The Brain in a Vat

The Brain in a Vat thought-experiment is most commonly used to illustrate global or Cartesian skepticism. You are told to imagine the possibility that at this very moment you are actually a brain hooked up to a sophisticated computer program that can perfectly simulate experiences of the outside world. Here is the skeptical argument. If you cannot now be sure that you are not a brain in a vat, then you cannot rule out the possibility that all of your beliefs about the external world are false. Or, to put it in terms of knowledge claims, we can construct the following skeptical argument. Let “P” stand for any belief or claim about the external world, say, that snow is white.
If I know that P, then I know that I am not a brain in a vat
I do not know that I am not a brain in a vat
Thus, I do not know that P.
The Brain in a Vat Argument is usually taken to be a modern version of René Descartes' argument (in the Meditations on First Philosophy) that centers on the possibility of an evil demon who systematically deceives us. The hypothesis has been the premise behind the movie The Matrix, in which the entire human race has been placed into giant vats and fed a virtual reality at the hands of malignant artificial intelligence (our own creations, of course).
One of the ways some modern philosophers have tried to refute global skepticism is by showing that the Brain in a Vat scenario is not possible. In his Reason, Truth and History (1981), Hilary Putnam first presented the argument that we cannot be brains in a vat, which has since given rise to a large discussion with repercussions for the realism debate and for central theses in the philosophy of language and mind. As we shall see, however, it remains far from clear how exactly Putnam’s argument should be taken and what it actually proves