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I'm currently studying the indirect approach to philosophical scepticism, and I'm struggling as to how you can say anything useful in this particular area of philosophy without dragging yourself into solipsism? For example, the philosophical sceptic may argue 'How can we know there are other people that have minds?'. It seems impossible to go anywhere with this point - what conclusion could you possibly arrive from it? I find it very difficult to understand because of two conflicting notions - whilst it seems impossible to prove that there are people that have minds, it would seem an absurd and ridiculous life to lead assuming that there are no other minds except my own. So what is one to do?

You say that 'it is impossible to prove that there are people that have minds'. But doesn't it depend on what standards of proof are required? If you insist on methods of proof that are 'demon-proof' (that is, are guaranteed to deliver truths in every possible scenario, including ones in which an evil demon is manipulating the evidence), then indeed you won't be able to prove that there are other minds (or that sun will rise tomorrow, or that there is a computer in front of you). But why ever set the standards of proof so high? There are plenty of methods of proof that are a very good guide to truth in the real world without being completely demon-proof. Isn't this enough for them to count as sources of knowledge? Of course, even if this much is agreed, plenty of awkward questions remain. Exactly how good do methods of proof need to be to yield knowledge? How can we find out which methods of proof satisfy those standards? And so on. But a first response to the threat of scepticism is surely to...

Is it possible that the Universe and how we perceive it are just fractions of what is really out there? How would we know that the universe is not some completely different place that we could not even begin to undestand or perceive? For example ants live their lives without ever knowing of our existence so how would we know that there is not a lot going on in this world that we can not sense?

The idea that our familiar universe is only a fraction of reality isn't just an abstract possibility. Many serious thinkers argue that this hypothesis is in fact strongly supported by physical theory. Two distinct sets of considerations are relevant here. One is to do with the interpretation of quantum mechanics. Quantum mechanics says that the world is basically chancy: nothing determines when a radioactive atom will decay, for example; this has a certain probability, and then either does or doesn't happen. However, it has proved surprisingly difficult to give a physically cogent account of quantum chance. Advocates of the Everettian interpretation of quantum theory (a.k.a. the 'many-worlds theory') maintain that the only viable theory is that the universe is constantly splitting into branches, one for each possible outcome of every chance event. At one level this is mind-spinningly extravagant: for starters, it means that each of us is constantly splitting into trillions of irreversibly...