Old evidence and new theories

Conclusion The discussion above indicates that there is some reason for optimism with regard to the project of incorporating logical-mathematical learning within Bayesianism, though it is obvious that there are many difficulties to be overcome. The biggest obstacle in this regard is overcoming the tension that exists between considerations of formal tractability and the desire to avoid demanding too much of rational agents. Jeffrey's solution seems more flexible in this regard than Garber's, but that may very well be because the general mechanisms underlying Jeffrey's rule of reparation have not been specified. In any case, in my view the verdict we should draw with regard to the problem of old evidence is a bit more pessimistic. Jeffrey's and Garber's solutions only address certain aspects of the problem, and thus can only provide partial solutions at best. The basic strategy of using logical-mathematical learning to induce a confirmation event does not completely evade the problem, which reemerges when the required logical-mathematical knowledge becomes old news. Thus, despite the solutions that have been offered to date, the problem of old evidence remains a fundamental challenge to the Bayesian point of view.This paper has benefited greatly due to valuable input from Bas van Fraassen, Richard Jeffrey, Alan Hájek, Gil Harman, Mike Thau, and Ned Hall.     

A new characterization of scientific theories

First, I discuss the older “theory-centered” and the more recent semantic conception of scientific theories. I argue that these two perspectives are nothing more than terminological variants of one another. I then offer a new theory-centered view of scientific theories. I argue that this new view captures the insights had by each of these earlier views, that it’s closer to how scientists think about their own theories, and that it better accommodates the phenomenon of inconsistent scientific theories.     

Patterns of Preference for Numerical and Verbal Probabilities

We report results of an experiment designed to test a principle formulated by Budescu and Wallsten (1995), that, when communicating uncertainty information, mode choices are sensitive to sources and degrees of vagueness. In addition, we examined subjects’ efficacy in using such uncertainty information as a function of communication mode, source, and vagueness. In phase one of the experiment, subjects in a dyad used precise (numerical) or imprecise (verbal) expressions to communicate to a remote partner precise or vague uncertainty about the likelihoods of events. Spinner outcomes were used to generate precise uncertainty while answers to almanac questions were used to elicit vague uncertainty. In phase two, subjects saw the events paired with their partners’ estimates of similar events, and were asked to gamble on one event from each pair. Communication mode preferences were measured as the relative frequency that subjects chose the numerical mode to either express or receive uncertainty information regarding the events. Efficacy was measured as the relative frequency that subjects choose from the pair the event associated with the objectively more probable uncertainty expression. Underlying uncertainty interacted with direction of communication to affect preferences for modes of expression of the probabilities. Subjects preferred precise (numerical) information, especially for precise events (spinners). For vague events (questions), their preference for precise (numerical) information was stronger when receiving than when communicating information. Similar preferences were reflected in the efficiency of subsequent gamble decisions based on the probability estimates. Specifically, decisions were more efficacious (i.e. consistent with Expected Utility) when degrees of precision in events and estimates matched. © 1997 by John Wiley & Sons, Ltd.     

Probabilities in implicit learning

The visual system possesses a remarkable ability in learning regularities from the environment. In the case of contextual cuing, predictive visual contexts such as spatial configurations are implicitly learned, retained, and used to facilitate visual search-all without one's subjective awareness and conscious effort. Here we investigated whether implicit learning and its facilitatory effects are sensitive to the statistical property of such implicit knowledge. In other words, are highly probable events learned better than less probable ones even when such learning is implicit? We systematically varied the frequencies of context repetition to alter the degrees of learning. Our results showed that search efficiency increased consistently as contextual probabilities increased. Thus, the visual contexts, along with their probability of occurrences, were both picked up by the visual system. Furthermore, even when the total number of exposures was held constant between each probability, the highest probability still enjoyed a greater cuing effect, suggesting that the temporal aspect of implicit learning is also an important factor to consider in addition to the effect of mere frequency. Together, these findings suggest that implicit learning, although bypassing observers' conscious encoding and retrieval effort, behaves much like explicit learning in the sense that its facilitatory effect also varies as a function of its associative strengths.     

Probabilities For Two Properties

Let R(X, B) denote the class of probability functions that are defined on algebra X and that represent rationally permissible degrees of certainty for a person whose total relevant background evidence is B. This paper is concerned with characterizing R(X, B) for the case in whichX is an algebra of propositions involving two properties and B is empty. It proposes necessary conditions for a probability function to be in R(X, B), some of which involve the notion of statistical dependence. The class of probability functions that satisfy these conditions, here denoted P_I, includes a class that Carnap once proposed for the same situation. Probability functions in P_I violate Carnap's axiom of analogy but, it is argued, that axiom should be rejected. A derivation of Carnap's model by Hesse has limitations that are not present in the derivation of P_I given here. Various alternative probability models are considered and rejected.     

Dynamic Update with Probabilities

Current dynamic-epistemic logics model different types of information change in multi-agent scenarios. We generalize these logics to a probabilistic setting, obtaining a calculus for multi-agent update with three natural slots: prior probability on states, occurrence probabilities in the relevant process taking place, and observation probabilities of events. To match this update mechanism, we present a complete dynamic logic of information change with a probabilistic character. The completeness proof follows a compositional methodology that applies to a much larger class of dynamic-probabilistic logics as well. Finally, we discuss how our basic update rule can be parameterized for different update policies, or learning methods.     

Theoretical inference and the new psychoanalytic theories of infancy.

Psychoanalytic developmental theory has been profoundly influenced by recent observational research on infants. Although it is commonly held that these new data refute earlier theories of infancy, an examination of the evidence indicates otherwise. Much of the disagreement between the two is based on differences over the definition of such concepts as "self" and "self/other differentiation" and over strategies of theoretical inference. Inferences about the subjective experience of infants are best viewed as theoretical postulates rather than empirical statements or metaphors.     

Revising Probabilities and Full Beliefs

Journal of Philosophical Logic - A new formal model of belief dynamics is proposed, in which the epistemic agent has both probabilistic beliefs and full beliefs. The agent has full belief in a...     

Taurek, Numbers and Probabilities

In his paper, “Should the Numbers Count?" John Taurek imagines that we are in a position such that we can either save a group of five people, or we can save one individual, David. We cannot save David and the five. This is because they each require a life-saving drug. However, David needs all of the drug if he is to survive, while the other five need only a fifth each. Typically, people have argued as if there was a choice to be made: either numbers matter, in which case we should save the greater number, or numbers don't matter, but rather there is moral value in giving each person an equal chance of survival, and therefore we should toss a coin. My claim is that we do not have to make a choice in this way. Rather, numbers do matter, but it doesn't follow that we should always save the greater number. And likewise, there is moral value in giving each person an equal chance of survival, but it doesn't follow that we should always toss a coin. In addition, I argue that a similar approach can be applied to situations in which we can save one person or another, but the chances of success are different.     

The No Probabilities For Acts-Principle

One can interpret the No Probabilities for Acts-Principle, namely that any adequate quantitative decision model must in no way contain subjective probabilities for actions in two ways: it can either refer to actions that are performable now and extend into the future or it can refer to actions that are not performable now, but will be in the future. In this paper, I will show that the former is the better interpretation of the principle.     

Conditionals Right and Left: Probabilities for the Whole Family

The fact that the standard probabilistic calculus does not define probabilities for sentences with embedded conditionals is a fundamental problem for the probabilistic theory of conditionals. Several authors have explored ways to assign probabilities to such sentences, but those proposals have come under criticism for making counterintuitive predictions. This paper examines the source of the problematic predictions and proposes an amendment which corrects them in a principled way. The account brings intuitions about counterfactual conditionals to bear on the interpretation of indicatives and relies on the notion of causal (in)dependence.     

Powers,Probabilities, and Tendencies

Philosophia - In this article, I aim at showing how powers may ground different types of probability in the universe. In Section 1 I single out several dimensions along which the probability of...