After treating true disjunction, the book’s “first kind” means affirming one side to deny the other. Its “second kind” means denying one side to affirm the other.
The later rules then become clear:
Exclusion of conjunction allows the first kind, not the second.
Exclusion of emptiness allows the second kind, not the first.
Mistaking the “first kind” for the “first alternative” would distort the argument. The division is by mode of inference, not by the position of the alternatives.
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Exceptive Syllogism: Valid Inferences from Connected and Disjunctive Conditionals
After treating true disjunction, the book’s “first kind” means affirming one side to deny the other. Its “second kind” means denying one side to affirm the other.
The later rules then become clear:
Exclusion of conjunction allows the first kind, not the second.
Exclusion of emptiness allows the second kind, not the first.
Mistaking the “first kind” for the “first alternative” would distort the argument. The division is by mode of inference, not by the position of the alternatives.