Epistemology

When the BBC held their Greatest Philosopher vote last year, there was only one possible choice for me: David Hume. Plato, Descartes, Kant? You can keep them; Hume’s the chap for me.

In the end, the Marxist vote kept Hume from his rightful place at the top of the poll, but he did come in second; not bad for a man who never held an academic post, and whose work was shunned by the prevailing orthodoxy of the day. His virtues, however, have been appreciated down the intervening centuries by many in the western philosophical tradition. They include a great clarity of thought and word, and a biting wit—in my view, his is the greatest employment of scholarly irony.

Hume’s response to the sceptical challenge can be seen as deeply pragmatic. We cannot truly believe the sceptic, and although our knowledge may be built on somewhat shaky foundations—the classic example being his demonstration of the impossibility of a proof for induction—we carry on regardless, because we can do nothing else. In effect, we shrug our shoulders and get on with it.

All this is well and good, but despite my admiration for Hume’s work, his theory of ideas and impressions is problematic. Obviously in a trivial sense everything begins with experience, because from the beginning we are experiencing. However, this should not count against the existence of a priori knowledge, such as that of mathematics or logic. The important thing about such knowledge is that it is independent of any particular set of experiences.

This problem, in fact, could be seen as the motivation behind Kant’s theory about the faculty of intuition: our mathematical intuitions are the impressions that our mathematical ideas are formed from.

Now, go and see what other people think about the second chapter of Hume’s first Enquiry.

This story in the Guardian is an instance of one of those strange journalistic tics: presenting the context of a story in a way consistent with the facts but bordering on the irrelevant.

“The Cambridge company [Autonomy] … developed a product to sort information based on the theories of an 18th century cleric,” writes Mark Tran. All of which is entirely true, but what does the fact that mathematician Thomas Bayes was an 18th century cleric really have to do with a business report about how well a software company is doing?

One might argue that it’s just an interesting fact that a reader could note in passing, and there’s a certain truth to this; if only more business articles were so horizon-broadening! However, if Mr. Tran had really wanted to provide a context for his brief remarks about statistical theory and fourth-quarter results, he could have done better. Much better.

Bayesianism, after all, is not some obscure concept rescued by archaeological software developers. It is an entirely mainstream theoretical tool used in a range of disciplines, from epistemology to spam-filtering. Pretensions to erudition, far from enlightening readers, generally only create misleading impressions. Journalists should remember that having the right balance of facts providing context to an article is just as important as ensuring those facts are correct.

Think back to school, and all the things you were taught. In science, at least, a lot of what you were taught (about protons and electrons, about genes and chemical reactions) wasn’t exactly false. But it often wasn’t exactly true, either. It was a simplification; an abstraction; a teaching aid, to bring you to the point of sophistication where you could handle a more complex model.

Philosophy is taught in much the same way. To learn philosophy (or rather, to do philosophy, for it can only be learnt by doing) is to walk on shifting sands. To understand anything, one must have reference points: fixed positions from which one can move.

To put it another way: we have to start somewhere. A baby does not just get up and run a hundred metre sprint; it crawls, eventually it walks, falls over, walks again, and finally begins to run. This primer is full of things which are initially taken for granted, but will later be questioned. Take them for granted, and begin to crawl. Leave running for later.

The Tripartite Theory

Epistemologists attempt to answer the question, “What is knowledge?” Here’s a really short answer: knowledge is a species of belief. Specifically, it’s a belief which is true.

Actually, “knowledge is true belief” isn’t generally accepted as covering it. Suppose I form a belief that Tony Blair is, at this very moment, picking his nose. As it happens, he is picking his nose. But I had no evidence, no reason to believe it. Did I know that he was picking his nose? Most people would say no; I was merely lucky.

The foundation of epistemology (by which I mean, firstly, the point from which most people start learning about epistemology, and secondly, a pretty good point to start from) is Plato’s Tripartite Theory of knowledge, which he outlines in the Theatetus. This claims that knowledge is justified true belief. On this account, if I say “I know that I am wearing shoes”, then for me to be correct (that is, for me to know that I am wearing shoes), the following conditions must obtain:

1. It must be true (I must really be wearing shoes)
2. I must believe it (I must believe that I am wearing shoes)
3. I must be justified in my belief (I must have some evidence or reason to believe that I am wearing shoes, for example, remembering putting them on this morning)

These conditions are individually necessary (all three must obtain) and jointly sufficient (you don’t need anything else) for knowledge.

Gettier problems

The Tripartite Theory stood up pretty well for over two thousand years, before running (like much else) into difficulties in the ’60s. In a paper entitled Is Justified True Belief Knowledge?, a philosopher named Edmund Gettier produced the first of what would become known as “Gettier counterexamples”. What follows is a Gettier counterexample I’ve just made up; they’re pretty simple to devise.

Damien is planning a bike ride into the country. His father, however, tells him that he has seen the weather forecast and it will rain later that day. Damien thus forms the belief that it will rain later in the day. In fact, Damien’s father was lying, because he wanted Damien to stay at home and help decorate the house; the weather forecast actually said that both that day, and the weeks to come, would be as dry as a bone. Later that day, freak weather conditions in the upper atmosphere cause a raincloud to form over Damien’s house. It begins to rain. Did Damien know it would rain?

Instinctively, the answer is no; he was (in the first place) deceived and (in the second) lucky. But what does the Tripartite Theory say? It was true that it rained later in the day; Damien believed it would rain; he was justified, because his father (in general a trustworthy soul) told him the weather forecast said it was rain. On that account, Damien did know.

At this point, we have two choices. Either we can say that it is possible to have “lucky knowledge”, where one ‘knows’ something simply because one has been lucky, or we can deny that the Tripartite Theory is always correct.

Intension & extension

All terms can be said to have two components: the intension (with an ‘S’, not a ‘T’) and the extension. If the term was ‘cat’, the extension would be the set of all cats. The intension of ‘cat’ is a definition: it describes what a cat is.

The extension of the term ‘knowledge’ is the set of all propositions that could possibly be known. The Tripartite Theory is an example of a purported intension; a definition of what knowledge is. But if we don’t accept the example above as being a case of knowledge, then the extension and the intension don’t match up properly, which means that one of them is wrong.

Further questions

Here are some avenues for discussion. Firstly, which of these things have we got wrong: the intension, or the extension? On the one hand, the idea that one can have lucky knowledge seems pretty dodgy (to me, at least). But on the other, why should we blindly accept our intuitions about whether a given proposition, under certain (usually imagined) circumstances is known or not? How could we amend or replace the Tripartite Theory (which does seem to basically work) in order to patch up its failings? Answers on a postcard (or maybe in the comments section)…

The Stanford Encyclopaedia of Philosophy is a good, free resource for anyone interested in these issues; this article in particular discusses some of the ideas I’ve mentioned here in a lot more depth and philosophical rigour.