Fallibility vs Infallibility

And binary.

This is another variant of the same old theme I keep rehashing.

If we have no perfect (infallible) knowledge, then we cannot know with certainty that we have no perfect/infallible knowledge. Even as fallible beings, we must know at least that--but then, we're not completely fallible after all. Just, mostly.

Maybe 99.99%.

...

In the mystical traditions, "one" is unity, "two" is a division (from a whole to distinct things). Dualistic thinking. If we had no powers of discrimination whatsoever, presumably we would experience all things as one giant homogeneous, indistinguishable conglomerate.

That is, assuming it is possible to "experience" at all without discriminating in some way or another. Don't our senses detect contrast best? When exposed to a single, unwavering stimulus, that stimulus loses its edge, its flavor, its ability to be sensed at all?

From the concept of "two"--of one thing distinct from another--we can build up, perhaps, the entirety of mathematics (and thus, we think, physics, nature, human thought) through binary; binary being a meaningful alternation between two distinguishable states (represented in computers as "0" and "1").

If we can reduce any piece of information to "yes" or "no" questions--true or false statements--then we can represent it as a series of bits. Just as, even before George Boole came along, logic traditionally separated all propositions into those which are the case and those which are not, knowing that some thing cannot both be the case and not be the case simultaneously. Presumably, a mind simply needs to know, from the list of infinite propositions, which are true, which false. (Perhaps we would need to know which propositions are senseless or lacking truth/false values too; but then we shouldn't have included them in the list to begin with.)

This would be sufficient for omniscience...? Leibniz thought so, or at least that God comprehended the universe through such eyes.

Infinity does seem to present a problem, among many other obstacles. Recursion, describing oneself while describing the universe.

And what about the infinity of imaginary possibilities? Are conditional/subjunctive statements "true" or "false"?