A Little History of Philosophy (Little Histories)

by Nigel Warburton

This style of reasoning goes from ‘All the swans I've seen are white’ to the conclusion ‘All swans are white.’ But clearly a swan that you haven't observed could turn out to be black. There are black swans in Australia, for example, and in many zoos around the world. So the statement ‘All swans are white’ doesn't follow logically from the evidence. Even if you have looked at thousands of swans and they were all white, it could still be false. The only way to prove conclusively that they are all white is to look at every single swan. If just one black swan exists, your conclusion ‘All swans are white’ will have been falsified. This is a version of the Problem of Induction, a problem that David Hume wrote about in the eighteenth century. Induction is very different from deduction. That is the source of the problem. Deduction is a type of logical argument where if the premises (the starting assumptions) are true the conclusion must be true. So, to take a famous example, ‘All men are mortal’ and ‘Socrates is a man’ are two premises from which the logical conclusion ‘Socrates is mortal’ follows. You would contradict yourself if you agreed that ‘All men are mortal’ and that ‘Socrates is a man’, but denied the truth of the statement ‘Socrates is mortal.’ That would be like saying ‘Socrates both is and is not mortal.’ One way of thinking about this is that with deduction the truth of the conclusion is somehow contained within the premises and logic just teases it out. Here's anoth...