Like most philosophers (though perhaps not most historians and sociologists of science), I think that knowledge requires truth, but it remains possible for someone to know something at one time and not to know it at a later time. Knowledge requires belief as well as truth, so a simple way that knowledge can be lost is if a person knows something but later for whatever reason stops believing it. Knowledge also requires warrant, and warrant may be lost. One possible example is where the warrant is forgotten. Suppose I prove a mathematical theorem. At that point I know that theorem to be true, but later I forget not only the proof but that I ever had a proof, though I retain the belief in the theorem. Here I would say (though I can imagine some philosophers resisting this) that I no longer know. Or maybe I don’t forget the warrant, but I acquire additional evidence that goes against my belief. Thus suppose I remember the proof, but it was quite tricky, and one day a much better mathematician that I...

One aspect of success is getting what you want, so if Mr. A wanted knowledge, and he got it, then he was successful. Indeed getting what you want is an aspect of success even if you don’t realise that you are getting it. For example, if I want to be a good role model for my children and I am, then I am successful, even if I mistakenly believe that I am a terrible role model. So even if Mr. A doesn’t realise that he is getting knowledge, if he is then he is successful. But maybe it’s not enough for success to get what you want; maybe what you want also has to have some value other than the value of being wanted. For example, some people would deny that a person who has managed to collect an enormous number of used matches is successful, even if that is what he wanted to achieve, on the grounds that what he wanted has no value. I’m not convinced that this is right – I think maybe the bare fact of wanting something gives it some value – but if one does accept the need for intrinsic value, then...

Almost everything we know we only know with the help of what others have told us. In that sense, testimony is our dominant source of knowledge. So it is somewhat surprising that the history of epistemology contains so little material on the epistemology of testimony. One reason for this neglect is the view that belief from testimony is fundamentally less secure than belief from reason or direct experience. Another is the view that, however important testimony may be, it is never the source of new knowledge, but only a way of distributing old knowledge. Both of these views are eminently disputable. One famous discussion of the epistemology of testimony is David Hume's chapter On Miracles in his Inquiry Concerning Human Understanding . For a good recent book, have a look at Tony Coady's Testimony.

Thomas Kuhn goes some way in this direction in his work on the nature of science. (You might have a look at his classic Structure of Scientific Revolutions , especially chapter ten .) It's not that he denied that there is an external world that sharply constrains what scientists can say; but he did hold that the structure of kinds and properties that scientific theories ascribe are not out there in the world independently of us but are something that the scientific community imposes on the empirical reality it is studying. Like Kant, Kuhn held that the empirical world is structured by the minds of those who study it. Only where Kant thought that the structure contributed by us could only take one form, Kuhn held that the human contribution changes with each scientific revolution. Thus Kuhn is Kant on wheels.

When we see or otherwise represent the world outside our minds, the act of representation is different from the object being represented. The object represented, say the Eiffel Tower, is something physical, but the act of representation is a thought -- something mental. This difference between that act of represenation and the object being represented might seem to entail that all representation introduces bias. The idea is that the act of representation must introduce something foreign to the object being represented, since the act is different from the object. But this is a bad argument. Of course there is no thinking without thinking; but it does not follow from this that we can only think about thinking, or that thinking always infects what we are thinking about. Just because the act is mental doesn't mean it represents the object as being mental. A postcard of the Eiffel Tower is flat, but it doesn't represent the Eiffel Tower as flat. Seeing the Eiffel Tower is a mental experience,...

Here are just a two brief reactions to your good question. First of all, maybe we do have an infinite number of beliefs. I believe a have fewer than three arms, and that I have fewer than four arms, and just maybe I believe that I have fewer than x arms, where x is any integer greater than two. But that is an infinite number of beliefs. Second of all, there can be belief that p without a belief that there is a belief that p. Dogs are good examples. Fido believes that there is food in his bowl, but he doesn't believe that he believes that he has food in his bowl, because he cannot entertain a thought like that. Dogs have beliefs, but they don't have the concept of belief. Perhaps people are like that two. Sure we, unlike Fido, can entertain the thought that there is a belief that there is food in the bowl, but maybe when you iterate the belief operator beyond a certain number of times, we lose conceptual grip.

If we take 'intuition' to mean something like what just seems right or wrong, then philosophy often seems to rely on intuition. One kind of case is when we are trying to analyse a concept. Take the concept of knowledge. We convince ourselves that knowledge is not quite the same as justified true belief, since if you believe that it's 10:45 because your normally reliable watch says so, you don't know it's 10:45 if in fact your watch stopped exactly twelve hours ago, even though your belief is true and justified. But notice that here the argument relies on our intuition that in this case you don't know the time. That seems the right answer, and philosophers lean on that feeling. Another kind of example is a situation in ethics where you decide what is right by playing your intuitions off against each other. It seems right that one shouldn't cause unnecessary suffering, and yet it also seems OK to eat meat. Then you come to believe that eating meat causes unecessary suffering. So for the sake of...

This doesn't address all of your question, but notice that if (as it seems) we can truly say that certain things do not exist, then there must also be true generalisations, since 'There are no A's' is equivalent to the generalisation that 'Everything is a non-A'. Thus 'Griffins do not exist' is equivalent to 'Everything is a non-griffin', and 'There are no non-black ravens' is equivalent to 'All ravens are black''.

This is not an easy question to answer, in part because it's not clear what it means 'to know what something is'. Still, various sensations may be candidates for things we know better than we can describe, sensations like headaches, the taste of pineapple, or the smell of rotten eggs. The reason is that we know what sensations are like by having them, not by having them described to us. It may seem harder to see how we could know what something like time is better than we can say, since time is not an experience. But there probably are things other than experiences that that we can know better than we can say. For example, I may be better at recognising a person in a crowd than in describing her.

I agree that a lucky guess is not knowledge. It's a true belief, but what seems to be missing is some justification for the belief. What is more surprising is that even a justified true belief may fail to be knowledge. Do you know what time it is right now? Have a look at your watch. Now you know, because you are justified in believing that your watch is working. Of couse if unbeknownst to you your watch has stopped, then you you don't know the time, because your belief about the time, though still justified, is false. But now suppose that, by sheer coincidence, your watch stopped exactly twelve hours ago. In that case your justified belief would be true! But still, you wouldn't know what time it is. Hey presto: that's a justified true belief that is not knowledge. Cases like these were brought to the attention of the philosphical world by Edmund Gettier in the 1960s, and they have prompted a large literature. For an article on Gettier cases, click here .