Disjunction: This integer is even or odd.
Exceptive premise: But it is not even.
Conclusion: Therefore it is odd.
This uses the other condition: even and odd exhaust the possibilities for integers, so both cannot be false.
Key distinction: the earlier argument used affirmation to deny the alternative; this one uses denial to establish the alternative. True disjunction licenses both patterns.
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Exceptive Syllogism: Valid Inferences from Connected and Disjunctive Conditionals
Disjunction: This integer is even or odd.
Exceptive premise: But it is not even.
Conclusion: Therefore it is odd.
This uses the other condition: even and odd exhaust the possibilities for integers, so both cannot be false.
Key distinction: the earlier argument used affirmation to deny the alternative; this one uses denial to establish the alternative. True disjunction licenses both patterns.