In this paper I argue three things: (1) that the interactionist view underlying Benacerraf's (1973) challenge to mathematical beliefs renders inexplicable the reliability of most of our beliefs in physics; (2) that examples from mathematical physics suggest that we should view reliability differently; and (3) that abstract mathematical considerations are indispensable to explanations of the reliability of our beliefs.

The standard theory of computation excludes computations whose completion requires an infinite number of steps. Malament-Hogarth spacetimes admit observers whose pasts contain entire future-directed, timelike half-curves of infinite proper length. We investigate the physical properties of these spacetimes and ask whether they and other spacetimes allow the observer to know the outcome of a computation with infinitely many steps.

This paper considers definitions of classical dynamical chaos that focus primarily on notions of predictability and computability, sometimes called algorithmic complexity definitions of chaos. I argue that accounts of this type are seriously flawed. They focus on a likely consequence of chaos, namely, randomness in behavior which gets characterized in terms of the unpredictability or uncomputability of final given initial states. In doing so, however, they can overlook the definitive feature of dynamical chaos—the fact that the underlying motion generating the behavior exhibits extreme trajectory instability. I formulate a simple criterion of adequacy for any definition of chaos and show how such accounts fail to satisfy it.

I argue that, contrary to some critics, the notion of conscious experience is a good candidate for denoting a distinct and scientifically interesting phenomenon in the brain. I base this claim mainly on an analysis of neuropsychological data concerning deficits resulting from various types of brain damage as well as some additional supporting empirical evidence. These data strongly point to the hypothesis that conscious experience expresses information that is available for global, integrated, and flexible behavior.

According to Marr's theory of vision, computational processes of early vision rely for their success on certain “natural constraints” in the physical environment. I examine the implications of this feature of Marr's theory for the question whether psychological states supervene on neural states. It is reasonable to hold that Marr's theory is nonindividualistic in that, given the role of natural constraints, distinct computational theories of the same neural processes may be justified in different environments. But to avoid trivializing computational explanations, theories must respect methodological solipsism in the sense that within a theory there cannot be differences in content without a corresponding difference in neural states.

This paper discusses a philosophical issue in taxonomy. At least one philosopher has suggested the taxonomic principle that scientific kinds are disjoint. An opposing position is defended here by marshalling examples of nondisjoint categories which belong to different, coexisting classification schemes. This denial of the disjointness principle can be recast as the claim that scientific classification is “interest-relative”. But why would anyone have held that scientific categories are disjoint in the first place? It is argued that this assumption is needed in one attempt to derive essentialism. This shows why the essentialist and interest-relative approaches to classification are in conflict.

According to a familiar argument, iterated prisoner's dilemmas of known finite lengths resolve for ideally rational and well-informed players: They would defect in the last round, anticipate this in the next to last round and so defect in it, and so on. But would they anticipate defections even if they had been cooperating? Not necessarily, say recent critics. These critics “lose” the backward-induction paradox by imposing indicative interpretations on rationality and information conditions. To regain it I propose subjunctive interpretations. To solve it I stress that implications for ordinary imperfect players are limited.

Relying on an analysis of the case of gravitational lensing, Hacking argues for a “modest antirealism” in astronomy. It is shown here that neither his scientific arguments nor his philosophical doctrines imply an antirealist conclusion. An alternative, realistic interpretation of gravitational lensing, and of the nature and history of astronomy more generally, is suggested.

Shown here is that a constraint used by Popper in The Logic of Scientific Discovery (1959) for calculating the absolute probability of a universal quantification, and one introduced by Stalnaker in “Probability and Conditionals” (1970, 70) for calculating the relative probability of a negation, are too weak for the job. The constraint wanted in the first case is in Bendali (1979) and that wanted in the second case is in Popper (1959).

When Bloor's Knowledge and Social Imagery was first published in 1976, it was not the first time that a “strong programme” in the sociology of knowledge was treated to a hostile reception by philosophers. But never before has such a dialectically unproductive encounter with philosophers led to such a methodologically fruitful response, for, when an array of positivist, historicist, Popperian, and realist philosophers argued against Bloor and his Edinburgh colleagues that normative accounts of scientific rationality could not be refuted by empirical accounts of what scientists do (see Brown 1984), an entire line of research was launched that sought to explain science without having to make reference to the philosophers' cherished norms. This is the field now known as Science and Technology Studies (STS). Although STS is normally taken to be intellectually centered in sociology, its main practitioners are just as likely to have been drawn from philosophy and the natural sciences (as in the case of the original Edinburgh School) as from the social sciences proper. The unmistakable mark of Bloor's influence is that, unlike the sociology of science most recognizable to sociologists (e.g., Merton 1973), the STS practitioner is committed to studying science in the same spirit of analytic detachment and epistemic neutrality as she would any other aspect of society. In practice, this has amounted to a preference for methods that incorporate “ethnographic distance” (e.g., Latour and Woolgar [1979] 1986), although in recent years theoretical debate has increasingly focused on the appropriate attitude that STS practitioners should adopt toward science, given their findings to date (see Pickering 1992, Fuller 1992b). I will return to this debate at the end of this essay.