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I’VE won the lottery. I haven’t checked my numbers yet, but I just know. You know what it’s like, when you just know you know.

Knowledge is a slippery concept: what we know, how we know we know it, what we know others know, what others know of what we know, how what we or they know differs from what we just believe. You would probably argue that, until I see the winning numbers, I can’t know I have won the lottery – I can only believe it. Yet how do you know that?

Read more: Inside knowledge: The biggest questions about facts, truth, lies and belief

Forget alternative facts: to get to the bottom of what we know and how we know we know it, delve into our special report on epistemology – the science of knowledge itself

Most of us make our way through life without peering too closely under the bonnet of epistemology – the theory of knowledge. “We manage it intuitively, we don’t have to reflect and calculate,” says , Canada, and author of Knowledge: A very short introduction.

But it rewards closer inspection. For a start, the degree to which we know stuff and know what others know is quite possibly what separates humans from everything else on the planet, from rocks to chimpanzees (see “Knowledge: Of chimps, curiosity and quantum mechanics“). It is certainly the lubricant of all human interactions. “We can cooperate, communicate and compete better if we know what others know and don’t know,” says Nagel. “Tracking states of knowledge can help you in the course of the argument, brace yourself against fallacies.”

“Knowing something is a far richer, more complex state than merely believing it”

Yet defining the basic currency of knowledge is surprisingly difficult. To know something you must first believe it, but that’s not enough: to make factual knowledge, that belief must also be true. “That is the one thing we’re all happy to accept,” says Nagel.

“True belief” is insufficient, though. A belief can be true just by chance, or we can arrive at a right answer via a wrong route. So epistemologists have traditionally added another condition for a true belief to count as knowledge: it must also be justified in some way. In the lottery example, the perceptual evidence of the numbers on my lottery ticket plus the testimonial evidence of, say, a broadcaster reading out the winning numbers creates the inferential knowledge that I have won – or not (see “Where knowledge comes from“).

Stop the clocks

For a long time, the conception of knowledge as a justified true belief ruled the roost. But then US philosopher Edmund Gettier put forward a couple of devastating counterexamples .

An example of a “Gettier problem” is someone glancing at a clock that says 12, at midday. The catch is that the usually reliable clock is broken, and is showing the right time only by chance. Our clock watcher believes it is midday, that belief happens to be true, and the stopped clock provides justification. But in fact no one knows it is midday – they just believe they know it.

Various attempts have been made since to tighten up the standards of justification to get round this sort of problem and provide a definition of knowledge everyone can agree on. But no one has quite yet nailed this one down. “It’s kind of an awkward question,” says Nagel.

In the end, though, an answer might not be the point. All these epistemological investigations point us to one fact that we are wont to forget: that knowing something is a far richer, more complex state than merely believing it. The ability to distinguish between fact and opinion, and to constantly question what we call knowledge, is vital to human progress, and something we cannot afford to let slip (see “Knowledge: How to tell truth from lies“).

“Knowing something is a mental state that locks you on to the truth,” says Nagel. What that lock is, though – well, we don’t really know.

This article appeared in print under the headline “What is knowledge?”