Solving a Paradox of Evidential Equivalence

David Builes presents a paradox concerning how confident you should be that any given member of an infinite collection of fair coins landed heads, conditional on the information that they were all flipped and only finitely many of them landed heads. We argue that if you should have any conditional credence at all, it should be 1/2.

The Bayesian Transition Theory

Chapter 4 discusses the Bayesian transition theory. The distinction is drawn between dynamics and kinematics, and it’s argued that the theory of rational inference belongs to the former rather than the latter. It’s shown that Jeffrey’s rule is thus not a rule of rational inference. Credence lent to a conditional is explained and compared to conditional credence. Two problems for Bayesian kinematics then come into focus: conditional credence is never changing in the model, nor is it ever the contact-point of rational shift-in-view. A natural conception of conditional commitment is then put forward and used to solve both these problems. Along the way it’s argued that modus-ponens-style arguments do not function in thought as logical syllogisms, since modus-ponens-style arguments specify obligatory paths forward in thought.

The Bayesian Model

Chapter 2 introduces the Bayesian Model of rational credence. The mathematical properties of classic probability are explained—their linearity, cardinality, and so on—as well as the use of probability functions to model mental states. A game with balls is created and diagrammed to make visually vivid how probability works. Venn diagrams and truth-tables are used to illustrate everything for the absolute beginner. Conditional Credence is explained with intuitive examples, and the standard ratio formula is introduced. A game with marbles is then created and diagrammed to pump intuition about change of probability, which leads directly to Jeffrey-style kinematics. The chapter closes by describing a notionally possible agent, Creda, whose psychology matches the Bayesian Model.

The Bayesian Theory of States

Chapter 3 is a critical discussion of the Bayesian theory of states. It argues that our psychology includes many more types of confidence than Bayesian credence. There is an extended discussion of the missing types of confidence—from both a functionalist and intuitive point of view. Conditional credence is discussed and it’s shown that the Bayesian way of thinking of it—baked into the formalism—is wrong. It is argued that conditional credence is a fundamental part of our rational psychology. Three attempts are then considered to generalize the Bayesian model: one uses midpoints of mathematical intervals, one uses midpoints along with 3-place psychological attitudes, and one uses richly membered sets of probability functions. It is argued that none of the generalizations work very well.

Internalism to the Rescue?

If meanings are interestingly like species, meanings are multitudes and what our words mean isn’t up to us. This chapter doesn’t deny that one finds things that can reasonably be labeled ‘meanings’ at the level of the individual, or that these are of theoretical interest. It does deny that internalist theorizing about meaning provides a way to resuscitate the notion of analyticity. It also argues that meanings turn out to be much like diachronic ensembles of mental states related by analogs of descent—i.e. analogous to species. The first half of this chapter discusses a popular response to ‘Two Dogmas’ and demonstrates that this response requires an untenable picture of meaning. The second half takes up an internalist response to Quine due to David Chalmers, who suggests we think of conceptual constancy only in the intrapersonal case, identifying it with constancy of conditional credence. Chalmers’ proposal is worth serious consideration. But even from an internalist perspective, it’s unacceptable.

Indicative conditionals

This chapter defends a probabilistic semantics for indicative conditionals and other logical operators. This semantics is motivated in part by the observation that indicative conditionals are context sensitive, and that there are contexts in which the probability of a conditional does not match the conditional probability of its consequent given its antecedent. For example, there are contexts in which you believe the content of ‘it is probable that if Jill jumps from this building, she will die’ without having high conditional credence that Jill will die if she jumps. This observation is at odds with many existing non-truth-conditional semantic theories of conditionals, whereas it is explained by the semantics for conditionals defended in this chapter. The chapter concludes by diagnosing several apparent counterexamples to classically valid inference rules embedding epistemic vocabulary.

STALNAKER’S THESIS IN CONTEXT

In this paper I present a precise version of Stalnaker’s thesis and show that it is both consistent and predicts our intuitive judgments about the probabilities of conditionals. The thesis states that someone whose total evidence is E should have the same credence in the proposition expressed by ‘if A then B’ in a context where E is salient as they have conditional credence in the proposition B expresses given the proposition A expresses in that context. The thesis is formalised rigorously and two models are provided that demonstrate that the new thesis is indeed tenable within a standard possible world semantics based on selection functions. Unlike the Stalnaker–Lewis semantics the selection functions cannot be understood in terms of similarity. A probabilistic account of selection is defended in its place.I end the paper by suggesting that this approach overcomes some of the objections often levelled at accounts of indicatives based on the notion of similarity.