Brian Cantwell Smith

Project on the foundations of computing

Many mainstay notions of programming practice remain in need of adequate conceptual analysis: symbol, representation, algorithm, information, effectiveness, implementation, object, abstraction, modularity, data, etc. The aim of the Foundations of Computing project is to develop a richly-textured foundational theory of computing that makes explicit our tacit understanding of these notions-intuitions that run deep in any working programmer. The first phase of the project involves analyzing six reigning models of computation: the Turing-theoretic notion of effective computability, cognitive science's conception of formal symbol manipulation, intuitions about rule-following and algorithm execution, the idea of a digital or discrete state machine, several models of information processing, and Newell & Simon's notion of a "physical symbol system". In spite of various well-known equivalence proofs, these models are all conceptually distinct, rest on separate intellectual footings, and apply to different real-world phenomena. Critical analysis shows, moreover, that not one of these models, nor any group in combination, can simultaneously meet three key criteria: (a) empirical adequacy, in the sense of doing justice to extant computational practice (e.g., explaining Microsoft Word); (b) conceptual adequacy, in the sense of discharging all unpaid intellectual debts, such as to semantics; and (c) cognitive adequacy, in the sense of explaining the content of the computational theory of mind. Nevertheless, the models rest on important intuitions and insights: such as about the constraints of concrete mechanism (implicit in the effective computability construal), and about the non-efficacy of at least some aspects of semantics (constitutive to the notion of formal symbol manipulation). The second phase of the project is to formulate a tenable alternative theory of computing, one that not only meets all three criteria, but also does justice to the intuitions underlying prior views. Achieving this goal, it is argued, requires developing a new metaphysics: one that, steering between realism and constructivism, provides new accounts of intentionality (semantics), ontology (objects), and "registration," a proposed replacement for the notion of representation. The results of the analysis of computation are being reported in a series of books, collectively entitled The Age of Significance: An Essay on the Foundations of Computation and Intentionality. The metaphysics to which the study has led is presented in On the Origin of Objects, M.I.T. Press, 1996.

Project on computational ontology

Real-world computer systems involve extraordinarily complex issues of identity. Often, objects that for some purposes are best treated as unitary, single, or "one", are for other purposes better distinguished, treated as several. Thus we have one program; but many copies. One procedure; many call sites. One call site; many executions. One product; many versions. One Web site; multiple servers. One url; several documents (also: several urls; one Web site). One file; several replicated copies (maybe synchronized). One function; several algorithms; myriad implementations. One variable; different values over time (as well as multiple variables; the same value). One login name; several users. And so on. Dealing with such identity questions is a recalcitrant issue that comes up in every corner of computing, from such relatively simple cases as Lisp's distinction between eq and equal to the (in general) undecidable question of whether two procedures compute the same function. The aim of the Computational Ontology project is to focus on identity as a technical problem in its own right, and to develop a calculus of generalized object identity, one in which identity -- the question of whether two entities are the same or different -- is taken to be a dynamic and contextual matter of perspective, rather than a static or permanent fact about intrinsic structure.