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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).
"The tiger (Subject) is (Copula) a four-footed (Immediate Predicate) animal." (Mediate Predicate) {"The tiger} is {a four-footed} animal." (Subject) (Copula) {(Immediate Predicate)} {(Mediate Predicate)} In order to have clear knowledge of the relation between a predicate and a subject, I can consider a predicate to be a mediate predicate. Between this mediate predicate or attribute, I can ...
At present, syllogism is used exclusively as the method used to reach a conclusion closely resembling the "syllogisms" of traditional logic texts: two premises followed by a conclusion each of which is a categorical sentence containing all together three terms, two extremes which appear in the conclusion and one middle term which appears in ...
Types of syllogism to which it applies include statistical syllogism, hypothetical syllogism, and categorical syllogism, all of which must have exactly three terms. Because it applies to the argument's form , as opposed to the argument's content, it is classified as a formal fallacy .
A syllogism is an argument that consists of at least three sentences: at least two premises and a conclusion. Although Aristotle does not call them "categorical sentences", tradition does; he deals with them briefly in the Analytics and more extensively in On Interpretation. [4]
Morley's categoricity theorem, a mathematical theorem in model theory; Categorical data analysis; Categorical distribution, a probability distribution; Categorical logic, a branch of category theory within mathematics with notable connections to theoretical computer science; Categorical syllogism, a kind of logical argument
A syllogism (Ancient Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also notable for its connections to theoretical computer science. [1] In broad terms, categorical logic represents both syntax and semantics by a category, and an interpretation by a functor.