On Certainty is a series of notes Wittgenstein took toward the end of his life on matters related to knowledge, doubt, skepticism, and certainty. Although the notes are not organized into any coherent whole, certain themes and preoccupations recur throughout.

On Certainty takes as its starting point Wittgenstein’s response to a paper given by G. E. Moore, called “A Proof of the External World.” In this paper, Moore tries to prove that there is a world external to our senses by holding up his hand and saying “here is a hand.” Wittgenstein admires the boldness of Moore’s approach, which implicitly questions the reasonableness of doubting such a claim, but he suggests that Moore fails because his claim that he knows he has a hand automatically invites the question of how he knows, a question that would embroil Moore in the sort of skeptical debate he wishes to avoid.

The idea of doubting the existence of a world external to our senses gains a foothold from the fact that any knowledge claim can be doubted, and every attempt at justification of a knowledge claim can also be doubted. Traditional epistemology has sought a bedrock of certain knowledge, knowledge that is immune to all possible doubt, but from Descartes to Moore, this search has always come across problems.

Wittgenstein asserts that claims like “here is a hand” or “the world has existed for more than five minutes” have the form of empirical propositions but that in fact they have more in common with logical propositions. That is, these sorts of propositions may seem to say something factual about the world, and hence be open to doubt, but really the function they serve in language is to serve as a kind of framework within which empirical propositions can make sense. In other words, we take such propositions for granted so that we can speak about the hand or about things in the world—these propositions aren’t meant to be subjected to skeptical scrutiny. At one point, Wittgenstein compares these sorts of propositions to a riverbed, which must remain in place for the river of language to flow smoothly, and at another, he compares them to the hinges of a door, which must remain fixed for the door of language to serve any purpose. The key, then, is not to claim certain knowledge of propositions like “here is a hand” but rather to recognize that these sorts of propositions lie beyond questions of knowledge or doubt.

Wittgenstein does not try to refute skeptical doubts about the existence of an external world so much as he tries to sidestep them, showing that the doubts themselves do not do the work they are meant to do. By suggesting that certain fundamental propositions are logical in nature, Wittgenstein gives them a structural role in language: they define how language, and hence thought, works. “Here is a hand” is an ostensive definition, meaning that it defines the word by showing an example. That statement explains how the word hand is to be used rather than making an empirical claim about the presence of a hand. If we begin to doubt these sorts of propositions, then the whole structure of language, and hence thought, comes apart. If two people disagree over whether one of them has a hand, it is unclear whether they can agree on anything that might act as a common ground on which they can debate the matter. Communication and rational thought are only possible between people when there is some sort of common ground, and when one doubts such fundamental propositions as “here is a hand,” that common ground shrinks to nothing. Skeptical doubts purport to take place within a framework of rational debate, but by doubting too much, they undermine rationality itself, and so undermine the very basis for doubt.

Behind Wittgenstein’s belief that “here is a hand” is an odd proposition, either to assert or to doubt, lies his insistence on the importance of context. The very idea of doubting the existence of the external world is a very philosophical activity. A philosopher can doubt away, but it is impossible to live out this sort of skepticism. In essence, skepticism only has a foothold when we abstract it from the activity of everyday life. Similarly, skepticism gains its foothold by doubting propositions like “here is a hand” when these propositions are abstracted from the activity of everyday life. According to Wittgenstein, a proposition has no meaning unless it is placed within a particular context. “Here is a hand,” by itself, means nothing, though those words might come to have meaning in the context of an anatomy class or of a parent teaching a child to speak. However, once we give propositions a particular context, the doubts cast by a skeptic lack the kind of generality that would throw the very existence of the external world into doubt. Only by removing language from all possible contexts, and hence rendering language useless, can skepticism function.