Bertrand Russell famously asked in The Problems of Philosophy: "Is there any knowledge in the world so certain that no one can doubt it?"
Descartes thought he'd got the answer when he deduced from the fact that he was doubting that he must therefore be thinking, and that if he was thinking then he must exist. And so, Cogito ergo sum - I think, therefore I am - the words that cast Western philosophy into a mode from which it did not recover for more than 300 years.
The Cogito sounds plausible, but it smells fishy. Wittgenstein thought that it started in the wrong place. After all, if, like Descartes, I am thinking about my capacity for systematic doubt, then this thinking must be going on in a language: and the notion of a private language doesn't make any sense. This argument pulls the rug from under the concept of Cartesian Privacy and shows that subjective things are not the most certain.
Besides, asked Wittgenstein, must I be thinking about my existence in order to demonstrate to myself my existence - or will any old thought do as well? It sounds odd to say, "I think it's raining, therefore I exist." It is surely bizarre to deduce one's existence from one's thoughts - as if I should deduce that I am thirsty because I find myself drinking a pint.
Every answer imaginable has been offered to the question of how we know what we know.
Is knowledge the result of sense impressions? But what of when our senses deceive us? It is possible that we are dreaming. You may be dreaming that you are reading this article right now. The whole world might be a dream. Everything could be different from the way we see it. What if all the world were only an illusion?
But hang on a minute. If everything is an illusion, where do we get the idea of "illusion"? To claim that everything is illusory is like saying that all money is counterfeit.
The concept of what is illusory requires for its meaning the concept that some things are genuine. So far, so good. But which bits of what we perceive are real and which not is still anybody's guess - isn't it?
Surely we know the truths of arithmetic? But these have been held to be trivial - which is not much comfort to the youngster struggling with his times tables. They are trivial in the sense that what goes on the right side of the "=" sign is only an alternative way of describing what goes on the left side.
Thus, arithmetic is only, as philosophers say in their jargon, "analytic" - true by means of the meaning of arithmetical expressions themselves. So we cannot get new knowledge from our use of words and symbols. To say that a bachelor is an unmarried man is only to put what we know already into different words.
There is another interesting thing about the problem of epistemology. It is hung about with a sort of buggeration factor, and this is because of the nature of language itself. If you say something - anything - the form of language makes it immediately possible that you can be contradicted.
Language is binary. That is to say, as soon as you declare: "It is!", you invite the response: "No, it isn't!" This helps to explain why it is that for every idealist, there is a materialist; for every naturalist, an intuitionist; and so on down all the gloomy corridors of binary bind. (But see Hegel, who makes a virtue out of this.)
It is like the Monty Python "room for an argument" sketch, where someone says: "Argument isn't just the automatic gainsaying of what the other person has said."
"Yes it is!"
"No it isn't!"
You can mug up on these interesting possibilities by reading Chomsky on the binary nature of language, and the educational psychologists' notion that everyone is born with "a primitive sense of the number two".
There are fascinating teleological speculations on this point. That our epistemology is bedevilled by the binary nature of our speech is only what we should expect: for one of the ancient titles of the devil is "Binarius", and if you look at the opening of the Book of Genesis you will see that God called everything that he had made "good" except for what he made on the second day. If the truth may be defined as p, then certainly the lie is not-p, the alternative. And another of the devil's titles is Father of Lies.
These sorts of serendipitous discoveries are grist to the mill of those cultural anthropologists who say that all our philosophising is only an explicit and over-literal way of talking about what was known to our ancient and primitive forebears intuitively - or should that be naturally?