We consider two categorical syllogisms, valid or invalid, to be equivalent if
they can be transformed into each other by certain transformations, going back to Aristotle, that preserve validity. It is shown that two syllogisms are
equivalent if and only if they have the same models. Counts are obtained for the number of syllogisms in each equivalence class. For a more natural
development, using group-theoretic methods, the space of syllogisms is
enlarged to include nonstandard syllogisms, and various groups of
transformations on that space are studied.