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 [unpublished]).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. (shrink)

Putnam and Searle famously argue against computational theories of mind on the skeptical ground that there is no fact of the matter as to what mathematical function a physical system is computing: both conclude (albeit for somewhat different reasons) that virtually any physical object computes every computable function, implements every program or automaton. There has been considerable discussion of Putnam's and Searle's arguments, though as yet there is little consensus as to what, if anything, is wrong with these arguments. In (...) the present paper we show that an analogous line of reasoning can be raised against the numerical measurement (i.e., numerical representation) of physical magnitudes, and we argue that this result is a reductio ad absurdum of the challenge to computational skepticism. We then use this reductio to get clearer about both (i) what's wrong with Putnam's and Searle's arguments against computationalism, and (ii) what can be learned about both computational implementation and numerical measurement from the shortcomings of both sorts of skeptical argument. (shrink)

I want to suggest that the major influence of classical arguments for embodiment like "The Embodied Mind" by Varela, Thomson & Rosch (1991) has been a changing of positions rather than a refutation: Cognitivism has found ways to retreat and regroup at positions that have better fortification, especially when it concerns theses about artificial intelligence or artificial cognitive systems. For example: a) Agent-based cognitivism' that understands humans as taking in representations of the world, doing rule-based processing and then acting on (...) them (sense-plan-act) is often limited to conscious decision processes; and b) Purely syntactic cognition is compatible with embodiment, or supplemented by embodiment (e.g. for 'grounding'). While the empirical thesis of embodied cognition ('embodied cognitive science') is true and the practical engineering thesis ('morphological computation', 'cheap design') is often true, the conceptual thesis ('embodiment is necessary for cognition') is likely false - syntax is often enough for cognition, unless grounding is really necessary. I conclude that it has become more sensible to integrate embodiment with traditional approaches rather than "fight for embodiment" or "against cognitivism". (shrink)

The dynamical hypothesis states that cognitive systems are dynamical systems. While dynamical systems play an important role in many cognitive phenomena, the dynamical hypothesis as stated applies to every system and so fails both to specify what makes cognitive systems distinct and to distinguish between proposals regarding the nature of cognitive systems. To avoid this problem, I distinguish several different types of dynamical systems, outlining four dimensions along which dynamical systems can vary: total-state versus partial-state, internal versus external, macroscopic versus (...) microscopic, and systemic versus componential, and illustrate these with examples. I conclude with two illustrations of partial-state, internal, microscopic, componential dynamicism. (shrink)

I show that the indeterminacy problem for computational structuralists is in fact far more problematic than even the harshest critic of structuralism has realised; it is not a bullet which can be bitten by structuralists as previously thought. Roughly, this is because the structural indeterminacy of logic-gates such as AND/OR is caused by the structural identity of the binary computational digits 0/1 themselves. I provide a proof that pure computational structuralism is untenable because structural indeterminacy entails absurd consequences - namely, (...) that there is only one binary computational digit. I conclude that accounting for individuation is a more important desiderata for a theory of computation than even that of triviality. -/- . (shrink)

I examine a major objection to the mechanistic view of concrete computation, stemming from an apparent tension between the abstract nature of computational explanation and the tenets of the mechanistic framework: while computational explanation is medium-independent, the mechanistic framework insists on the importance of providing some degree of structural detail about the systems target of the explanation. I show that a common reply to the objection, i.e. that mechanistic explanation of computational systems involves only weak structural constraints, is not enough (...) to save the standard mechanistic view of computation—it trivialises the appeal to mechanism, and thus makes the account collapse into a purely functional view. I claim, however, that the objection can be put to rest once the account is appropriately amended: computational individuation is indeed functional, while mechanistic explanation plays a role in accounting for computational implementation. Since individuation and implementation are crucial elements in a satisfying account of computation in physical systems, mechanism keeps its central importance in the theory of concrete computation. Finally, I argue that my version of the mechanistic view helps to provide a convincing reply to a powerful objection against non-semantic theories of concrete computation: the argument from the multiplicity of computations. (shrink)

Computational implementations are special relations between what is computed and what computes it. Though the word “isomorphism” appears in philosophical discussions about the nature of implementations, it is used only metaphorically. Here we discuss computation in the precise language of abstract algebra. The capability of emulating computers is the defining property of computers. Such a chain of emulation is ultimately grounded in an algebraic object, a full transformation semigroup. Mathematically, emulation is defined by structure preserving maps (morphisms) between semigroups. These (...) are systematic, very special relationships, crucial for defining implementation. In contrast, interpretations are general functions with no morphic properties. They can be used to derive semantic content from computations. Hierarchical structure imposed on a computational structure plays a similar semantic role. Beyond bringing precision into the investigation, the algebraic approach also sheds light on the interplay between time and computation. (shrink)

In this paper, we address the question of what current computers are from the point of view of human-computer interaction. In the early days of computing, the Turing machine (TM) has been the cornerstone of the understanding of computers. The TM defines what can be computed and how computation can be carried out. However, in the last decades, computers have evolved and increasingly become interactive systems, reacting in real-time to external events in an ongoing loop. We argue that the TM (...) does not provide a mechanistic explanation for interactive computing. The reason is that the fundamental phenomena relevant to interactive computing are out of the scope of classical computability theory. Part of the explanatory power of the TM relies on what we propose to call an execution model. An execution model belongs to a level of abstraction where it is possible to describe both the functional architecture and the execution in mechanistic terms. An updated execution model is warranted to provide the minimal mechanistic description for interactive computation as a counterpart of what the TM could explain regarding Church-Turing computation. It would support an explanation of the ubiquitous computing devices we know - those interacting with humans, e.g., through digital interfaces. We show that such a model is not available within interactive models of computation and that relevant abstractions and concerns are available in computer engineering but need to be identified and gathered. To fill this void, we propose to reflect on the level of abstraction required to support the mechanistic description of an interactive execution and propose some preliminary requirements. (shrink)

This paper seeks to understand machine cognition. The nature of machine cognition has been shrouded in incomprehensibility. We have often encountered familiar arguments in cognitive science that human cognition is still faintly understood. This paper will argue that machine cognition is far less understood than even human cognition despite the fact that a lot about computer architecture and computational operations is known. Even if there have been putative claims about the transparency of the notion of machine computations, these claims do (...) not hold out in unraveling machine cognition, let alone machine consciousness (if there is any such thing). The nature and form of machine cognition remains further confused also because of attempts to explain human cognition in terms of computation and to model/simulate (aspects of) human cognitive processing in machines. Given that these problems in characterizing machine cognition persist, a view of machine cognition that aims to avoid these problems is outlined. The argument that is advanced is that something becomes a computation in machines only when a human interprets it, which is a kind of semiotic causation. From this it follows that a computing machine is not engaged in a computation unless a human interprets what it is doing; instead, it is engaged in machine cognition, which is defined as a member or subset of the set of all possible mappings of inputs to outputs. The human interpretation, which is a semiotic process, gives meaning to what a machine does, and then what it does becomes a computation. (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)

I examine the abstraction/representation theory of computation put forward by Horsman et al., connecting it to the broader notion of modeling, and in particular, model-based explanation, as considered by Rosen. I argue that the ‘representational entities’ it depends on cannot themselves be computational, and that, in particular, their representational capacities cannot be realized by computational means, and must remain explanatorily opaque to them. I then propose that representation might be realized by subjective experience (qualia), through being the bearer of the (...) structure of abstract objects that are represented. (shrink)

In spite of their practical importance, the connections between technology and mathematics have not received much scholarly attention. This article begins by outlining how the technology–mathematics relationship has developed, from the use of simple aide-mémoires for counting and arithmetic, via the use of mathematics in weaving, building and other trades, and the introduction of calculus to solve technological problems, to the modern use of computers to solve both technological and mathematical problems. Three important philosophical issues emerge from this historical résumé: (...) how mathematical knowledge depends on technology, the definition of the hybrid concept of a computation, and the usefulness of mathematics in technology. Each of these issues is briefly discussed, and it is shown that in order to analyze them, we need to combine tools and ideas from both the philosophy of technology and the philosophy of mathematics. In conclusion, it is argued that much more of interest can be found in the historically and philosophically unexplored terrains of the technology–mathematics relationship. (shrink)