Brian Cantwell Smith
on "What Is Computing?"

Smith, Brian Cantwell (2002), "The Foundations of Computing", in Scheutz, Matthias (ed.), Computationalism: New Directions (Cambridge, MA: MIT Press): 23–58. (*)

1. The major question in the philosophy of computer science is:
   • What is computation?

   and the answer is that it is a lot more than the theory of Turing machines.

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2. Computing is:
   1. empirical
      • "computation in the wild" includes every aspect of the nature and use of computing and computers
      • [including things like iPads and Facebook]

   2. conceptual
      • computing and computers are intimately related to issues in semantics (interpretation, representation)
      • [TMs probably fit in here]

   3. cognitive
      • theory of computation must provide a foundation for theory of mind (computational cognitive science)
      • [TT & CRA fit in here]

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3. 9 Theses about Computation:
   • (C2) A theory of computation needs a full theory of semantics and intentionality.
     • [By "intentionality", I think Smith means what the 19th-century cognitive scientist Franz Brentano meant,
       namely: "directedness to an object", i.e., "being about something".]

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   • (C1) However, none of the following provide such a theory:

     1. effective computability;
        —what can, can't, or is impractical to be done by abstract machine

     2. execution of algorithms, or rule following
        (including recipes)

     3. calculation of functions
        —behavior of taking I/P & producing O/P

     4. digital state machines
        —automata with finite sets of states

     5. information processing
        —storing, manipulating, displaying "information"

     6. physical symbol systems
        —computer's interaction with symbols depends on physical implementation

     7. formal symbol manipulation by machine without regard to meaning
        • (C3)
          • Formal symbol manipulation separates the syntactic and semantic domains
          • But real-world computational processes are "participatory"
            • i.e., the syntax and semantics of real-world computational processes intersect
              1. Computers get I/P from, & must act in (i.e., produce O/P to), the real world.

              2. Computers are part of the real-world
                 • some computer-internal symbols refer to other computer-internal symbols, some to external objects;
                 • some computer-external symbols refer to computer-internal ones, some to other external objects.

        • (C6) Computation is not formal in any of the following senses of "formal":
          • anti-semantic
            • syntax is independent of semantics

          • syntactic
            • e.g., proof-theory only relies on pattern matching and symbol manipulation

          • determinate or well-defined (i.e., not vague),
            • e.g., digital or discrete

          • mathematical
            • [Russell: "Pure mathematics consists entirely of such asseverations as that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing…. It's essential not to discuss whether the proposition is really true, and not to mention what the anything is of which it is supposed to be true…. If our hypothesis is about anything and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."
              ( Mysticism and Logic (1917), Ch. 4.)]

          • analytic method
            • [Perhaps related to Simon's theory of how to analyze complexity "hierarchically", i.e., recursively; see Simon, Herbert A. (1962), "The Architecture of Complexity", Proceedings of the American Philosophical Society 106(6) (December 12): 467–482; reprinted as Simon 1996, Ch. 8.]

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   • (C4) TMs don't use marks to represent numbers;
              they use numbers to represent marks!
     • [syntax concerns mark-manipulation;
       the real world of math concerns number-manipulation
       (semantics is the study of the relation between them)]

     • ["In science, we use numbers to represent ‘stuff’
       computation only studies marks"]

     • Corollary:
       The theory of computation is "a theory [i.e., a language] of how … patches of the world in one physical configuration [can] change into another physical configuration" (p.42)

     • (C5) I.e., computability theory is a mathematical theory of the flow of causality

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   • (C7) A theory of computation needs a full theory of ontology
     • For a beginning, see Smith 1996.

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   • (C8)
     1. Computers are not natural kinds.
     2. There can be no theory of computation.

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   • (C9) Therefore, the existence of computation is extremely important,
              because any theory of it will be a theory of intentional artifacts, hence a theory of everything!