 Work on logic continued for the next couple of centuries, though most of it was lost and had little influence. But the topic of empty terms was squarely faced, and solutions that were given within the Medieval tradition were consistent with [SQUARE]. I rely here on Ashworth 1974, 201–02, who reports the most common themes in the context of post-medieval discussions of contraposition. One theme is that contraposition is invalid when applied to universal or empty terms, for the sorts of reasons given by Buridan. The O form is explicitly held to lack existential import. A second theme, which Ashworth says was the most usual thing to say, is also found in Buridan: additional inferences, such as contraposition, become valid when supplemented by an additional premise asserting that the terms in question are non-empty.