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How much complexity had to be added to human thought...

...to make us able to think of the infinite?

Uh, that's intended as a rhetorical question. Thought of the infinite is not more complex than other thought. If you think otherwise, then may I ask you: in order to be of the infinite, must thought itself be infinitely complex? If not consider whether such thought is actually SIMPLER than a lot of thoughts that we and other animals may have in a day. Yet thought of the infinite is qualitatively different, higher, than those other, more complex thoughts. In fact, it is a necessary condition for having a genuinely mathematical thought... as well as any other sort of thematization of what is or may be universally and necessarily true.

But let me unpack the above just a little. Consider how math presupposes the ability to think of a kind of infinite. Straight lines in geometry for example, are conceived of as being the same no matter how small you go. The possibility of infinite precision is implicit in the concept of a line. Maybe there's something like that with numbers: 1,2,3,4... oh yes: we think of the number line as continuing indefinitely.

Something analogous characterizes all reflection on the universality and necessity of our knowledge of general truths.


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