It is important to have an adequate model of uncertainty, since decisions must be made before the uncertainty can be resolved. For instance, flood defenses must be designed before we know the future distribution of flood events. It is standardly assumed that probability theory offers the best model of uncertain information. I think there are reasons to be sceptical of this claim. I criticise some arguments for the claim that probability theory is the only adequate model of uncertainty. In particular (...) I critique Dutch book arguments, representation theorems, and accuracy based arguments. Then I put forward my preferred model: imprecise probabilities. These are sets of probability measures. I offer several motivations for this model of uncertain belief, and suggest a number of interpretations of the framework. I also defend the model against some criticisms, including the so-called problem of dilation. I apply this framework to decision problems in the abstract. I discuss some decision rules from the literature including Levi’s E-admissibility and the more permissive rule favoured by Walley, among others. I then point towards some applications to climate decisions. My conclusions are largely negative: decision making under such severe uncertainty is inevitably difficult. I finish with a case study of scientific uncertainty. Climate modellers attempt to offer probabilistic forecasts of future climate change. There is reason to be sceptical that the model probabilities offered really do reflect the chances of future climate change, at least at regional scales and long lead times. Indeed, scientific uncertainty is multi-dimensional, and difficult to quantify. I argue that probability theory is not an adequate representation of the kinds of severe uncertainty that arise in some areas in science. I claim that this requires that we look for a better framework for modelling uncertainty. (shrink)

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...) the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)

According to the traditional Bayesian view of credence, its structure is that of precise probability, its objects are descriptive propositions about the empirical world, and its dynamics are given by conditionalization. Each of the three essays that make up this thesis deals with a different variation on this traditional picture. The first variation replaces precise probability with sets of probabilities. The resulting imprecise Bayesianism is sometimes motivated on the grounds that our beliefs should not be more precise than the evidence (...) calls for. One known problem for this evidentially motivated imprecise view is that in certain cases, our imprecise credence in a particular proposition will remain the same no matter how much evidence we receive. In the first essay I argue that the problem is much more general than has been appreciated so far, and that it’s difficult to avoid without compromising the initial evidentialist motivation. The second variation replaces descriptive claims with moral claims as the objects of credence. I consider three standard arguments for probabilism with respect to descriptive uncertainty—representation theorem arguments, Dutch book arguments, and accuracy arguments—in order to examine whether such arguments can also be used to establish probabilism with respect to moral uncertainty. In the second essay, I argue that by and large they can, with some caveats. First, I don’t examine whether these arguments can be given sound non-cognitivist readings, and any conclusions therefore only hold conditional on cognitivism. Second, decision-theoretic representation theorems are found to be less convincing in the moral case, because there they implausibly commit us to thinking that intertheoretic comparisons of value are always possible. Third and finally, certain considerations may lead one to think that imprecise probabilism provides a more plausible model of moral epistemology. The third variation considers whether, in addition to conditionalization, agents may also change their minds by becoming aware of propositions they had not previously entertained, and therefore not previously assigned any probability. More specifically, I argue that if we wish to make room for reflective equilibrium in a probabilistic moral epistemology, we must allow for awareness growth. In the third essay, I sketch the outline of such a Bayesian account of reflective equilibrium. Given that this account gives a central place to awareness growth, and that the rationality constraints on belief change by awareness growth are much weaker than those on belief change by conditionalization, it follows that the rationality constraints on the credences of agents who are seeking reflective equilibrium are correspondingly weaker. (shrink)

There is a growing interest in the foundations as well as the application of imprecise probability in contemporary epistemology. This dissertation is concerned with the application. In particular, the research presented concerns ways in which imprecise probability, i.e. sets of probability measures, may helpfully address certain philosophical problems pertaining to rational belief. The issues I consider are disagreement among epistemic peers, complete ignorance, and inductive reasoning with imprecise priors. For each of these topics, it is assumed that belief can be (...) modeled with imprecise probability, and thus there is a non-classical solution to be given to each problem. I argue that this is the case for peer disagreement and complete ignorance. However, I discovered that the approach has its shortcomings, too, specifically in regard to inductive reasoning with imprecise priors. Nevertheless, the dissertation ultimately illustrates that imprecise probability as a model of rational belief has a lot of promise, but one should be aware of its limitations also. (shrink)

How can self-locating propositions be integrated into normal patterns of belief revision? Puzzles such as Sleeping Beauty seem to show that such propositions lead to violation of ordinary principles for reasoning with subjective probability, such as Conditionalization and Reflection. I show that sophisticated forms of Conditionalization and Reflection are not only compatible with self-locating propositions, but also indispensable in understanding how they can function as evidence in Sleeping Beauty and similar cases.

Physicist J. Richard Gott uses the Copernican principle that “we are not special” to make predictions about the future lifetime of the human race, based on how long the human race has been in existence so far. We show that the predictions which can be derived from Gott’s argument are less strong than one might be inclined to believe, that Gott’s argument illegitimately assumes that the human race will not last forever, that certain versions of Gott’s argument are incompatible with (...) Bayesian conditionalization, and that Gott’s argument is self-refuting. -/- *****Note: For Bradley Monton's up-to-date thoughts on Gott's argument, see his _Philosophical Quarterly_ paper co-authored with Brian Kierland, "How To Predict Future Duration from Present Age".*****. (shrink)

I restate the Sleeping Beauty probabilistic paradox and offer an overview of the ongoing discussions that aim at resolving the problem. I summarize and eventually criticize briefly the various views: neutral position, Bayesian thirdism, non-Bayesian thirdism, traditional halfism, as well as the new halfism of credence conservation, a somewhat neglected but interesting point of view. I try at the same time to clarify some essential notions, to introduce the main actors of the debate, and to anticipate its evolution.

This is a defense of the doctrine of scientific realism. SR is defined through the following two claims: Most essential unobservables posited by the well-established current scientific theories exist independently of our minds. We know our well-established scientific theories to be approximately true. I first offer positive argumentation for SR. I begin with the so-called 'success arguments' for SR: 1) scientific theories most of the times entail successful predictions; 2) science is methodologically successful in generating empirically successful theories. SR explains (...) these facts via inference to the best explanation. I combine Hacking's experimental argument for entity realism with Salmon's common-cause principle. I take entity realism to be foundational to SR: one may believe in the existence of some theoretical entities without believing in any particular theory in which these are embedded. Its motivation comes from experimental practice, where the manipulation of these entities often relies on incompatible theoretical accounts. The underdetermination topic is thereafter discussed. Several attempts to distinguish between an observable and an unobservable realm are critically discussed, as well as the possibility that for any given theory, there are empirically equivalents generated by means of algorithms. I present extensive argumentation to the effect that such algorithmic rivals are not to be taken seriously. Social constructivism is being critically treated. I proceed by distinguishing between a metaphysical, a semantic, and an epistemic variant of SC. I conclude that only a moderate metaphysical constructivism can stand on its own feet. Its claim is merely that some facts about the world are socially constructed. I finish with a plea for a selective SR, able to do justice to the presence of both instrumentalism and modest constructivism in scientific practice. (shrink)

Cosmology raises novel philosophical questions regarding the use of probabilities in inference. This work aims at identifying and assessing lines of arguments and problematic principles in probabilistic reasoning in cosmology. -/- The first, second, and third papers deal with the intersection of two distinct problems: accounting for selection effects, and representing ignorance or indifference in probabilistic inferences. These two problems meet in the cosmology literature when anthropic considerations are used to predict cosmological parameters by conditionalizing the distribution of, e.g., the (...) cosmological constant on the number of observers it allows for. However, uniform probability distributions usually appealed to in such arguments are an inadequate representation of indifference, and lead to unfounded predictions. It has been argued that this inability to represent ignorance is a fundamental flaw of any inductive framework using additive measures. In the first paper, I examine how imprecise probabilities fare as an inductive framework and avoid such unwarranted inferences. In the second paper, I detail how this framework allows us to successfully avoid the conclusions of Doomsday arguments in a way no Bayesian approach that represents credal states by single credence functions could. -/- There are in the cosmology literature several kinds of arguments referring to self- locating uncertainty. In the multiverse framework, different "pocket-universes" may have different fundamental physical parameters. We don’t know if we are typical observers and if we can safely assume that the physical laws we draw from our observations hold elsewhere. The third paper examines the validity of the appeal to the "Sleeping Beauty problem" and assesses the nature and role of typicality assumptions often endorsed to handle such questions. -/- A more general issue for the use of probabilities in cosmology concerns the inadequacy of Bayesian and statistical model selection criteria in the absence of well-motivated measures for different cosmological models. The criteria for model selection commonly used tend to focus on optimizing the number of free parameters, but they can select physically implausible models. The fourth paper examines the possibility for Bayesian model selection to circumvent the lack of well-motivated priors. (shrink)

Dawid, DeGroot and Mortera showed, a quarter century ago, that any agent who regards a fellow agent as a peer--in particular, defers to the fellow agent's prior credences in the same way that she defers to her own--and updates by split-the-difference is prone to diachronic incoherence. On the other hand one may show that there are special scenarios in which Bayesian updating approximates difference splitting, so it remains an important question whether it remains a viable response to ``generic" peer update. (...) We look at arguments by two teams of philosophers against difference splitting. (shrink)

A large number of essays address the Sleeping Beauty problem, which undermines the validity of Bayesian inference and Bas Van Fraassen's 'Reflection Principle'. In this study a straightforward analysis of the problem based on probability theory is presented. The key difference from previous works is that apart from the random experiment imposed by the problem's description, a different one is also considered, in order to negate the confusion on the involved conditional probabilities. The results of the analysis indicate that no (...) inconsistency takes place, whereas both Bayesian inference and 'Reflection Principle' are valid. (shrink)

Assuming that votes are independent, the epistemically optimal procedure in a binary collective choice problem is known to be a weighted supermajority rule with weights given by personal log-likelihood-ratios. It is shown here that an analogous result holds in a much more general model. Firstly, the result follows from a more basic principle than expected-utility maximisation, namely from an axiom (Epistemic Monotonicity) which requires neither utilities nor prior probabilities of the ‘correctness’ of alternatives. Secondly, a person’s input need not be (...) a vote for an alternative, it may be any type of input, for instance a subjective degree of belief or probability of the correctness of one of the alternatives. The case of a profile of subjective degrees of belief is particularly appealing, since here no parameters such as competence parameters need to be known. (shrink)

This thesis focuses on expressively rich languages that can formalise talk about probability. These languages have sentences that say something about probabilities of probabilities, but also sentences that say something about the probability of themselves. For example: (π): “The probability of the sentence labelled π is not greater than 1/2.” Such sentences lead to philosophical and technical challenges; but can be useful. For example they bear a close connection to situations where ones confidence in something can affect whether it is (...) the case or not. The motivating interpretation of probability as an agent's degrees of belief will be focused on throughout the thesis. -/- This thesis aims to answer two questions relevant to such frameworks, which correspond to the two parts of the thesis: “How can one develop a formal semantics for this framework?” and “What rational constraints are there on an agent once such expressive frameworks are considered?”. (shrink)

This paper shows that any view of future contingent claims that treats such claims as having indeterminate truth values or as simply being false implies probabilistic irrationality. This is because such views of the future imply violations of reflection, special reflection and conditionalization.

Knowledge entails the truth of the proposition known; that which is merely believed may be false. If I have beliefs about your beliefs, then I may believe that some of your beliefs are false. I may believe, for example, that you mistakenly believe that it is now raining outside. This is a coherent belief for me, though not for you. You cannot coherently believe that you believe falsely that it is raining, and this despite the fact that your having that (...) false belief is clearly a logical possibility. The proposition is, for you, a kind of doxastic blindspot. (shrink)

In this brief note I show how to model conceptual change, logical learning, and revision of one's beliefs in response to conditional information such as indicative conditionals that do not express propositions.

In the current debate on the concept of probability in the Everett interpretation of quantum mechanics Saunders and Wallace argue for a notion of pre-measurement uncertainty whilst Greaves and Myrvold attempt to do without uncertainty altogether. Both these approaches are controversial and I suggest a middle way. I develop in detail an argument which Wallace has hinted at and Greaves has seen as beside the point in order to show that Vaidman’s concept of post-measurement uncertainty has more relevance to pre-measurement (...) decision making than has hitherto been generally recognised. Further, Vaidman uncertainty leads naturally to another form of post-measurement uncertainty which clarifies the process of experimental confirmation of quantum mechanics in the Everett picture. I also stress the importance of Sider’s theory of transtemporal identity in making Everett’s multiverse intelligible. (shrink)