I'm inclined to think that there are, and perhaps must be, things that humans can't understand because of the limitations of our brains. Now, the term 'understand' might mean (i) 'understand at all (i.e., at least partly)' or (ii) 'understand completely'. On interpretation (ii), it's pretty clear that there are things we can't understand, because our finite brains can't grasp all of the infinitely many facts there are about even as ordinary a thing as my car. What's my car's exact mass right now? (No rounding allowed!) Even on interpretation (i), there may be things that humans can't understand. The only organ with which we can hope to understand something is our brain. Why wouldn't our brain's finite capacity for information storage, calculation, and so on, be accompanied by a finite capacity for understanding things? Indeed, Colin McGinn has conjectured that some of the central problems of philosophy have endured for so long because, although they have solutions, our species lacks the ability...

You take issue with the way the content of the man's belief is being described in this case: you suggest that the content of his belief is the more specific (1) 'There is a sheep 200 yards out there' rather than the less specific (2) 'There is a sheep out there'. If we're worried about the actual content of the man's belief, then (1) strikes me as unrealistically specific: 200 yards rather than 201 yards? But never mind that. We can easily use (1) to generate a Gettier case: suppose that the man validly deduces that (2) from his belief that (1) and thereby comes to believe that (2). Valid deduction is one way in which we come to believe things. If he's justified in believing that (1) even though (1) is false, then presumably he's justified in believing that (2) by validly deducing (2) from (1). So he's justified in believing that (2), and (2) is true because of a sheep he can't see. So he has a justified, true belief that (2) yet doesn't know that (2).

You asked, "Can we know for sure that the external world exists?" That will depend, of course, on what's required for such knowledge. Some philosophers have said that such knowledge requires a successful proof of the existence of the external world, but many other philosophers (especially in the last few decades) have said that no such proof is required. For those who think a proof is required, G.E. Moore famously (or infamously) offered one: see this link . If you investigate Moore's proof at that link and in other places on the web, I think you'll get a sense of how the proof you offered might be received by various philosophers.

Very interesting (if tantalizingly brief) question. There's reason to think that all human beings rely on their memories for any knowledge they possess. One might think I can know at least some facts about my present-tense experiences without relying on my memory, but what facts could those be? For example, if I'm to know that I have a headache (when I do have one), arguably I must know what counts as a headache, and isn't that something I once learned and now remember? Descartes (1596-1650) was very sensitive to the role of memory in human knowledge. He famously argued that (a) only if you're aware of the existence of a benevolent God do you have sufficient reason to trust your memory, and that (b) without sufficient reason to trust your memory you know virtually nothing. Both (a) and (b), and Descartes's arguments for them, can of course be questioned. You'll find more at this link .

Your question asks about your knowledge of your own certainty : "How do you know that you are sure...?" That's a question about your knowledge of your own mind rather than about your knowledge of your parentage. So I think the best answer is "By introspection -- by looking inward -- and perhaps also by examining your own behavior for signs that you're unsure that the people you take to be your parents are in fact your parents." If, instead, you meant to ask how you can be sure that the people you take to be your parents aren't impostors, then you might have to seek DNA evidence (in the case of biological parents) or adoption records and other documents (in the case of adoptive parents). There's also a facetious answer: "Of course your parents are your parents -- that's a tautology!"

"Is there any way of answering this question without an innate idea of God?" Yes! I recommend starting with the detailed SEP entry on skepticism .

I'll try to answer the second of your three interesting questions. The proponent of the dream argument for skepticism (imagine rehearsing this argument to yourself) could say, "For all I know, this allegedly scientific claim about right and left hemispheres is merely more stuff from my dream; I can't tell that it's not. Even if it's a true claim, I can't know that it's true until I rule out the possibility that I'm merely dreaming it up." If so, then Bruce Wayne's reasoning wouldn't be an effective reply to the dream argument. This isn't to say that it's clear sailing for the dream argument. My view, for which I argue here , is that the dream argument is self-defeating unless it's no different from (and hence no improvement on) the evil demon argument.

I congratulate you on your interest in philosophy at the age of 16 -- in this case, your interest in epistemology (the theory of knowledge) and, within epistemology, the issue of skepticism . You posed your question in terms of certainty. I said in response to Question 4721 that the term 'certain' works in a way that allows you to be certain that some proposition P is true even though it's logically possible that P is false. But you raised a harder question: Can you be certain that P is true when the evidence you now have is the same evidence you'd have if P were false? This question is hotly debated: there are plausible grounds for answering "No" and plausible grounds for answering "Yes." You might start your investigation by reading Peter Klein's SEP article on skepticism . It's long and challenging, but I think it will reward your patience. I recommend paying particular attention to Klein's discussion of the concept of evidence. (By the way, I don't think particle...

Your questions are so terse that I can't be confident I'm interpreting them as you intended. But I'm inclined to answer them "Yes" and "Yes." If by "reason" you mean "deductively valid reasoning," then reason is infallible in the sense that it's guaranteed never to lead us from truth to falsity. Even so, however, we're fallible in our use of reason: we can think that some bit of reasoning is deductively valid and be mistaken about that (within limits: some reasoning is so basic that it would make no sense to think we could be mistaken about its validity). Still, deductive reasoning differs from other ways of forming beliefs in that when it's properly employed it can't lead us into error. Can reason alone help us understand everything? Yes, with emphasis on help . We can apply deductive reasoning to the inputs we get from our senses, from introspection, from memory, from our traffic in concepts, etc., to see what those inputs imply, to see what their content is, to understand them...

I'd question your assumption that solipsism "cannot be disproven to 100% certainty," unless by "disproven to 100% certainty" you mean "shown to be logically impossible," but in that case I'd question your use of "disproven to 100% certainty." I think the latter phrase, or something close to it, has a use in our language, and therefore a conventional meaning, and its meaning isn't the same as "shown to be logically impossible." That is, I think we use the phrase in such a way that something can be disproven to 100% certainty without being shown to be logically impossible. Furthermore, although they don't quite convince me, some argue that solipsism can be shown to be logically impossible because it requires the existence of a "private language," something that's allegedly incoherent. For (much) more on that argument, you might start with this SEP article .