The Existential Assumption & the Square of Opposition Discussion

In the classical and medieval version of the Square of Opposition, the truth of an A-proposition entails the truth of the corresponding I-proposition.  So, if “All horses are mammals” are true, then “At least one horse is a mammal” is true.  Why is this called “the existential assumption”?  And is it a good assumption to make?Up to 20 points for your comment, and 10 for your reply to someone else.

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The reason why it is called the existential assumption is because it implies that some class is not empty, which means that there is at least one member of the class. I would agree that it is a good assumption because of the fact that horses are real subjects that exist in the world and are categorized as mammals. In addition, we could swap the subject with the predicate in the I-claim and see if the meaning is preserved or not. According to the material within the Module Two, when we mean “at least one”, we could use “some'” to indicate that there could also be more than one. Based on this rule, the claim “At least a horse is a mammal” can be rewritten as “Some horses are mammals”. Next, we could swap the subject and the object and come up with a claim as “Some mammals are horses“, which seems to be valid and is also applicable to reality. Edited by An Hsuan Kung on Sep 18 at 2:51pm