Valid: This shape is a triangle or a square; it is a triangle; therefore it is not a square.
Invalid: This shape is a triangle or a square; it is not a triangle; therefore it is a square.
A circle refutes the second inference: it is neither a triangle nor a square. The relation only excludes their conjunction; it does not eliminate every third possibility.
With the same “or” statement, a different kind of exceptive premise changes what may validly be concluded.
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Exceptive Syllogism: Valid Inferences from Connected and Disjunctive Conditionals
Valid: This shape is a triangle or a square; it is a triangle; therefore it is not a square.
Invalid: This shape is a triangle or a square; it is not a triangle; therefore it is a square.
A circle refutes the second inference: it is neither a triangle nor a square. The relation only excludes their conjunction; it does not eliminate every third possibility.
With the same “or” statement, a different kind of exceptive premise changes what may validly be concluded.