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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.

Do the dynamics of a physical system determine what function the system computes? Except in special cases, the answer is no: it is often indeterminate what function a given physical system computes. Accordingly, care should be taken when the question ‘What does a particular neuronal system do?’ is answered by hypothesising that the system computes a particular function. The phenomenon of the indeterminacy of computation has important implications for the development of computational explanations of biological systems. Additionally, the phenomenon lends some support to the idea that a single neuronal structure may perform multiple cognitive functions, each subserved by a different computation. We provide an overarching conceptual framework in order to further the philosophical debate on the nature of computational indeterminacy and computational explanation.

Is the mathematical function being computed by a given physical system determined by the system’s dynamics? This question is at the heart of the indeterminacy of computation phenomenon (Fresco et al. [unpublished]). A paradigmatic example is a conventional electrical AND-gate that is often said to compute conjunction, but it can just as well be used to compute disjunction. Despite the pervasiveness of this phenomenon in physical computational systems, it has been discussed in the philosophical literature only indirectly, mostly with reference to the debate over realism about physical computation and computationalism. A welcome exception is Dewhurst’s ([2018]) recent analysis of computational individuation under the mechanistic framework. He rejects the idea of appealing to semantic properties for determining the computational identity of a physical system. But Dewhurst seems to be too quick to pay the price of giving up the notion of computational equivalence. We aim to show that the mechanist need not pay this price. The mechanistic framework can, in principle, preserve the idea of computational equivalence even between two different enough kinds of physical systems, say, electrical and hydraulic ones.

There has been an ongoing conflict regarding whether reality is fundamentally digital or analogue. Recently, Floridi has argued that this dichotomy is misapplied. For any attempt to analyse noumenal reality independently of any level of abstraction at which the analysis is conducted is mistaken. In the pars destruens of this paper, we argue that Floridi does not establish that it is only levels of abstraction that are analogue or digital, rather than noumenal reality. In the pars construens of this paper, we reject a classification of noumenal reality as a deterministic discrete computational system. We show, based on considerations from classical physics, why a deterministic computational view of the universe faces problems (e.g., a reversible computational universe cannot be strictly deterministic).

What is nontrivial digital computation? It is the processing of discrete data through discrete state transitions in accordance with finite instructional information. The motivation for our account is that many previous attempts to answer this question are inadequate, and also that this account accords with the common intuition that digital computation is a type of information processing. We use the notion of reachability in a graph to defend this characterization in memory-based systems and underscore the importance of instructional information for digital computation. We argue that our account evaluates positively against adequacy criteria for accounts of computation.

The phenomenon of digital computation is explained (often differently) in computer science, computer engineering and more broadly in cognitive science. Although the semantics and implications of malfunctions have received attention in the philosophy of biology and philosophy of technology, errors in computational systems remain of interest only to computer science. Miscomputation has not gotten the philosophical attention it deserves. Our paper fills this gap by offering a taxonomy of miscomputations. This taxonomy is underpinned by a conceptual analysis of the design and implementation of conventional computational systems at various levels of abstraction. It shows that ‘malfunction’ as it is typically used in the philosophy of artefacts only represents one type of miscomputation.

3D printing is a process of producing solid objects of various shapes (e.g., spare plastic parts for cars) from a digital model by adding successive layers of material. More recently, 3D bioprinting technology has been used for producing living tissues and organs. 3D bioprinting provides another avenue to analyze the increasingly informational nature of physical objects and the ethical challenges it brings. It uses both specific information provided by the “digital model” and the instructional information of its printing program. While bioprinting holds promise to alleviate shortages of certain biological tissues, in this paper we begin to address ethical challenges that arise, in particular, from the possible avenues of exploiting this information and questions about ownership and quality of as well as accessibility to this information. Further, we suggest that 3D bioprinting brings some urgency to addressing philosophical questions about personal identity.

Which notion of computation (if any) is essential for explaining cognition? Five answers to this question are discussed in the paper. (1) The classicist answer: symbolic (digital) computation is required for explaining cognition; (2) The broad digital computationalist answer: digital computation broadly construed is required for explaining cognition; (3) The connectionist answer: sub-symbolic computation is required for explaining cognition; (4) The computational neuroscientist answer: neural computation (that, strictly, is neither digital nor analogue) is required for explaining cognition; (5) The extreme dynamicist answer: computation is not required for explaining cognition. The first four answers are only accurate to a first approximation. But the "devil" is in the details. The last answer cashes in on the parenthetical "if any" in the question above. The classicist argues that cognition is symbolic computation. But digital computationalism need not be equated with classicism. Indeed, computationalism can, in principle, range from digital (and analogue) computationalism through (the weaker thesis of) generic computationalism to (the even weaker thesis of) digital (or analogue) pancomputationalism. Connectionism, which has traditionally been criticised by classicists for being non-computational, can be plausibly construed as being either analogue or digital computationalism (depending on the type of connectionist networks used). Computational neuroscience invokes the notion of neural computation that may (possibly) be interpreted as a sui generis type of computation. The extreme dynamicist argues that the time has come for a post-computational cognitive science. This paper is an attempt to shed some light on this debate by examining various conceptions and misconceptions of (particularly digital) computation.

It is common in cognitive science to equate computation (and in particular digital computation) with information processing. Yet, it is hard to find a comprehensive explicit account of concrete digital computation in information processing terms. An information processing account seems like a natural candidate to explain digital computation. But when ‘information’ comes under scrutiny, this account becomes a less obvious candidate. Four interpretations of information are examined here as the basis for an information processing account of digital computation, namely Shannon information, algorithmic information, factual information and instructional information. I argue that any plausible account of concrete computation has to be capable of explaining at least the three key algorithmic notions of input, output and procedures. Whist algorithmic information fares better than Shannon information, the most plausible candidate for an information processing account is instructional information.

This paper deals with the question: what are the key requirements for a physical system to perform digital computation? Time and again cognitive scientists are quick to employ the notion of computation simpliciter when asserting basically that cognitive activities are computational. They employ this notion as if there was or is a consensus on just what it takes for a physical system to perform computation, and in particular digital computation. Some cognitive scientists in referring to digital computation simply adhere to Turing’s notion of computability. Classical computability theory studies what functions on the natural numbers are computable and what mathematical problems are undecidable. Whilst a mathematical formalism of computability may perform a methodological function of evaluating computational theories of certain cognitive capacities, concrete computation in physical systems seems to be required for explaining cognition as an embodied phenomenon. There are many non-equivalent accounts of digital computation in physical systems. I examine only a handful of those in this paper: (1) Turing’s account; (2) The triviality “account”; (3) Reconstructing Smith’s account of participatory computation; (4) The Algorithm Execution account. My goal in this paper is twofold. First, it is to identify and clarify some of the underlying key requirements mandated by these accounts. I argue that these differing requirements justify a demand that one commits to a particular account when employing the notion of computation in regard to physical systems. Second, it is to argue that despite the informative role that mathematical formalisms of computability may play in cognitive science, they do not specify the relationship between abstract and concrete computation.

This paper deals with the question: What are the criteria that an adequate theory of computation has to meet? (1) Smith's answer: it has to meet the empirical criterion (i.e. doing justice to computational practice), the conceptual criterion (i.e. explaining all the underlying concepts) and the cognitive criterion (i.e. providing solid grounds for computationalism). (2) Piccinini's answer: it has to meet the objectivity criterion (i.e. identifying computation as a matter of fact), the explanation criterion (i.e. explaining the computer's behaviour), the right things compute criterion, the miscomputation criterion (i.e. accounting for malfunctions), the taxonomy criterion (i.e. distinguishing between different classes of computers) and the empirical criterion. (3) Von Neumann's answer: it has to meet the precision and reliability of computers criterion, the single error criterion (i.e. addressing the impacts of errors) and the distinction between analogue and digital computers criterion. (4) "Everything" computes answer: it has to meet the implementation theory criterion by properly explaining the notion of implementation.

Artefacts do not always do what they are supposed to do, due to a variety of reasons, including manufacturing problems, poor maintenance, and normal wear-and-tear. Since software is an artefact, it should be subject to malfunctioning in the same sense in which other artefacts can malfunction. Yet, whether software is on a par with other artefacts when it comes to malfunctioning crucially depends on the abstraction used in the analysis. We distinguish between “negative” and “positive” notions of malfunction. A negative malfunction, or dysfunction, occurs when an artefact token either does not (sometimes) or cannot (ever) do what it is supposed to do. A positive malfunction, or misfunction, occurs when an artefact token may do what is supposed to do but, at least occasionally, it also yields some unintended and undesirable effects. We argue that software, understood as type, may misfunction in some limited sense, but cannot dysfunction. Accordingly, one should distinguish software from other technical artefacts, in view of their design that makes dysfunction impossible for the former, while possible for the latter.

Piccinini defends a mechanistic account of physical computation intended to distinguish computing from non-computing systems (for both artificial and natural systems). This account—drawing on the m...

What is computation? This question may seem, at a first glimpse, trivial and uninteresting. There has already been a long discussion about this subject back in the mid-twentieth century. The discussion produced many extensionally equivalent models of computation, such as Turing machines, lambda calculus, cellular automata, Post machines and recursive functions.

It seems incontrovertible that information processing is fundamental to cognitive function. As already observed in Chapter 1, one explanatory strategy for a theory of cognition to take is to view some of the agent’s internal states and processes as carrying information about those relevant aspects of its body and external states of affairs in negotiating its environment (Bechtel, 1998, p. 297). Natural cognitive agents produce new information that is intended, amongst other things, to deal with a variety of environments. It is unsurprising then that semantic accounts of computation that underlie CTM view digital computing systems as engaging in information processing at the symbol level (cf. the FSM and PSS accounts).

In the present chapter, we examine the views of two well-known and influential philosophers concerning the ubiquitous character of concrete computation. They both share a common objective, namely, the falsification of the computationalist thesis that cognition is computational. But in order to accomplish this objective, they in effect undermine the demarcation of digital computation as a subject matter. For, by their lights, there is no fact of the matter about what digital computation is. On their view, every physical object implements any number of programs and, hence, computes every Turing-computable function.

In this chapter, we explore the possible criteria for evaluating the adequacy of candidate accounts of concrete digital computation. According to proponents of CTM, cognition is computational. Before we can judge the plausibility of any particular CTM, we need to understand what notion of computation this theory employs. Although there are extant accounts of computation, any of which may, in principle, serve as a basis for CTM, it is not clear that they are all equivalent or even adequate as accounts of computation proper. By proposing a plausible alternative to Smith’s adequacy criteria, our goal here is to resist his discouraging claim that no adequate account of computation proper is possible.

In this final chapter, we conclude the book with four theses. First, in Section 8.1, we argue that in the course of nontrivial computation, typically, only implicit intrinsic and mathematical representations are processed. Then, in Section 8.2, we argue that any computational explanation of cognition is unintelligible without a commitment to a single interpretation of ‘digital computation’ as defined by a given account thereof. In Section 8.3, we argue that a blanket dismissal of the key role computation plays in cognitive science is unwarranted. We also argue that the thesis that computationalism, connectionism and dynamicism are mutually exclusive is wrong.

Computability as an abstract notion, underlying any physical digital computation, was the focus of intense interest during the 1930s by mathematicians such as Godel (1931), Turing (1936), Church (1936) and Post (1936). According to Turing’s analysis, digital computation is the process of effectively calculating the values of a function by some purely mechanical procedure executed by a TM. He argued that computation is reducible to carrying out a calculation by following instructions.

This chapter examines some accounts according to which external semantic content is inherent to the computational process, and so any computational explanation entails content ascription to the explanandum. The goal of these accounts is clear: by ascribing semantic content to digital computing systems proper, proponents of the semantic view of computation aim to explain cognition computationally.

This paper deals with the question: what are the key requirements for a physical system to perform digital computation? Oftentimes, cognitive scientists are quick to employ the notion of computation simpliciter when asserting basically that cognitive activities are computational. They employ this notion as if there is a consensus on just what it takes for a physical system to compute. Some cognitive scientists in referring to digital computation simply adhere to Turing computability. But if cognition is indeed computational, then it is concrete computation that is required for explaining cognition as an embodied phenomenon. Three accounts of computation are examined here: 1. Formal Symbol Manipulation. 2. Physical Symbol Systems and 3.The Mechanistic account. I argue that the differing requirements implied by these accounts justify the demand that one commits to a particular account when employing the notion of digital computation in regard to physical systems, rather than use these accounts interchangeably.

Wolf and White address different aspects of the paper and in this present reply space only permits making two brief remarks. Starting with White’s intriguing observation: digital computation without erasing information is possible. This clearly has important implications for real-world digital computing systems, since they can be designed and constructed in a more energy efficient manner, if information erasure operations are kept to a minimum. Yet, avoiding information erasure operations completely in the course of computation is another matter. At least prima facie, this introduces difficulties relating to memory storage. Information is conveyed by data and (particularly persistent) data in computing systems occupy space. However, computation that only adds new information without erasing any one will inevitably require infinite memory space. Whilst idealised Turing machines have this capacity by definition, real-world computing systems do not. The second remark is about control information in digital computing systems. White omits the fifth requirement from the list of requirements, which an information processing system has to meet to qualify as a computing system. However, it is the capacity of the physical system to actualise control information that shoulders much of the burden in terms of distinguishing nontrivial digital computing systems from trivial ones. This requirement is the main focus of Wolf’s commentary. Unlike factual information, instructional information is fully compatible with control information. Questions, requests and commands (the building blocks needed for an adequate explanation of concrete digital computation) are examples of control information, since their information processing function involves making something happen. Interestingly, whilst discrete connectionist networks lack any controller unit, they still actualise control information. Typically, the pattern of activating of a set of units depends on the previous activation pattern (in some other possibly overlapping set of units), the weighted connections between the two sets and the units’ threshold functions for combining these weighted influences. Therefore, discrete connectionist