The Foundations of Computing

Draft: version 0,94 (b) Not for distribution, citation, or … Comments welcome The Foundations of Computing Brian Cantwell Smith* Computer and Cognitive Science Departments Indiana University, Bloomington, in 47405 usa Will computers ever be conscious? Is it appro- 1. Empirical: It must do justice to computa- priate—correct, illuminating, ethical—to un- tional practice (e.g., be capable of explaining derstand people in computational terms? Will Microsoft Word: the program, its construc- quantum, dna, or nanocomputers radically alter tion, maintenance, and use); our conception of computation? How will com- 2. Conceptual: It must discharge all intellectual puting affect science, the arts, intellectual his- debts (e.g., to semantics), so that we can un- tory? derstand what it says, where it comes from, I have never known how to answer these what it costs; and questions, because I have never been sure what computation is. More than twenty-five years 3. Cognitive: It must provide a tenable founda- ago, this uncertainty led me to undertake a tion for the computational theory of long-term investigation of the foundations of mind—the thesis, sometimes known as “cog- computer science and artificial intelligence. nitivism,” that underlies artificial intelligence That study is now largely complete. My aim in and cognitive science. this paper is to summarise some of the results.1 The first, empirical, requirement, of doing justice to practice, helps to keep the analysis 1. Project grounded in real-world examples. It is hum- bling, too, since the computer revolution so reli- The overall goal has been to develop a compre- ably adapts, expands, dodges expectations, and hensive theory of computation. Since the outset, in general outstrips our theoretical grasp. But I have assumed that such an account must meet the criterion’s primary advantage is to provide a three criteria: vantage point from which to question the legit- imacy of all extant theoretical perspectives. For I 1This paper is largely excerpted from, and is intended to take it as a tenet that what Silicon Valley treats serve as an introduction to, a series of books that collec- as computational, is computational; to deny that tively report, in detail, on the study identified in the would be considered sufficient grounds for re- opening paragraphs. The study of computing is presented jection. But no such a priori commitment is in The Age of Significance: Volumes I–VI (Smith, forthcom- ing); the metaphysical territory to which that study leads, given to any story about computation—includ- in On the Origin of Objects (Smith 1996). ing the widely-held Turing-theoretic conception Copyright © 1996 Brian Cantwell Smith *Brian Cantwell Smith <[email protected]> T H E F O U N D A T I O N S O F C O M P U T I N G of computability that currently goes by the equate theory of computation must provide a name “the theory of computation.” I also reject tenable foundation for a theory of mind, is of a all proposals that assume that computation can somewhat different character. Like the second, be defined. By my lights, an adequate theory it is more a metatheoretic requirement on the must make a substantive empirical claim about form or status of the theory than a constraint on what I call computation in the wild:2 that erup- substantive content. In committing myself to tive body of practices, techniques, networks, honor the criterion, however, I make no ad- machines, and behavior that has so palpably vance commitment to cognitivism’s being true revolutionized late twentieth century life. or false. I just want to know out what it says. The second, “conceptual” criterion, that a That is not to say that the content of cogni- theory own up to—and as far as possible re- tivism is left open. Cognitivism’s fundamental pay—its intellectual debts, is in a way no more thesis—that the mind is computational—is than standard theoretical hygiene. But it is im- given substance by the first, empirical criterion. portant to highlight, for two intertwined rea- Cognitivism, that is—at least as I read it—is not sons. First, it turns out that several candidate a theory-laden proposal, in the sense of framing theories of computing (including the official specific hypotheses about what computers are. mathematical “theory of computation” taught Rather, it has more an ostensive character: that in computer science departments), as well as people (i.e., us) are computers in whatever way many of the reigning but largely tacit ideas that computers (i.e., those things over there) are about computing held in surrounding disci- computers, or at least in whatever way some of plines,3 implicitly rely, without explanation, on those things are computers. such substantial, recalcitrant notions as repre- It follows that any theoretical formulation of sentation and semantics. Second, which only cognitivism is doubly contingent. Thus consider makes the matter worse, there is a wide-spread Newell and Simon’s (1976) popular “physical tendency throughout the surrounding in- symbol system hypothesis,” according to which tellectual terrain to point to computation as a human intelligence is claimed to consist of possible theory of those very recalcitrant notions. physical symbol manipulation, or Fodor’s (1975, Unless we ferret out all such dependencies, and 1980) claim, that thinking consists of formal lay them in plain view, we run the risk of en- symbol manipulation, or Dreyfus’ (1993) asser- dorsing accounts that are either based on, or tion that cognitivism (as opposed to connec- give rise to, vicious circularity. tionism) requires the explicit manipulation of The third “cognitive” condition, that an ad- explicit symbols. Not only do these writers make a hypothetical statement about people, that 2Borrowed from Hutchins’ Cognition in the Wild (1995). they are physical, formal, or explicit symbol 3A notable example of such a far-from-innocent assump- manipulators, respectively; they do so by mak- tion is the common idea that “computation” is the funda- ing a hypothetical statement about computers, mental notion, with a “computer” simply being any phy- that they are in some essential or illuminating sical device that carries out a computation. It turns out, on spection, that this assumption builds in a residually way characterisable in the same way. Because I dualist stance towards the mind/body problem—some- take the latter claim to be as subservient to em- thing I eventually want to argue against, and probably not pirical adequacy as the former, there are two a claim that anyone should want to build into their theo- ways in which these writers could be wrong. In ries as a presumptive but inexplicit premise. Page 2 Copyright © 1996 Brian Cantwell Smith T H E F O U N D A T I O N S O F C O M P U T I N G claiming that people are formal symbol ma- 4. Digital state machines (DSM): the idea of nipulators, for example, Fodor would naturally an automata with a finite disjoint set of inter- be wrong if computers were formal symbol ma- nally homogeneous machine states—as paro- nipulators and people were not. But he would died in the “clunk, clunk, clunk” gait of a also be wrong, even though cognitivism itself 1950’s cartoon robot; might still be true, if computers were not formal 5. Information processing (IP): what is in- symbol manipulators, either. volved in storing, manipulating, displaying, In sum, cognitive science is, like computer and otherwise trafficking in information, science, hostage to what I call the constitutive whatever that might be; and project: formulating a true and satisfying theory 6. Physical symbol systems (PSS): the idea, of computing that honors these three criteria. made famous by Newell and Simon, that, Needless to say, no one of them is easy to meet. somehow or other, computers interact with (and perhaps also are made of) symbols in a 2. Six Construals of Computation way that depends on their mutual physical embodiment. Some might argue that we already know what computation is. That in turn breaks into two By far the most important step in getting to the questions: (i) is there a story—an account that heart of the foundational question, I believe, is people think answers the question of what com- to recognize that these construals are all concep- puters are; and (ii) is that story right? tually distinct. In part because of their great fa- With regards to the first question, the an- miliarity (we have long since lost our inno- swer is not no, but it is not a simple yes, either. cence), and in part because “real” computers More than one idea is at play in current theo- seem to exemplify more than one of them—in- retic discourse. Over the years I have found it cluding those often-imagined but seldom-seen convenient to distinguish six construals of com- Turing machines, complete with controllers, putation, each requiring its own analysis: read-write heads, and long tapes—it is sometimes uncritically thought that all six can be 1. Formal symbol manipulation (FSM): the viewed as rough synonyms, as if they were dif- idea, derivative from a century’s work in for- ferent ways of getting at the same thing. Indeed, mal logic & metamathematics, of a machine this conflationary tendency is rampant in the manipulating symbolic or (at least poten- literature, much of which moves around among tially) meaningful expressions without regard them as if doing so were intellectually free. But to their interpretation or semantic content; that is a mistake. The supposition that any two 2. Effective computability (EC): what can be of these construals amount to the same thing, done, and how hard it is to do it, mechani- let alone all six, is simply false.

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