Do we have a name for the following axiom?: We can never know for sure whether we know everything that exists

Question

Let's assume that our words and sentences are able to describe the truth. It is clear that whatever we know - even if we have knowledge about an entire universe and every position and momentum of its particles - we are inherently determined to not know whether we know really everything. It implies that we cannot prove anything because it would require a complete knowledge which we cannot know we have. That implies that we are never going to be able to know the absolute truth. In other words, we are never going to be able to know the absolute truth because it would require knowing everything. (Even if we knew everything, we are not able to know that we know everything and therefore we are inherently determined just to assume that something is true.)

Yet it seems to me that we are actually able to know one absolute truth, which is the following:

We know for sure that we cannot know whether we know everything and therefore we cannot know anything for sure.

I know that I am contradicting myself but this problem seems to me rather peculiar. Am I touching on some problem of an incompleteness theorem? What do you think about my reasoning? Since it is just my reasoning, would you please give me some reference to it?

Answer 1

Do we have a name for the following axiom?: We can never know for sure whether we know everything that exists

Yup, I'd call that incompleteness.

It's not precisely what the term "incompleteness" originally meant, within the minimal ontology in which it was conceived, but it's essentially mappable to it.

---

Yet it seems to me that we are actually able to know one absolute truth, which is the following:

We know for sure that we cannot know whether we know everything and therefore we cannot know anything for sure.

If you believe that your own thoughts are inviolate, existing as abstract entities that're inherently valid, then incompleteness isn't an issue; you know absolutely true things because we're assuming that they're absolutely true, and you can use those absolutely true things to establish other absolutely true things through logical construction.

Then, it'd be more precise to phrase your claim like this:

We can't be sure about anything except for those things we've established through purely logical construction.

Then that claim is itself knowable as absolutely true because it was established through use of such logic. And that logic is itself absolutely true because it just is because we-said-so.

Incompleteness doesn't really become problematic until we stop regarding our minds as inviolate. Once we start questioning our most basic beliefs or/and our thought processes, then we have a problem because we don't have absolute truths to build everything else upon.

At this point, the claim

• We can't be sure about anything except for those things we've established through purely logical construction.

reduces to

• We can't be sure about anything.

because we no longer hold anything to automatically get a pass as being "purely logical".

Then is the claim that "We can't be sure about anything." self-contradictory?

I'd see it as consistent. I mean, the entire point is that we can't be sure about anything, even what some might regard as purely abstract logic. So even if we attempt to think the claim out, and establish its apparent consistency and good-standing, we can't be sure that the thoughts we used to validate it weren't themselves somehow corrupted, or that we may've misremembered something.

Answer 2

The OP makes the following claim:

Yet it seems to me that we are actually able to know one absolute truth, which is the following:

We know for sure that we cannot know whether we know everything and therefore we cannot know anything for sure.

However, do we really know that? That is actually the conclusion of an argument which rests on some premises which are assumed. Is that argument valid? Here is one of the premises:

It is clear that whatever we know - even if we have a knowledge about an entire universe and every position and momentum of a its particles - we are inherently determined to not know whether we know really everything.

It seems clear that we do not know everything, but we also have this assumption:

Let's assume that our words and sentences are able to describe the truth.

That assumption means that our words and sentences are bearers of truth. Surely there is at least one of those words or sentences that we do know. Even Descartes had "I think therefore I am".

That we don't know everything seems true. However, there do appear to be things that we do know given that our words and sentences are assumed to be truth bearers and Descartes gave us an example of something we do know. So we cannot conclude from that true statement that we do not know everything that we do not know anything. That conclusion would be a false statement. If a true antecedent implies a false consequent the conditional statement is false making the argument invalid.