Original: Every cat is an animal.
Step 1: Complement the subject “cat” to “noncat.”
Step 2: Complement the predicate “animal” to “nonanimal.”
Step 3: Put “nonanimal” first and “noncat” second.
Result: Every nonanimal is a noncat. No cat can be a nonanimal, so the result follows. This illustrates valid contraposition of a universal affirmative.
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Contraposition: Classical Rules, Validity and the Later Convention
Original: Every cat is an animal.
Step 1: Complement the subject “cat” to “noncat.”
Step 2: Complement the predicate “animal” to “nonanimal.”
Step 3: Put “nonanimal” first and “noncat” second.
Result: Every nonanimal is a noncat. No cat can be a nonanimal, so the result follows. This illustrates valid contraposition of a universal affirmative.