n. an instance of a form of reasoning in which a conclusion is drawn (whether validly or not) from two given or assumed propositions (premises), each of which shares a term with the conclusion, and shares a common or middle term not present in the conclusion (e.g., all dogs are animals; all animals have four legs; therefore all dogs have four legs). ∎  deductive reasoning as distinct from induction: logic is rules or syllogism. DERIVATIVES: syl·lo·gis·tic / ˌsiləˈjistik/ adj. syl·lo·gis·ti·cal·ly / ˌsiləˈjistik(ə)lē/ adv.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"syllogism." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. 19 Sep. 2018 <http://www.encyclopedia.com>.

"syllogism." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. (September 19, 2018). http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/syllogism-0

"syllogism." The Oxford Pocket Dictionary of Current English. . Retrieved September 19, 2018 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/syllogism-0

Learn more about citation styles

Citation styles

Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

Notes:
  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.

syllogism

syllogism argument expressed in the form of two propositions called the premisses and a third called the conclusion. XIV. ME. silogisme, occas. silogime — OF. sil(l)ogisme, earlier silogime (mod. syllogisme) or L. syllogismus — Gr. sullogísmós, f. sullogizesthai, intensive of logízesthai reckon, compute, conclude, f. lógos discourse, consideration, account; see SYL-, -ISM. So syllogistic XVII. — L. syllogisticus — Gr. sullogístikós. syllogize XV. — OF. sil(l)ogiser — late L. syllogizāre — Gr. sullogizesthai.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"syllogism." The Concise Oxford Dictionary of English Etymology. . Encyclopedia.com. 19 Sep. 2018 <http://www.encyclopedia.com>.

"syllogism." The Concise Oxford Dictionary of English Etymology. . Encyclopedia.com. (September 19, 2018). http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/syllogism-1

"syllogism." The Concise Oxford Dictionary of English Etymology. . Retrieved September 19, 2018 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/syllogism-1

Learn more about citation styles

Citation styles

Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

Notes:
  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.

syllogism

syllogism Logical argument consisting of three categorical propositions: two premises and a conclusion. It was devised by Aristotle to establish the conditions under which the conclusion of a deductive inference is valid or not valid. A valid conclusion can only come from premises that are logically related to each other. Examples of syllogisms are as follows: All men are mortal; John is a man; therefore John is mortal (valid); All trees have leaves; a daffodil has leaves; therefore a daffodil is a tree (invalid).

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"syllogism." World Encyclopedia. . Encyclopedia.com. 19 Sep. 2018 <http://www.encyclopedia.com>.

"syllogism." World Encyclopedia. . Encyclopedia.com. (September 19, 2018). http://www.encyclopedia.com/environment/encyclopedias-almanacs-transcripts-and-maps/syllogism

"syllogism." World Encyclopedia. . Retrieved September 19, 2018 from Encyclopedia.com: http://www.encyclopedia.com/environment/encyclopedias-almanacs-transcripts-and-maps/syllogism

Learn more about citation styles

Citation styles

Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

Notes:
  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.

syllogism

syllogism an instance of a form of reasoning in which a conclusion is drawn (whether validly or not) from two given or assumed propositions (premises) that each share a term with the conclusion, and that share a common or middle term not present in the conclusion (e.g. all dogs are animals; all animals have four legs; therefore all dogs have four legs).

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"syllogism." The Oxford Dictionary of Phrase and Fable. . Encyclopedia.com. 19 Sep. 2018 <http://www.encyclopedia.com>.

"syllogism." The Oxford Dictionary of Phrase and Fable. . Encyclopedia.com. (September 19, 2018). http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/syllogism

"syllogism." The Oxford Dictionary of Phrase and Fable. . Retrieved September 19, 2018 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/syllogism

Learn more about citation styles

Citation styles

Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

Notes:
  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.

Syllogism

SYLLOGISM

A syllogism is an artificial, logical arrangement of a natural deductive process known as argumentation. It was invented and perfected by aristotle, although other Greek thinkers, particularly Theophrastus, the Stoics and the Megarians, made substantial additions. In the Middle Ages the syllogism became identified with scholastic method, and it was much ridiculed by the founders of modern science in the 17th century. Recent studies, however, including those in symbolic logic, have vindicated the concern of ancient and medieval thinkers for this instrument of human thought. In its apodictic form, or dem onstration, the syllogism is man's most powerful device for the attainment of truth and certitude (see logic, history of).

Nature and Kinds of Syllogism. The argumentation expressed by a syllogism involves three elements: the antecedent, or truth already known; the conclusion or new truth; and the inference of the mind connecting these two. In the syllogism, the antecedent is made up of propositions called premises, usually two in number. The conclusion is also a proposition, preceded by a "therefore" to signify the act of inference. While inference itself is not artificial, since it is a natural act of the mind (called rea soning), the forced disposition of the antecedent and conclusion according to logical laws is artificial, that is, it is imposed on the mind by mind itself in order to attain truth more easily and with less error. Thus syllogism is a logical tool that makes the natural deductive process more accurate, much as learning to eat correctly is an artificial imposition that assists the natural process of nutrition.

The two principal types of syllogism are the categorical and the hypothetical. The difference lies in the formal structure and the type of inference, as is explained below.

Categorical Syllogism. The categorical syllogism is defined as an argumentation in which two terms are compared with a third term in the antecedent, and the conclusion states that the two terms agree or do not agree with each other. An example is the following:

All things composed of matter are corruptible.

But all men are things composed of matter.

Therefore all men are corruptible.

In this example, the first two propositions constitute the antecedent; the proposition "Therefore all men are corruptible" is the conclusion. The subject term of the conclusion, "men," is the minor term and the premise that contains this term is called the minor premise. The predicate term, "corruptible," is the major term and the premise that contains it is called the major premise. The term repeated in both premises but not found in the conclusion, that is, "things composed of matter," is known as the middle term.

The categorical syllogism is validated by two basic principles of logic, the so-called dictum de omni and dictum de nullo. The first states that whatever is distributively and universally predicated of some subject must be affirmed of all included under that subject; the second states that whatever is universally and distributively denied of a subject must be denied of all included under that subject (see predication). These principles are similar to the mathematical propositions: two things equal to a third are equal to each other, and two things not equal to a third are not equal to each other.

Rules for the Syllogism. From the nature of the categorical syllogism certain laws follow that govern its use. These may be summarized as follows: (1) There can be only three terms in such a syllogism, one of which (the middle term) cannot appear in the conclusion. From this law, logicians deduce that only four "figures" of the categorical syllogism are possible. The following shows the four figures of the categorical syllogism and the possible arrangements of the subject term (S), the predicate term (P) and the middle term (M):

(2) A term in the conclusion cannot have a wider extension than in the premises, for the effect cannot be greater than the cause. (3) The middle term must be used universally at least once, otherwise one cannot be certain that this subject term is included under this predicate term. (4) If one premise is negative or particular, the conclusion must be negative or particular. (5) When both premises are negative or particular, no conclusion is possible.

Mnemonics and the Laws. When these rules are applied to the various figures of the categorical syllogism, only a limited number of forms, or moods, are found to be valid within each figure. These valid moods can be recognized with the aid of the following mnemonics or memory aids, devised by logicians for this purpose:

First Figure: Barbara, Celarent, Darii, Ferio.

Second Figure: Cesare, Camestres, Festino, Baroco.

Third Figure: Darapti, Felapton, Disamis, Datisi, Bocardo, Ferison.

Fourth Figure: Bamalip, Calemes, Dimatis, Fesapo, Fresison.

The first three vowels in these mnemonics indicate whether the major premise, the minor premise, and conclusion, in order, are A, E, I, or O (see proposition). Some of the consonants, similarly, indicate how various moods can be reduced to the four basic moods of the first figure. The first figure is considered the most perfect, because it best illustrates the principles on which the categorical syllogism is based, while the mood Barbara, being composed of three universal affirmative propositions, is regarded as the most perfect form of the first figure.

Related Forms. The polysyllogism is a series of categorical syllogisms so arranged that the conclusion of the previous syllogism becomes a premise of the next. The enthymeme is a categorical syllogism with one premise merely implied; it is employed with great effect in rhet oric. The singular syllogism, called an expository syllogism if the singular term is the middle term, is a post-Aristotelian development; its validity as a form of categorical syllogism is controverted. The sorites is a categorical syllogism resulting from a concatenation of middle terms. The modal syllogism is made up of propositions that have a modality apart from being true or false, such as, necessary, possible, or problematical; while not much discussed in traditional logic, it is undergoing extensive development in symbolic logic (see logic, symbolic; mode).

Hypothetical Syllogism. The hypothetical syllogism is defined as an argumentation that has a hypothetical proposition as a major premise. Hence the basic forms of this syllogism derive from the forms of the hypothetical proposition, namely, conditional, disjunctive and alternative. The conditional syllogism, most important among the hypotheticals, has two valid figures: one posits the condition in the minor premise, and then posits the conditioned in the conclusion; the other denies the conditioned in the minor premise, and denies the condition in the conclusion. The frequent use of the other possibilities constitutes the fallacy of consequence.

See Also: deduction; first principles; proof;

Bibliography: i. m. bochenski, A History of Formal Logic, tr. i. thomas (Notre Dame, Ind. 1961). s. caramella, Enciclopedia filosofica, 4 v. (Venice-Rome 1957) 4:615620. r. eisler, Wörterbuch der philosophischen Begriffe, 3 v. (4th ed. Berlin 192730) 2:757771. j. a. oesterle, Logic: the Art of Defining and Reasoning (2d ed. Englewood Cliffs, N.J. 1963). v. e. smith, The Elements of Logic (Milwaukee 1957). e. d. simmons, The Scientific Art of Logic (Milwaukee 1961).

[e. bondi]

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"Syllogism." New Catholic Encyclopedia. . Encyclopedia.com. 19 Sep. 2018 <http://www.encyclopedia.com>.

"Syllogism." New Catholic Encyclopedia. . Encyclopedia.com. (September 19, 2018). http://www.encyclopedia.com/religion/encyclopedias-almanacs-transcripts-and-maps/syllogism

"Syllogism." New Catholic Encyclopedia. . Retrieved September 19, 2018 from Encyclopedia.com: http://www.encyclopedia.com/religion/encyclopedias-almanacs-transcripts-and-maps/syllogism

Learn more about citation styles

Citation styles

Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

Notes:
  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.