Online research in philosophy

Systems involving many interacting variables are at the heart of the natural and social sciences. Causal language is pervasive in the analysis of such systems, especially when insight into their behavior is translated into policy decisions. This is exemplified by economics, but to an increasing extent also by biology, due to the advent of sophisticated tools to identify the genetic basis of many diseases. It is argued here that a regularity notion of causality can only be meaningfully defined for systems with linear interactions among their variables. For the vastly more important class of nonlinear systems, no such notion is likely to exist. This thesis is developed with examples of dynamical systems taken mostly from mathematical biology. It is discussed with particular reference to the problem of causal inference in complex genetic systems, systems for which often only statistical characterizations exist.

The question whether cognition is subserved by internal processes in the brain (internalism) or extends in to the world (active externalism) has been vigorously debated in recent years. I show how internalist and externalist ideas can be pursued in a common framework, using (1) open dynamical systems, which allow for separate analysis of an agent's intrinsic and embodied dynamics, and (2) supervenience functions, which can be used to study how low-level dynamical systems give rise to higher-level dynamical structures.

We show that, given standard assumptions about classical dynamical systems, Lewis' conception of possible worlds is incompatible with classical physics in that it would imply that all dynamical systems were integrable.

The proposed model is put forward as a template for the dynamical systems approach to embodied cognition. In order to extend this view to cognitive processing in general, however, two limitations must be overcome. First, it must be demonstrated that sensorimotor coordination of the type evident in the A-not-B error is typical of other aspects of cognition. Second, the explanatory utility of dynamical systems models must be clarified.

The subject of this chapter is the identity of individual dynamical objects and properties. Two problems have dominated the literature: transtemporal identity and the relation between composition and identity. Most traditional approaches to identity rely on some version of classification via essential or typical properties, whether nominal or real. Nominal properties have the disadvantage of producing unnatural classifications, and have several other problems. Real properties, however, are often inaccessible or hard to define (strict definition would make them nominal). I suggest that classification should be in terms of dynamical properties of systems, starting with individual systems rather than classes, and working up by abstractions that fit causal generalities. The advantage of this approach is that individuality is testable and revisable as we come to know more about systems. Another advantage is that if anything is real, then it is the dynamical. Once I have presented this approach in general, I will show that the central concept of dynamical cohesion (the "dividing glue") is amenable to giving a principled account of individuation as a process, at the same time explaining the origin of diversity. Some other advantages of this approach are presented, including how it can be used as a basis for testable classifications. This last has moral implications, since cohesion at the individual and the social levels, and their interactions, can impinge on proper moral decisions.

The dynamical systems approach in cognitive science offers a potentially useful perspective on both brain and behavior. Indeed, the importation of formal tools from dynamical systems research has already paid off for our field in many ways. However, like some other theoretical perspectives in cognitive science, the dynamical systems approach comes in both moderate or pragmatic and “fundamentalist” varieties (Jones & Love, 2011). In the latter form, dynamical systems theory can rise to some stirring rhetorical heights. However, as argued here, it also triggers a number of serious and specific reservations.

In Robert West’s talk last week, dynamical systems theory (DST) was applied to a specific problem involving interacting symbolic systems, without much reference to how those systems are embodied or related to other types of systems. Despite this level of abstraction, DST can yield interesting results, though one might be left wondering if it really leads to understanding, or what it all means. In particular, Robert noted problems he has in convincing referees that the sort of explanation he gave can give a useful understanding, and that it doesn’t invoke dubious notions with its references to emergence, holism, and mathematical openness.

Cognitive agents are dynamical systems but not quantitative dynamical systems. Quantitative systems are forms of analogue computation, which is physically too unreliable as a basis for cognition. Instead, cognitive agents are dynamical systems that implement discrete forms of computation. Only such a synthesis of discrete computation and dynamical systems can provide the mathematical basis for modeling cognitive behavior.

Cognitive systems are wilder than today's dynamical systems theory can handle. Cognitive systems might be tamed in principle, but the very notion of a dynamical system will change in the process.

.  Interpreted dynamical systems are dynamical systems with an additional interpretation mapping by which propositional formulas are assigned to system states. The dynamics of such systems may be described in terms of qualitative laws for which a satisfaction clause is defined. We show that the systems Cand CL of nonmonotonic logic are adequate with respect to the corresponding description of the classes of interpreted ordered and interpreted hierarchical systems, respectively. Inhibition networks, artificial neural networks, logic programs, and evolutionary systems are instances of such interpreted dynamical systems, and thus our results entail that each of them may be described correctly and, in a sense, even completely by qualitative laws that obey the rules of a nonmonotonic logic system.