An Introduction to the Philosophy of Science

observation is ever completely precise. There is always an element of uncertainty. All laws of science are, in this sense, statistical

The law does not predict what will happen on any one roll, nor does it say what is certain to happen on sixty rolls. It asserts that, if a great many rolls are made, each face can be expected to appear about as often as any other face. Because there are six equally probable faces, the probability of rolling any one face is %. Probability is used here in a statistical sense, to mean relative frequency in the long run, and not in the logical or inductive sense, which I call degree of confirmation

For example, a statistical law states that, if a cubical die is rolled sixty times, a given face may be expected to be uppermost on about ten of the rolls.

A statistical law, however, states only a probability distribution for the values of a magnitude in individual cases.

assertion that, when the bar is heated to a certain temperature, its length increases by a certain amount, is a quantitative assertion. A quantitative deterministic law always states that, if certain magnitudes have certain values, another magnitude (or one of the former magnitudes at a different time) will have a certain value. In brief, the law expresses a functional relation between the values of two or more magnitudes

I object to this reasoning, because I think it involves a confusion between determination in the theoretical sense, in which an event is determined by a previous event according to laws (which means no more than predictability on the basis of observed regularities), and compulsion.

Predictability and compulsion are two entirely different things

CAUSALITY” and “causal structure of the world” are terms I prefer to use in an extremely wide sense. Causal laws are those laws by which events can be predicted and explained. The totality of all these laws describes the causal structure of the world.

Neurath, for instance, said that it would be a sin against empiricism to speak of laws as true

But this is not, I suspect, what scientists mean when they speak of a basic law of nature. By “basic law”, they mean something that holds in nature regardless of whether any human being is aware of it.