Russell's Epistemic Responsibility — Epoche B2
Three Questions About Uncertain Inference, and Which One Russell Answered Russell's Human Knowledge [1] : Its Scope and Limits (1948) is often treated as a late and unsuccessful book: an attempt at a theory of probable inference that was overtaken within a generation by the Bayesian apparatus. The verdict rests on a confusion. Three different questions travel under the heading of probable inference, and Russell was answering the second while the apparatus that supposedly superseded him answers the first. They are not competitors. This essay separates the three, places Russell's postulates where they belong, and argues that his failure was real but lay elsewhere than where his critics put it. It is at the third question, and it is the failure Hume identified [2] . That conclusion can be denied: a Bayesian will say the second question should not be asked at all, and that objection is taken up near the end. The three questions The first question is about form. Given a body of evidence and a hypothesis, what is the correct way to move from one to the other? Call this the coherence question. It asks what constraints a rational person's confidences must satisfy. The second is about the world. What must reality be like for inferences of that form to lead us right more often than not? Call this the reliability question. A rule of inference can be impeccably coherent and still take us nowhere if the universe is not the sort of place in which past regularities indicate future ones. The third is about entitlement. Whatever the answer to the second question, what right have we to believe it? Call this the justification question. These come apart. A perfectly coherent agent may be systematically wrong; a reliable rule may be one we have no independent reason to trust; and an answer to the third question would settle Hume's problem, which the first two leave exactly where it was. What Russell was doing The sixth part of Human Knowledge sets out five postulates of scientific inference: that things persist for a while in roughly their present state; that there are causal lines which can be traced separately; that causal influence is transmitted continuously through space and time; that similar structures ranged about a centre commonly have a common origin; and that observed regularities can be extended by analogy to unobserved cases. Russell's argument for the list is not that these are self-evident. It is conditional. Scientific inference, as actually practised, delivers probable conclusions; if the world did not satisfy something like these principles it would not; therefore anyone who accepts the practice is committed to them. He is doing what a mathematician does in finding the weakest axioms sufficient for a body of results. He is also careful about probability itself, distinguishing mathematical probability, which is a matter of proportions in a class and obeys a calculus, from degree of credibility, which is what attaches to a proposition on given evidence and which he does not assume obeys the same calculus. That distinction is not a confusion. It is a refusal to assume the thing later work assumed. So the common complaint, that Russell lacked a technique for handling uncertainty, misses its target. He was not trying to supply one. He was asking what the world must be like for any such technique to be worth using. An older classification, and the same difficulty The dialectic here is not peculiar to modern philosophy of science. The later Mohists, writing in China in the third century before the common era, produced the most developed classification of non-demonstrative argument in the ancient world. The Xiao Qu chapter of the Mozi distinguishes four modes [3] , which A. C. Graham renders as illustrating [4] , in which a case is explained by another; parallelising, in which two sentences of like form are put side by side; adducing, in which one turns an opponent's own accepted case against him; and extending, in which a claim granted in some cases is carried over to cases not yet granted. What is striking is the accompanying warning. The Mohists observe that arguments of these kinds alter as they proceed, become precarious as they are turned about, fail when carried far, and drift from their starting point; so one must be careful with them. Their examples are exact. A white horse is a horse, and riding a white horse is riding a horse: the parallel holds. Her younger brother is a handsome man, and loving her younger brother is not loving a handsome man: the parallel fails. The two arguments have the same shape. The Mohists drew the conclusion that the modes must be used with attention to the particular case, and they did not offer a principle that would separate the good extensions from the bad. That is the reliability question arising in a tradition with no notion of probability at all, and it shows that the question is not an artefact of Russell's framework. Enumerating the valid-looking forms of uncertain inference leaves untouched the question of when extending a pattern is a good idea, and no amount of care about form supplies it. What the Bayesian framework provides The modern answer to the first question is the probabilistic one. A rational agent's confidences are degrees of belief obeying the axioms of probability, and evidence is accommodated by conditionalising: on learning that E, the new confidence in H becomes the old confidence in H given E. Dutch book arguments support the first requirement by showing that an agent whose degrees of belief violate the axioms will accept a set of bets that loses whatever happens; Howson and Urbach set out both the axioms and that argument as the framework's own case for itself [5] . This is a genuine achievement and it is an answer to the coherence question. It is worth being clear about what it does not touch. Coherence is compatible with any prior whatever. An agent who begins convinced that the future will not resemble the past can obey every axio