• One distinction (which is discussed on pp. 33-35) is among meanings that might be assigned to the term probability. He considers three: the concept of probability as “relative frequency” and concepts of probability referred to as “subjective” and “logical.” I’ll add a fourth and suggest a way of relating these concepts to one another.

According to both the subjective and logical concepts of probability, the laws of probability set requirements for the rationality of our degrees of belief. In the subjective concept of it, probability is just a measure of the degree of conviction one has in a given statement. The logical concept regards it instead as something that provides grounds for degrees of conviction. It is built into the logical concept of probability not only what is required for one’s degrees of belief to be coherent but also what is required for them to be correct; and thus the standard laws of probability do not, according to it, exhaust the truths about probability that can be regarded as logical. While, according to the both views, if you assign a 70% chance to rain on the basis of given evidence, you must assign a 30% chance to dry weather if you are to be rational; according to the logical view, it can be a truth of logic that certain evidence gives rain a 70% chance (or a 68% chance, or …); indeed, it is a truth of logic, on this view, that a given claim has a certain probability even when considered apart from particular evidence.

The idea of probability as relative frequency treats probability as a feature of nature. In the strictest sense, this view can be distinguished from a view of probability as a natural “propensity.” When it is distinguished from propensity, probability as relative frequency is tied to us in the sense that it refers to the relative frequency of actual occurrences, occurrences in the world we are part of (as opposed to other possible worlds allowed by the laws of nature). Since the actual occurrences at any given time can be quite accidental, the relative frequency that is considered is usually something like relative frequency in the long run. On the other hand, when understood as propensity, probability is not the relative frequency of occurrences (even in the long run) but rather some feature of nature that causes these relative frequencies. From this point of view, relative frequencies are merely our evidence of what the probability is.

This way of understanding these four concepts can be summarized in the following table:

	tied to us	independent of us
probability as a measure of conviction	subjective probability	logical probability
probability as a natural quantity	relative frequency	propensity

• Okasha’s second distinction (which is discussed on pp. 36-39) is between two roles that the concept of probability plays. One role is as a concept that figures in the content of science; some scientific laws, for example, concern probabilities. The other role is as a measure of the degree of support for statements by evidence. You might think of these two roles as probability in laws vs. probability of laws. This distinction has connections to the first one: probability as relative frequency and probability as propensity are the natural competitors for the first role, and the subjective and logical conceptions of probability are the natural competitors for the second role.