Epistemology
In the field of epistemology, Putnam is known for his "brain in a vat" thought experiment (a modernized version of Descartes' evil demon hypothesis). The argument is that one cannot coherently state that one is a disembodied "brain in a vat" placed there by some "mad scientist".
This follows from the causal theory of reference. Words always refer to the kinds of things they were coined to refer to, thus the kinds of things their user, or the user's ancestors, experienced. So, if some person, Mary, were a "brain in a vat", whose every experience is received through wiring and other gadgetry created by the "mad scientist", then Mary's idea of a "brain" would not refer to a "real" brain, since she and her linguistic community have never seen such a thing. Rather, she saw something that looked like a brain, but was actually an image fed to her through the wiring. Similarly, her idea of a "vat" would not refer to a "real" vat. So, if, as a "brain in a vat", she were to say "I'm a brain in a vat", she would actually be saying "I'm a brain-image in a vat-image", which is incoherent. On the other hand, if she is not a "brain in a vat", then saying that she is still incoherent, but now because she actually means the opposite. This is a form of epistemological externalism: knowledge or justification depends on factors outside the mind and is not solely determined internally.
Putnam has clarified that his real target in this argument was never skepticism, but metaphysical realism. Since realism of this kind assumes the existence of a gap between how man conceives the world and the way the world really is, skeptical scenarios such as this one (or Descartes' Evil demon) present a formidable challenge. Putnam, by arguing that such a scenario is impossible, attempts to show that this notion of a gap between man's concept of the world and the way it is, is in itself absurd. Man cannot have a "God's eye" view of reality. He is limited to his conceptual schemes. Metaphysical realism is therefore false, according to Putnam.
Read more about this topic: Hilary Putnam