Intertheoretic Reduction

In this article, I explore how connectionism might expand its role in second language acquisition (SLA) theory by showing how some symbolic models of bilingual and second language lexical memory can be reduced to a biologically realistic (i.e., neurally plausible) connectionist model. This integration or hybridization of the two models follows the principles of what philosophers of science call intertheoretic reduction. Such a reduction serves two important purposes: It expands the explanatory scope of the symbolic models and it explains how some features of these models can actually emerge through learning in neural systems. To this end, I present a connectionist simulation of experimental data and show both the general feasibility of such a reduction and the specific manner in which the salient phenomenological distinction between form and meaning may be an emergent product of cortical memory processes. I argue this intertheoretic reduction of the symbolic to the neural serves an important goal of SLA, as these neural models can provide the theory of learning lacking in symbolic models of SLA.

Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important and well-known case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In defense of this claim, I offer evidence from mathematical practice, and I respond to contrary suggestions due to Steinhart, Maddy, Kitcher and Quine. I then show how, even if set-theoretic reductions are generally not explanatory, set theory can nevertheless serve as a legitimate and successful foundation for mathematics. Finally, some implications of my thesis for philosophy of mathematics and philosophy of science are discussed. In particular, I suggest that some reductions in mathematics are probably explanatory, and I propose that differing standards of theory acceptance might account for the apparent lack of unexplanatory reductions in the empirical sciences.

According to Gold and Stoljar, one cannot both consistently be reductionist about psychoneural relations and invoke concepts developed in the psychological sciences. I deny the utility of their distinction between biological and cognitive neuroscience, suggesting that they construe biological neuroscience too rigidly and cognitive neuroscience too liberally. Then I reject their characterization of reductionism: reductions need not go down past neurobiology straight to physics, and cases of partial, local reduction are not neatly distinguishable from cases of mere implementation. Modifying the argument from unification-as-reduction, I defend a position weaker than the radical, but stronger than the trivial neuron doctrine.

ABSTRACT: 'New wave' reductionism aims at advancing a kind of reduction that is stronger than unilateral dependency of the mental on the physical. It revolves around the idea that reduction between theoretical levels is a matter of degree, and can be laid out on a continuum between a 'smooth' pole (theoretical identity) and a 'bumpy' pole (extremely revisionary). It also entails that both higher and lower levels of the reductive relationship sustain some degree of explanatory autonomy. The new wave predicts that reductions of folk psychology to neuroscience will be located in the middle of this continuum; as neuroscientific evidence about mental states checks in, theoretical folk psychology will therefore be moderately revised. However, the model has conceptual problems which preclude its success in reviving reductionism, and its commitment to a syntactic approach wrecks its attempt to rescue folk psychology. Moreover, the architecture of the continuum operates on a category mistake that sneaks in an eliminativist conclusion. I argue that new wave reductionism therefore tends to be eliminativism in disguise.

In 1973, Nickles identified two senses in which the term 'reduction' is used to describe the relationship between physical theories: namely, the sense based on Nagel's seminal account of reduction in the sciences, and the sense that seeks to extract one physical theory as a mathematical limit of another. These two approaches have since been the focus of most literature on the subject, as evidenced by recent work of Batterman and Butterfield, among others. In this paper, I discuss a third sense in which one physical theory may be said to reduce to another. This approach, which I call 'dynamical systems (DS) reduction,' concerns the reduction of individual models of physical theories rather than the wholesale reduction of entire theories, and specifically reduction between models that can be formulated as dynamical systems. DS reduction is based on the requirement that there exist a function from the state space of the low-level (more encompassing) model to that of the high-level (less encompassing) model that satisfies certain general constraints and thereby serves to identify quantities in the low-level model that mimic the behavior of those in the high-level model -but typically only when restricted to a certain domain of parameters and states within the low-level model. I discuss the relationship of this account of reduction to the Nagelian and limit-based accounts, arguing that it is distinct from both but exhibits strong parallels with a particular version of Nagelian reduction, and that the domain restrictions employed by the DS approach may, but need not, be specified in a manner characteristic of the limit-based approach. Finally, I consider some limitations of the account of reduction that I propose and suggest ways in which it might be generalised. I offer a simple, idealised example to illustrate application of this approach; a series of more realistic case studies of DS reduction is presented in another paper.

This study attempts to spell out more explicitly than has been done previously the connection between two types of formal correspondence that arise in the study of quantum-classical relations: one the one hand, deformation quantization and the associated continuity between quantum and classical algebras of observables in the limit → 0, and, on the other, a certain generalization of Ehrenfest's Theorem and the result that expectation values of position and momentum evolve approximately classically for narrow wave packet states. While deformation quantization establishes a direct continuity between the abstract algebras of quantum and classical observables, the latter result makes in-eliminable reference to the quantum and classical state spaces on which these structures act -specifically, via restriction to narrow wave packet states. Here, we describe a certain geometrical re-formulation and extension of the result that expectation values evolve approximately classically for narrow wave packet states, which relies essentially on the postulates of deformation quantization, but describes a relationship between the actions of quantum and classical algebras and groups over their respective state spaces that is non-trivially distinct from deformation quantization. The goals of the discussion are partly pedagogical in that it aims to provide a clear, explicit synthesis of known results; however, the particular synthesis offered aspires to some novelty in its emphasis on a certain general type of mathematical and physical relationship between the state spaces of different models that represent the same physical system, and in the explicitness with which it details the above-mentioned connection between quantum and classical models.

This paper challenges a popular thesis which we call the explanatory primitiveness thesis (for short, EPT), namely, the thesis that identities leave no logical space wherein explanatory questions may be formulated and explanatory gaps may reside. We argue that while EPT is, in all likelihood, flawless when the relevant domain consists of identity statements flanked by proper names of individuals it is a mistake to hold that the thesis generalizes to cover all identity statements. In particular, we argue that EPT fails decisively with respect to an important class of identity statements, viz., those in which natural kinds are identified across different theoretical levels (i.e., the so-called inter-level type-identities). If correct, our result shows EPT to be much more limited in scope than is usually supposed. Moreover, and perhaps more significantly, it shows that there is no inherent absurdity in the idea that certain type-identity statements, in particular psychophysical type-identity statements, suffer from an explanatory gap.