When I went to graduate school in the 1990s, the mainstream assumptions were that (1) computation properly so called is digital and its limits are defined by classical computability theory, and (2) the debate in cognitive science was between “classical” (LOT) digital computation and “nonclassical” (connectionist in the narrow sense) digital computation. (Some people knew about so-called “analog computation” but they barely ever mentioned it.) To this day, many people still seem to accept these assumptions. For example, Brian Scholl is a distinguished psychologist who spoke at the recent PSA meeting in Pittsburgh; he sounded like he operates under these assumptions.
One lesson of the last 20 years or so of literature on physical computation is that these assumptions are wrong and badly misleading.
First, there is a lot more to computation than digital computation. Analog computation has seen a resurgence of interest and the field of computer science itself has further expanded to include quantum computation and various other unconventional models of computation that are nondigital in various ways. Therefore, we need a broad notion of computation that encompasses digital computation, analog computation, etc. as species.
Second, the debate in cognitive science should be broader as well, between different kinds of computation. In a 2013 paper with biophysicist Sonya Bahar, I have argued that neural computation, in general, is not digital; therefore, theories of cognition need to be formulated in terms of (what we know about or expect to be possible via) neural computation. This is one of the cornerstones of my book Neurocognitive Mechanisms. Many others have written on these topics. While they may disagree on this or that detail, I’m not aware of any refutation of our argument. On the contrary, informed writers on neural computation seem to more or less agree that neural computation, in general, is not digital and needs to be understood in its own right.
I say this mostly for the benefit of young scholars as well as people with a serious interest in the theory of cognition. Be aware that the debate has shifted and literature that is older than 10 years is often obsolete, and even some recent literature is badly misinformed. There are plenty of good people with excellent recent work in this area, including but not limited to Oron Shagrir, Marcin Milkowski, Corey Maley, Francis Egan, Matteo Colombo, Dimitri Coelho Mollo, David Kaplan, Mazviita Chirimuuta, Brendan Ritchie, David Barack.
For what it’s worth, Matteo Colombo and I have just finished a brief introduction to The Computational Theory of Mind for Cambridge Elements, which is now under review and will hopefully help bring more people up to date.