Michael Rescorla

When P(E) > 0, conditional probabilities P(H|E)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(H|E)$$\end{document} are given by the ratio formula. An agent engages in ratio conditionalization when she updates her credences using conditional probabilities dictated by the ratio formula. Ratio conditionalization cannot eradicate certainties, including certainties gained through prior exercises of ratio conditionalization. An agent who updates her credences only through ratio conditionalization risks permanent certainty in propositions against which she has overwhelming evidence. To avoid this undesirable consequence, I argue that we should supplement ratio conditionalization with Kolmogorov conditionalization, a strategy for updating credences based on propositions E such that P(E) = 0. Kolmogorov conditionalization can eradicate certainties, including certainties gained through prior exercises of conditionalization. Adducing general theorems and detailed examples, I show that Kolmogorov conditionalization helps us model epistemic defeat across a wide range of circumstances.

A striking thesis lies at the core of Davidson's philosophy: when we attribute intentional content to another creature's mental states and speech acts, we must treat the creature as largely conforming to our own rational norms. I will discuss how this thesis informs Davidson's treatment of rationality and intentionality. After reviewing some historical background, I present basic aspects of Davidson's position. I then examine various worries about the position. I conclude by highlighting some key Davidsonian insights into rationality.

Conditionalization governs how to reallocate credence in light of new evidence. One prominent argument in favor of Conditionalization holds that an agent who violates it is vulnerable to a diachronic Dutch book: a series of acceptable bets offered at multiple times that inflict a sure loss. van Fraassen argues that an agent who violates the Principle of Reflection is likewise vulnerable to a diachronic Dutch book. He concludes that agents should conform to both Conditionalization and Reflection. Some authors reply that Reflection is implausible and hence that there must be something wrong with diachronic Dutch book arguments. Other authors try to isolate a principled difference between the Dutch book argument for Conditionalization and the Dutch book argument for Reflection, such that the former argument may succeed even though the latter fails. I pursue a version of this strategy. I contend that, once we properly elucidate the notion of sure loss, non‐reflectors are not vulnerable to a sure loss. An agent who violates Reflection is not thereby subject to a diachronic Dutch book. Appearances to the contrary result from an unmotivated focus upon an overly narrow set of gambling scenarios.

Lewis proved a Dutch book theorem for Conditionalization. The theorem shows that an agent who follows any credal update rule other than Conditionalization is vulnerable to bets that inflict a sure loss. Lewis’s theorem is tailored to factive formulations of Conditionalization, i.e. formulations on which the conditioning proposition is true. Yet many scientific and philosophical applications of Bayesian decision theory require a non-factive formulation, i.e. a formulation on which the conditioning proposition may be false. I prove a Dutch book theorem tailored to non-factive Conditionalization. I also discuss the theorem’s significance.

Conditionalization is a norm that governs the rational reallocation of credence. I distinguish between factive and non-factive formulations of Conditionalization. Factive formulations assume that the conditioning proposition is true. Non-factive formulations allow that the conditioning proposition may be false. I argue that non-factive formulations provide a better foundation for philosophical and scientific applications of Bayesian decision theory. I furthermore argue that previous formulations of Conditionalization, factive and non-factive alike, have almost universally ignored, downplayed, or mishandled a crucial causal aspect of Conditionalization. To formulate Conditionalization adequately, one must explicitly address the causal structure of the transition from old credences to new credences. I offer a formulation of Conditionalization that takes these considerations into account, and I compare my preferred formulation with some prominent formulations found in the literature.

The perceptual system estimates distal conditions based upon proximal sensory input. It typically exploits information from multiple cues across and within modalities: it estimates shape based upon visual and haptic cues; it estimates depth based upon convergence, binocular disparity, motion parallax, and other visual cues; and so on. Bayesian models illuminate the computations through which the perceptual system combines sensory cues. I review key aspects of these models. Based on my review, I argue that we should posit co-referring perceptual representations corresponding to distinct sensory cues. For example, the perceptual system represents a distal size using a representation canonically linked with vision and a distinct representation canonically linked with touch. Distinct co-referring perceptual representations represent the same denotation, but they do so under different modes of presentation. Bayesian cue combination models demonstrate that psychological explanation of perception should attend to mode of presentation and not simply to denotation.

This paper discusses how to update one’s credences based on evidence that has initial probability 0. I advance a diachronic norm, Kolmogorov Conditionalization, that governs credal reallocation in many such learning scenarios. The norm is based upon Kolmogorov’s theory of conditional probability. I prove a Dutch book theorem and converse Dutch book theorem for Kolmogorov Conditionalization. The two theorems establish Kolmogorov Conditionalization as the unique credal reallocation rule that avoids a sure loss in the relevant learning scenarios.

Interventionism is a theory of causal explanation developed by Woodward and Hitchcock. I defend an interventionist perspective on the causal explanations offered within scientific psychology. The basic idea is that psychology causally explains mental and behavioral outcomes by specifying how those outcomes would have been different had an intervention altered various factors, including relevant psychological states. I elaborate this viewpoint with examples drawn from cognitive science practice, especially Bayesian perceptual psychology. I favorably compare my interventionist approach with well-known nomological and mechanistic theories of psychological explanation.

In this dissertation, I explore the relation between language and thought. I criticize theories that explain the representational dimension of language in terms of the representational dimension of thought. I also investigate the prospects for theories that treat neither thought nor language as explanatorily prior to the other. ;The first chapter, "The Diversity of Representational Content," examines one of the most important arguments for treating thought as explanatorily prior to language. Many creatures seemingly lack language while manifesting serious cognitive activity. These examples of non-linguistic cognition apparently favor treating thought as explanatorily prior to language. In response to this argument, I urge that non-linguistic creatures display proto-thought rather than genuine thought. Genuine thought involves propositional content, while proto-thought involves different types of representational content. Once we distinguish proto-thought from genuine thought, we can maintain that genuine thought intimately involves language even though proto-thought does not. ;In the next two chapters, "The Norms of Reasoned Discourse" and "Why Should I Speak the Truth?", I develop a theory of assertion. I argue that assertion falls under irreducibly linguistic norms: the norms of reasoned discourse. When speakers violate these norms, they cease to reason correctly with one another. ;In the final chapter, "The Code Conception of Language," I deploy my theory of assertion against the conception of language propounded by Paul Grice and David Lewis. Grice and Lewis hold that sentences inherit content from the thoughts they communicate. For instance, a simplified form of the view holds that the sentence "Frank is hungry" inherits content from the belief that Frank is hungry because it serves to transmit that belief. This approach, which currently enjoys widespread popularity, treats thought as explanatorily prior to language. I argue that the approach ignores the norms of reasoned discourse and therefore enshrines a false theory of assertion

Turing computation over a non-linguistic domain presupposes a notation for the domain. Accordingly, computability theory studies notations for various non-linguistic domains. It illuminates how different ways of representing a domain support different finite mechanical procedures over that domain. Formal definitions and theorems yield a principled classification of notations based upon their computational properties. To understand computability theory, we must recognize that representation is a key target of mathematical inquiry. We must also recognize that computability theory is an intensional enterprise: it studies entities as represented in certain ways, rather than entities detached from any means of representing them

The central philosophical task posed by conventions is to analyze what they are and how they differ from mere regularities of action and cognition. Subsidiary questions include: How do conventions arise? How are they sustained? How do we select between alternative conventions? Why should one conform to convention? What social good, if any, do conventions serve? How does convention relate to such notions as rule, norm, custom, practice, institution, and social contract? Apart from its intrinsic interest, convention is important because philosophers frequently invoke it when discussing other topics. A favorite philosophical gambit is to argue that, perhaps despite appearances to the contrary, some phenomenon ultimately results from convention. Notable candidates include: property, government, justice, law, morality, linguistic meaning, necessity, ontology, mathematics, and logic

Dialectical egalitarianism holds that every asserted proposition requires defence when challenged by an interlocutor. This view apparently generates a vicious 'regress of justifications', since an interlocutor can challenge the premises through which a speaker defends her original assertion, and so on ad infinitum . To halt the regress, dialectical foundationalists such as Adler, Brandom, Leite, and Williams propose that some propositions require no defence in the light of mere requests for justification. I argue that the putative regress is not worrisome and that egalitarianism can handle it quite satisfactorily. I also defend a positive view that combines an anti-foundationalist conception of dialectical interaction with a foundationalist conception of epistemic justification.

This paper further develops the non-restrictive dialectical perspective. Many philosophers hold that truthfulness is somehow constitutive of assertion. I argue against this view while simultaneously attempting to ground truthfulness in assertion’s essential features. I argue that truthfulness is the prima facie best way to avoid decisive counter-arguments against what one says. Moreover, avoiding decisive counter-arguments is a constitutive goal of rational dialectic. Thus, while truthfulness is not constitutive of assertion, it is the rational default strategy for achieving a goal that is constitutive of assertion.

A striking thesis lies at the core of Davidson‟s philosophy: when we attribute intentional content to another creature‟s mental states and speech acts, we must treat the creature as largely conforming to our own rational norms. I will discuss how this thesis informs Davidson‟s treatment of rationality and intentionality. After reviewing some historical background, I present basic aspects of Davidson‟s position. I then examine various worries about the position. I conclude by highlighting some key Davidsonian insights into rationality.

Under what conditions does a physical system implement or realize a computation? Structuralism about computational implementation, espoused by Chalmers and others, holds that a physical system realizes a computation just in case the system instantiates a pattern of causal organization isomorphic to the computation’s formal structure. I argue against structuralism through counter-examples drawn from computer science. On my opposing view, computational implementation sometimes requires instantiating semantic properties that outstrip any relevant pattern of causal organization. In developing my argument, I defend anti-individualism about computational implementation: relations to the social environment sometimes help determine whether a physical system realizes a computation. 1 The Physical Realization Relation2 Semantics and Computational Implementation3 Conforming to Instructions4 Implementing a Computer Program4.1 The denotational semantics of Scheme4.2 Worries about intentionality4.3 Worries about the natural numbers5 Implementing a Machine Model6 Bounded Structuralism7 Triviality Arguments8 Anti-individualism about Computational Implementation

Dialectical foundationalists, including Adler, Brandom, Leite, and Williams, claim that some asserted propositions do not require defense just because an interlocutor challenges them. By asserting such a proposition, the speaker shifts the burden of proof to her interlocutor. Dialectical egalitarians claim that all asserted propositions require defense when challenged. I elucidate the dispute between dialectical foundationalists and egalitarians, and I defend a broadly egalitarian stance against several prominent objections.

I argue that maps do not feature predication, as analyzed by Frege and Tarski. I take as my foil (Casati and Varzi, Parts and places, 1999), which attributes predication to maps. I argue that the details of Casati and Varzi’s own semantics militate against this attribution. Casati and Varzi emphasize what I call the Absence Intuition: if a marker representing some property (such as mountainous terrain) appears on a map, then absence of that marker from a map coordinate signifies absence of the corresponding property from the corresponding location. Predication elicits nothing like the Absence Intuition. “F(a)” does not, in general, signify that objects other than a lack property F. On the basis of this asymmetry, I argue that attaching a marker to map coordinates is a different mode of semantic composition than attaching a predicate to a singular term.