Can you elaborate on your conclusion? I'm unsure as to how this creates a paradoxical cycle, if the premise is that you know nothing.
I can try. The premises weren't "that you know nothing", the premises were those of your opening argument + finite humans.
Premise 1: In order to know anything, must be able to validate the correctness of your knowledge through some method.
Premise 2: In order to know that your method of validation is correct, you must use a method of validation on your method.
Premise 3: Each method of validation must be unique, since we will not accept circular reasoning.
Premise 4: Humans are finite.
Conclusion 1: p2+p3 => After validating the original method, the second method must be validated, by a third, unique method of validation, which in turn is not valid until we validate it with a fourth, unique method, and we can see from this pattern that an infinite amount of validation methods are required, since stopping at any arbitrary value will leave us with the final method of validation
unvalidated, and as such the entire chain fails.
Conclusion 2: c1 + p4 => Since an infinite validation chain is required, and humans are finite, humans are not capable of validating anything.
Conclusion 3: c2 + p1 => Since humans cannot validate anything, but validation is required to know anything, humans cannot know anything.
The alternative would be like adding zero to an integer, in hopes of changing it (winning the argument). Although, adding 0 will never actually do anything.
Be careful with your analogies. Obviously a + 0 = a, but this is a unique property of the group of numbers under addition. If you take matrices as an example, you can have ab = 0, where both a and b are non-zero.
then his claim can't be true since his claim was claiming knowledge he didn't have.
It could still be true, despite the fact that he has no knowledge as to its accuracy or falsity. Same thing can happen with any claim. Happens all the time on game shows:
Bob: okay susie, we have two doors for you, one has a prize and one has nothing
Susie: oh I want door number two bob, door number two,
I know it's door number two!
Bob: are you sure you don't want door number one?
Susie: oh I'm sure bob, I want door number two!
Bob: okay, let's show her what's behind door number two!
*game show person opens door*
Bob: a new car!!!
Did Susie really have any knowledge of which door was correct? No, probably not. But she claimed to know. A claim has nothing to do with knowledge, the proof that backs up the claim is where the knowledge is at. If we ask Susie "how did you know it was door number two?" And she says "oh I just knew" then obviously it was luck, random statistical probability, but if she answers "I snuck back there earlier and saw it was door number two" then of course she had some knowledge of the state of things.
Really though, when it comes to skeptics, and they tell you that you can't know anything, punch them in the mouth. Then, when they say "what the fuck dude, why'd you punch me in the mouth?" respond with "Well, according to you, you don't know I punched you in the mouth"
In my personal opinion, skepticism only comes from a misguided belief that people can't know anything because our sense data is not impervious to illusion, so they have to disbelieve EVERYTHING because it's all at risk of being false, when in reality, maybe only a small portion of our sense data is corrupted. On top of that, we can reasonably extrapolate from experience to know when our sense data is corrupt. Like when you watch a magician, your sense data tells you that he put a person in the box, and that person dissapeared. Your reasonable extrapolation tells you this is a situation where more than sense data is needed, so you don't believe the sense data. On the other hand, you go down to your local grocery story to buy a carton of milk. Last week the price was 2.79, and this week the price is 3.49. Your sense data tells you that this sign changed forms. No, of course not, you know the person running the store came over and changed the sign sometime in the last week.
None.