From dynamic disbeliefs to causality and chance
Wolfgang Spohn belongs to a generation of German analytic philosophers educated by Professor Wolfgang Stegmüller at the University of Munich. He wrote his master thesis on conditional deontic logic in 1973, doctoral dissertation on decision theory and probabilistic causality in 1976 and his Habilitationsschrift on causality in 1983. Continuing his academic career in Regensburg, Bielefeld and Konstanz, Spohn has become one of the leading European experts in philosophical logic, formal epistemology and philosophy of science.
In Causation, Coherence and Concepts, Spohn has collected 16 of his most important essays in theoretical philosophy. The topics include a dynamic theory of doxastic states, the definition of causation, Bayesian nets, induction and lawlikeness, coherentist epistemology, a priori knowledge and metaphysical necessity, concept formation and conceptual change. Many papers have their roots in the Habilitationsschrift of 1983, which formulated an account of belief change in terms of what are now called “ranking functions”. The publication of the articles in their original form (in spite of some repetition) allows the reader to see clearly how Spohn has applied, with admirable consistency and formal rigour, this basic tool in various applications in epistemology and philosophy of science. The excellent Introduction illuminates his path to more general issues in metaphysics, philosophy of language and philosophy of mind. With a carefully prepared Subject Index, the book is a rich source of original ideas and exact results about many important themes within contemporary philosophy.
A ranking function K expresses ordinal degrees of disbelief. For a proposition A, K(A) is the minimum of values K(w) for possible worlds w in A. K(A) = 0 means that A is not believed to be false. If K(A) = n > 0, then A is disbelieved with grade n. For each proposition A, K(A) = 0 or K(−A) = 0 or both. Proposition A is believed if its negation is positively disbelieved, i.e. K(−A) > 0. The rank of the disjunction A ∨ B is the minimum of K(A) and K(B). Conditional disbelief is defined by K(w/A) = K(w) − K(A). The law of conjunction states that K(A ∧ B) = K(A) + K(B/A). The belief function β associated with K is then defined by β(A) = K(−A) − K(A) and β(B/A) = K(−B/A) − K(B/A). The result of A, n-conditionalisation is defined so that A (rather than −A, as the misprint states on p. 30) is believed with firmness n.
Spohn’s ranking functions K are related to George Shackle’s degrees of potential surprise. They lead to non-probabilistic belief functions β that take both positive and negative values and replace additivity by the minimum operation. As a novelty with respect to Shackle, Spohn’s definition of conditionalisation leads to a dynamic theory of belief. It gives a way of formulating the principles of belief revision which is an alternative to Peter Gärdenfors’s relation of epistemic entrenchment and Adam Grove’s semantics in terms of similarity spheres. The relation to the AGM approach of belief revision is stated only briefly in a footnote on p. 31. Spohn has discussed this topic in more detail in his article “Ranking Functions, AGM style” in the 1999 Gärdenfors Festschrift.
The relations of positive relevance and independence can be stated by the function K in a convenient way. Spohn uses skilfully this fact in his definition of direct causes (Chapters 2 and 3). The basic idea—the cause “raises the epistemic or metaphysical rank” of the effect—can be worked out in a parallel way in deterministic and probabilistic cases. Indirect causes are then defined by the transitive closure of direct causes. Relations to Wesley Salmon’s and Nancy Cartwright’s studies on probabilistic causality are discussed. Spohn’s account turns out to be almost identical—with some differences explained in Chapter 4—with the theory of Bayesian nets and their causal interpretation, developed by Judea Pearl, Clark Glymour and Peter Spirtes et al. in the late 1980s.
The relation of reason and its variants are defined by the belief function β and hence by the ranking function K: A is a reason for B if and only if β(B/A) > β(B/−A). This notion is used in Chapter 9 to give a brief account of causal explanation and scientific understanding.
In Spohn’s approach, causation is a “covertly epistemological notion”, analysed in terms of a subject’s doxastic state and degrees of disbelief. Is such a subject-relative basis sufficient or legitimate for our understanding of the concept of causation? In what sense can causal relations be asserted to be objective or independent of any observer? Spohn tells us that he did not want to publish his Habilitationsschrift without an answer to this fundamental problem. The proposed solution is given in Chapter 5, where he attempts to uncover the sense in which causation can be understood as an “objectification of inductive schemes”. He appeals to the idea that each ranking function K can be associated with a “causal law” L that expresses as material conditionals the statements about sufficient and necessary direct causes relative to K. Then, L has objective truth conditions in the actual world. This construction from K to L is reversible for a special class of ranking functions, “fault counting functions”, which tell us how many times the law L is violated in each possible world w. This is an interesting proposal, but it can be debated whether the regularity L is strong enough to really express objective causation. Instead of counting false instances, disbelief in law L could also be defined by the number of kinds of counterexamples to L—this would be comparable to measures of truthlikeness (see Niiniluoto: Truthlikeness, Kluwer, 1987).
Spohn is of course aware of non-subjective approaches that analyse causation in terms of deterministic and probabilistic laws, counterfactual conditionals, causal necessities or objective chances (propensities). In pursuing his own programme, he does not extensively go through these alternatives. But in Chapter 8, he gives a very illuminating critical discussion of David Lewis’s Principal Principle about chance–credence relations. Spohn rejects Lewis’s doctrine of Humean supervenience, which takes the complete theory of chances in world w to supervene on the totality of particular facts in w, and favours “Humean projection” which treats chance as an objectification of credence. His proposal about “natural modalities” is adopted from Bruno de Finetti’s representation theorem, which shows how an exchangeable subjective probability measure can be expressed as a mixture of Bernoulli measures. While de Finetti himself never accepted the existence of chances, I J Good and others have interpreted his theorem as a proof that exchangeable subjective probabilities converge to an objective probability measure with increasing evidence. This strategy of objectification seems to be more interesting and powerful than the reduction of causation to material implications.
According to Spohn, the notion of a law is also covertly epistemological (Chapters 6–8). Hence, his characterisation of lawlikeness concerns the confirmation of laws by their single instances. For this purpose, Spohn needs a theory of induction. He states boldly that the theory of inductive inference is “no more and no less” than the dynamic theory of belief revision. But when he works out this idea, he reduces enumerative induction to the principles of positive and non-negative instantial relevance which state that the next instance of a law is confirmed by positive singular evidence. This move is familiar from Rudolf Carnap’s inductive logic: Carnap had to focus on instance confirmation, since genuine generalisations have a priori and a posteriori zero probability in his system. Instead, Jaakko Hintikka showed in the 1960s how inductive generalisations can be handled within inductive logic: universal generalisations receive non-zero probabilities even in infinite domains, and the posterior probability of a lawlike generalisation grows rapidly towards the maximal value one with positive evidence.
Spohn argues that “Carnap’s problem of the null confirmation of universal generalisations disappears in the ranking theoretic context”, as for symmetric cases “there is no difference between belief in the next instance and belief in the universal generalisation about all further instances”. Indeed, if G is a universal generalisation, then the negation −G of G is an infinite disjunction and your degree of disbelief K(−G) in −G is the minimum of the degrees of disbelief in the instances of −G. Spohn further suggests that lawlikeness is expressed by “the persistent attitude”, where your belief in further positive instances is unaffected by negative ones. With irony directed to Karl Popper, the mark of laws is not their falsifiability by negative instances, as only accidental generalisations are shattered by falsifying instances. He concludes with an elegant de Finetti style representation of inductive attitudes as mixtures of persistent attitudes.
I am not quite convinced by this argument. If G is believed, then K(G) = 0 and K(−G) > 0. Thus, we may have β(G) > 0 for universal generalisations. But if i is a negative instance of G, then the conditional rank K(−G/i) of −G given i is dropped to zero, which means that G is not any more believed given i. In this sense, G is falsified or “shattered” by i. Moreover, repeated negative instances without positive ones should eventually lead to a positive belief in −G. If our beliefs in the further positive instances of G, i.e. disbeliefs in the negative instances of G, are unaffected by i, there is after all an important difference between beliefs in the law and its instances. So what I find missing in Spohn’s instantial approach is the direct application of the belief function β to a Hintikka style dynamic study of inductive generalisation.
Chapters 9–11 discuss the function of reasons in a coherence theory of knowledge. As the relation of reason is symmetric and not transitive, it provides a useful tool for analysing the notion of a coherent doxastic state. Spohn argues that there is a defeasible a priori relation between perceptual appearance and observational belief (Chapter 11) and likewise between a disposition and its manifestation (Chapter 12). Here, it would be important to further develop the dynamics of coherence. For this purpose, Spohn’s framework could be adapted to the so-called non-prioritised belief revision, where the received input information is not taken for granted but its acceptability is weighed against other propositions.
Given Spohn’s early interest in decision theory and game theory, his framework can be expected to give interesting results about causal decision theory. However, Newcomb’s problem is mentioned only in passing (109). The pragmatist idea that beliefs are sources for action is missing in the articles of Spohn’s collection, but action theory could give a possible direction for his further studies. It could also help to show how experimentation and other ways of manipulating reality can give us knowledge about causal relations.
Since the 1990s, Spohn has been more and more attracted with issues in the philosophy of language. His most important study, written with Ulrike Haas-Spohn, defends the thesis that “concepts are beliefs about essences” (Chapter 14).
The final articles are contributions to the programme of “two-dimensional semantics” which has been developed within “mature” analytic philosophy since the 1970s by Saul Kripke, Hilary Putnam, David Kaplan, Robert Stalnaker and David Chalmers. The key idea is the clear separation of epistemological and ontological aspects of meaning or between epistemic necessity (unrevisable a priori) and metaphysical necessity, associated with a correspondence or “the EO-map” between them. Spohn’s own way of proceeding by “objectification” from doxastic states to causation and from credence to chance illustrate his idea of the EO-map and the direction of its “diagonal”.
In the Introduction, Spohn ventures into some speculative remarks about the two-dimensional semantics. He suggests that complete epistemic possibilities are Lewisian possible worlds or “maximal individuals”, while complete ontic possibilities are Wittgensteinian worlds or “maximal states of affairs”. The former are governed by a pragmatist or coherentist notion of truth, the latter by the correspondence theory of truth. But then he adds that the former are Kantian noumenal worlds and the latter Kantian phenomenal words. To me this sounds perplexing, as one might rather expect to find Kant’s noumenal things in themselves in the ontic worlds and his phenomena among the epistemic possibilities.