Wolfgang Spohn

Ordinal Conditional Functions: A Dynamic Theory of Epistemic States

Many of the philosophically most interesting notions are overtly or covertly epistemological. Overtly epistemological notions are, of course, the concept of belief itself, the concept of subjective probability, and, presumably the most important, the concept of a reason in the sense of a theoretical reason for believing something. Covertly epistemological notions are much more difficult to understand; maybe, they are not epistemological at all. However, a very promising strategy for understanding them is to try to conceive of them as covertly epistemological. One such notion is the concept of objective probability;1 the concept of explanation is another. A third, very important one is the notion of causation, which has been epistemologically problematic ever since Hume. Finally, there is the notion of truth. Many philosophers believe that there is much to be said for a coherence theory of truth or internal realism; they hold some version of the claim that something for which it is impossible to get a true reason cannot be true, and that truth is therefore covertly epistemological.

A general non-probabilistic theory of inductive reasoning

Publisher Summary Probability theory, epistemically interpreted, provides an excellent account of inductive reasoning. A fundamental reason for the epistemological success of probability theory is that there exists a well-behaved concept of conditional probability. However, still people have, and have reasons for, various concerns over probability theory. One of these is the notion of plain belief. Probability theory, however, offers no formal counterpart to this notion. It seems that the formal representation of plain belief has to take a nonprobabilistic route. Indeed, representing plain belief seems easy enough: simply represent an epistemic state by the set of all propositions believed true in it or by the conjunction of all propositions believed true in it. |However, this does not yet provide a theory of induction—an answer to the question how epistemic states so represented are changed through information or experience. There is a convincing partial answer: If the new information is compatible with the old epistemic state, the new epistemic state is simply represented by the conjunction of the new information and the old beliefs. It is, however, important to complete the answer and to cover this case, too; otherwise plain belief would not be represented as corrigible. When epistemic states are represented by the conjunction of all propositions believed true in it, the answer cannot be completed; and though there is a lot of fruitful work, no other representation of epistemic states has been proposed that provides a complete solution to this problem.

The laws of belief : ranking theory and its philosophical applications

Preface 1. Introduction 2. Belief and Its Objects 3. The Probabilistic Way 4. The Representation of Belief: Some Standard Moves 5. Ranking Functions 6. Reasons and Apriority 7. Conditional Independence and Ranking Nets 8. The Measurement of Ranks 9. Supposing, Updating, and Reflection 10. Ranks and Probabilities 11. Comparisons 12. Laws and Their Confirmation 13. Ceteris Paribus Conditions and Dispositions 14. Causation 15. Objectification 16. Justification, Perception, and Consciousness 17. The A Priori Structure of Reasons Bibliography Name Index Subject Index

WHERE LUCE AND KRANTZ DO REALLY GENERALIZE SAVAGE'S DECISION MODEL

In this paper I shall somewhat investigate several formulations of decision theory from a purely quantitative point of view, thus leaving aside the whole question of measurement. Since almost any foundational work on decision theory strives at proving nicer and nicer measurement results and representation theorems, I feel obliged to give a short explanation of my self-imposed limitation. The first and best reason for it is that I have not got anything new to say about measurement, and the second is that one need not say anything: It was hard work to convince economists that cardinalization is possible and meaningful. This was accomplished by proving existence and uniqueness theorems establishing the existence of cardinal functions (e.g. subjective utilities and probabilities) unique up to certain transformations that mirror ordinal concepts (e.g. subjective preferences) in a certain way. And surely, such theorems provide an excellent justification for the use of cardinal concepts. The eagerness in the search for representation theorems, however, is not really understandable but on the supposition that they are the only justification of cardinal concepts, and this assumption is merely a rather dubious conjecture. After all, philosophers of science have been debating about theoretical concepts for at least 40 years, and, though the last word has not yet been spoken, they generally agree that it is possible to have meaningful, yet observationally undefinable theoretical notions.1 And the concepts of subjective probability and utility are theoretical notions of decision theory. Thus if philosophers of science are right, they need not necessarily be proved observationally definable by representation theorems for being meaningful. 2 For that reason I consider quantitative decision models fundamental for decision theory and measurement as part of the confirmation or testing theory of the quantitative models. Of course, the latter is important for evaluating the former, but there may be different (e.g. conceptual) grounds for finding one quantitative decision model more satisfac

An Analysis of Hansson's Dyadic Deontic Logic

Introduction and summaryRecently, Bengt Hansson presented a paper about dyadic deontic logic,2 criticizing some purely axiomatic systems of dyadic deontic logic and proposing three purely semantical systems of dyadic deontic logic which he confidently called dyadic standard systems of deontic logic (DSDL1–3). Here I shall discuss the third by far most interesting system DSDL3 which is operating with preference relations. First, I shall describe this semantical system (Sections 1.1–1.3). Then I shall give an axiomatic system (Section 1.4) which is proved to be correct (Section 2) and complete (Section 3) with respect to Hanssons semantics. Finally, in face of these results Hanssons semantics will be discussed from a more intuitive standpoint. After emphasizing its intuitive attractiveness (Section 4.1) I will show that two objections often discussed in connection with preference relations do not apply to it (Section 4.2 and 4.3); more precisely, I will show that the connectedness condition for preference relations can be dropped and that, in a sense, it is not necessary to compare two possible worlds differing in infinitely many respects. (What exactly is meant by this, will become clear later on.) Yet there is a third objection to Hanssons semantics which points to a real intuitive inadequacy of DSDL3. A way of removing this inadequacy, which corresponds to Hanssons own intuitions as well as to familiar metaethical views, is suggested, but not technically realized (Section 4.4). In the last section (section 4.5) I shall briefly show that DSDL3 is decidable, as expected.

The measurement of ranks and the laws of iterated contraction

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.

Causation : an alternative

The paper builds on the basically Humean 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 pre-emption. It finally indicates how the accounts profound epistemic relativization induced by ranking theory can be undone. 1. Introduction2. Variables, propositions, time3. Induction first4. Causation5. Redundant causation6. Objectivization Introduction Variables, propositions, time Induction first Causation Redundant causation Objectivization

A Reason for Explanation: Explanations Provide Stable Reasons

Why ask ‘Why?’ Whence our drive for explanation? This is a bewildering question because it is hard to see what an answer might look like. I well remember having learnt in undergraduate courses that explanation is the supreme goal of science. So who would dare ask for more? Some fortunately did.1 One prominent answer is that (scientific) explanation yields (scientific) understanding; and surely, we want to understand things. It is this answer which this paper is about.

Laws, Ceteris Paribus Conditions, and the Dynamics of Belief

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. Likewise, the issue about ceteris paribus conditions is essentially about how we epistemically deal with exceptions. Hence, ranking theory with its resources of defeasible reasoning seems ideally suited to explicate these points 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 Finettis representation theorems can be directly transformed into an account of confirmation of laws thus conceived.

How to make Sense of Game Theory

Game theory and decision theory are congenial, or so at least one would expect from their akin subject matter and their akin basic concepts and methods. And this expectation is justified by first inspection of the standard accounts of these theories: Decision theory investigates rational behaviour of single persons in isolation; game theory is concerned with the rationality of mutually dependent decisions of several persons; thus game theory is the more embracing theory, leaving to decision theory the special case of one-person games or, according to a rather unfortunate phrase, of games against nature.