Papers

This paper gives a detailed formal characterization of dependency equilibria — a novel solution concept for games that provides a natural extension of Nash equilibria to strategic interactions where the standard assumption of non-cooperative game theory of the causal independence of the players’ choices is retained, but the assumption of their probabilistic independence is forgone. Hence, players’ beliefs may be entangled, i.e., permit probabilistic dependencies between their choices, in which case they maximize conditional expected utility (in contrast to correlated equilibria, where players maximize posterior unconditional expected utility). We demonstrate how this novel equilibrium concept can account for seeming out-of-equilibrium behavior in a variety of experimentally and socially relevant games. We further provide lower and upper bounds for the existence of dependency equilibria, determine epistemic conditions for their obtaining, and demonstrate how certain simple iterative belief revision algorithms can lead players into a common dependency equilibrium state.

This is a German version of No. 92, completely restructured and rewritten for a German audience of legal philosophers. It avoids formalities, should be broadly understandable, and is closer to the legal practice (although the distance is still large). So, this paper is perhaps more recommendable than the original No. 92. Formal details, though, are only contained in No. 92.

The paper starts from the observation that laws are full of conditional norms or obligations, the defeasible character of which prevents representing them by the material implication of classical logic. Material implication almost never adequately represents ordinary “if, then”; in particular, it can account neither for the legal syllogism nor for the practical syllogism ubiquitous in ordinary reasoning. In order to do better, the paper pursues a far-reaching analogy between beliefs (held by a person) and norms (held by an alleged authority). The analogy shows in doxastic and deontic logic. It extends to the Ramsey test, which is usually taken to be the basic explanation of conditionals, i.e., “if, then” sentences, to its treatment in the dynamic setting of belief revision theory and its normative counterpart, and thus to conditional logic and conditional deontic logic. A reflection of Chisholm’s paradox reveals a principled ambiguity in our normative talk; norms may be taken in a purely normative or in a fact-regarding way. In order to account for this ambiguity, the analogy must be further developed within so-called ranking theory which completes the dynamic perspective suggested by the Ramsey test and insufficiently explained in belief revision theory. Only in this account, fact-regarding norms can be explicated. In this way, finally, Chisholm’s paradox can be resolved, and the legal and the practical syllogism can be adequately represented. The paper attempts throughout to keep the connection to legal theorizing and argumentation.

Fitelson and McCarthy (2014) have proposed an accuracy measure for confidence orders which favors probability measures and Dempster-Shafer belief functions as accounts of degrees of belief and excludes ranking functions. Their accuracy measure only fines mistakes in confidence comparisons. We propose an alternative accuracy measure that also rewards correct confidence comparisons. It thus respects both parts of William James' maxim: Belief Truth! Shun Error! The alternative results in a criterion that we call prioritized accuracy optimization (PAO). It turns out that precisely confidence orders representable by two-sided ranking functions satisfy PAO. The point is not to argue that PAO is the better accuracy goal. The point is only that ranking theory, too, can be supported by accuracy considerations. Thus, those considerations by themselves cannot decide about rational formats for degrees of belief, but are part and parcel of an overall normative assessment of those formats.

The paper is motivated by the need of giving an account for the practical syllogism as a piece of defeasible reasoning. Such an account is missing so far. To meet the need, the paper develops a far-reaching parallel between epistemic and deontic reasoning. Deontic logic works like epistemic or rather doxastic logic. Dyadic deontic logic and contrary-to-duty obligations work like belief revision theory and counterfactual logic. The parallel continues to ranking theory, which was so far only epistemically interpreted, to a normative or deontic interpretation of ranking theory which is elaborated here for the first time. Only on that level, we can distinguish and account for  two kinds of ought, for so-called purely normative and fact-regarding obligations (in analogy to intrinsic and extrinsic utilities in decision theory). The purely normative obligations (and their contrary-to-duty fall-backs) are represented by a purely normatively interpreted ranking function. The central proposal then is to represent the fact-regarding obligations (and their fall-backs) by a combination of the purely normative and an epistemic ranking function. Such a combination is possible only at the level of ranking theory and not on the two preceding and therefore deficient levels. Moreover, it is argued that this combination must be the sum of the purely normative and the epistemic function (as suggested in qualitative decision theory). The paper defends this proposal with a comparative discussion of some critical examples and some other distinctions made in the literature, where it develops both, disambiguating and unifying power. In particular, it can plausibly account for Chisholm's paradox of contrary-to-duty obligations and for the defeasible nature of the practucal syllogism. Finally, it displays the possibility of jointly developing the logic of purely normative and of fact-regarding normative defeasible reasoning, but must acquiesce in pointing out the difficulties of completing the logic of the fact-regarding side.

This is one of a pair of discussion notes comparing some features of the account of causation in Spohn’s Laws of Belief (2012) with the “interventionist” account in Woodward’s Making Things Happen (2003). This note locates the core difference of the accounts in the fact that Woodward’s account follows an epistemological order, while Spohn’s follows a conceptual order. This unfolds in five further differences: (i) type- vs. token-level causation, (ii) reference to time, (iii) actual/counterfactual intervention vs. epistemic/suppositional wiggling, (iv) a circular vs. a circle-free conception of the circumstances of a direct causal relation, and (v) absolute vs. model-relative causation.

Knightian uncertainty is not a special kind of uncertainty; it’s just uncertainty. And it raises the issue how we may model uncertainty. The paper gives a brief overview over non-probabilistic measures of uncertainty, starting with Shackle’s functions of potential surprise and mentioning non-additive probabilities, Dempster–Shafer belief functions, etc. It arrives at an explanation of ranking theory as a further uncertainty model and emphasizes its additional epistemological virtues, which consist in a representation of belief, i.e., of taking something to be true (which is the basic notion of traditional epistemology and admits of degrees as well), together with a full dynamic account of those beliefs. The final section addresses the issue how these uncertainty measures and in particular ranking theory may be used within a decision theoretic context. The novel information is that ranking theory has a decision theoretic extension at all.

This talk (in German) explains my not too optimistic 2017 view of the past and present situation of philosophy of science not only in Konstanz, but also in Germany and worldwide. The general view may be interesting, but the local Konstanz stories are definitely informative.

Objective standards for justification or for being a reason would be desirable, but inductive skepticism tells us that they cannot be presupposed. Rather, we have to start from subjective-relative notions of justification and of being a reason. The paper lays out the strategic options we have given this dilemma. The paper explains the requirements for this subject-relative notion and how they may be satisfied. Then it discusses four quite heterogeneous ways of providing more objective standards, which combine without guaranteeing complete success.

This paper deals with the epistemology and auto-epistemology of temporal self-location and forgetfulness in probabilistic terms. After explicitly stating the underlying algebraic or propositional framework, it proposes two rules of probability change through our inner sense of time and generally describes how conditionalization works with respect to indexical information. It suggests a rule for rearranging beliefs after forgetting (and other unfavorable epistemic changes). After rehearsing standard auto-epistemology in terms of the reflection principle and its consequences, it moreover studies the auto-epistemology of those non-standard epistemological changes. Thus, it generalizes the reflection principle to the indexical case and to an even more general version that is free from the informal restrictions that are commonly assumed. All these principles are illustrated with various examples: the prisoner, the new riddle of induction, Sleeping Beauty, and finally Shangri-La. 

This paper is an elaboration of my Frege Lecture, within the Frege colloquium at GAP.9 for the award of the Frege Prize of the Gesellschaft für Analytische Philosophie on Sept. 16, 2015. It argues that the modalities come into the world by being projections or objectivizations of our epistemic constitution. Thus it is a statement of Humean projectivism. In fact, it goes beyond Simon Blackburn’s version. It is also designed as a comprehensive counter-program to David Lewis’ program of Humean supervenience. In detail, the paper explains: (1) Already the basic fact that the world is a world of states of affairs is due to the nature of our epistemic states. (2) Objects (and properties and relations), which figure in states of affairs and which embody metaphysical modality, are constitutable by their essential properties and in fact constituted by us according to our ontological policies. (3) What the facts are, to which the correspondence notion of truth refers, is determined by applying an epistemic or pragmatic notion of truth to the world. (4) Causation is a specific objectivization of our conditional beliefs. (5) Nomicity is a ‘habit of belief’ (Ramsey), a specific way of generalizing epistemic attitudes. This covers the basic metaphysical and natural modalities. The paper attempts to convey that talking of projection or objectivization is not just imagery, but a constructively realizable program. The paper essentially refers to various other papers of mine, most notably No. 85, 82, 77, 61, 60, 56, and 27, and chs. 12, 14 and 15 of my book The Laws of Belief.

This paper is an elaboration of my Lakatos lecture on May 9, 2013, at the ceremony for the Lakatos Award 2012. It is about the pragmatic notion of truth, according to which what we believe in the ideal limit of inquiry is true. Hence, it refers to the dynamics of belief and thus to theoretical rationality. Thereby, truth and rationality are inexorably intertwined; neither can be explained without the other, and each contributes to substantiating the other.

“Enumerative Induction”: This is a philosophical paper about enumerative induction, a basic rule of inductive or defeasible reasoning. It shows that it is almost satisfactorily accounted for in probability theory, which, however, is plagued by the problem of null confirmation of laws. It is even more adequately in ranking theory, which can explain that it specifically applies to laws, as opposed to accidental generalizations. This has consequences for Goodman's new riddle of induction as well as the often claimed apriority of the uniformity of nature. The paper certainly deals with the foundations of formal rationality and should be of interest not only to philosophers, but also to the Artificial Intelligence community, which is deeply engaged in inductive reasoning as well. So, it is a suitable contribution in this Festschrift.

„Wie Wünsche zweiter Stufe praktisch relevant werden“: Harry Frankfurt has forcefully argued how closely freedom of will is connected with second order desires and volitions. However, neither he himself nor the subsequent literature has accounted for the rational role of second order desires, of their logic, as it were. They remain an intuitive phenomenon without theory. The paper elaborates in an informal way how these second order desires could adopt an important constructive role in rational decision theory, a role which standard decision theory fails to define as well.

„Three Kinds of Worlds and Two Kinds of Truth“: This paper argues for three kinds of possible worlds: Wittgensteinian totalities of facts, Lewisian worlds or universes, concrete objects of maximal essence, and the world, a concrete object of minimal essence. It moreover explains that correspondence truth applies to Wittgensteinian totalities and pragmatic truth to Lewisian universes. And it finally argues that this conceptualization lays proper foundations to two-dimensional semantics. This includes a critical discussion of David Chalmers' conception of two-dimensional semantics.

„The Epistemic Account of Ceteris Paribus Conditions“: The paper focuses on interpreting ceteris paribus conditions as normal conditions. After discussing six basic problems for the explication of normal conditions and seven interpretations that do not well solve those problems I turn to what I call the epistemic account. According to it the normal is, roughly, the not unexpected. This is developed into a rigorous constructive account of normal conditions, which makes essential use of ranking theory and in particular allows to explain the phenomenon of multiply exceptional conditions. Finally, this static account is extended to a schematic dynamic model of how we may learn about those normal and (multiply) exceptional conditions.

“Conditionals: A Unified Ranking-Theoretic Perspective”: The paper takes an expressivistic perspective, i.e., it takes conditionals of all sorts to primarily express (features of) conditional beliefs. Therefore it is based on what it takes to be the best account of conditional belief, namely ranking theory. It proposes not to start looking at the bewildering linguistic phenomenology, but first to systematically study the various options of expressing features of conditional belief. Those options by far transcend the Ramsey test and include relevancies of various kinds and in particular the so-called “circumstances are such that” reading, under which also all conditionals representing causal relations can be subsumed. In this way a unifying perspective on the many kinds of conditionals is offered. The final section explains the considerable extent to which truth conditions for conditionals, which may seem lost in the expressivistic or epistemic perspective, may be recovered.

„50 Jahre Gettier: Reichen Vielleicht”: A critical concern of this paper is to emphasize how little the unclarities of the three basic concepts truth, belief, and justification of Plato’s analysis of knowledge are mastered up to the present day. This applies as well to the unclarities of the so-called modal analyses of knowledge with respect to their reference to (counterfactual) conditionals and to normal conditions. A constructive concern is to at least suggest how helpful ranking theory could be in coming to terms with those unclarities. This finally leads to a possible answer to the issue what the surplus value of knowledge over mere true beliefs may be.

„How Essentialism Properly Understood Might Reconcile Realism and Social Constructivism”: The paper attempts to reconcile realism and constructivism (i) by endorsing an essentialist conception of the individuation of objects, (ii) by pointing to the conventional character of the essential/accidental distinction, (iii) by noticing that conventions may still leave room for the empirical investigation of essential properties, and (iv) by observing that despite this conventionality realism need not be derogated in any way. The final section points to some consequences for social ontology.

“A Priori Principles of Reason“: This paper presents various a priori principles of reason: a basic empiricist principle, as it is called here, some coherence principles, principles about the connection between truth and reason, etc. They are familiar, indeed venerable. What the paper will add are precise explications of those principles and rigorous relations between them. Just in order to make you curious, in the end a weak principle of causality will be derived from a principle characteristic of pragmatic truth. This connection sounds surprising, and in view of the recent persistent silence on the principle of causality this result is certainly alerting.

“AGM, Ranking Theory, and the Many Ways to Cope with Examples”: The paper first explains how the ranking-theoretic belief change or conditionalization rules entail all of the standard AGM belief revision and contraction axioms. Those axioms have met a lot of objections and counter-examples, which thus extend to ranking theory as well. The paper argues for a paradigmatic set of cases that the counter-examples can be well accounted for with various pragmatic strategies while maintaining the axioms. So, one point of the paper is to save AGM belief revision theory as well as ranking theory. The other point, however, is to display how complex the pragmatic interaction of belief change and utterance meaning may be; it should be systematically and not only paradigmatically explored.

"A Ranking-Theoretic Approach to Conditionals": Conditionals somehow express conditional beliefs. However, conditional belief is a bi-propositional attitude that is generally not truth-evaluable, in contrast to unconditional belief. Therefore, the paper opts for an expressivistic semantics for conditionals, grounds this semantics in the arguably most adequate account of conditional belief, i.e., ranking theory, and dismisses probability theory for that purpose, because probabilities cannot represent belief. Then, various expressive options are explained in terms of ranking theory, with the intention to set out a general interpretive scheme that is able to account for the most variegated usage of conditionals. The Ramsey test is only the first option. Relevance is another, familiar, but little understood item, which comes in several versions. The paper adds a further family of expressive options, which is able to subsume also counterfactuals and causal conditionals, and indicates at the end how this family allows to partially recover truth conditions for conditionals.

The alleged principled difference between human sciences (social sciences and humanities) and natural sciences is much discussed for more than 100 years. The paper first discusses some accounts of this difference, which appear unsatisfactory to me. In preparing its main thesis, it then distinguishes normativity from an external third-person perspective and an internal first-person perspective. In the external perspective normativity is an empirical phenomenon, in the internal perspective it is genuine and irreducible. The paper then discusses the extent to which sciences are involved in normative issues in the internal sense. Issues in research agenda and methodology are normative for all of the sciences in the same way. But only human sciences deal with objects, i.e., human beings, as having an internal normative perspective. It is argued then that the human sciences, even when only doing their empirical business properly, are inextricably entangled in normative issues in the internal sense, like their objects of investigation themselves. This is in my view their essential difference to the natural sciences. The final section argues that this view is well compatible with a materialist view that everything in the world including normativity supervenes on the physical constitution of the world.

The Structural Model Approach to causation has become very prominent in the last 10 years. It attempts to improve on other accounts of deterministic causation and appears promising because of its proximity to scientific practice. This paper gives an essentially descriptive comparison between it and the ranking-theoretic account which I endorse for more than two decades. Because they look similar, they are easily compared. Nevertheless I find no less than 15 minor and major points in which the two accounts diverge. This long list intends to remind of the many open issues in the theory of causation, and it might suggest that the weight of argument ultimately favors the ranking-theoretic approach.

“Multiple Contraction Revisited”: Multiple contraction consists in giving up several beliefs at once. The treatments of multiple contraction in AGM belief revision theory have remained unsatisfactory. The paper proposes a clear, plausible, and general model for multiple contraction in ranking-theoretic terms according to which multiple contraction turns out to reduce to single contractions. The belief set multiply contracted by {A1, …,An} is just the intersection of all the belief sets singly contracted by Ai (i = 1, …, n).

"Reversing 30 Years of Discussion: Why Causal Decision Theorists Should One-Box": This paper aims at rationalizing drinking the toxin in the Toxin puzzle and one-boxing in Newcomb’s problem within the realms of causal decision theory. These actions standardly maximize conditional expected utlity, since the conditional probabilities of the outcomes probabilistically depend on the actions. Traditional causal decision theory interprets this dependence as a causal one and takes this as a correct reason for rejecting it. Within the partially elaborated so-called reflexive decision theory, however, this dependence is causally interpreted as induced by a common cause relation; upon reflection, the decision situation itself turns out to be a common cause of the rational action as well as the outcome. And, so the paper argues, rational decisions have to take this kind of common cause relation into account in terms of conditional expected utility.

In my paper No. 42, I have first introduced and developed the novel notion of a dependency equilibrium for game theory. There I have done so on the basis of a quite sophisticated account of probabilistic causation, which is not really required for this purpose. In the present paper I give a much simpler and intuitive explanation of dependency equilibria, of their potential and their relevance, and of the fallacies behind taking them as meaningless or confused. It is the most recommendable introduction into this novel concept.

"Two-Dimensional Truth": The paper identifies two major strands of truth theories, ontological and epistemological ones and argues that both are of equal primacy and find their home within two-dimensional semantics. Contrary to received views, it argues further that epistemological truth theories operate on Lewisian possible worlds and ontological truth theories on Wittgensteinian possible worlds and that both are mediated by the so-called epistemic-ontic map the further specification of which is of utmost philosophical importance.

"Why the Received Models of Considering Preference Change Must Fail": First, the paper discusses the extent to which preference change is a topic of normative rationality; it confirms as one main issue the economists’ search for a rational decision rule in cases in which the agent himself envisages to have changing preferences. Then it introduces so-called global decision models and shows that all the received economic models for dealing with preference change have that shape. The final section states two examples for global decision models, one with extrinsic, belief-induced and one with intrinsic preference change, and interprets each of them in two different scenarios in which different strategies are intuitively reasonable – the point being that global decision models cannot provide sufficient information for stating adequate decision rules. What the missing information might be is at least indicated at the end.

"A Priori Reasons: Two Difficult Notions and an Even More Difficult Connection": Contrary to received views, I propose in this paper to understand both apriority and justification (or rather having and giving reasons), from the dynamic perspective of belief change. This will provide us with the basic explication of the notion of a reason and with the basic distinction of unrevisable and defeasible apriority. And it will lead us to new and instructive connections between reasons and apriority.

"Dependency Equilibria": This paper introduces a new equilibrium concept for normal form games called dependency equilibrium; it is defined, exemplified, and compared with Nash and correlated equilibria in Sections 2–4. Its philosophical motive is to rationalize cooperation in the one shot prisoners’ dilemma. A brief discussion of its meaningfulness in Section 5 concludes the paper.

Ranking theory delivers an account of iterated contraction; each ranking function induces a specific iterated contraction behavior. The paper shows how to reconstruct a ranking function from its iterated contraction behavior uniquely up to multiplicative constant and thus how to measure ranks on a ratio scale. Thereby, it also shows how to completely axiomatize that behavior. The complete set of laws of iterated contraction it specifies amend the laws hitherto discussed in the literature.

In truth-conditional semantics, concepts are usually explicated as (diagonal) intensions of predicates or relations. Hence: different intensions, different concepts. Concepts cannot literally change; a concept can only be replaced by another. This is against intuition according to which a concept, like most other things, can change while staying the same. This little paper discusses five ways how to account for this intuition, the last one being my favorite.

The paper argues that the objects of belief should not be conceived as sets of possible worlds or propositions of set of centered possible worlds or egocentric propositions (this is the propositional conception), but rather as sets of pairs consisting of a centered world and a sequence of objects (this is the intentional conception of the objects of belief). The paper explains the deep significance of this thesis for the framework of two-dimensional semantics, indeed for any framework trying to adequately relate semantics and epistemology (which is here construed as what I call the Congruence Principle). I give three arguments for this thesis, two preliminary indecisive ones by way of examples, and third theoretical one alluding to a deep principle of philosophical psychology (which I call the Invariance Prinicple). This paper is an improved and up-dated version of my paper No. 25. It will appear in Causation, Cohrence, and Concepts. A Collection of Essays of mine.

The paper proposes to amend structuralism in mathematics by saying what places in a structure and thus mathematical objects are. They are the objects of the canonical system realizing a categorical structure, where that canonical system is a minimal system in a specific essentialistic sense. It would thus be a basic ontological axiom that such a canonical system always exists. This way of conceiving mathematical objects is underscored by a defense of an essentialistic version of Leibniz’ principle according to which each object is uniquely characterized by its proper and possibly relational essence (where “proper” means “not referring to identity”).

"Five Questions on Formal Philosophy": Like the other authors in the volume, I was asked for my reflections on the character of (formal) philosophy by answering the following five questions: 1. Why were you initially drawn to formal methods? 2. What example(s) from your work illustrates the role formal methods can play in philosophy? 3. What is the proper role of philosophy in relation to other disciplines? 4. What do you consider the most neglected topics and/or contributions in late 20th century philosophy? 5. What are the most important problems in philosophy and which are the prospects for progress?

"The Core of Free Will": The paper pleads for compatibilism by distinguishing the first-person’s normative and the observer’s empirical perspective. In the normative perspective one’s own actions are uncaused and free, in the empirical perspective they are caused and may be predetermined. Still, there is only one notion of causation that is able to account for the relation between the causal conceptions within the two perspectives. The other main idea for explicating free will by explaining free actions or intentions as appropriately caused in a specified way is acknowledged, but not discussed. The paper finally argues that the normative and the empirical perspective are on a par; none is prior; even from within the empirical perspective the normative perspective is ineliminable.

"A Survey of Ranking Theory": The paper gives an up-to-date survey of ranking theory. It carefully explains the basics. It elaborates on the ranking theoretic explication of reasons and their balance. It explains the dynamics of belief statable in ranking terms and indicates how the ranks can thereby be measured. It suggests how the theory of Bayesian nets can be carried over to ranking theory. It indicates what it might mean to objectify ranks. It discusses the formal and the philosophical aspects of the tight relation and the complementarity of ranks and probabilities. It closes with comparative remarks on predecessors and other philosophical proposals as well as formal models developed in AI.

"Chance and Necessity: From Humean Supervenience to Humean Projection": This paper attempts to develop a projectivistic understanding of chance or objective probability or partial determination. It does so by critically examining David Lewis’ philosophy of probability and his defense of Humean Supervenience, building thereupon the constructive projectivistic alternative, which will basically be a suitable reinterpretation of de Finetti’s position. Any treatment of the topic must show how it extends to natural necessity or deterministic laws or full determination in perfect parallel. The paper indicates at the end how this demand can be met.

"Anmerkungen zum Begriff des Bewusstseins": The paper explains and defends its core thesis that p is a possible content of consciousness of a at time t if and only if it is metaphysically necessary that p iff a believes at t that p. It argues that this thesis adequately captures phenomenal consciousness as well as intentional consciousness (of our propositional attitudes) and perhaps self-consciousness. It argues that the thesis is a traditional one, in a way. And it finally points to some remarkable epistemological consequences of its thesis.

"Isaac Levi's Potentially Surprising Epistemological Picture": This paper compares the epistemological conception of Isaac Levi with mine. We are joined in both giving a constructive answer to the relation of belief and probability, without reducing one to the other. However, our constructions differ in at least nine more or less important ways, all discussed in the paper. In particular, the paper explains the similarities and differences of Shackle's functions of potential surprise, as used by Levi, and my ranking functions in formal as well as in philosophical respects. The appendix explains how ranking and probability theory can be combined in the notion of a ranked probability measure (or probabilified ranking function).

"Ist Philosophie eine Wissenschaft?": I give a positive answer to the title question - by defending six claims: (1) Philosophy must in any case maintain the claim to be a scientific discipline. (2) There are many close relations between philosophy and specific disciplines showing that they are at least similar in kind; all are part of our best ways of theorizing about the world. (3) There is a lot of 'normal science' in philosophy, not less useful than other normal science. (4) This has the effect of raising the scholarly standards in philosophy. (5) There is still progress and improvement in philosophy, even concerning the 'big questions', but only with the help of 'scientific' methods. (6) There is a peculiar dialectics between the philosophy of big questions and the philosophy as normal science; both depend on one another.

"Enumerative Induction and Lawlikeness": The paper is based on ranking theory, a theory of degrees of disbelief (and hence belief). On this basis, it explains enumerative induction, the confirmation of a law by its positive instances, which may indeed take various schemes. It gives a ranking theoretic explication of a possible law or a nomological hypothesis. It proves, then, that such schemes of enumerative induction uniquely correspond to mixtures of such nomological hypotheses. Thus, it shows that de Finetti's probabilistic representation theorems may be transformed into an account of confirmation of possible laws and that enumerative induction is equivalent to such an account. The paper concludes with some remarks about the apriority of lawfulness or the uniformity of nature.

"Causation: An Alternative": The paper builds on the basically Humean general idea that A is a cause of B iff A and B both occur, A precedes B, and A raises the metaphysical or epistemic status of B given the obtaining circumstances. It argues that in pursuit of a theory of deterministic causation this 'status raising' is best explicated not in regularity or counterfactual terms, but in terms of ranking functions. On this basis, it constructs a rigorous theory of deterministic causation that successfully deals with cases of overdetermination and preemption. It finally indicates how the account's profound epistemic relativization induced by ranking theory can be undone.

"On the Objectivity of Facts, Beliefs, and Values": This paper arose from a comment to the talk of Tara Smith at the Pittsburgh-Konstanz Colloquium in October 2002. Now it is a self-contained text precisely about what the title indicates. It is a somewhat mixed bag, but a nice read.

"Laws Are Persistent Inductives Schemes": The characteristic difference between laws and accidental generalizations lies in our epistemic or inductive attitude towards them. This idea has taken various forms and dominated the discussion about lawlikeness in the last decades. Hence, ranking theory with its resources of formalizing defeasible reasoning or inductive schemes seems ideally suited to explicate the idea in a formal way. This is what the paper attempts to do. Thus it will turn out that a law is simply the deterministic analogue of a sequence of independent, identically distributed random variables. This entails that de Finetti's representation theorems can be directly transformed into an account of confirmation of laws thus conceived. Theorem and proof are, however, fully and precisely stated only in paper No. 52.

"Burge macht uns weis: ein Zirkel bei Grice": This paper is a brief comment on Mark Siebel's contribution to the present volume. In his famous paper "Individualism and the Mental" Tyler Burge suggests that the equally famous Gricean account of linguistic meaning is circular and cannot offer a reduction of semantics to psychology. Siebel argues that this suggestion is mistaken. I try to make clear that there is a point in Burge's suggestion: namely that the Gricean account can hold out its reductionistic promise only if it additionally provides an account of narrow as opposed to wide content.

"Laws, Ceteris Paribus Conditions, and the Dynamics of Belief": The paper develops an account of lawlikeness on the basis of ranking theory (cf. No. 15 and, e.g., No. 39). A universal generalization is a law not because of its content, but only insofar a certain inductive attitude is taken towards its instantiations, an attitude which I describe as being persistent as opposed to being shaky. Thereby, a conception of lawlikeness widely found in the literature receives a precise explication (for the first time, as far as I know). In effect, a law thus turns out to be the ranking analogue of a sequence of independent and identically distributed stochastic variables. This entails that de Finetti's account of the confirmation of statistical hypotheses can be immediately carried over to the case of deterministic laws. The paper also explains that laws explicated in ranking terms are perfectly suited for accommodating ceteris paribus conditions in various senses. The final section offers brief comparative remarks about the other papers in this Erkenntnis issue.

"Carnap versus Quine, or Aprioristic versus Naturalized Epistemology, or a Lesson from Dispositions": In his influential paper "Epistemology Naturalized" Quine argues that Carnap's failure to define disposition predicates and his subsequent preference for reduction sentences naturally lead to an entirely naturalized epistemology. This conclusion is too hasty, I object. Applying the account of dispositional predicates developed in No. 26 I defend Carnap's aprioristic epistemology against Quine's attacks.

"Die vielen Facetten der Rationalitätstheorie": The paper is essentially an updated and abbreviated version of No. 21. It specifies the general scheme of what is assessed as rational relative to what. It gives a very brief overview over the various fields of rationality theory ensuing from this scheme. It explains how rationality theory can be both, a normative and an empirical theory, and why the normative perspective is ineliminable (a fact which entails that psychology cannot be entirely naturalized).

"Lehrer Meets Ranking Theory": Keith Lehrer's sophisticated epistemology is essentially based on a four-place relation: A is more reasonable to accept given C than B given D. The only formal account of this relation compatible with Lehrer's requirements is provided by ranking theory as developed by me in No. 15 (but see also No. 39). However given this account, justified acceptance as defined by Lehrer reduces to acceptance and knowledge as defined by Lehrer reduces to true acceptance. Thus, Lehrer's theory is trivialized. The final section discusses possible consequences to be drawn from these results.

"A Brief Comparison of Pollock's Defeasible Reasoning and Ranking Functions": For more than 20 years John Pollock is elaborating a detailed account of defeasible reasoning. Ranking theory as developed by me in No. 15 (but see also No. 39) offers such an account, too. The paper first gives a very brief informal sketch of the two accounts. It then explains that the basic difference is that Pollock's theory is entirely computational, whereas mine is located at a regulative level. It continues to argue that Pollock's theory cannot bridge this difference and that its normative condition is therefore deficient. The final section shows, by contrast, that ranking theory provides ample means to bridge the difference.

"Dependency Equilibria and the Causal Structure of Decision and Game Situations": The paper attempts to rationalize cooperation in the one-shot prisoners' dilemma (PD). It starts by introducing (and preliminarily investigating) a new kind of equilibrium (differing from Aumann's correlated equilibria) according to which the players' actions may be correlated (sect. 2). In PD the Pareto-optimal among these equilibria is joint cooperation. Since these equilibria seem to contradict causal preconceptions, the paper continues with a standard analysis of the causal structure of decision situations (sect. 3). The analysis then raises to a reflexive point of view according to which the agent integrates his own present and future decision situations into the causal picture of his situation (sect. 4). This reflexive structure is first applied to the toxin puzzle and then to Newcomb's problem, showing a way to rationalize drinking the toxin and taking only one box with-out assuming causal mystery (sect. 5). The latter result is finally extended to a rationalization of cooperation in PD (sect. 6).

"Bayesian Nets Are All There Is To Causal Dependence": The paper displays the similarity between the theory of probabilistic causation developed by Glymour et al. since 1983 and mine developed since 1976: the core of both is that causal graphs are Bayesian nets. The similarity extends to the treatment of actions or interventions in the two theories. But there is also a crucial difference. Glymour et al. take causal dependencies as primitive and argue them to behave like Bayesian nets under wide circumstances. By contrast, I argue the behavior of Bayesian nets to be ultimately the defining characteristic of causal dependence.

"Vier Begründungsbegriffe": The paper distinguishes four basic notions of one assumption or proposition being a reason for (or justifying) another: a deductive notion, a computational notion, a causal notion, and a positive relevance notion (as first defended by me in No. 10). After setting these notions within three important distinctions of present-day epistemology - knowledge vs. belief, internalistic vs. externalistic, and normative vs. naturalized epistemology - and after explaining why I tend to be a normative internalist belief theorist, I compare the four notions and argue that the positive relevance notion is the most adequate and fruitful one.

"Deterministic Causation": The paper is the most complete presentation of my views on deterministic causation. It develops the deterministic theory in terms of ranking functions in perfect parallel to my theory of probabilistic causation (as was claimed to be possible in No. 17) and thus unites the two aspects. It also argues that the theory presented is superior to regularity and counterfactual theories of causation, in particular by giving a natural account of causal overdetermination. Since it presents a subjectivistic theory of causation, in a Humean spirit, it closes with briefly summarizing my account of how to objectify this theory of causation (which is fully presented in No. 20).

"Über die Struktur theoretischer Gründe": The paper sets out something like a scheme behind my various epistemological papers (Nos. 15, 18, 26, 27, 28, and 32): by explaining the relations I see between the dynamics of belief, reasons and apriority, by introducing a number of basic general principles concerning the structure of reasons (such as a ban of dogmatism, the Schein-Sein-Prinzip, a special and a general coherence principle, a weak and a strong discoverability principle, a weak and strong principle of the coherence of truth, and a weak and a very weak principle of causality), by explaining the relations between these principles, and by relating the principles to familiar doctrines like the verifiability theory of meaning, the unity of science, or internal realism.

"Die Logik und das Induktionsproblem": The paper explains my view that the venerable problem of induction is tantamount to the question of how to revise or change our beliefs or doxastic states. It thus emphasizes the importance and fruitfulness of general theories of belief revision. Moreover, it gives a very elementary introduction to my theory of ranking functions which I still believe to be the best general theory about how to revise plain beliefs, i.e., the set of propositions held to be true.

"Concepts Are Beliefs about Essences": The most promising strategy to understand (sentential) narrow contents or (subsentential) concepts seems to be to conceive them as primary intensions or diagonals within the epistemologically reinterpreted character theory of Kaplan. However, this strategy seems to founder either at Block's dilemma between a too syntacticist or too holistic understanding of narrow contents and concepts or at Schiffer's problem that the character theory depends on functional role semantics without adding anything to it. The paper defends a way of steering midway of Block's dilemma without recourse to functional role semantics, a way perfectly summarized in its title.

"Ranking Functions, AGM Style": The paper first points out that ranking functions are superior to AGM belief revision theory in two crucial respects, i.e. in solving the problem of iterated belief revision and in giving an adequate account of doxastic independence (this was indeed why ranking function were developed in No. 15). Second, it shows how ranking functions are uniquely reflected in iterated belief change. More precisely, it specifies conditions on threefold contractions which suffice to represent contractions by a ranking function uniquely up to multiplication by a positive integer (a result independently obtained by Matthias Hild). Thus, an important advantage AGM theory was always claimed to have over ranking functions proves to be spurious.

"A Rationalization of Cooperation in the Iterated Prisoner's Dilemma": The paper is essentially a short version No. 33 which emphasizes in particular how the ideas developed there may be used to shed new light on the iterated prisoner's dilemma (and on iterated Newcomb's problem). (However, I have withdrawn the final section; see No. 42.)

"Strategic Rationality": The paper argues that the standard decision theoretic account of strategies and their rationality or optimality is much too narrow, that strategies should rather condition future action to future decision situations (a point of view already developed in my Grundlagen der Entscheidungstheorie, sect. 4.4), that practical deliberation must therefore essentially rely on a relation of superiority and inferiority between possible future decision situations, that all this allows to substantially broaden the theory of practical rationality, that a long list of points attended to in the literature can be subsumed under the broadened perspective (including a novel view on the iterated prisoner's dilemma and on iterated Newcomb's problem, which, however, is revised in No. 42), and that the task to complete and systematize this list indeed forms a fruitful research programme.

"Two Coherence Principles": The paper proposes two principles of coherence (thus taking up work started in No. 18). The latter indeed serves as a weak, but precise explication of the notion of coherence as it is used in the current epistemological discussion. After discussing their epistemological setting, the paper considers four ways of establishing these principles. They may be inferred neither from enumerative induction, nor from the nature of propositions as objects of belief, nor in a Kantian way from self-consciousness. Rather, I propose a fairly rigorous way to infer them from an even more fundamental rationality principle of non-dogmatism and an elementary theory of perception.

"Die Philosophie und die Wissenschaften": In this paper I try to give a popular characterization of how I would like to conceive of philosophy, how closely current philosophy is intertwined with many neighboring fields, and why philosophy is nevertheless essentially different.

"Lewis' Principal Principle ist ein Spezialfall von van Fraassens Reflexion Principle": The paper explains how Lewis' (old) Principal Principle (which tries to specify the most basic connection between subjective probability, credence, and objective probability, chance) may be conceived and derived as a special case of van Fraassen's Reflexion Principle (which specifies a fundamental relation between present and future subjective probabilities).

"Wo stehen wir heute mit dem Problem der Induktion?": The paper gives a broad overview of the current state of the discussion of the problem of induction, explains the importance of general formal treatments, and argues that its normative status cannot be dissolved into naturalized epistemology.

"How to Understand the Foundations of Empirical Belief in a Coherentist Way": The central claim of the paper is, roughly, that the fact that it looks to somebody as if p is a defeasibly a priori reason for assuming that p (and vice versa), for any person, even for the perceiver himself. As a preparation, it outlines a doxastic conception suitable to explicate this claim and explains how to analyse dispositions within this conception. Since an observable p has the disposition to look as if p, this analysis generalizes to the central claim which is then argued to be at the bottom of coherentism. Thus, the defense of the claim supports coherentism as opposed to foundationalism and at the same time provides an answer to skepticism about the external world.

"The Character of Color Terms: A Materialist View": The paper analyzes the meaning of color terms within the framework of Kaplan's character theory (which, when generalized to a treatment of hidden indexicality or dependence on the context world, can perfectly accommodate Kripke's notions of apriority and of (metaphysical) necessity). It explains this framework and why it might be fruitfully applied to color terms. Then it defends six theses: that (1) the predicate "is red" and (2) even the relation "appears red to" are hidden indexicals (i.e., have, as used in English, different extensions in different context worlds), that (3) the phenomenal, the comparative, and the epistemic reading of "appears red to" are not three different readings, but reflect the context world dependence of this term, that (4) the statement "x is red iff x would appear red to most English-speaking people under normal conditions" is a priori in English, but analytic only in one reading and not in another, and that these observations account well for the epistemology of color terms and allow us to be metaphysically conservative by claiming that our context world is presumably such that (5) the statement "x appears red to y iff x (appropriately) causes y to be in a certain (disjunctive) neural state N" is necessarily true and (6) the statement "x is red iff the reflectance spectrum of the surface of x is of some (disjunctive) kind R" is necessarily true as well.

As the heading indicates, the paper has two different topics, put in relation in the paper. The first topic is to explain the notions of apriority = epistemic necessity, metaphysical necessity, and analyticity as introduced by Kripke and explicable in Kaplan’s and Stalnaker’s framework of two-dimensional semantics. The second topic is developed by means of the example of disposition predicates, at which logical empiricism eventually foundered. It is that there also is another kind of apriority which I later call defeasible apriority (this is the first paper where I develop this distinction). So-called reduction sentences for disposition predicates are my prime example for defeasible apriority. It shows at the same time that not only sentences or propositions, but also reason relations between propositions can be defeasibly a priori. The paper also discusses what all of this means for the relation between a disposition and its (ontological) basis. And it concludes with an outlook concerning the relevance of defeasible apriority for the issue of skepticism (a point further developed in my paper No. 28).

"Über die Gegenstände des Glaubens": The paper deals with the question of how to conceive the objects of belief. It emphasizes its epistemological importance, defends to conceive these objects as semantic contents, characterizes such contents as sets of doxastic alternatives, and explains them in an individualistic way as narrow contents. It claims moreover that doxastic alternatives (and thus narrow contents) need structure: they do not consist only of a possible world, or of a possible world, a subject, and a time (as required for the representation of belief de se and de nunc); they must rather contain a (finite) sequence of objects, too. It offers three arguments for this claim and points to some fundamental philosophical consequences of it.

The paper attempts to clarify the relation between three different accounts of certainty as (i) unrevisability or infallibility, (ii) apriority, and (iii) analyticity, which are confused in analytic philosophy since Quine’s “Two Dogmas of Empiricism”.

"On the Properties of Conditional Independence": As the paper explains, it is crucial to epistemology in general and to the theory of causation in particular to investigate the properties of conditional independence as completely as possible. The paper summarizes the most important results concerning conditional independence with respect to two important representations of epistemic states, namely (strictly positive) probability measures and ranking functions (still called natural conditional functions in Nos. 15 and 16). It finally adds some new observations and thus supplements Nos. 6 and 15.

"On Reichenbach's Principle of the Common Cause": The paper asks: What does Reichenbach's Principle of the Common Cause say? What is its philosophical significance? And most importantly: Is the principle true? To answer this, one must first consider how one might at all argue about the principle. One can do so by way of examples or more theoretically; this is the main intent of the paper. Based on the explication of probabilistic causation proposed in Nos. 6 and 17 it is shown that a variant of the principle is provable within a classical framework. This variant is finally argued to be essentially adequate.

"Wie kann die Theorie der Rationalität normativ und empirisch zugleich sein?": The paper argues that the theory of (theoretical and practical) rationality is subject to a double reflective equilibrium. On the one hand, there is a purely normative discussion that tries to settle on some normative theory of rationality. On the other hand, empirical theorizing about human cognitive and practical behavior has to find its optimum as well in which rationality figures as a kind of intramental causality. However, there is a positive and a negative rationality presumption: roughly, whenever people show behavior A or non-A and A is rationally assessible, then A is rational or, respectively, irrational. Hence, the two equilibria are connected and have to be chosen so as to fit together. The paper elaborates on how this might work out and which overall picture of rationality thus emerges.

"Causal Laws are Objectifications of Inductive Schemes": Since my theory of causation operates in a Humean spirit on a subjectivistic base (causes are explained only relative to ranking functions which represent doxastic states), I must address the question how causation can still be an objective relation. This is what is done in the paper. First, it briefly introduces ranking theory and the explication of causation based on it. Then it explains what it means to objectify a certain feature of ranking functions: the feature is objective to the extent in which propositions (which are objectively true or false) can be associated with that feature and in which a ranking function can be uniquely reconstructed from the propositions associated with how it realizes that feature. It is shown, roughly, that, in contrast to the reason relation as it obtains relative to a ranking function, the causal relation can be objectified under certain illuminating conditions. Hence, my final answer is that a causal law is a proposition which can be true or false and has the logical form of a law of succession, and with which a particular inductive behavior (= ranking function) is uniquely associated via the above objectification.

"The Utility of Pleasure is a Pain for Decision Theory": The paper claims that Joseph Butler's criticism of hedonism still presents a serious problem. It shows that a subject's intrinsically evaluated states (called satisfactive states in the paper) are caused not only by external states of affairs, but usually also by the subject's prior utility functions for these external states of affairs. It shows further that this entails an essential incompleteness of received decision theory because the derivation of expected utilities of such external states of affairs and thus finally of acts is thereby caught in a vicious circle. The paper proposes to solve the problem by a kind of equilibrium model, and it shows that this has important consequences for hedonism and the relation between satisfaction and utility, for our conception of practical rationality and practical reasons, and for our notions of intrinsic, extrinsic, and true desires or utilities. (The German version is slightly less condensed than the English version.)

"A Reason for Explanation: Explanations Provide Stable Reasons": The general idea of the paper is to provide independent characterizations of scientific explanation and of scientific understanding and thereby to confirm or prove that the former yields the latter. After the beginnings of a deterministic theory of causation on the basis of No. 15 (according to which causes are a particular kind of conditional reasons; see No. 10), taking A to (causally) explain B is explicated as believing A to be a cause of B. The paper then speculates about some principles concerning reasons and their connection to truth, the strongest of which roughly says, in accordance with Putnam's internal realism, that for each true proposition there is a true ultimately stable reason. Knowing ultimately stable reasons is defended as one good way of capturing what is said about scientific understanding. So, the argument is completed by the observation that, on the basis of the given explications, having an explanation is (almost) equivalent to knowing a stable reason.

This is the paper where I have finally fixed my opinion on probabilistic causation. I did not find reasons to essentially change it (although it is further clarified in the papers No. 41 and 42 and in particular in my book The Laws of Belief (OUP 2012), ch. 14, which is the most comprehensive presentation of my theory of causation building upon the present paper).

It first introduces the formal framework. It then distinguishes between direct and indirect causation, a distinction which is key to overcoming the circularity objections raised by Cartwright (1979) against the possibility of defining causation in probabilistic terms, but which is rarely directly tackled in the literature. So, I first explicate direct causation: A is a direct cause of B iff A is (probabilistically) positively relevant to B given the history up to B without A. I defend this explication since my dissertation in 1976. Then I discuss three desiderata on causation simpliciter, i.e., direct or indirect causation: the structural condition of transitivity (or alternative conditions), the idea that each cause is in some sense positively relevant to its effect, and the idea that causal chains are in some sense Markov chains. Any two of the three desiderata, however they are exactly specified, are in conflict. I argue, pace Suppes (1970), that the best way out of these dilemmas is to assume transitivity, i.e., to define causation simpliciter as the transitive closure of direct causation. The paper concludes by exploring under which conditions causation so defined satisfies the other two desiderata.

(The causal Bayes net theory, which has become dominant in the meantime, is only about causal dependence between variables, although it follows from my account of direct causation. Only later it addresses causation between events under the label “actual causation”, though without utilizing the distinction between direct and indirect causation.)

"A General Non-Probabilistic Theory of Inductive Reasoning": This is a useful condensed version of No. 15, additionally explaining that ranking functions cannot be subsumed under Dempster-Shafer belief functions.

"Ordinal Conditional Functions. A Dynamic Theory of Epistemic States": It is natural and important to have a formal representation of plain belief, according to which propositions are held true, or held false, or neither. (In the paper this is called a deterministic representation of epistemic states). And it is of great philosophical importance to have a dynamic account of plain belief. AGM belief revision theory seems to provide such an account, but it founders at the problem of iterated belief revision, since it can generally account only for one step of revision. The paper discusses and rejects two solutions within the confines of AGM theory. It then introduces ranking functions (as I prefer to call them now; in the paper they are still called ordinal conditional functions) as the proper (and, I find, still the best) solution of the problem, proves that conditional independence w.r.t. ranking functions satisfies the so-called graphoid axioms, and proposes general rules of belief change (in close analogy to Jeffrey's generalized probabilistic conditionalization) that encompass revision and contraction as conceived in AGM theory. Indeed, the parallel to probability theory is amazing. Probability theory can profit from ranking theory as well since it is also plagued by the problem of iterated belief revision even if probability measures are conceived as Popper measures (see No. 11). Finally, the theory is compared with predecessors which are numerous and impressive, but somehow failed to explain the all-important conditional ranks in the appropriate way.

This little note is a kind of supplement to Kamlah's larger paper in the same issue. I contend that the relatively unproblematic side of probability is subjective probability and the really problematic side is objective probability. In my view the latter should be understood as a result of our attempts at objectivizing our subjective probabilities. In this note, I have nothing specific to say about these attempts. I only put them into a larger context, namely the general problem of objectivizing our mental and in particular our epistemic attitudes and their contents, a problem the ramifications of which may be observed at many places.

"Die fünf Stufen einer Theorie der Bedeutung": The paper describes the embracive theoretical scheme that inspires the Gricean account of linguistic meaning.

"The Representation of Popper Measures": The paper shows that all and only - additive Popper measures can be, indeed uniquely, represented by so-called dimensionally well-ordered families of - additive probability measures.

"Deterministic and Probabilistic Reasons and Causes": The ultimate aim of the paper is to provide for a unified account of direct causation. It starts by explicating the relation of one proposition being a reason for another as the first being positively relevant for the second. The explication is given in probabilistic terms and in deterministic terms, i.e., relative to a representation of epistemic states in which propositions are held true or false or neither (Deterministic positive relevance is here still based on the epistemic interpretation of conditionals, though I knew already that the theory presented in No. 15 is more adequate for this purpose). By examining Suppes' probabilistic theory of causation and amending it with the observation that there are not only spurious and indirect, but also hidden causes, I arrive at the conclusion that direct causes must be understood as conditional reasons: a cause is a reason for its direct effect conditional on the whole past of the effect with the exception of the cause. This lays foundations to No. 6 and to a unified account of probabilistic and deterministic causation. The theory is extended to indirect causation in No. 17.

"Probabilistic Causality: From Hume via Suppes to Granger": The paper observes that the theory of causal dependence developed in No. 6 and more extensively justified in No. 10 is very similar to C.W.J. Granger's account of causal dependence prominent in econometrics.

"How to Make Sense of Game Theory": The paper examines the extent to which game theory can be derived from a strictly Bayesian or decision theoretic point of view, since this is the only way to gain a unified theory of practical rationality. It observes that no such derivation exists and criticizes the standard arguments for the rationality of equilibrium strategies in two-person zero-sum games. It then proposes the beginnings of the theory or rationalizability (as it has been called later on) and observes its restrictions. It continues with pleading for a strict distinction of action rationality and epistemic rationality (which are confounded in game theory). The final critical discussion of Harsanyi's stance concludes that issues of epistemic rationality are independent and need to be explicitly considered in game theory and proposes to explain the subjective probabilities of the players, as they are assumed in game theory, as evolving in Bayesian game learning processes. (The postscript of the German version adds some comparative remarks on Skyrms' theory of practical deliberation.)

"Analogy and Inductive Logic: A Note on Niiniluoto": The first part of the note makes some critical remarks on Niniluoto (1981) (in the same issue), arriving at the conclusion that the systems proposed by Niiniluoto fail to satisfy symmetry, positive instantial relevance, and the Reichenbach axiom, and are thus more defective than seems acceptable. As I try to show in the second constructive part, positive instantial relevance and the Reichenbach axiom may be regained for analogical inference. The note closes with some general skeptical remarks to the effect that by trying to accommodate analogy considerations inductive logic regresses to subjectivism.

"Stochastic Independence, Causal Independence, and Shieldability": The aim of the paper is to explicate causal independence and Reichenbach's screening-off relation, or equivalently, causal dependence and direct causal dependence (always taken as relations between sets of factors or variables) in probabilistic terms along the lines of Suppes' probabilistic theory of causality, which is amended by the observation that there are not only spurious and indirect, but also hidden causes. The notion central to the explication is that of conditional stochastic or probabilistic independence, for which the graphoid axioms, as they have been called later on, are proved to hold (see also No. 23). The adequacy of the explication is supported by proving some intuitively expected theorems, such as that unions of sets of factors causally independent from some other set are causally independent from that set as well, or that partitions into probabilistic independent parts are equivalent with partitions into causally independent parts. (Much of the paper is contained already in my Ph.D. thesis of 1976, published as Grundlagen der Entscheidungstheorie, 1978. However, the theory of indirect causal dependence developed in the paper is essentially revised in No. 17.)

"Where Luce and Krantz Do Really Generalize Savage's Decision Model": The aim of the paper is a comparison of the decision models of Savage, Fishburn, Jeffrey and Luce & Krantz. Savage's model turns to represent subjective values and beliefs in a restricted way by implicitly assuming special probabilities for consequences and valuewise independence between world states and consequences. Fishburn's model overcomes both restrictions. The models of Jeffrey and Luce & Krantz are argued to be inadequate because they assume acts to be probabilistically assessed. A reinterpretation of the model of Luce & Krantz and a determination of the (intrinsic) utility function underlying their expected utility function yields the unexpected result that it generalises Savage's model with respect to utilities and not, as intended, with respect to probabilities.

"An Analysis of Hansson's Dyadic Deontic Logic": Bengt Hansson has proposed a semantics of dyadic or conditional deontic logic in terms of preference relations (in Noûs 3, 1969). This paper presents an axiomatic system and proves it to be correct, complete, and decidable (a result obtained after, but independently of D. Lewis, Counterfactuals, 1973). The subsequent informal discussion emphasizes the intuitive attractiveness of Hansson's semantics, refutes two objections against it, and finally focusses on a real intuitive inadequacy which can only be removed in a temporal frame by restricting Hansson's semantics to formulae expressing future obligations.