Real knowledge is to know the extent of one’s own ignorance. —Confucius

What if we are being radically deceived? What if I am no more than a brain kept alive in a vat and fed with stimuli by a mad scientist? What if my life is but a dream or computer simulation? Like the prisoners in Plato’s cave, I would be experiencing not reality itself, but a mere facsimile. I couldn’t be said to know anything at all, not even that I was being deceived. Given the choice between a life of limitless pleasure as a brain in a vat and a genuine human life along with all its pain and suffering, most people opt for the latter, suggesting that we value truth and authenticity, and, by extension, that we value knowledge for its own sake.

But even if we’re not being deceived, it is not at all clear that we can have any knowledge of the world. Much of our everyday knowledge comes from the use of our senses, especially sight. ‘Seeing is believing’, as the saying goes. French is one of many languages that has two verbs for ‘to know’: savoir and connaître, where connaître implies a kind of direct, privileged kind of knowledge acquired through sense experience. But appearances, as we all know, can be deceptive: a stick held under water appears to bend, the hot tarmac in the distance appears like a sparkling lake, and almost 40% of the normal population have experienced hallucinations of some kind, such as hearing voices. Our sense impressions are also subject to manipulation, as, for example, when a garden designer uses focal points to create an illusion of space. My mind interprets a certain wavelength as the colour red, but another animal or even another person may interpret it as something entirely else. How do I know that what I experience as pain is also what you experience as pain? You may react as I do, but that need not mean that you are minded like I am, or even that you are minded at all. All I might know is how the world appears to me, not how the world actually is.

Beyond my immediate environment, much of what I count as knowledge is so-called testimonial knowledge, that is, knowledge gained by the say-so of others, often teachers, journalists, and writers. If a piece of testimonial knowledge conflicts with our worldview, we tend, in the absence of non-testimonial evidence, to check it against other forms of testimony. If a friend tells me that Melbourne is the most populous city in Australia, I might carry out an Internet search and find that it is actually Sydney, even though I have never been to Australia and cannot be sure of what I read on the Internet.

Knowing that Sydney is the most populous city in Australia is a case of declarative (or propositional) knowledge, knowledge that can be expressed in declarative sentences or propositions. I know, or think that I know, that ‘Prince Harry is married to Meghan Markle’, ‘Paris is the capital of France’, and ‘democracy is the least worst form of government’. Apart from declarative knowledge, I also have know-how, for example, I know how to cook and how to drive a car. The relationship between knowing that and knowing how is not entirely clear, though it may be that knowing how collapses into multiple instances of knowing that.

For me to know something, say, that Mount Athos is in Greece, it must be the case that (1) I believe that Mount Athos is in Greece, and (2) Mount Athos is actually in Greece. In short, knowledge is true belief. True beliefs are better than false beliefs because they are, in general, more useful. Some beliefs, such as that my wine has been poisoned, are more useful than others, such as that my neighbour has 423 stamps in her collection. Some true beliefs, such as that I am a coward, can even be unhelpful, and we deploy a number of psychological mechanisms such as repression and rationalization to keep them out of mind. Inversely, some false beliefs, such as that my country or football team is the best, can be helpful, at least for my mental health. But on the whole we should seek to maximize our true beliefs, especially our useful or otherwise valuable true beliefs, while minimizing our false beliefs.

If knowledge is true belief, it is not any kind of true belief. People with paranoid psychosis often believe that they are being persecuted, for example, that the government is trying to have them killed. Clearly, this cannot count as knowledge, even if, by coincidence, it happens to be true. More generally, beliefs that are held on inadequate grounds, but by luck happen to be true, fall short of knowledge. In the Meno, Plato compares these true beliefs, or ‘correct opinions’, to the statues of Daedalus, which run away unless they can be tied down ‘with an account of the reason why’, whereupon they become knowledge. Knowledge, therefore, is not mere true belief, but justified true belief. Knowledge as justified true belief is called the tripartite, or three-part, theory of knowledge. Setting aside any intrinsic value that it may have, knowledge is more useful than mere true belief because it is more stable, more reliable.

Fine, but what does justification demand? I justify my belief in manmade global warming by the current scientific consensus as reported by the press. But what justifies my belief in the current scientific consensus, or in the press reports that I have read? Justification seems to involve an infinite regress, such that our ‘justified’ true beliefs have no solid foundation to rest upon. It may be that some of our beliefs rest upon certain self-justifying foundational beliefs such as the famous I think therefore I am of Descartes. But few beliefs are of this kind, and those that are seem unrelated to the bulk of my beliefs. In practice, most of our beliefs seem to rest upon a circular or circuitous chain of justification, which, if large enough, might be held to constitute adequate justification. The problem, though, is that people can choose to live in different circles.

People typically justify, or try to impose, their beliefs by means of arguments. Arguments provide reasons (or premises) in support of a particular claim or conclusion. There are two broad kinds of argument, deductive and inductive. In a deductive or ‘truth-preserving’ argument, the conclusion follows from the premises as their logical consequence. In an inductive argument, the conclusion is merely supported or suggested by the premises. More often than not, arguments are implicit, meaning that their rational structures are not immediately apparent and need to be made explicit by analysis.

A deductive argument is valid if the conclusion flows from the premises, regardless of the truth or falsity of the premises.

All organisms with wings can fly. (Premise 1, False)

Penguins have wings. (Premise 2, True)

Therefore, penguins can fly. (Conclusion, False)

This deductive argument is valid, even if it is unsound. For a deductive argument to be both valid and sound, all of its premises have to be true.

All mammals are warm-blooded. (Premise 1, True)

Bats are mammals. (Premise 2, True)

Therefore, bats are warm-blooded. (Conclusion, True)

Though a deductive argument appears to bring out a truth, that truth was already contained in the premises. For an inductive argument, the equivalent of soundness is cogency. An inductive argument is cogent if its premises are true and they render the truth of the conclusion probable. Every flamingo that I’ve ever seen has been pink. Therefore, it’s very probable that all flamingos are pink, or that flamingos are generally pink.

A third form of reasoning, abductive reasoning, involves inference to the best explanation for an observation or set of observations, for example, diagnosing a disease from a constellation of symptoms. But once broken down, abductive reasoning can be understood as a shorthand form of inductive reasoning.

Obviously, arguments often fall short. A logical fallacy is some kind of defect in an argument, and may be unintentional or intentional (with the aim to deceive). A formal fallacy is a deductive argument with an invalid form: the argument is invalid regardless of the truth of its premises. An informal fallacy is an argument that can only be identified by an analysis of the content of the argument. Informal fallacies are frequently found in inductive arguments, and often turn on the misuse of language, for example, using an ambiguous word with one meaning in one part of the argument and another in another (fallacy of equivocation). Informal fallacies can also distract from the weakness of the argument, or appeal to the emotions rather than to reason: “Will someone please think of the children!”

Science principally proceeds by induction, through the study of large and representative samples. An important problem with inductive reasoning is that the observations involved do not in themselves establish its validity, except by induction! A turkey that is fed every morning without fail expects to be fed every morning, until the day the farmer wrings its neck. For this reason, induction has been called ‘the glory of science and the scandal of philosophy’. This is an even bigger problem than it seems, since inductive arguments usually supply the premises for deductive arguments, which, as we have seen, are merely a priori. The 20th century philosopher Karl Popper argued that science actually proceeds by deduction, by making bold generalizations and then seeking to falsify them (or prove them wrong). He famously argued that if a proposition cannot be falsified, then it is not in the realm of science. But if Popper is right, then science could never tell us what is, but only what is not.

As we have seen, justification is hard to come by. But there is another problem lurking in the tripartite theory of knowledge. In 1963, Edmund Gettier published a two-and-a-half page paper showing that it is possible to hold a justified true belief without this amounting to knowledge. Here is my own example of a Gettier-like case. Suppose I am sleeping in my bed one night. Suddenly, I hear someone trying to unlock the front door. I call the police to share my belief that I am about to be burgled. One minute later, the police arrive and apprehend a burglar at my door. But it was not the burglar who made the noise: it was a drunken student who, coming home from a party, mistook my house for his own. While my belief was both true and justified, I did not, properly speaking, have knowledge. Responses to the Gettier problem typically involve elaborating upon the tripartite theory, for example, stipulating that luck or false evidence should not be involved. But these elaborations seem to place the bar for knowledge far too high.

As Gettier made clear, it is not so easy to identify instances of knowledge. Instead of defining the criteria for knowledge and, from these criteria, identifying instances of knowledge, it might be easier to work the other way, that is, begin by identifying instances of knowledge and, from these instances, derive the criteria for knowledge. But how can we identify instances of knowledge without having first defined the criteria for knowledge? And how can we define the criteria for knowledge without having first identified instances of knowledge? This Catch-22, in one form or another, seems to lie at the bottom of the problem of knowledge.