From "Bayes' Arrows" interview by Richard Martin, thoughtful comments by CMU philosopher Clark Glymour – on causality:

Try to plan getting out of a room by computing the probability that you try to turn the doorknob conditional on the doorknob turning ... versus ... computing the probability that the knob will turn given that you try to turn the knob. The conditional probabilities are different. Causality makes the difference, and is why when planning to get out of a room, we use the second, and not the first, conditional probability. For planning actions and policy interventions, probability is useless without causality. Once upon a time yellowed fingers were highly correlated with lung cancer later in life. The surgeon general recommended against smoking; he did not recommend that people wear gloves to prevent yellowed fingers.

... and on probability and science:

Bayesian statistics is two things: a useful technology and a bundle of mythology. A Bayesian data analyst almost never, and I mean almost never, inquires as to her degrees of belief: she makes mathematically convenient and not absurd assumptions and goes on. She tests the resilience of the outcomes she obtains by varying those assumptions–the prior probabilities, the penalties in a model score, etc. Essentially, her "prior probabilities" are just a measure to guide through a search space of alternative possible values for parameters in a model or models. The measure is adaptive, in the sense that it alters (by Bayes Rule) as data are acquired. It is subjective, in the sense that there is no best adaptive measure for guiding search, but there are better and worse adaptive measures. Generally, the measures are nobody's degrees of belief.

The facts we are really talking about when we talk of probabilities in science is estimates of "large" but finite sample frequencies. "Large" is of course vague. Frequentist textbooks often fudge their introductions this way. Then they go on to give a mathematical theory of "probabilities" that are estimated from finite sample frequencies. The mathematics hides the vagueness of the fundamental notion.

Probability in its mathematical form is about nothing, and so about any domain you may want it to be about. The same is true of logic, and of causality. Those three notions are the intangible bedrocks of science, and of rationality.

... and on the reality of causality:

Anyone who seriously thought causation is a fiction, a social creation of some kind unlike the everyday facts of the world ... such a person would be paralyzed, without reason for planning any one action rather than another. To get out of my office, shall I open the doorknob or wait for the doorknob to open? If I move my legs will I find myself at the door? If I move to an apartment with thin walls, will I hear my neighbors, and they me? I don't care so much whether people say broccoli tastes good; it makes a bad taste in my mouth. An ad hominem: people who say causality is a fiction are not doing much thinking.

... and on Bayes nets and graphical causal models:

Causes are relations between events: one event is a cause of another, or not. In science, causes are usually regarded as general, repeatable relations among variable quantities or properties: if one variable changes values will it, in all circumstances of a specifiable kind, produce changes in other variable quantities? A trivial example: if lobsters are boiled, do their carapaces change color (not trivial for the lobsters)?

Graphical causal models represent distinct variables as points and a direct causal relation between two variables as a directed line between one point and the other. By itself, this is just a convenient picture (of a kind people often produce spontaneously when asked to depict causal relations). When appropriately combined with the theory of probability, however, it is much more: an effective guide to predicting the effects of interventions that deliberately and directly change one or more of the variables (and hence, through the effects of the variables directly intervened upon, change other variables that they influence), and a framework that allows systematic investigations of the circumstances in which causal relations can be discovered.

(cf Correlations and Causality (2000-04-09), Epistemological Enginerooms (2000-08-10), Problems of Knowledge (2010-07-29), Causal Inference in Statistics (2018-09-16), Think Better - Three Keys (2019-06-05), Chance, Cause, Clash (2021-01-21), ...) - ^z - 2022-07-31