Paul knew which horse would win the Derby. At least, he felt certain he knew, and when he had felt this certainty in the past, he had never been wrong.
Paul's conviction was not based on studying the horses' form. Nor could he see the future unfolding in a vision. Rather, the name of the winning horse would just come to him, as he rode back and forth on his rocking horse, which he had really outgrown.
It was not that Paul won all his bets (or those made on his behalf by the adults who shared his secret). Sometimes he was less sure, and on other occasions he didn't really know at all and just guessed. But he never bet a large amount in those circumstances. When he was completely sure, however, he put down almost all the money he had. The method had never let him down yet.
Oscar, one of his adult collaborators, had no doubt that Paul possessed an uncanny ability, but he was not sure that Paul really knew the winners. It wasn't enough that Paul had always won so far. Unless he knew why he had got it right, the foundations of his belief were far too shaky to hold true knowledge. However, that did not stop Oscar from betting some of his own money on Paul's tips.
Sources: 'The Rocking-Hourse Winner' by D.H. Lawrence (1926); lectures by Michael Proudfoot
Baggini, J., The Pig That Wants to Be Eaten, 2005, p. 118.
As Plato defined it, knowledge is justified true belief. But how has our young horserace handicapper Paul come by his own belief in his "knowledge"? A few lucky bets? Some strong feeling? Is that justified? For the rest of us, we've seen far too many instances of betting at the tracks to know that predictions by bettors are rarely right more than at levels of random chance (once odds are accounted for). We don't see people go on miraculous winning streaks that prove they are somehow much better at this than everyone else. So we think Paul is being silly and it's only a matter of time before one of his big bets on a "sure thing" goes wrong and he goes bust.
In both Paul's case and in our own, however, everyone is relying on inductive reasoning for their beliefs. The Oxford English Dictionary defines induction as: the process of inferring a general law or principle from the observation of particular instances. Paul has seen his method work in the past; he thinks the general law is that it will work in the future. We've seen bettors fail in the past; we think they'll all fail in the future. Who's to say who's right? As the Stanford Encyclopedia of Philosophy entry on the induction problem says, "What distinguishes good from bad inductions?"
It turns out there's not a great answer to this question as induction has never been fully justified. The Ancient Greek skeptic Sextus Empiricus was possibly the first to question the validity of inductive reasoning when he wrote:
"When they propose to establish the universal from the particulars by means of induction, they will effect this by a review of either all or some of the particulars. But if they review some, the induction will be insecure, since some of the particulars omitted in the induction may contravene the universal; while if they are to review all, they will be toiling at the impossible, since the particulars are infinite and indefinite."
That's the problem of induction known as generalising—i.e., trying to define "the properties of a class of objects based on some number of observations of particular instances of that class (for example, the inference that "all swans we have seen are white, and, therefore, all swans are white", before the discovery of black swans)." But there is a second common objection to induction as well.
David Hume is perhaps the most famous philosopher attached to this part of the induction problem. He said there was no justification for "presupposing that a sequence of events in the future will occur as it always has in the past (for example, that the laws of physics will hold as they have always been observed to hold)." Hume called this the principle of "uniformity of nature", but to rely on it by simply pointing to past examples of the uniformity of nature was merely begging the question in a vicious circularity.
For practical purposes, people just accept this and rely on the uniformity of nature until proven otherwise. So far, that has worked. But really, philosophers know we cannot Know this will always be true.
When talking about this issue though, it's important to point out how philosopher Karl Popper proposed we can get around it. He held that:
"Induction has no place in the logic of science. Science in his view is a deductive process in which scientists formulate hypotheses and theories that they test by deriving particular observable consequences. Theories are not confirmed or verified. ... The best we can say of a hypothesis is that up to now it has been able to show its worth, and that it has been more successful than other hypotheses. ... This appraisal of the hypothesis relies solely upon deductive consequences (predictions), which may be drawn from the hypothesis: There is no need even to mention “induction”."
Popper said this meant the scientific method relied on falsifiability, or the liability of a theory to counterexample. Highly falsifiable theories thus make stronger assertions and are in general more informative.
So we may use the iterative nature of the scientific method to tease out causes, inventing new and different experiments that rule out other causes until we are "sure" we have isolated the true cause. At least to the best of our present abilities. And it must be said that we've been using this method to improve the scientific method as well—gradually emphasising repeatability, independent observations, falsifiability, double blind methodology, etc.—all the time trying to correct for the fallacies our senses and reason are susceptible to. But as I've pointed out several times on this blog, this all means our knowledge is only ever probabilistic so we must act with confidence and caution appropriate to the probability, being especially careful in realms where knowledge is uncertain and consequences of error are large.
So, it looks like Paul's belief that he can pick the horsies is a theory that isn't justified and has generally been falsified by other gamblers in the past. I, therefore, wouldn't put my own money behind him. But then again, we aren't really told how these winners "come to him" while he's on his hobby horse so maybe there's a hidden cause there that is new to us. I guess we'll just have to wait and see...