In everyday life, we change our beliefs all the time. In philosophy, belief change is less common, because the beliefs in question are often very deep-seated and indeed in some cases -- for example the belief tables don't disappear when you blink -- effectively unrevisable. But if you want a personal example of philosophical belief-change, I used to think that it was fine to eat veal and ordinary (i.e. not free-range) chicken. Then I made the mistake of teaching a couse on applied ethics, and I changed my mind. Or if that seems too ordinary for you, I used to think that the content of my beliefs must be fixed by what is going on in my brain or mind. Then I read Putnam and Kripke...

Reading these questions might just make you more aware; thinking about them just might make you more intelligent.

Here is an additional (and very ahistorical) reason for studying some history of philosophy. The best philosophers of the past had more philosophical talent than any philosopher now living.

Much of it is consistency checking, and this involves playing off our intuitions against each other and trying to get rid of contradictions in our beliefs. The good news is consistency is a necessary condition for truth: if our beliefs are inconsistent they cannot all be true. The bad news is that consistency is not a sufficient condition for truth: there can be more than one system, where each system is interally consistent but where the systems are inconsistent with each other. But consistency turns out to be a suprisingly demanding constraint, particularly as you expand the set of beliefs in play, a set that will for example include scientific as well as philosophical claims. And notice that science too has limitations. Is is not as if observed reality enables scientists to prove their theories. They have a problem similar to the philosophers' problem of mutiple consistent systems. For no matter how much data a scientist gathers, there will always be in principle many theories that are...

Lexicography and conceptual analysis must anyway be different, since a good dictionary has lots of good definitions, while philosophers are hard pressed to give a correct conceptual analysis of any of the concepts that centrally concern them. One reason for this may be that conceptual analysis tries to go deeper than lexicography, to give the underlying contours of a concept. Take the concept of knowledge. My dictionary defines knowledge as 'the facts, feelings or experiences known by a person or group of people'. Not very deep, because it uses 'known' in the definition. Philosophers try to avoid that sort of circle. The traditional philosophical definition of knowledge is 'justified true belief', which probably avoids a circle; but it is also wrong. Like pretty much every philosophical analysis, it is both too narrow and too broad. Thus you can know without having a justification, say if you just see something, and you can have a justified true belief without knowing, because it may still be just...

This is a surprisingly difficult question to answer. There are a number of answers that seem to have something going for them, but also face various difficulties We might say that science is empirical, based on observation and experiment, whereas you can do philosophy with your eyes closed. But some parts of science are highly conceptual and far removed from the data, and on the other side a number of philosophers have denied that philosophy or any other form of inquiry could be entirely independent of empirical evidence. We might say that science concerns how things are while philosophy concerns how things ought to be. But although questions about how we ought to act and what we ought to believe are central to philosophy, there are also other, more descriptive aspects of philosophy, such as metaphysical questions about what sorts of things exist. We might say that science asks questions that we know in principle how to answer, whereas philosophy asks questions which, although they seem...

Here is one reason why one limited form of competition in philosophy (and many other areas of inquiry) is good. Faced with a philosophical problem, our best bet is to propose a possible solution, criticise it, and on that basis to try to improve it, or improve on it. But almost all philosophers are better at criticising other people's ideas than their own. So competition yields an epistemic advantage. Karl Popper proposed this kind of methodology of 'conjectures and refutations' as the key to inquiry, especially in science. Although there is a lot I would criticize (sic) in Popper, I think he is right to emphasise the importance of trying to find the weak points in the best ideas people can come up with.

How do you even know they have the question? But if what you are asking is how philosophers know that an answer they propose is in fact the right answer, then the question is big and complicated. Here is a short partial answer. Philosophers are good at finding contradictions between different things we are inclined to believe, and one way they test their answers is seeing whether they can be integrated into a consistent system. Consistency is no guarantee of truth, but inconsistency is a guarantee of falsehood.

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You have put it very well: exposing those mysteries is a deep pleasure of philosophy. That is one of the reasons that the great skeptical arguments -- arguments that seem to show that we have no reason to believe anything we have not seen, or anything outside ourselves, or even that our thoughts have any content -- are fascinating. They do cause a chill up the spine. The feeling of having solved the problem (a feeling I rarely have) is difficult to compare with the feeling of wonder at the problem. But if you are by disposition a philosopher you will not be inclined to wallow in the wonder; instead it will drive you to try to solve the problem.