Because of my common sense, I know, as I type this, that I have hands; but presumably a disembodied, and therefore handless, brain-in-a-vat might think so too, as a result of its experiences being so arranged that they resembled mine, down to the smallest detail—so, perhaps I am such a brain-in-a-vat? My problem is that if I do not know that that is very unlikely (or impossible)—and how could I examine its likelihood?—then I can hardly justify my belief that I have hands; so I would not know (for sure) that my hands exist. That is a problem because one naturally feels that one’s confidence in such everyday propositions is fully justified, somehow.
...... But therefore we have G E Moore’s common sense refutation of such Cartesian scepticism (and Humean scepticism can be treated similarly, e.g. see my A Pair of ‘Sceptical’s): All such stupefying scenarios can be known to be impossible because one really can know that one’s hands (knees, feet etc.) certainly do exist. That is an almost complete refutation—only a scientific question remains. Sceptical scenarios are seemingly rational possibilities that are not made sufficiently unlikely by the empirical evidence, whence even when we are not tempted by the scepticism, they naturally raise such scientific questions as: How do we know that we have hands?
...... Insofar as we think of our knowledge of the external world as being constructed indirectly, from nerve-signals coming from sensory organs external to our brains, it is quite mysterious (in view of such sceptical scenarios) how our natural confidence in our knowledge of the ordinary things around could be justified. Nonetheless the foundations of our scientific knowledge are surely our common sense certainties (e.g. as we perform experiments), so we cannot really question them, we can only seek their scientific justification. Now, scientific questions require scientific answers and of course, as a philosopher of mathematics I don’t have a scientific answer, but what I can do is speculate.
...... The scientific answer would surely be some theory devised to account for scientific observations of the relevant phenomena, so we might ask ourselves: What would be relevant here? Well, in what ways might we become directly acquainted with things? A clue comes, it seems to me, from our need to explain the direct mind-brain interaction (since something else that is common sense is Cartesian dualism), because quantum mechanics is likely to be a key component of that explanation. If so, then (wavefunctions being spread out) we might expect direct knowledge of external objects to be possible too, and so the relevant phenomena could well include the micro-psychokinetic (the ‘micro’ means that the mind interacts directly with chance phenomena in the external world, i.e. not levitation).
...... Of course, common sense also tells us that the paranormal is not worth investigating. After all, such things are investigated, by reputable sceptics and by believers, and nothing ever comes of it. But then, a socio-economic explanation for that might involve that word ‘reputable’—I don’t want to delve into such issues here because they are intrinsically complicated (as political issues are). I’ll just observe that if I’m right (and why not?) then the paranormal would, insofar as it occurs, be the extremity of something quite normal (much as superfluids are), varying in the usual way of such biological things (and insofar as it does not occur—e.g. poltergeists—its plausibility could be similarly explained, i.e. via the ubiquity of something that is both obscure and like the fiction). After all, the empirical evidence is not inconsistent with lesser degrees of the so-called sixth sense being surprisingly common (e.g. consider the sense of being stared at, which would probably have been selected for if our underlying physics does allow it; cf. this recent research).
...... Just as Humean scepticism motivates our taking seriously what is common sense, that there are laws of nature (indicated by the correlations due to them), by verging upon a reductio of their non-existence (of there being only the correlations), so Cartesian scepticism motivates our taking seriously what is common sense, that we are directly acquainted with such natural kinds as hands (e.g. via a process akin to the mind-brain interaction), by verging upon a reductio of its non-existence (of our having only an indirect acquaintance with our own hands).