Syllogisms {categorical syllogism} can have major premise, minor premise, and conclusion. Major premise and minor premise share term. For example, "all a are b" is major premise. "c is a" is minor premise. Therefore, "c is b" {conclusion}, because both premises share term a.
negative
Categorical syllogism can have only one negative premise, and then conclusion must be negative.
quantifier
Categorical syllogisms can have premises about all, some, or none, in four forms: "All A are B", "No A are B", "Some A are B", or "Some A are not B". Verb must be "to be".
First, statement states All, Some, or No {quantifier, syllogism}. Noun phrase {subject class} follows quantifier. Verb {copula, syllogism} follows subject class. Second noun phrase {predicate class} follows copula. Therefore, categorical syllogism has three terms: two noun phrases and copula.
types
Categorical syllogisms have four types {figure, syllogism}. All A are B, C is A, and so C is B {first figure of syllogism}. All B are A, C is A, and so C is B {second figure of syllogism}. All B are A, A is C, and so C is B {third figure of syllogism}. All A are B, A is C, and so C is B {fourth figure of syllogism}.
The four types can use "All", "Some", or "No", making twelve categorical syllogisms. With "Some" in conclusion {particular statement}, only one premise can have "All" or "No" {universal statement}.
errors
Errors can be in categorical syllogisms. Major premise can be untrue. Syllogism can reverse major premise. Terms can be ambiguous. Middle term can be ambiguous {ambiguous middle}. For example, A is B(1) is true, B(2) is C is true, so A is C is true.
Mathematical Sciences>Logic>Syllogism
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Date Modified: 2022.0224