Categorical proposition

distributedDistribution of termscategoricalcategorical propositionsDistributionundistributeduniversal affirmativecategorical assertionscategorical sentencecategorical statement
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).wikipedia
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Proposition

propositionspropositionalclaim
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).
Aristotelian logic identifies a proposition as a sentence which affirms or denies a predicate of a subject with the help of a 'Copula'.

Square of opposition

subcontrarycontradictoriescontraries
In philosophical logic, the square of opposition is a diagram representing the relations between the four basic categorical propositions.

Syllogism

syllogisticcategorical syllogismsyllogisms
The study of arguments using categorical statements (i.e., syllogisms) forms an important branch of deductive reasoning that began with the Ancient Greeks.
Despite this very general definition, in Prior Analytics Aristotle limits himself to categorical syllogisms that consist of three categorical propositions.

Predicate (grammar)

predicatepredicatespredication
In each row of the following chart, S corresponds to the subject of the example sentence, and P corresponds to the predicate.

Logic

logicianlogicallogics
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).

Argument

logical argumentargumentsproof
The study of arguments using categorical statements (i.e., syllogisms) forms an important branch of deductive reasoning that began with the Ancient Greeks.

Deductive reasoning

deductiondeductivedeductive logic
The study of arguments using categorical statements (i.e., syllogisms) forms an important branch of deductive reasoning that began with the Ancient Greeks.

Ancient Greece

Greekancient Greekancient Greeks
The study of arguments using categorical statements (i.e., syllogisms) forms an important branch of deductive reasoning that began with the Ancient Greeks.

Aristotle

AristotelianAristotelesAristote
It has been suggested that statements of the form "Some A are not B" would be less problematic if stated as "Not every A is B," which is perhaps a closer translation to Aristotle's original form for this type of statement.

George Boole

BooleBoole, GeorgeBoole, G
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.

First-order logic

predicate logicfirst-orderpredicate calculus
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.

Natural language

linguisticnaturalnatural languages
Sentences in natural language may be translated into standard form.

Subject (grammar)

subjectsubjectsgrammatical subject
In each row of the following chart, S corresponds to the subject of the example sentence, and P corresponds to the predicate.

Venn diagram

Venn diagramsLogic diagramVenn
Although not developed here, Venn diagrams are sometimes helpful when trying to understand the distribution of terms for the four forms.

Singular term

single personsingularterm
But if, as an example, this group of "some politicians" were defined to contain a single person, Albert, the relationship becomes clearer.

Peter Geach

P. T. GeachPeter Thomas GeachGeach
Peter Geach and others have criticized the use of distribution to determine the validity of an argument.

Domain of discourse

universe of discoursedomainarea of interest
This refers to every element under consideration which is not an element of the class.

Complement (set theory)

complementset differencecomplements
Class complements are very similar to set complements.

Term logic

Aristotelian logicscholastic logictraditional logic

Inductive reasoning

inductioninductiveinductive logic
If one observes 100 swans, and all 100 were white, one might infer a universal categorical proposition of the form All swans are white.

Converse (logic)

converseconverselyConversion (logic)
For the categorical proposition All S are P, the converse is All P are S.