Please excuse my parentheses; I hope they don't obscure my answer. As I understand it, an inference is (deductively) valid if and only if there's no possible world in (or at) which the premise(s) is (are) true and the conclusion is false. So "Socrates is a man; therefore, there's at least one man" is a deductively valid inference, since there's no possible world in (or at) which the premise is true and the conclusion is false. Ditto for the inference "Socrates exists; Socrates doesn't exist; therefore, snow is green": Barring equivocation, there's no possible world in (or at) which the premises are both true, and so there's no possible world in (or at) which the premises are both true and the conclusion is false.

Could you or the Demon even understand what he tells you? The Demon tells you (a) that he has predicted what you'll eat for lunch. Of course, now that he's told you that, what he's really told you is (b) that he has predicted what you'll eat for lunch given that he's told you (a). Notice that (b) isn't the same item of information as (a). But wait. If he's told you (b), then really what he's told you is (c) that he has predicted what you'll eat for lunch given that he's told you (b). Notice that (c) isn't the same item of information as (b) or (a). And so the regress continues, forever. Therefore, I wonder if anyone can understand the story you've sketched well enough to see what the story implies or what's consistent with it. In this article , my co-author and I raised a similar worry in regard to Newcomb's problem, a famous problem in rational decision theory that also involves a predictor. But I'm not sure anyone else was convinced by our argument! In any case,...

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 .

I strongly doubt it! I think it's a very good bet that we human beings will continue to improve our understanding of the universe, but I strongly doubt that our understanding will ever become perfect, that there will come a time at which we've answered every meaningful question about it. Certainly there's no evidence from the history of science that such a day will come. Quite the contrary. Every time scientists have thought that the end is in sight, that soon no further important questions would remain in some domain, a revolution has occurred to open unforeseen avenues of inquiry. Here's a trivial reason why the possibility of further inquiry won't end. Suppose we answer the 'final question'; call it 'FQ'. Why did we ask FQ? That question is meaningful and has to be distinct from FQ. Call it 'FQ*'. Why did we ask FQ*? And so on. A less trivial reason stems from the widely held assumption that at least some aspects of our universe are contingent rather than absolutely necessary. If...

Interestingly, something like the converse of your question was asked and answered at Question 4669, linked here . The earlier question was " Is 'understanding' a proposition necessary, but not sufficient, for 'believing' that same proposition?" Whether it's psychologically possible for someone to believe a given proposition without understanding the proposition will depend on whether it's even conceptually possible, i.e., whether it could even make sense to describe someone that way. When asking whether something is conceptually possible, philosophers often consult their linguistic intuitions. So you might ask whether you would sincerely assert something of the form "So-and-so believes that p but doesn't understand it." I myself wouldn't. Now maybe that shows only that such statements are unassertible rather than conceptually false, but I think it's conceptually confused to describe someone as believing a proposition without understanding it. If it is, then the answer to your second...

Your question engages at least three areas of philosophy: metaphysics, epistemology, and philosophy of mind. The answers are as deep and detailed as those areas, i.e., as deep and detailed as you want to go. But maybe a short answer will do for now. Someone claims, apparently sincerely, that the government is controlling him by means of radio signals sent to his dental fillings. (1) He's "in contact with reality," in that respect, only if the government is in fact doing what he claims. (2) There's no good reason to believe it is, and good reasons to believe it isn't (his relative unimportance, the nature of radio signals, the nature of neurons, etc.). If we're justified in drawing conclusions about any empirical issue, I'd say we're therefore justified in concluding that he isn't in contact with reality in that respect. (3) I'm no psychiatrist, but my sense is that losing "contact" with reality requires being impervious to evidence in a special way; not just any false belief, even if persistently...

Philosophers, especially lately, have had a lot to say about this topic. You might start with this SEP entry , and I recommend looking at this recent anthology . Fortunately (or unfortunately, if you wanted a short answer!), there's a large and growing literature on the topic. Enjoy.

Warning: I grind my methodological ax a bit in these answers. 1. "Does it follow from the fact that he got excited from breaking the rules that he broke the rules for the sake of breaking the rules rather than the excitement it generated?" No: it doesn't follow; the former doesn't logically imply the latter. A philosopher (indeed, any decent reasoner who understands the question) can answer that one. 2. "Are there other reasons why breaking the rules might be exciting other than a desire to break the rules for its own sake?" I can't see why not, but here you're better off asking a psychologist, someone who studies people's actual motivations in a systematic way. 3. "Maybe he got excitement from stealing the peaches because it was risky or because he wanted to challenge authority or to feel less confined by rules." Maybe so. For more than "Maybe so," you'd again need to consult someone with psychological insight into rule-breakers in general and (if possible) this rule-breaker in particular...

I'd say that C. I. Lewis's strict implication is very much alive in contemporary philosophy, although often called by different names, such as "logical entailment" or "logical implication." Philosophers frequently claim (or deny) that some proposition "entails" another, by which they very often seem to mean "strictly implies." Material implication, unlike strict implication, is a truth-functional relation between propositions: given only the classical truth-values of two propositions, you can tell which one materially implies the other (material implication will run in at least one direction between them, if not both). By contrast, strict implication isn't truth-functional: it requires asking about the truth-values that propositions take in worlds other than the actual world, which invites philosophical controversy. As a result, strict implication is a less clear-cut relation than material implication. So despite its unintuitive features (which, as you say, Lewis criticized), material...