Paul Bartha

In contemporary epistemology, there are two broad approaches to conceptualizingbelief. According to the qualitative conception, belief is all or nothing; an agenteither believes some proposition, or she does not. This is often referred to as fullbelief. Alternatively, according to the quantitative conception, belief comes by degrees;an agent can partly believe a proposition, having a lower or higher degree ofconfidence in its truth. This is often referred to as partial belief. In my dissertation,I explore the connection between full and partial belief.In chapters 2 and 3, I focus on a paradox that arises when we try to understandfull belief as having a sufficient degree of partial belief, namely the Lottery Paradox.Briefly, in a large enough lottery, my degree of belief that my ticket will lose issufficient for full belief that it will lose. The same can be said for all of the tickets.This puts me in the awkward position of believing of each ticket that it will lose,but also believing that there is a winning ticket. In Chapter 2 I examine a formalsystem, Ranking Theory, that models both full and partial belief while avoiding theLottery Paradox. I argue, however, that in doing so it is an implausible model ofour beliefs about fair lotteries. In Chapter 3 I show how we can avoid the LotteryParadox by treating belief as contrastive–what we believe depends on what we areconsidering as alternatives.Turning from formal to applied epistemology, in chapters 4 and 5 I examinehow the relation between full and partial belief has practical consequences in twoareas–the use of statistical evidence in legal contexts, and the epistemic evaluationof conspiracy theories. Recently some have argued that the use of statistical evidencein legal contexts shows that we cannot formally reduce full belief to partialbelief. Using the contrastive method introduced in Chapter 3, I demonstrate that this is not correct. Continuing with the idea of contrastive belief, in Chapter 5, I examine the epistemology of conspiracy theories through a contrastive Bayesian lens.

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The dissertation investigates the nature of partial beliefs and norms governing their use. One widely accepted (though not uncontested) norm for partial belief change is Bayesian conditionalization. Information theory provides a far-reaching generalization of Bayesian conditionalization and gives it a foundation in an intuition that pays attention principally to information contained in probability distributions and information gained with new evidence. This generalization has fallen out of favour with contemporary epistemologists. They prefer an eclectic approach which sometimes conflicts with norms based on information theory, particularly the entropy principles of information theory. The principle of maximum entropy mandates a rational agent to hold minimally informative partial beliefs given certain background constraints; the principle of minimum cross-entropy mandates a rational agent to update partial beliefs at minimal information gain consistent with the new evidence. The dissertation shows that information theory generalizes Bayesian norms and does not conflict with them. It also shows that the norms of information theory can only be defended when the agent entertains sharp credences. Many contemporary Bayesians permit indeterminate credal states for rational agents, which is incompatible with the norms of information theory. The dissertation then defends two claims: (1) the partial beliefs that a rational agent holds are formally expressed by sharp credences; and (2) when a rational agent updates these partial beliefs in the light of new evidence, the norms used are based on and in agreement with information theory. In the dissertation, I defuse a collection of counter-examples that have been marshaled against entropy principles. More importantly, building on previous work by others and expanding it, I provide a coherent and comprehensive theory of the use of information theory in formal epistemology. Information theory rivals probability theory in formal virtue, theoretical substance, and coherence across intuitions and case studies. My dissertation demonstrates its significance in explaining the doxastic states of a rational agent and in providing the right kind of normativity for them.

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I discuss the implications of Simpson’s paradox for epistemology and decision theory. In Chapter One I outline the paradox, focussing on its identification, nature, and type of reasoning that it involves. In Chapter Two I discuss the view that Simpson’s paradox is resolved by means of graph-based causal analysis. In Chapter Three I outline a major problem (hitherto unacknowledged) that Simpson’s paradox poses for the probabilistic Bayesian theory of evidence. I make a proposal to split the probabilistic concept of evidence into a causal and a news-value kind of evidence, tracking causal probabilities under an intervention, and tracking overall probabilistic relevance under conditioning. In Chapters Four and Five I apply the proposal to two further areas of concern. In Chapter Four I defend a unified causal view of Simpson’s paradox. In Chapter Five I defuse a problem about counterfactual force of evidence. In Chapters Six and Seven I discuss Simpson’s paradox and the sure thing principle in decision theory. I then conclude in Chapter Eight.

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Philosophers subscribing to particular principles of statistical inference and evidence need to be aware of the limitations and practical consequences of the statistical approach they endorse. The framework proposed (for statistical inference in the field of medicine) allows disparate statistical approaches to emerge in their appropriate context. My dissertation proposes a decision theoretic model, together with methodological guidelines, that provide important considerations for deciding on clinical trial conduct. These considerations do not amount to more stopping rules. Instead, they are principles that address the complexity of interpreting and responding to interim data, based on a broad range of epistemic and ethical factors. While they are not stopping rules, they would assist a Data Monitoring Committee in judging its position with regard to necessary precautionary interpretation of interim data. By vindicating a framework that accommodates a wide range of approaches to statistical inference in one important setting (clinical trials), my results pose a serious challenge for any approach that advocates a single, universal principle of statistical inference.

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