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. 24 Feb. 2018 <http://www.encyclopedia.com>.

"syllogism." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. (February 24, 2018). http://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/syllogism

"syllogism." The Columbia Encyclopedia, 6th ed.. . Retrieved February 24, 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. 24 Feb. 2018 <http://www.encyclopedia.com>.

"syllogism." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. (February 24, 2018). http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/syllogism-0

"syllogism." The Oxford Pocket Dictionary of Current English. . Retrieved February 24, 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. 24 Feb. 2018 <http://www.encyclopedia.com>.

"syllogism." The Concise Oxford Dictionary of English Etymology. . Encyclopedia.com. (February 24, 2018). http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/syllogism-1

"syllogism." The Concise Oxford Dictionary of English Etymology. . Retrieved February 24, 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. 24 Feb. 2018 <http://www.encyclopedia.com>.

"syllogism." World Encyclopedia. . Encyclopedia.com. (February 24, 2018). http://www.encyclopedia.com/environment/encyclopedias-almanacs-transcripts-and-maps/syllogism

"syllogism." World Encyclopedia. . Retrieved February 24, 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. 24 Feb. 2018 <http://www.encyclopedia.com>.

"syllogism." The Oxford Dictionary of Phrase and Fable. . Encyclopedia.com. (February 24, 2018). http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/syllogism

"syllogism." The Oxford Dictionary of Phrase and Fable. . Retrieved February 24, 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.