a thing as neither existent nor nonexistent, neither necessary nor possible nor impossible, and other such mental suppositions that do not entail the possibility of their existence in external reality. Thus, one can conceive an infinite line or surface, shapes of ever-increasing size without limit, and infinite dimensions. The possibility of conceiving something infinite in the mind does not entail its possibility in external reality. The opponents themselves concede the impossibility of bodies of infinite magnitude, infinite dimensions, and infinitely many causes and effects, although all these can be conceived in the mind.

If they are told:

“Likewise, conceiving infinitely many numbers, or an infinite sequence of numerical values, some greater than others, does not demonstrate that what is conceived in the mind can exist in external reality,”

their counterargument is invalidated.

Someone who counters the conception of infinitely many numbers with the conception of infinitely many shapes, and conceives differences in magnitude in the latter just as in the former, would be more justified than someone who counters differences in the numbers of orbits with differences between numerical values.

For if it is said:

“Multiplying one without limit yields less than multiplying two,”

one may reply:

“If we suppose a line one palm-width across and infinite in length, and another one cubit across and infinite in length, the palm-width line is smaller. And if we suppose spherical bodies, each the size of a human head, with no limit to their number, and others, each the size of the celestial sphere, whose number is not