Franz Huber

"This book is the first of two volumes on belief and counterfactuals. It consists of six of a total of eleven chapters. The first volume is concerned primarily with questions in epistemology and is expository in parts. Among others, it provides an accessible introduction to belief revision and ranking theory. Ranking theory specifies how conditional beliefs should behave. It does not tell us why they should do so nor what they are. This book fills these two gaps. The consistency argument tells us why conditional beliefs should obey the laws of ranking theory by showing them to be the means to attaining the end of holding true and informative beliefs. The conditional theory of conditional belief tells us what conditional beliefs are by specifying their nature in terms of non-conditional belief and counterfactuals. In addition, the book contains several novel arguments, accounts, and applications. These include an argument for the thesis that there are only hypothetical imperatives and no categorical imperatives; an account of the instrumentalist understanding of normativity, or rationality, according to which one ought to take the means to one's ends; as well as solutions to the problems of conceptual belief change, logical learning, and learning conditionals. A distinctive feature of the book is its unifying methodological approach: means-end philosophy. Means-end philosophy takes serious that philosophy is a normative discipline, and that philosophical problems are entangled with each other. It also explains the importance of logic to philosophy, without being a technical theory itself"--

The thesis of this paper is that we can justify induction deductively relative to one end, and deduction inductively relative to a different end. I will begin by presenting a contemporary variant of Hume ’s argument for the thesis that we cannot justify the principle of induction. Then I will criticize the responses the resulting problem of induction has received by Carnap and Goodman, as well as praise Reichenbach ’s approach. Some of these authors compare induction to deduction. Haack compares deduction to induction, and I will critically discuss her argument for the thesis that we cannot justify the principles of deduction next. In concluding I will defend the thesis that we can justify induction deductively relative to one end, and deduction inductively relative to a different end, and that we can do so in a non-circular way. Along the way I will show how we can understand deductive and inductive logic as normative theories, and I will briefly sketch an argument to the effect that there are only hypothetical, but no categorical imperatives.

This paper presents a new analysis of C.G. Hempel’s conditions of adequacy for any relation of confirmation [Hempel C. G. (1945). Aspects of scientific explanation and other essays in the philosophy of science. New York: The Free Press, pp. 3–51.], differing from the one Carnap gave in §87 of his [1962. Logical foundations of probability (2nd ed.). Chicago: University of Chicago Press.]. Hempel, it is argued, felt the need for two concepts of confirmation: one aiming at true hypotheses and another aiming at informative hypotheses. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative hypotheses. I then show that one can have Hempel’s cake and eat it too. There is a logic that takes into account both of these two conflicting aspects. According to this logic, a sentence H is an acceptable hypothesis for evidence E if and only if H is both sufficiently plausible given E and sufficiently informative about E. Finally, the logic sheds new light on Carnap’s analysis.

Recent accounts of actual causation are stated in terms of extended causal models. These extended causal models contain two elements representing two seemingly distinct modalities. The first element are structural equations which represent the or mechanisms of the model, just as ordinary causal models do. The second element are ranking functions which represent normality or typicality. The aim of this paper is to show that these two modalities can be unified. I do so by formulating two constraints under which extended causal models with their two modalities can be subsumed under so called which contain just one modality. These two constraints will be formally precise versions of Lewissystem of weights or priorities” governing overall similarity between possible worlds.

This paper starts by indicating the analysis of Hempel's conditions of adequacy for any relation of confirmation (Hempel, 1945) as presented in Huber (submitted). There I argue contra Carnap (1962, Section 87) that Hempel felt the need for two concepts of confirmation: one aiming at plausible theories and another aiming at informative theories. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative theories. The main part of the paper consists in working out the claim that one can have Hempel's cake and eat it too - in the sense that there is a logic of theory assessment that takes into account both of the two conflicting aspects of plausibility and informativeness. According to the semantics of this logic, a is an acceptable theory for evidence β if and only if a is both sufficiently plausible given β and sufficiently informative about β. This is spelt out in terms of ranking functions (Spohn, 1988) and shown to represent the syntactically specified notion of an assessment relation. The paper then compares these acceptability relations to explanatory and confirmatory consequence relations (Flach, 2000) as well as to nonmonotonic consequence relations (Kraus et al., 1990). It concludes by relating the plausibility-informativeness approach to Carnap's positive relevance account, thereby shedding new light on Carnap's analysis as well as solving another problem of confirmation theory

Crupi et al. propose a generalization of Bayesian confirmation theory that they claim to adequately deal with confirmation by uncertain evidence. Consider a series of points of time t0, . . . , ti, . . . , tn such that the agent’s subjective probability for an atomic proposition E changes from Pr0 at t0 to . . . to Pri at ti to . . . to Prn at tn. It is understood that the agent’s subjective probabilities change for E and no logically stronger proposition, and that the agent updates her subjective probabilities by Jeffrey conditionalization. For this specific scenario the authors propose to take the difference between Pr0 and Pri as the degree to which E confirms H for the agent at time ti , C0,i. This proposal is claimed to be adequate, because.

Philosophically, one of the most important questions in the enterprise termed confirmation theory is this: Why should one stick to well confirmed theories rather than to any other theories? This paper discusses the answers to this question one gets from absolute and incremental Bayesian confirmation theory. According to absolute confirmation, one should accept ''absolutely well confirmed'' theories, because absolute confirmation takes one to true theories. An examination of two popular measures of incremental confirmation suggests the view that one should stick to incrementally well confirmed theories, because incremental confirmation takes one to (the most) informative (among all) true theories. However, incremental confirmation does not further this goal in general. I close by presenting a necessary and sufficient condition for revealing the confirmational structure in almost every world when presented separating data.

This paper discusses an almost sixty year old problem in the philosophy of science -- that of a logic of confirmation. We present a new analysis of Carl G. Hempel's conditions of adequacy (Hempel 1945), differing from the one Carnap gave in §87 of his Logical Foundations of Probability (1962). Hempel, it is argued, felt the need for two concepts of confirmation: one aiming at true theories and another aiming at informative theories. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative theories. We then show that one can have Hempel's cake and eat it, too: There is a (rank-theoretic and genuinely nonmonotonic) logic of confirmation -- or rather, theory assessment -- that takes into account both of these two conflicting aspects. According to this logic, a statement H is an acceptable theory for the data E if and only if H is both sufficiently plausible given E and sufficiently informative about E. Finally, the logic sheds new light on Carnap's analysis (and solves another problem of confirmation theory).

Philosophers typically rely on intuitions when providing a semantics for counterfactual conditionals. However, intuitions regarding counterfactual conditionals are notoriously shaky. The aim of this paper is to provide a principled account of the semantics of counterfactual conditionals. This principled account is provided by what I dub the Royal Rule, a deterministic analogue of the Principal Principle relating chance and credence. The Royal Rule says that an ideal doxastic agent’s initial grade of disbelief in a proposition \(A\) , given that the counterfactual distance in a given context to the closest \(A\) -worlds equals \(n\) , and no further information that is not admissible in this context, should equal \(n\) . Under the two assumptions that the presuppositions of a given context are admissible in this context, and that the theory of deterministic alethic or metaphysical modality is admissible in any context, it follows that the counterfactual distance distribution in a given context has the structure of a ranking function. The basic conditional logic V is shown to be sound and complete with respect to the resulting rank-theoretic semantics of counterfactuals

Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, that is, by employing tools from logic and mathematics. The goal of this entry is to give the reader an overview of the formal tools available to epistemologists for the representation of belief. A particular focus will be the relation between formal representations of qualitative belief and formal representations of quantitative degrees of belief.

We argue that a semantics for counterfactual conditionals in terms of comparative overall similarity faces a formal limitation due to Arrow’s impossibility theorem from social choice theory. According to Lewis’s account, the truth-conditions for counterfactual conditionals are given in terms of the comparative overall similarity between possible worlds, which is in turn determined by various aspects of similarity between possible worlds. We argue that a function from aspects of similarity to overall similarity should satisfy certain plausible constraints while Arrow’s impossibility theorem rules out that such a function satisfies all the constraints simultaneously. We argue that a way out of this impasse is to represent aspectual similarity in terms of ranking functions instead of representing it in a purely ordinal fashion. Further, we argue against the claim that the determination of overall similarity by aspects of similarity faces a difficulty in addition to the Arrovian limitation, namely the incommensurability of different aspects of similarity. The phenomena that have been cited as evidence for such incommensurability are best explained by ordinary vagueness.

The problem addressed in this paper is “the main epistemic problem concerning science”, viz. “the explication of how we compare and evaluate theories [...] in the light of the available evidence” (van Fraassen, BC, 1983, Theory comparison and relevant Evidence. In J. Earman (Ed.), Testing scientific theories (pp. 27–42). Minneapolis: University of Minnesota Press). Sections 1– 3 contain the general plausibility-informativeness theory of theory assessment. In a nutshell, the message is (1) that there are two values a theory should exhibit: truth and informativeness—measured respectively by a truth indicator and a strength indicator; (2) that these two values are conflicting in the sense that the former is a decreasing and the latter an increasing function of the logical strength of the theory to be assessed; and (3) that in assessing a given theory by the available data one should weigh between these two conflicting aspects in such a way that any surplus in informativeness succeeds, if the shortfall in plausibility is small enough. Particular accounts of this general theory arise by inserting particular strength indicators and truth indicators. In Section 4 the theory is spelt out for the Bayesian paradigm of subjective probabilities. It is then compared to incremental Bayesian confirmation theory. Section 4 closes by asking whether it is likely to be lovely. Section 5 discusses a few problems of confirmation theory in the light of the present approach. In particular, it is briefly indicated how the present account gives rise to a new analysis of Hempel’s conditions of adequacy for any relation of confirmation (Hempel, CG, 1945, Studies in the logic of comfirmation. Mind, 54, 1–26, 97–121.), differing from the one Carnap gave in § 87 of his Logical foundations of probability (1962, Chicago: University of Chicago Press). Section 6 adresses the question of justification any theory of theory assessment has to face: why should one stick to theories given high assessment values rather than to any other theories? The answer given by the Bayesian version of the account presented in section 4 is that one should accept theories given high assessment values, because, in the medium run, theory assessment almost surely takes one to the most informative among all true theories when presented separating data. The concluding section 7 continues the comparison between the present account and incremental Bayesian confirmation theory.