A skeptical worry known as ‘the indeterminacy of computation’ animates much recent philosophical reflection on the computational identity of physical systems. On the one hand, computational explanation seems to require that physical computing systems fall under a single, unique computational description at a time. On the other, if a physical system falls under any computational description, it seems to fall under many simultaneously. Absent some principled reason to take just one of these descriptions in particular as relevant for computational explanation, (...) widespread failure of computational explanation would appear to follow. This paper advances a new solution to the indeterminacy of computation. Very roughly, I argue that the computational identity of a physical system is determinate relative to a contextually specified way of regarding that system computationally—known as a labelling scheme. When a system simultaneously implements multiple computations, it does so relative to different labelling schemes. But relative to a fixed labelling scheme, a physical system has a unique computational identity. I argue that this relativistic conception of computational identity vindicates computational explanation in the face of simultaneous implementation. (shrink)

The received view of computation is methodologically bifurcated: it offers different accounts of computation in the mathematical and physical cases. But little in the way of argument has been given for this approach. This article rectifies the situation by arguing that the alternative, a unified account, is untenable. Furthermore, once these issues are brought into sharper relief we can see that work remains to be done to illuminate the relationship between physical and mathematical computation.

Computational complexity theory is a subfield of computer science originating in computability theory and the study of algorithms for solving practical mathematical problems. Amongst its aims is classifying problems by their degree of difficulty — i.e., how hard they are to solve computationally. This paper highlights the significance of complexity theory relative to questions traditionally asked by philosophers of mathematics while also attempting to isolate some new ones — e.g., about the notion of feasibility in mathematics, the $\mathbf{P} \neq \mathbf{NP}$ (...) problem and why it has proven hard to resolve, and the role of non-classical modes of computation and proof. (shrink)

This paper makes a novel linkage between the multiple-computations theorem in philosophy of mind and Landauer’s principle in physics. The multiple-computations theorem implies that certain physical systems implement simultaneously more than one computation. Landauer’s principle implies that the physical implementation of “logically irreversible” functions is accompanied by minimal entropy increase. We show that the multiple-computations theorem is incompatible with, or at least challenges, the universal validity of Landauer’s principle. To this end we provide accounts of both ideas in terms of (...) low-level fundamental concepts in statistical mechanics, thus providing a deeper understanding of these ideas than their standard formulations given in the high-level terms of thermodynamics and cognitive science. Since Landauer’s principle is pivotal in the attempts to derive the universal validity of the second law of thermodynamics in statistical mechanics, our result entails that the multiple-computations theorem has crucial implications with respect to the second law. Finally, our analysis contributes to the understanding of notions, such as “logical irreversibility,” “entropy increase,” “implementing a computation,” in terms of fundamental physics, and to resolving open questions in the literature of both fields, such as: what could it possibly mean that a certain physical process implements a certain computation. (shrink)

The semantic view of computation is the claim that semantic properties play an essential role in the individuation of physical computing systems such as laptops and brains. The main argument for the semantic view rests on the fact that some physical systems simultaneously implement different automata at the same time, in the same space, and even in the very same physical properties. Recently, several authors have challenged this argument. They accept the premise of simultaneous implementation but reject the semantic conclusion. (...) In this paper, I aim to explicate the semantic view and to address these objections. I first characterize the semantic view and distinguish it from other, closely related views. Then, I contend that the master argument for the semantic view survives the counter-arguments against it. One counter-argument is that computational individuation is not forced to choose between the implemented automata but rather always picks out a more basic computational structure. My response is that this move might undermine the notion of computational equivalence. Another counter-argument is that while computational individuation is forced to rely on extrinsic features, these features need not be semantic. My reply is that the semantic view better accounts for these extrinsic features than the proposed non-semantic alternatives. (shrink)

Cognitive science givescomputational explanationsof the brain. Philosophers have treated these explanations as if they simply claim that the brain computes. We have therefore assumed that to understand how and why computational explanation works, we must understand what it is to compute. In contrast, I argue that we can understand computational explanation by describing the resources it brings to bear on the study of the brain. Specifically, I argue that it introduces concepts and formalisms that complement cognitive science's modeling goals. This (...) allows us to understand computational explanation without having to debatewhat it isto compute. (shrink)

Computational physical systems may exhibit indeterminacy of computation (IC). Their identified physical dynamics may not suffice to select a unique computational profile. We consider this phenomenon from the point of view of cognitive science and examine how computational profiles of cognitive systems are identified and justified in practice, in the light of IC. To that end, we look at the literature on the underdetermination of theory by evidence and argue that the same devices that can be successfully employed to confirm (...) physical hypotheses can also be used to rationally single out computational profiles, notwithstanding IC. (shrink)

We show that the so-called Multiple-Computations Theorem in cognitive science and philosophy of mind challenges Landauer’s Principle in physics. Since the orthodox wisdom in statistical physics is that Landauer’s Principle is implied by, or is the mechanical equivalent of, the Second Law of thermodynamics, our argument shows that the Multiple-Computations Theorem challenges the universal validity of the Second Law of thermodynamics itself. We construct two examples of computations carried out by one and the same dynamical process with respect to which (...) Landauer’s principle implies contradictory predictions concerning the entropy increase. Our two examples are based on a weak version of the Multiple-Computations Theorem, which is quite uncontroversial, and therefore they amount to a clear refutation of the universal validity of Landauer’s Principle. We consider some responses to this argument that do not attempt to single out one computation over the others, and we show that they do not work. We further consider ways out of the argument by externalist approaches supporting the computational theory of the mind who propose that the interaction of a computing system with the environment is enough to select a single computation over the others. We show on physical grounds that this approach fails too. We then reverse the direction of our challenge and formulate a dilemma for supporters of the computational theory of the mind: they must reject the causal closure of physic; or else they must accept on a priori grounds that Landauer’s Principle and the Second Law of thermodynamics are not universally valid. Finally, we present our version of a type–type mind-brain identity theory called Flat Physicalism, which is based on the paradigm case of statistical mechanics, and we show that it circumvents the challenge from Landauer’s Principle and the Multiple-Computations Theorem and does not fall prey to our dilemma. (shrink)