Much of the current thought concerning mathematical ontology and epistemology follows Quine and Putnam in looking to the indispensable application of mathematics in science. A standard assumption of the indispensability approach is some version of confirmational holism, i.e., that only “sufficiently large” sets of beliefs “face the tribunal of experience.” In this paper I develop and defend a distinction between a pure mathematical theory and a mathematized scientific theory in which it is applied. This distinction allows for the possibility that pure mathematical theories are systematically insulated from such confirmation in virtue of their being distinct from the “sufficiently large” blocks of scientific theory that are empirically confirmed.

In this paper I argue that category theory ought to be seen as providing the language for mathematical discourse. Against foundational approaches, I argue that there is no need to reduce either the content or structure of mathematical concepts and theories to the constituents of either the universe of sets or the category of categories. I assign category theory the role of organizing what we say about the content and structure of both mathematical concepts and theories. Insofar, then, as the structuralist sees mathematics as talking about structures and their morphology, I contend that category theory furnishes a framework for mathematical structuralism.

We first examine Howard's analysis of the Bell factorizability condition in terms of ‘separability’ and ‘locality’ and then consider his claims that the violations of Bell's inequality by the statistical predictions of quantum mechanics should be interpreted in terms of ‘nonseparability’ rather than ‘nonlocality’ and that ‘nonseparability’ implies the failure of spacetime as a principle of individuation for quantum-mechanical systems. We will argue that his argument for the first claim is less than compelling and that any argument for the second claim will be interpretation-dependent and, hence, not generally valid.

If observation is ‘theory-laden’, how can there be ‘observationally equivalent theories’? How can the observations ‘laden’ by one theory be ‘the same as’ those ‘laden’ by another? The answer might lie in the expressibility of observationally equivalent theories in a common mathematical formalism.

GRW models of the physical world are criticized in the literature for involving wave function “tails” that allegedly create fatal interpretive problems and even compromise standard arithmetic. I find such objections both unfair and misguided. But not all is well with the GRW approach. One complaint I articulate in this paper does not have to do with tails as such but with the specific way in which past physical structures linger forever in the total GRW wave function. By pushing the total proposal towards either the “Many Worlds” approach or the Bohmian approach, this feature diminishes extant GRW claims to preferability. I suggest, however, that the problem here is just an artifact of the particular and ultimately optional genre of collapse mechanism chosen by GRW.

The status of a causal approach to EPR-Bell nonlocal correlations in terms of a counterfactual framework for causation is considered. It is argued that when the relativistic spacetime structure of the events is taken into due account, the adoption of this approach is best motivated by the assumption of a preferred frame of reference, an assumption that seems even more in need of justification than the causal theory itself.

Ruetsche (1996) has argued that van Fraassen's (1991) Copenhagen Variant of the Modal Interpretation (CVMI) gives unsatisfactory accounts of measurement and of state preparation. I defend the CVMI against Ruetsche's first argument by using decoherence to show that the CVMI does not need to account for the measurement scenario which Ruetsche poses. I then show, however, that there is a problem concerning preparation, and the problem is more serious than the one Ruetsche focuses on. The CVMI makes no substantive predictions for the everyday processes we take to be measurements.

Phase transitions are well-understood phenomena in thermodynamics (TD), but it turns out that they are mathematically impossible in finite SM systems. Hence, phase transitions are truly emergent properties. They appear again at the thermodynamic limit (TL), i.e., in infinite systems. However, most, if not all, systems in which they occur are finite, so whence comes the justification for taking TL? The problem is then traced back to the TD characterization of phase transitions, and it turns out that the characterization is the result of serious idealizations which under suitable circumstances approximate actual conditions.

In the usual procedure of deriving equilibrium thermodynamics from classical statistical mechanics, Gibbsian fine-grained entropy is taken as the analogue of thermodynamical entropy. However, it is well known that the fine-grained entropy remains constant under the Hamiltonian flow. In this paper it is argued that we need not search for alternatives for fine-grained entropy, nor do we have to reject Hamiltonian dynamics, in order to solve the problem of the constancy of fine-grained entropy and, more generally, to account for the non-equilibrium part of the laws of thermodynamics. Rather, we have to weaken the requirement that equilibrium be identified with a stationary probability distribution.

Much controversy surrounds the question of what ought to be the proper definition of ‘singularity’ in general relativity, and the question of whether the prediction of such entities leads to a crisis for the theory. I argue that a definition in terms of curve incompleteness is adequate, and in particular that the idea that singularities correspond to ‘missing points’ has insurmountable problems. I conclude that singularities per se pose no serious problem for the theory, but their analysis does bring into focus several problems of interpretation at the foundation of the theory often ignored in the philosophical literature.

Gauge theories are theories that are invariant under a characteristic group of “gauge” transformations. General relativity is invariant under transformations of the diffeomorphism group. This has prompted many philosophers and physicists to treat general relativity as a gauge theory, and diffeomorphisms as gauge transformations. I argue that this approach is misguided.

In a pair of articles (1996, 1997) and in his recent book (1998), Miklos Redei has taken enormous strides toward characterizing the conditions under which relativistic quantum field theory is a safe setting for the deployment of causal talk. Here, we challenge the adequacy of the accounts of causal dependence and screening off on which rests the relevance of Redei's theorems to the question of causal good behavior in the theory.

The recent work of Paul Teller and Sunny Auyang in the philosophy of Quantum Field Theory (QFT) has stimulated the search for the fundamental entities in this theory. In QFT, the classical notion of a particle collapses. The theory does not only exclude classical, i.e., spatiotemporally identifiable particles, but it makes particles of the same type conceptually indistinguishable. Teller and Auyang have proposed competing ersatz-ontologies to account for the ‘loss of particles’: field quanta vs. field events. Both ontologies, however, suffer from serious defects. While quanta lack numerical identity, spatiotemporal localizability, and independence of basis-representations, events—if understood as concrete measurement events—are related to the theory only statistically. I propose an alternative solution: The entities of QFT are events of the type ‘Quantum system, S, is in quantum state, Ψ‘. These are not point events, but Davidsonian events, i.e., they can be identified by their location within the causal net of the world.

Lennox and Wilson (1994) critique dispositional accounts of selection on the grounds that such accounts will class evolutionary events as cases of selection whether or not the environment constrains population growth. Lennox and Wilson claim that pure r-selection involves no environmental checks on growth, and that accounts of natural selection ought to distinguish between the two sorts of cases. I argue that Lennox and Wilson are mistaken in claiming that pure r-selection involves no environmental checks, but suggest that two related cases support their substantive complaint, namely that dispositional accounts of selection have resources insufficient for making important distinctions in causal structure.

According to Philip Kitcher, scientific unification is achieved via the derivation of numerous scientific statements from economies of argument schemata. I demonstrate that the unification of selection phenomena across domains in which it is claimed to occur—evolutionary biology, immunology and, speculatively, neurobiology—is unattainable on Kitcher's view. I then introduce an alternative method for rendering the desired unification based on the concept of a mechanism schema. I conclude that the gain in unification provided by the alternative account suggests that Kitcher's view is defective.

“Modern History” versions of the etiological theory claim that in order for a trait X to have the proper function F, individuals with X must have been recently favored by natural selection for doing F (Godfrey-Smith 1994; Griffiths 1992, 1993). For many traits with prototypical proper functions, however, such recent selection may not have occurred: traits may have been maintained due to lack of variation or due to selection for other effects. I examine this flaw in Modern History accounts and offer an alternative etiological theory, the Continuing Usefulness account, which appears to avoid such problems.

This paper is a defense of “explanatory pluralism” (i.e., the view that some events can be correctly explained in two distinct ways). To defend pluralism, I identify two distinct (but compatible) styles of explanation in paleobiology. The first approach (“actual sequence explanation”) traces out the particular forces that affect each species. The second approach treats the trend as “passive” or “random” diffusion away from a boundary in morphological space. I argue that while these strategies are distinct, some trends are correctly explained in both ways. Further, since neither strategy can be reduced or eliminated from paleobiology, we should accept that both strategies can provide correct explanations for a single trend.

Donald Campbell has long advocated a naturalist epistemology based on a general selection theory, with the scope of knowledge restricted to vicarious adaptive processes. But being a vicariant is problematic because it involves an unexplained epistemic relation. We argue that this relation is to be explicated organizationally in terms of the regulation of behavior and internal state by the vicariant, but that Campbell's selectionist approach can give no satisfactory account of it because it is opaque to organization. We show how organizational constraints and capacities are crucial to understanding both evolution and cognition and conclude with a proposal for an enriched, generalized model of evolutionary epistemology that places high-order regulatory organization at the center.

In this paper I provide a metatheoretical analysis of speech perception research. I argue that the central turning point in the history of speech perception research has not been well understood. While it is widely thought to mark a decisive break with what I call “the alphabetic conception of speech,” I argue that it instead marks the entrenchment of this conception of speech. In addition, I argue that the alphabetic conception of speech continues to underwrite speech perception research today and moreover that it functions as a dogma which ought to be rejected.