Abstract
This paper deals with the question: how is computation best individuated?
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The semantic view of computation: computation is best individuated by its semantic properties.
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The causal view of computation: computation is best individuated by its causal properties.
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The functional view of computation: computation is best individuated by its functional properties.
Some scientific theories explain the capacities of brains by appealing to computations that they supposedly perform. The reason for that is usually that computation is individuated semantically. I criticize the reasons in support of this view and its presupposition of representation and semantics. Furthermore, I argue that the only justified appeal to a representational individuation of computation might be that it is partly individuated by implicit intrinsic representations.
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Notes
Phillip Staines suggested avoiding the use of the term external in this context. An ‘independent’ knower here escapes the effects of discouraging objections. One might argue for instance that a knower can be engaged in a form of virtual reality, in which case it is not clear cut whether he is in fact external to the computing mechanism.
Arguably, connectionist networks significantly extend the received notion of computation, and are thus individuated differently than classic computation (or symbolic computation). Indeed, these networks enrich the discipline of computer science with new and interesting computational architectures and learning algorithms. Nevertheless, in my opinion, they are not radically different from classic symbolic computation and I do not have space to discuss them in detail in this paper.
It is thus easy to see, for example, why some may interpret the “functional view of computation” as machine functionalism, an important theory in the philosophy of mind. The functional view of computation is labelled as such following Piccinini’s mechanistic account of computation, where a function is determined by what it is for (i.e., teleofunctionalism in a computational context).
In fairness to Fodor, he thinks that computational states are defined over representations, but denies that the content of representations affects the computational individuation. He maintains that what matters to computational individuation is only syntactic properties (Shagrir 2001, p. 370, fn. 2, and personal correspondence).
Copeland (1996, pp. 350–351) defines two necessary conditions for the honesty feature. First, the labelling scheme L must not be ex post facto. Second, the interpretation associated with the model must secure the truth of appropriate counterfactuals concerning the machine's behaviour.
It may be worthwhile noting that Piccinini’s mechanistic account of computation does not reduce computing mechanisms to nothing more than their sub-components. It is rather meant to support an account that appeals to the mechanism’s sub-components, their functions and the particular way that they are organized together.
The term “cognitive science” can be interpreted in many ways. On a narrow interpretation of this term, it is used to encompass the three predominant views in the philosophy of mind: computationalism, connectionism and dynamicism. On a broader interpretation, it is used to also include disciplines such as neuroscience, cognitive psychology, linguistics, biology, computer science, sociology and artificial intelligence. Depending on the interpretation of this term, it may de-emphasise or even exclude outright key factors like consciousness, emotions, etc. Throughout this paper the term “cognitive science” should be interpreted in the narrow sense.
Put another way, the computational identity of a system is context-dependent: it depends on the syntactic structure the system implements while performing a given task (Shagrir 1999, p. 142). The underlying function being computed in that context determines the computational identity of the system.
The emphasis in the second argument is on functions computed, whereas in the third argument it is on tasks. The purpose of computational task is to compute a certain function. Consequently, both arguments are susceptible to similar criticisms.
A “cognitive system” here refers to systems in the broad sense that have cognitive capacities such as reception and processing of information, thinking, representation of knowledge, memory, natural language etc.
A computational function performing addition over the positive integers would be functionally equivalent to one performing addition over the even positives. However, these functions differ in their domains. It is not simply a matter of an external knower supplying some consistent interpretation of the functions in question. There is a fact of the matter about what the canonical interpretation of a computing circuit is, and it comes specifically from the designer's interpretation. Moreover, the context is then not what the inputs and outputs are, but rather the design context.
The representational theories of consciousness reviewed henceforth should not be confused with the three approaches of computation discussed before.
Intrinsic representations in this context are the referents of symbols that are internal (intrinsic) to the computing mechanism. Extrinsic representations are referents of external symbols, data or objects. The intrinsic representations are thus knower-independent (e.g., computer instructions that contain addresses of memory registers, which in turn contain representations of other instructions) as opposed to extrinsic representations that are knower-dependent (i.e., a knower assigns external semantics to the symbols).
“Constant time” has a particular meaning in computer science. It is also known as O(1) time, and describes the computation time of a function when the time needed to solve it is bounded by a value, which does not depend on the size of the data it is given as input.
See Kirsh (1991) for a detailed critical analysis of our existing intuitions and explanations of explicitness and implicitness of information. These concepts are examined in the context of computation, where he exposes their problematic usage in the explanatory frameworks of both computation and cognition. My assumption is that the criterion proposed by Kirsh (1991, p. 360) for explicitness of representation is satisfactory.
Anyone, who uses the Google search engine, may be prompted by Google to ‘respond’ to a question of some form (such as ‘did you mean flying cargo?’). This does not entail that the underlying computation that occurred behind the scenes demonstrated an understanding per se of the searched term. It is rather a process built into the search engine that allows it to ‘guess’ what the user might have meant, when few or no ‘hits’ were found.
In some ways biological computers are analogous to connectionist systems. They are both distributed systems by nature, in which a population of autonomous agents follows simple local rules. Some connectionists systems operate by employing learning algorithms, but receive their information pre-programmed by a human designer and generate output, which requires human interpretation. However, in the case of biological computers they get their input from the environment in which they are situated. Accordingly, their output is dependent on an open-ended evolutionary dynamic process. (Bedau 2003, pp. 198–199). Nevertheless, this is yet to be proven. This research is still in its infancy stages, and only time will tell if researchers succeed in harnessing natural selection to take its course on biological computers. And the harnessing of natural selection to modify computing mechanisms is where I think it departs from computation proper.
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Acknowledgements
Thanks to Axel Cleeremans, David Rosenthal, Gualtiero Piccinini, Joseph Agassi and Oron Shagrir for useful comments on earlier drafts of this paper. An earlier version of this text was presented at the 2007 AAP (NZ) conference in Auckland, NZ. I am especially grateful to Phillip Staines for his helpful comments and ongoing support.
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In the context of this paper, ‘individuated’ may be interpreted as ‘distinguished’. Thus, the main question can be rephrased to read: how is computation best distinguished from non-computational phenomena? I do not explicitly discuss the criteria for distinguishing computation from non-computation in this paper (see for example, Fresco 2008).
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Fresco, N. Explaining Computation Without Semantics: Keeping it Simple. Minds & Machines 20, 165–181 (2010). https://doi.org/10.1007/s11023-010-9199-6
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DOI: https://doi.org/10.1007/s11023-010-9199-6