The Idealized Mind (2025) distinguishes between computational modeling, where computational models are used to study target systems, and the additional practice of showing that neural systems literally perform computations. The former is a legitimate scientific practice. The latter is problematic.
Because computational neuroscientists take neural systems to be computational systems, Maley thinks that a core task for philosophers of neuroscience is to figure out what it might mean for a neural system to compute. According to Maley, this project “likely depends on a theory of what, if anything, it is for any system to compute.” I’m sceptical about this for at least two reasons. First, there isn’t any sight of a general theory of computation – certainly not one to be found in the philosophy of neuroscience and cognitive science. Second, even if one were to find such a general theory, I’m unconvinced it will be applicable to the brain. As in my response to Egan’s commentary, there is no reason to reject the claim that we can build computer-based models that compute a Laplacian of a Gaussian (LoG) to arbitrary precision, i.e., with any chosen finite precision. However, we have good reasons to reject the claim that nervous systems compute a LoG, since a LoG involves several key mathematical idealizations. I agree with Maley’s observation that “[p]erhaps computation is not something that natural systems can ever engage in, but at the very least, we have a lot of artificial, or engineering, systems that engage in computation.” Nervous systems are natural systems. In The Idealized Mind, I defend the view: based on computational models of the mind and brain, we don’t have any evidence to support the metaphysical claim that nervous systems compute.
Discussions about physical computation is about implementation (as Maley notes). The received view characterizes physical computation in terms of mathematical computation. A crucial question is: what conditions must a concrete system satisfy to be a computational system? The mathematical theory of computation is well-understood in the abstract (Chalmers 1994). It is not well understood in concreto, certainly not in the sciences of the mind and brain. Maley states: “A computation is defined by an abstract, formal characterization, such as a Turing machine or some other finite automaton. A physical system computes when it implements a given automaton …” Maley also states: “There is a very real sense in which computational characterizations such as automata are idealized with respect to the physical systems that implements them.” In The Idealized Mind, I argue: if the abstract, formal characterization of computation is idealized, then no physical system can implement such an abstract, formal characterization.
Maley’s main worry is that “Kirchhoff’s take on computation … seems to imply that there are no physical systems that could ever really compute anything.” I don’t think I commit to anything that strong. Let’s ask: can a computer literally compute a LoG? Not in the mathematical sense. As I argue in my forthcoming book, The Idealized Brain: Uniting Philosophy of Science and Computational Neuroscience (MIT Press), the mathematical formulation of a LoG assumes: (i) a continuous Gaussian distribution with infinite support; (ii) exact second-order derivatives; and (iii) real numbers with infinite precision. An actual computer cannot compute the mathematical formulation of a LoG. This is obvious for a couple of reasons: (a) a computer can’t store the full Gaussian; nor (b) can a computer take an exact derivate in the calculus sense. An ideal computer can compute all these functions. A physical computer can approximate them. Does this mean I’m committed to the view that no physical system computes? I don’t think so. Let me quickly refer to Hardy-Weinberg equilibrium discussed in The Idealized Mind (see my response to Drayson for elaboration). It models biological populations as infinite. Can a physical computer encode an infinite population? It can’t, because it has finite ‘memory’. Yet, a physical computer operating on genotypic frequencies deterministically can compute the limit equations to arbitrary precision – just as a computer can compute a LoG to arbitrary precision. Hence, while a computer can’t compute a mathematical idealization, it does not follow (as far as I can tell) that no physical system computes. Yet, we have no evidence that neural systems compute.
References
Chalmers, David. The Conscious Mind. New York: Oxford University Press.
Kirchhoff, Michael. 2025. The Idealized Mind: From Model-based Science to Cognitive Science. Cambridge, MA: The MIT Press.