Principles of scientific method: Notes on Lectures by Dr K.R. Popper given at the University of Otago, 22–26 May 1945; Lecture 4. Probability - Popper, Karl (New Zealand Science Review, 2012)
Consideration of probability is necessary to finish up the case against induction.If we say that a certain hypothesis is probable, we may mean: • I think this hypothesis good (a subjective judgement), or I hope this hypothesis may not be falsified pretty soon; • probability in a more technical sense, i.e. something which follows laws of mathematical probability theory. For example, the probability of an event happening plus probability of an event not happening – 1 (probability of an event happening is never greater than one), e.g. dice throwing. Right back to Hume we find the idea that inductively one cannot derive a law, but just a high probability of a law, i.e. it seems that one can have a watering down of law. For example, we could determine say 90 per cent of all men drink tea, Socrates is a man, therefore a 90 percent conclusion that Socrates drinks tea. This is the simplest way to show that there is a prima facie view that by inductivism we could establish the probability of a hypothesis.