A single physical process may often be described equally well as computing several different mathematical functions—none of which is explanatorily privileged. How, then, should the computational identity of a physical system be determined? Some computational mechanists hold that computation is individuated only by either narrow physical or functional properties. Even if some individuative role is attributed to environmental factors, it is rather limited. The computational semanticist holds that computation is individuated, at least in part, by semantic properties. She claims that (...) the mechanistic account lacks the resources to individuate the computations performed by some systems, thereby leaving interesting cases of computational indeterminacy unaddressed. This article examines some of these views, and claims that more cases of computational indeterminacy can be addressed, if the system-environment interaction plays a greater role in individuating computations. A new, long-arm functional strategy for individuating computation is advanced. (shrink)

Turner argues that computer programs must have purposes, that implementation is not a kind of semantics, and that computers might need to understand what they do. I respectfully disagree: Computer programs need not have purposes, implementation is a kind of semantic interpretation, and neither human computers nor computing machines need to understand what they do.

In a recent article in this Journal, Fumagalli argues that economists are provisionally justified in resisting prominent calls to integrate neural variables into economic models of choice. In other articles, various authors engage with Fumagalli’s argument and try to substantiate three often-made claims concerning neuroeconomic modelling. First, the benefits derivable from neurally informing some economic models of choice do not involve significant tractability costs. Second, neuroeconomic modelling is best understood within Marr’s three-level of analysis framework for information-processing systems. And third, (...) neural findings enable choice modellers to confirm the causal relevance of variables posited by competing economic models, identify causally relevant variables overlooked by existing models, and explain observed behavioural variability better than standard economic models. In this paper, I critically examine these three claims and respond to the related criticisms of Fumagalli’s argument. Moreover, I qualify and extend Fumagalli’s account of how trade-offs between distinct modelling desiderata hamper neuroeconomists’ attempts to improve economic models of choice. I then draw on influential neuroeconomic studies to argue that even the putatively best available neural findings fail to substantiate current calls for a neural enrichment of economic models. (shrink)

Bayesian reverse-engineering is a research strategy for developing three-level explanations of behavior and cognition. Starting from a computational-level analysis of behavior and cognition as optimal probabilistic inference, Bayesian reverse-engineers apply numerous tweaks and heuristics to formulate testable hypotheses at the algorithmic and implementational levels. In so doing, they exploit recent technological advances in Bayesian artificial intelligence, machine learning, and statistics, but also consider established principles from cognitive psychology and neuroscience. Although these tweaks and heuristics are highly pragmatic in character and (...) are often deployed unsystematically, Bayesian reverse-engineering avoids several important worries that have been raised about the explanatory credentials of Bayesian cognitive science: the worry that the lower levels of analysis are being ignored altogether; the challenge that the mathematical models being developed are unfalsifiable; and the charge that the terms ‘optimal’ and ‘rational’ have lost their customary normative force. But while Bayesian reverse-engineering is therefore a viable and productive research strategy, it is also no fool-proof recipe for explanatory success. (shrink)

Are all three of Marr's levels needed? Should they be kept distinct? We argue for the distinct contributions and methodologies of each level of analysis. It is important to maintain them because they provide three different perspectives required to understand mechanisms, especially information-processing mechanisms. The computational perspective provides an understanding of how a mechanism functions in broader environments that determines the computations it needs to perform. The representation and algorithmic perspective offers an understanding of how information about the environment is (...) encoded within the mechanism and what are the patterns of organization that enable the parts of the mechanism to produce the phenomenon. The implementation perspective yields an understanding of the neural details of the mechanism and how they constrain function and algorithms. Once we adequately characterize the distinct role of each level of analysis, it is fairly straightforward to see how they relate. (shrink)

We consider approaches to explanation within the cognitive sciences that begin with Marr's computational level or Marr's implementational level and argue that each is subject to fundamental limitations which impair their ability to provide adequate explanations of cognitive phenomena. For this reason, it is argued, explanation cannot proceed at either level without tight coupling to the algorithmic and representation level. Even at this level, however, we argue that additional constraints relating to the decomposition of the cognitive system into a set (...) of interacting subfunctions are required. Integrated cognitive architectures that permit abstract specification of the functions of components and that make contact with the neural level provide a powerful bridge for linking the algorithmic and representational level to both the computational level and the implementational level. (shrink)