Here is one hand is an epistemological argument created by George Edward Moore in reaction against philosophical skepticism and in support of common sense.
The argument takes the following form:
G. E. Moore wrote A Defence of Common Sense and Proof of an External World. For the purposes of these essays, he posed skeptical hypotheses, such as "you may be dreaming" or "the world is 5 minutes old", and then provided his own response to them. Such hypotheses ostensibly create a situation where it is not possible to know that anything in the world exists. These hypotheses take the following form:
Where S is a subject, sp is a skeptical possibility, such as the brain in a vat hypothesis, and q is a knowledge claim about the world:
Moore does not attack the skeptical premise; instead, he reverses the argument from being in the form of modus ponens to modus tollens. This logical maneuver is often called a G. E. Moore shift or a Moorean shift. His response takes the following form:
Moore famously put the point into dramatic relief with his 1939 essay Proof of an External World, in which he gave a common sense argument against skepticism by raising his right hand and saying "here is one hand," and then raising his left and saying "and here is another". Here, Moore is taking his knowledge claim (q) to be that he has two hands, and without rejecting the skeptic's premise, seeks to prove that we can know the skeptical possibility (sp) to be untrue.
Moore's argument is not simply a flippant response to the skeptic. Moore gives, in Proof of an External World, three requirements for a good proof: (1) the premises must be different from the conclusion, (2) the premises must be demonstrated, and (3) the conclusion must follow from the premises. He claims that his proof of an external world meets those three criteria.