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Valid Categorical Syllogisms^†

† Without further conditions stated, the syllogisms in the final two rows are not considered valid in modern logic where empty sets are permitted. Those in the sixth row only hold if the class M is nonempty (i.e., there is an element x such that x belongs to M). The lone argument in the seventh row only holds if P is nonempty.

Examples of Invalid Categorical Syllogisms

Caution: These are not forms of valid reasoning. They are collected here only to put the reader on alert (see Exercise 4.3).

Valid Arguments Involving Conditional Statements

Modus Ponens

P implies Q

P

∴Q

Modus ...