Assume that every human is an animal. Choose something that is not an animal. If it were human, the universal premise would make it an animal, contradicting our choice.
It therefore cannot be human. That is precisely what “Every nonanimal is nonhuman” says.
The converse is not a word trick; it follows from the inclusion expressed by the original universal proposition.
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Contraposition: Classical Rules, Validity and the Later Convention
Assume that every human is an animal. Choose something that is not an animal. If it were human, the universal premise would make it an animal, contradicting our choice.
It therefore cannot be human. That is precisely what “Every nonanimal is nonhuman” says.
The converse is not a word trick; it follows from the inclusion expressed by the original universal proposition.