It seems reasonable to open a book such as this with a simple question: What is scepticism? According to Webster's, it is “an attitude of doubt or disposition toward incredulity in general or in regard to something particular”. So scepticism relates to doubt; but what is it to ‘doubt’ or to have a ‘doubting attitude’? Mention scepticism to anyone who has been subjected to an introductory course on ‘The Problems of Philosophy’ and they will probably recall that there are a number of arguments that seem to show that we can doubt, and therefore don't know, many if not all of the things we claim to know. As such, what it is to doubt is associated with certain sorts of thought-experiments like the idea that right now you or I might be dreaming, or a disembodied brain floating around in a vat of nutrients linked up to a supercomputer.