Holly Andersen

A finer-grained delineation of a given explanandum reveals a nexus of closely related causal and non-causal explanations, complementing one another in ways that yield further explanatory traction on the phenomenon in question. By taking a narrower construal of what counts as a causal explanation, a new class of distinctively mathematical explanations pops into focus; Lange’s characterization of distinctively mathematical explanations can be extended to cover these. This new class of distinctively mathematical explanations is illustrated with the Lotka–Volterra equations. There are at least two distinct ways those equations might hold of a system, one of which yields straightforwardly causal explanations, and another that yields explanations that are distinctively mathematical in terms of nomological strength. In the first case, one first picks out a system or class of systems, and finds that the equations hold in a causal–explanatory way. In the second case, one starts with the equations and explanations that must apply to any system of which the equations hold, and only then turns to the world to see of what, if any, systems it does in fact hold. Using this new way in which a model might hold of a system, I highlight four specific avenues by which causal and non-causal explanations can complement one another. _1_. Introduction _2._ Delineating the Boundaries of Causal Explanation _2.1._ Why construe causal explanation narrowly? The land of explanation versus grain-focusing _2.2._ Reasons to narrow the scope of causal explanation _3._ Broadening the Scope of Mathematical Explanation _4._ Lotka–Volterra: Same Model, Different Explanation Types _4.1._ General biocide in the Lotka–Volterra model _4.2._ Two ways a model can hold, yielding causal versus mathematical explanations _5._ Four Complementary Relationships between Mathematical and Causal Explanation _5.1._ Slight reformulations of explananda _5.2._ Causal distortion of idealized mathematical models _5.3._ Partial explanations requiring supplementation _5.4._ Explanatory dimensionality _6._ Conclusion

Shadworth Hodgson offers an account of how philosophy relates to science - both physical and psychological - in which three different conceptions of time can be identified. He distinguishes the methods of philosophy, involving analysis of the contents of immediate consciousness, and of science, which presumes the existence of the world of common sense. Hodgson holds that philosophical analysis of immediate consciousness, or the analysis of a present moment in the experience, provides the ultimate justification for knowledge in science. Time as an object of study in science must be distinguished from the temporal structure of immediate consciousness. Time as a target of scientific study is thus differentiable into time in physical science, and time in psychology, where the temporal characteristics of consciousness can be studied, but only from a perspective external to that consciousness. Each of those scientific conceptions of time still presupposes and are evidentially dependent on the analysis of immediate consciousness, itself already temporal. The result is that time as a fundamental unit of experience could not, even in principle, conflict with time as studied in science, because it is presupposed by and the evidential base for claims about time in science.

People's doings as agents in the world are irreducibly temporally extended, involving both time itself as well as various representations of temporality. There are three distinct elements this chapter disentangles in order to draw out the connections between them: temporal experience, agency, and representation. It outlines some of the key issues that arise when agency and temporality are considered jointly. The chapter traces out some intriguing paths for future work from the tangle of issues involved in the representation of time in agency. The issue of time and agency in psychology and the cognitive sciences are also covered. The chapter explores the implication of the dissociation between agency and the sense of agency. It explores options for developing a parallel project to that of explaining the Edmund Husserl's tripartite structure of time consciousness, a project capable of grounding the intentional content of temporal representations involved in agency in neurophysiological processes.