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Each premise and the conclusion can be of type A, E, I or O, and the syllogism can be any of the four figures. A syllogism can be described briefly by giving the letters for the premises and conclusion followed by the number for the figure. For example, the syllogism BARBARA below is AAA-1, or "A-A-A in the first figure".
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).
categorical syllogism A form of deductive reasoning in Aristotelian logic consisting of three categorical propositions that involve three terms and deduce a conclusion from two premises. category In mathematics and logic, a collection of objects and morphisms between them that satisfies certain axioms, fundamental to category theory. category ...
Sometimes a syllogism that is apparently fallacious because it is stated with more than three terms can be translated into an equivalent, valid three term syllogism. [2] For example: Major premise: No humans are immortal. Minor premise: All Greeks are people. Conclusion: All Greeks are mortal.
Syllogistic fallacies – logical fallacies that occur in syllogisms. Affirmative conclusion from a negative premise (illicit negative) – a categorical syllogism has a positive conclusion, but at least one negative premise. [11] Fallacy of exclusive premises – a categorical syllogism that is invalid because both of its premises are negative ...
Therefore, a judgment is a declarative sentence, which is a categorical proposition. Example: The tiger is four-footed. A predicate can also have its own predicate. In the example, the predicate "four-footed" can, itself, have the further predicate "animal." One of these predicates is immediately and directly connected to the subject or thing.
A polysyllogism is a complex argument (also known as chain arguments of which there are four kinds: polysyllogisms, sorites, epicheirema, and dilemmas) [1] that strings together any number of propositions forming together a sequence of syllogisms such that the conclusion of each syllogism, together with the next proposition, is a premise for the next, and so on.
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; Categorical proposition, a part of deductive reasoning; Categorization; Categorical perception