NO OBSERVER, NO OBJECT:

On the one hand, Kant says, our reason tells us that as we home in on a substance we will eventually come to a unit that cannot be further divided, for if we didn't, there would be nothing out of which the world and everything in it is composed. On the other hand, our reason also tells us that such a simple substance, if we find it, occupies space; and if it occupies space, that space must be divisible.

In formulating the antinomies, Kant was inspired by Zeno. Zeno's paradoxes purport to prove the impossibility of motion. To get from Point A to Point B, a traveler must first cross to a Point C halfway between them. Prior to that, though, he or she must cross Point D halfway between A and C, and so on infinitely, such that the traveler never in fact moves.

In both Zeno's paradoxes and Kant's antinomies, an act of observation engenders an apparent contradiction in the very knowledge it produces. As it turns out, it is this very same apparent contradiction that we see at work in the uncertainty principle. While any and all observations contain this inherent paradox, it becomes visible only when pushed to the extreme, either of logic or of the physical world.

In a story published in his 1941 collection "Fictions," Borges created just such an extreme scenario. His character in that story, Funes, has a memory so perfect that he perceives every moment in time as entirely distinct, unrelated to those coming before or after. Consequently, he is incapable of overlooking minor differences in order to connect the impressions of one moment in time to those of the next. He becomes frustrated at our how language generalizes, at how we use the same word, "dog," to refer to a four-legged creature facing one direction at 3:14 and facing another direction at 3:15.

While Borges may have been inspired by examples of prodigious memory, pushed to such impossible extremes the example of Funes reveals the paradox at the heart of any and all knowledge of the world: namely, that there can be no such thing as a pure observation, one free of the changes imposed by time.

What Funes shows is that, at its most basic level, any observation requires a synthesis of impressions over time. Furthermore, the process by which the synthesis takes place, the media through which it is processed, and the entity doing the synthesizing are all essential aspects of the knowledge being produced. This is, in a nutshell, the first part of Kant's 1781 opus magnum, "The Critique of Pure Reason."

Kant had been challenged -- awoken from his dogmatic slumber, as he said -- by the empiricist David Hume's assertion that we could never infer any certain knowledge about, for instance, laws of causality, because we are limited to knowing what our senses can learn about the world at any given moment. We may know that the sun is rising now, he famously argued, but cannot infer with any certainty that it will rise again tomorrow.

Follow @brothersjudd