One construal of convergent realism is that for each clear question, scientific inquiry eventually answers it. In this paper we adapt the techniques of formal learning theory to determine in a precise manner the circumstances under which this ideal is achievable. In particular, we define two criteria of convergence to the truth on the basis of evidence. The first, which we call EA convergence, demands that the theorist converge to the complete truth “all at once”. The second, which we call AE convergence, demands only that for every sentence in the theorist's language, there is a time at which the theorist settles the status of the sentence. The relative difficulties of these criteria are compared for effective and ineffective agents. We then examine in detail how the enrichment of an agent's hypothesis language makes the task of converging to the truth more difficult. In particular, we parametrize first-order languages by predicate and function symbol arity, presence or absence of identity, and quantifier prefix complexity. For nearly each choice of values of these parameters, we determine the senses in which effective and ineffective agents can converge to the complete truth on an arbitrary structure for the language. Finally, we sketch directions in which our learning theoretic setting can be generalized or made more realistic.

It is widely supposed that the scientists in any field use identical standards for evaluating theories. Without such unity of standards, consensus about scientific theories is supposedly unintelligible. However, the hypothesis of uniform standards can explain neither scientific disagreement nor scientific innovation. This paper seeks to show how the presumption of divergent standards (when linked to a hypothesis of dominance) can explain agreement, disagreement and innovation. By way of illustrating how a rational community with divergent standards can encourage innovation and eventually reach consensus, recent developments in geophysics are discussed at some length.

In quantum field theory divergent expressions are “discarded”, leaving finite expressions which provide the best predictions anywhere in science. In fact, this “renormalization procedure” involves no mystery or illegitimate operations. This paper explains, in terms accessible to non-experts, how the procedure really works and explores some different ways in which physicists have suggested that one understand it.

The suggestion that cognition is holistic has become a prominent criticism of optimism about the prospects for cognitive science. This paper argues that the standard motivation for this holism, that of epistemological holism, does not justify this pessimism. An illustration is given of how the effects of epistemological holism on perception are compatible with the view that perceptual processes are highly modular. A suggestion for generalizing this idea to conceptual cognitive processing is made, and an account of the holists' failure is offered.

To infer the state of a cause from the states of its effects, independent lines of evidence are preferable to dependent ones. This familiar idea is here investigated, the goal being to identify its presuppositions. Connections are drawn with Reichenbach's (1956) and Salmon's (1984) discussions of the principle of the common cause.

I defend the historical definition of “function” originally given in my Language, Thought and Other Biological Categories (1984a). The definition was not offered in the spirit of conceptual analysis but is more akin to a theoretical definition of “function”. A major theme is that nonhistorical analyses of “function” fail to deal adequately with items that are not capable of performing their functions.

Many physicalists are committed to an austere dichotomy: either beliefs, desires and intentions are scientifically respectable or attributions of such attitudes are all false. One physicalist, Daniel Dennett, offers a third alternative, which seems to permit a kind of instrumentalism concerning attitudes. I argue that Dennett's attempt to reconcile an instrumentalistic account of attributions of attitudes with a thoroughgoing physicalism founders on unresolvable conflicts between his official theory and his actual treatment of key concepts. As a result, instrumentalism concerning attitudes is exposed as inadequate to be a genuine alternative to the physicalist's dichotomy.

L. J. Savage and I. J. Good have each demonstrated that the expected utility of free information is never negative for a decision maker who updates her degrees of belief by conditionalization on propositions learned for certain. In this paper Good's argument is generalized to show the same result for a decision maker who updates her degrees of belief on the basis of uncertain information by Richard Jeffrey's probability kinematics. The Savage/Good result is shown to be a special case of the more general result.

In their paper “Why Gibbs Phase Averages Work—The Role of Ergodic Theory” (1980), David Malament and Sandy Zabell attempt to explain why phase averaging over the microcanonical ensemble gives correct predictions for the values of thermodynamic observables, for an ergodic system at equilibrium. Their idea is to bypass the traditional use of limit theorems, by relying on a uniqueness result about the microcanonical measure—namely, that it is uniquely stationary translation-continuous. I argue that their explanation begs questions about the relationship between thermodynamic equilibrium and statistical equilibrium; I argue in addition that any account which supports their view of the relationship between these two notions of equilibrium will likely use the limit theorems in traditional ways, and thereby bypass the explanation they offer.

In “Events and Causality” Mark Steiner argues that though Bertrand Russell was right to claim that the laws of physics do not express causal relations, nevertheless, Russell was wrong to suppose that therefore causality plays no role in physics. I argue that Steiner misses the point of Russell's argument for the first of these claims, and because of this Steiner's argument against the second fails to controvert it. Steiner fails to see that Russell's argument against causation, is in fact an argument against the existence of causal directionality or asymmetry. Steiner gives no reason to suppose physical theory requires this asymmetry after all.

Recently, Nathan (1986) criticized Bar-Hillel and Falk's (1982) analysis of some classical probability puzzles on the grounds that they wrongheadedly applied mathematics to the solving of problems suffering from “ambiguous informalities”. Nathan's prescription for solving such problems boils down to assuring in advance that they are uniquely and formally soluble—though he says little about how this is to be done. Unfortunately, in real life problems seldom show concern as to whether their naturally occurring formulation is or is not ambiguous, does or does not allow for unique formalization, etc. One step towards dealing with such problems intelligently is to recognize certain common cognitive pitfalls to which solvers seem vulnerable. This is discussed in the context of some examples, along with some empirical results.