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- Categorical_proposition abstract "In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the subject term) are included in another (the predicate term). The study of arguments using categorical statements (i.e., syllogisms) forms an important branch of deductive reasoning that began with the Ancient Greeks.The Ancient Greeks such as Aristotle identified four primary distinct types of categorical proposition and gave them standard forms (now often called A, E, I, and O). If, abstractly, the subject category is named S and the predicate category is named P, the four standard forms are:All S are P. (A form)No S are P. (E form)Some S are P. (I form)Some S are not P. (O form)A surprisingly large number of sentences may be translated into one of these canonical forms while retaining all or most of the original meaning of the sentence. Greek investigations resulted in the so-called square of opposition, which codifies the logical relations among the different forms; for example, that an A-statement is contradictory to an O-statement; that is to say, for example, if one believes "All apples are red fruits," one cannot simultaneously believe that "Some apples are not red fruits." Thus the relationships of the square of opposition may allow immediate inference, whereby the truth or falsity of one of the forms may follow directly from the truth or falsity of a statement in another form.Modern understanding of categorical propositions (originating with the mid-19th century work of George Boole) requires one to consider if the subject category may be empty. If so, this is called the hypothetical viewpoint, in opposition to the existential viewpoint which requires the subject category to have at least one member. The existential viewpoint is a stronger stance than the hypothetical and, when it is appropriate to take, it allows one to deduce more results than otherwise could be made. The hypothetical viewpoint, being the weaker view, has the effect of removing some of the relations present in the traditional square of opposition.Arguments consisting of three categorical propositions — two as premises and one as conclusion — are known as categorical syllogisms and were of paramount importance from the times of ancient Greek logicians through the Middle Ages. Although formal arguments using categorical syllogisms have largely given way to the increased expressive power of modern logic systems like the first-order predicate calculus, they still retain practical value in addition to their historic and pedagogical significance.".
- Categorical_proposition wikiPageExternalLink categorical_propositions.htm.
- Categorical_proposition wikiPageExternalLink catlogic.
- Categorical_proposition wikiPageID "2418429".
- Categorical_proposition wikiPageLength "16365".
- Categorical_proposition wikiPageOutDegree "21".
- Categorical_proposition wikiPageRevisionID "682567703".
- Categorical_proposition wikiPageWikiLink Ancient_Greece.
- Categorical_proposition wikiPageWikiLink Ancient_Greeks.
- Categorical_proposition wikiPageWikiLink Argument.
- Categorical_proposition wikiPageWikiLink Aristotle.
- Categorical_proposition wikiPageWikiLink Categorical_syllogism.
- Categorical_proposition wikiPageWikiLink Category:Propositions.
- Categorical_proposition wikiPageWikiLink Category:Term_logic.
- Categorical_proposition wikiPageWikiLink Complement_(set_theory).
- Categorical_proposition wikiPageWikiLink Deductive_reasoning.
- Categorical_proposition wikiPageWikiLink Domain_of_discourse.
- Categorical_proposition wikiPageWikiLink First-order_logic.
- Categorical_proposition wikiPageWikiLink George_Boole.
- Categorical_proposition wikiPageWikiLink Immediate_inference.
- Categorical_proposition wikiPageWikiLink Logic.
- Categorical_proposition wikiPageWikiLink Peter_Geach.
- Categorical_proposition wikiPageWikiLink Proposition.
- Categorical_proposition wikiPageWikiLink Square_of_opposition.
- Categorical_proposition wikiPageWikiLink Syllogism.
- Categorical_proposition wikiPageWikiLink Term_logic.
- Categorical_proposition wikiPageWikiLink Venn_diagram.
- Categorical_proposition wikiPageWikiLinkText "Categorical proposition".
- Categorical_proposition wikiPageWikiLinkText "Categorical proposition#Distribution".
- Categorical_proposition wikiPageWikiLinkText "categorical assertions".
- Categorical_proposition wikiPageWikiLinkText "categorical proposition".
- Categorical_proposition wikiPageWikiLinkText "categorical".
- Categorical_proposition wikiPageWikiLinkText "universal affirmative".
- Categorical_proposition hasPhotoCollection Categorical_proposition.
- Categorical_proposition wikiPageUsesTemplate Template:Cite_book.
- Categorical_proposition wikiPageUsesTemplate Template:Empty_section.
- Categorical_proposition wikiPageUsesTemplate Template:Incomplete.
- Categorical_proposition wikiPageUsesTemplate Template:Main.
- Categorical_proposition wikiPageUsesTemplate a.
- Categorical_proposition wikiPageUsesTemplate Template:No2.
- Categorical_proposition wikiPageUsesTemplate Template:Partial.
- Categorical_proposition wikiPageUsesTemplate Template:Refimprove.
- Categorical_proposition wikiPageUsesTemplate Template:Reflist.
- Categorical_proposition wikiPageUsesTemplate Template:Sfn.
- Categorical_proposition wikiPageUsesTemplate Template:Yes.
- Categorical_proposition subject Category:Propositions.
- Categorical_proposition subject Category:Term_logic.
- Categorical_proposition hypernym Proposition.
- Categorical_proposition type Article.
- Categorical_proposition type Article.
- Categorical_proposition type Statement.
- Categorical_proposition type Statement.
- Categorical_proposition comment "In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the subject term) are included in another (the predicate term).".
- Categorical_proposition label "Categorical proposition".
- Categorical_proposition sameAs Kategorisches_Urteil.
- Categorical_proposition sameAs Proposición_categórica.
- Categorical_proposition sameAs Kategorinen_arvostelma.
- Categorical_proposition sameAs m.07bpsp.
- Categorical_proposition sameAs Q1735817.
- Categorical_proposition sameAs Q1735817.
- Categorical_proposition wasDerivedFrom Categorical_proposition?oldid=682567703.
- Categorical_proposition isPrimaryTopicOf Categorical_proposition.