 There are four levels in Kilvington’s secundum imaginationem analyses. These levels may be classified according to their increasing abstraction and decreasing probability. On the first level, there are imaginary cases which are potentially observable and which might occur in nature, such as Socrates’ becoming white. On the second level are imaginary cases which cannot be observed, even though they belong to the natural order. These cases illustrate the necessary consequences of the application of rules properly describing natural phenomena—the best example being the Earth’s rectilinear motion, which is caused by its desire to unite the center of gravity with its own center. On the third level are cases not observable but theoretically possible, such as reaching infinite speed in an instant. The fourth level concerns cases that are only theoretically possible. Kilvington uses the last two groups of imaginable, i.e., hypothetical cases to reveal inconsistencies in received theories, especially from Aristotle, demonstrating mathematically the paradoxes that arise from Aristotle’s laws of motion. If hypothetical cases do not involve contradiction, there is no reason to reject them or exclude them from the realm of speculation (see Jung 2016).