I recently had occasion to think further about Wittgenstein's On Certainty when a correspondent asked me by e-mail to help him understand it as he was wrestling with it for the first time. What follows is my effort to do that. Note that it includes a substantial amount of text laying out the background to the issue Wittgenstein was addressing as it occurs in the Western philosophical tradition since I believe one cannot fully appreciate Wittgenstein's effort here without understanding the reason it matters. After all, what normal person is going to ask how he or she can be sure there's an external world in which we reside (that it's not just all in our minds, a remarkable illusion as it were) unless he or she is a philosopher? Here goes then:
G. E. Moore once claimed that he knew there was an external world (beyond his own mind, i.e., his perceptions, conceptions, etc.) because he could raise a hand and show it when asked (the physical body being part of the external world, the thoughts and our awareness of it being the "internal"). 'I know I have a hand,' he said (I'm paraphrasing), 'because here is one hand and here is another' at which point he held up his second. Moore's was an argument from common sense. Wittgenstein, as he lay dying, was asked to say something about that (though Sean assures me that he actually began the text somewhat earlier and merely completed his remarks -- to the extent Wittgenstein ever completed anything -- on his death bed, remarks which were then edited and published by his executors). The text was eventually published as On Certainty. In that little book, he takes off from Moore's "argument" to explore what it means to say we are certain of anything.
Background
Typically in classical western philosophy, certainty of anything was assumed to be warranted for what could be proved to the satisfaction of a credible observer/listener. Absent that, you could not claim to be certain (to know something beyond the possibility of doubting it). Now there are basically two ways to prove anything: deductively (by reasoning from unassailable premises) and inductively by relying on the evidence of our senses to come to reliable conclusions as suggested by the preponderance of that evidence.
However, some experiential information was presumed to be so basic as to require no reasoning (on the inductive model) at all (e.g., our sense perceptions themselves) so, on this view, there are three kinds of knowledge (i.e., information of which we can be certain):
1) Our raw sense data (smells, sights, tastes, feels and sounds) -- no proof required as they are givens
2) Claims about the world we construct from those sense data (in combination) via inductive reasoning (to suggest probable truth)
3) The ideas we develop by deductive reasoning (drawing indubitable conclusions from claims we already ACCEPT as true -- based either on inductive judgments or because we count them as unquestionable premises for some other reason, i.e, being some kind of given)
But this leads to some problems.
Most of what we think we know is inductive in nature and so only weakly "known" (given the uncertainties of experience). If the idea of certainty involves what can be known without any possibility of doubt, then it starts to look like nothing significant can be known that way at all. And so we are moved to doubt most everything around us.
Decartes had argued that that was what must happen and that to deal with it, to gain certain knowledge, we must go back to what is so basic that to doubt it is inconceivable. He formulated his famous proposition, "Cogito ergo sum" ("I think, therefore I am") as something fitting that bill. His Cogito amounts to a recognition that the very act of doubting is an affirmation of being and so the fact there is a doubter, a thinking being capable of doubting, is itself not doubtable to the doubter. Therefore we have at least one claim of which we can be absolutely certain. Descartes proposed to build an edifice of belief on this indubitable foundation and argued that everything we know about the world must be shown to stand on this bedrock -- or else we cannot be certain of anything.
To explain the world in which we exist, Descartes, who assumed but did not argue for the truth of that world, asserted that it must consist of two fundamental types of stuff, mind and matter, and that God brings them together in human brains. (Hence Descartes' famous dualism.)
The Irish philosopher, Bishop George Berkeley, addressed Descartes' claims by arguing that, if the thinking self is all that can be known with certainty, as Descartes had proposed, then the thinker qua the mind was all that we can be certain exists, making the mind primary in any effort to describe the world. The material world, the world of physical things, must therefore be no more than a mental construct. Thus, and as seen in some eastern traditions, Berkeley thought the world secondary to the mind which turns out to be the stuff of reality while physical phenomena have a status akin to dreams, hallucinations, etc.
The Scottish philosopher, David Hume, challenged that by suggesting that we could no more know about what we thought of as minds than we could know about the physical world itself. The mind, he argued, only looks like a unified entity to us on reflection, but if you really consider the facts you'll see there is no real self to be found, no mind as thing we can pick out referentially or describe, and no way, in fact, of even reasoning with certainty from one thing to the next (the conclusions of induction, he suggested, amounting to no more than guesswork and judgments formed by habit).
Hume's approach led to the challenge of radical skepticism, which amounts to a complete rejection of any kind of knowledge at all.
Everything we know is merely illusion, this thinking goes. Western philosophy was subsequently deeply troubled over this division between idealism (Berkeley) and radical skepticism (Hume) and many thinkers arose to try to reconcile the different positions.
Western Philosophy's Response to the Challenge of Radical Skepticism
Immanuel Kant, a German philosopher, was the most successful. He developed a complex philosophy that basically said we really can't know anything beyond what we can rationally think about since our rational or conceptual categories are givens in the same sense that our perceptions are. Within rational thought though, he suggested, we can and do know a lot. He relegated skepticism to the realm beyond conceptual knowledge (which he defined in terms of the synthesis of raw perceptual data and our conceptual categories with which we sort and manage the inputted perceptions which we receive from the external world).
In doing this he sought to delineate the boundaries of what could be known, pushing the idea of skepticism (that nothing can really be known) to the periphery. His approach is sometimes referred to as transcendental idealism in that he did not deny that mind might be primary (as Berkeley thought), but only that we can know whether it is or isn't -- since such knowledge necessarily lies outside the boundaries of what we can think about, i.e., it "transcends" the knowable. His solution is generally thought to have been powerful but many thought it inelegant and it did not put the matter of radical skepticism to rest for philosophy in the Western tradition.
Western philosophy, after Kant, moved in two main directions. The empiricists in the English speaking world put their faith in the knowledge we get from our senses and grappled with the implicit skepticism arising from Hume's analysis by reliance on common sense and a call to practicality. This still left the metaphysical problem of knowledge and certainty unresolved however. European thinkers tended to embrace Kant's new idealism, which was not so simplistic as Berkeley's, as the proper solution to the mind vs. matter problem, leading to German Idealism which reached its apogee in Hegel, and, later, the Existentialists who personalized the philosophical enterprise, re-focusing it on questions of self and the experience of being, while relegating questions about what the world is really like and what we can hope to know about it (the subject matter of earlier philosophers) to the sidelines. In the Empiricist tradition philosophy was given a back seat to science while in the European tradition philosophy moved off in a markedly different direction.
In the English speaking world, Empiricism remained strong even though German Idealism exerted significant influence until the late 19th/early 20th centuries when a group of science-oriented English philosophers arose (Whitehead, Russell, Moore, etc.) to strike down the excesses of Idealism which seemed to be spinning off into ever more arcane notions of being and diverging from the progress science, a set of empirical disciplines, had been making. Thinkers like Russell wanted to re-connect the two knowledge disciplines (science and philosophy) but, among other things, they were faced with the Humean problem of knowledge itself: what did it mean to know anything; how could we know anything; how could we differentiate between what we really knew and only thought we knew; how can knowledge be differentiated from opinion?
Russell worked to build a metaphysical picture of the universe that reflected the findings of modern science and Moore wrestled with what we could know and how we could be certain we knew it. Wittgenstein, who grew up in Austria, came from a culture in which German Idealism was dominant but was early on attracted to the work of the German logician Gottlob Frege who was doing work with logic to lay out what it meant to know anything, i.e., how logic sorts and expresses knowledge. Russell was doing similar work with logic in England and Wittgenstein was directed to Russell by Frege. He became Russell's student and Moore's colleague.
Wittgenstein's Early Thinking
Wittgenstein's early work was in the metaphysical vein Russell had been pursuing: sorting out what could be known and how based on an analysis of what the world was. His first book, the Tractatus Logico-Philosophicus, attempted to lay out the bounds of knowledge by exploring what we can logically say and what cannot be said. Adopting a somewhat Kantian approach (albeit with more elegance), he attempted to plot the boundaries of language, eventually concluding, as Kant did, that beyond language lie things we cannot know.
Unlike Kant, however, who relegated the unknown (what is beyond any possible human categorization) to a vast dark field (the Noumenon) that we could not reach (while offering other rationalistic reasons for affirming faith, God, ethical behavior, etc.), Wittgenstein suggested that there were other ways than words to get at what was linguistically beyond us. Near the end of his Tractatus, Wittgenstein pointed (albeit without being explicit about it) to behaviors (the gestures and rituals of ethics, aesthetics, faith, etc.).
The Later Wittgenstein
But Wittgenstein eventually abandoned this semi-metaphysical approach ("semi" because it rejected metaphysics via an exercise in metaphysics!) to deny the efficacy of the metaphysical enterprise entirely. Instead of suggesting that there is a linguistic arena within which knowledge could be achieved and another, beyond language, with its own type(s) of knowing, and seeking to say something about these two areas as he did with the logical edifice he constructed in his Tractatus, he came to conclude that the proper focus of philosophy is not the things we cannot say but language itself (as in what we do with words). He thus shifted from a focus on language-as-logic to language-as-behavior, the study of what we can know and think, as seen in the behavioral possibilities of language (the various "language games" he thought made up any given natural language).
On Certainty, his answer to Moore, explores the different things we mean when we speak of being certain and shows that we don't always mean it as logicians and past philosophers have thought.
To be certain is a state of mind, a condition of unwillingness to doubt, whatever the basis for that unwillingness. In that book he shows that there are different reasons not to doubt different things and that, just because we cannot be certain of something for one kind of reason, it doesn't follow that we cannot be certain for another, often quite different, sort of reason.
If you do mathematics you get answers by following the rules of mathematics, for instance. As long as you know those rules and can follow them, you have certainty in the truth (correctness) of your answers. The same is the case for logic.
Empirical certainty, however, is a game with other rules than mathematics and logic, rules which involve accepting the preponderance of evidence rather than holding out for something on a par with the certainty found in the mathematics or logic games.
Radical skepticism makes much of the apparently less certain outcomes of empirical inquiry than are achieved in mathematical or logical inquiry, but Wittgenstein's view is that that is just to apply the wrong paradigm. In On Certainty he shows how it is abnormal and absurd to seek to know empirical facts with deductive certainty, the kind that is relied on in logic and mathematics, and that to do so is to mix up the games you are playing.
The problem of radical skepticism, however, is not merely the impossibility of being certain about particular facts (for which common sense or experience can supply adequate justification for all practical purposes). It's about whether we can be certain of the underlying beliefs on which empirical facts are seen to rest.
Of course, we have evidence of an external world. But what makes such evidence itself reliable? If the external world is, itself, false (illusory) then the evidence of the elements which exist within it and constitute it cannot be thought reliable either. If we cannot have certainty of our underlying beliefs, the skeptic argues, then how can we be certain of any particular fact known based on them? If we cannot prove there is an external world, then how can the facts of an external world ever be taken as true, either in themselves or as evidence for anything else?
The result is collapse of the game which leads to the apparently self-defeating conclusions of radical skepticism.
The Hinge on Which the Doors of Knowledge Swing
But Wittgenstein suggested that the underlying beliefs of empirical knowledge (which underpin particular empirical claims) are just explicit statements of the rules of the empirical game. When stated explicitly, they effectively do not denote or even prove those rules. They express them.
But, if they are just rules, why must we play by them and not some others? His answer is that: 1) they are the rules we have (though we might have had others under other conditions); and 2) they have a history of working for us, given the conditions we currently live under ("Everything is in favor of it, nothing against it," as he puts it in On Certainty). Thus Wittgenstein gives us the notion of hinge statements, i.e., statements which EXPRESS the underpinnings of everything else we do and say and upon which the rest hinges.
The truth of particular empirical claims HINGEs on belief in the reliability of the underpinning claims (the expressions of the rules of that game). We don't need to prove or verify their veracity because they are the basis on which other things are proved and verified. They take their truth from the fact that the game, which belief in them makes possible, is seen to work. We take hinge statements to be true, not because we have proved them individually, or expect to, but because, as with the rules of a chess game, if we did not play by them, then the rest of what we do and say could not work. You can't play chess by following baseball's rule book or by just making it up as you go along.
This is the core insight of On Certainty and the one that gets at G. E. Moore's overly simplistic reliance on common sense as a response to the challenge of radical skepticism. That is, Wittgenstein shows WHY common sense is in play, why it works for us, rather than simply asserting common sense as the antidote to radical skepticism's attack. Moore's answer to the radical skeptic, to invoke common sense, is ultimately a failure because the radical skeptic essentially denies common sense and not even Moore can refute a claim simply by affirming what the claim denies!
Wittgenstein offered an analysis which shows why "common sense" IS reliable, i.e., it's a matter of following the rules which make playing the game possible.
A radical skeptic, if he is to act on the premises of his belief, could not play the necessary game and so would simply fail to function in the world. In a sense he would be judged insane if he were, indeed, to act on his belief in the ultimate uncertainty of everyday reality.
But Wittgenstein's insight here rests on his still more wide reaching insight (as seen in his other major work, The Philosophical Investigations) that our words, including words used to represent ideas like certainty, are not monoconceptual notions (they are not atomic, unanalyzable concepts) but are multifaceted in their meanings, uses and implications (see his points about meaning residing in the uses we put our words to and the family resemblance nature of meanings).
So the fact that we cannot have logical or mathematical type certainty of every claim we act on with belief does not imply that we must therefore doubt such claims, discard belief (assume uncertainty).
For Wittgenstein the idea of certainty is not confined to a single paradigm (the logical/mathematical one) which, of course, put him at loggerheads with his former teacher, Russell, who tried in his heyday to establish a basis for mathematical and empirical certainty in terms of logic (he sought to demonstrate that mathematics rests on the rules of logic in his early work and, in his later idea of Logical Atomism, he sought to develop an ideal -- rigorously logical -- language to express knowledge claims about the world with scientific precision, i.e., without any ambiguity).
Wittgenstein's departure from Russellian thinking blazed a new trail for western philosophy, one that took it away from the old excessive reliance on logic and toward an example-based account of what we really do and say.