on "What Is Computing?"

Last Update: 22 April 2010
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Smith, Brian Cantwell (2002),
"The Foundations of Computing",
in
Scheutz, Matthias (ed.), *Computationalism: New Directions* (Cambridge,
MA: MIT Press): 23–58.
(*)

- 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.

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

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

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

- 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".]

- [By "intentionality", I think Smith means what
the 19th-century cognitive scientist
Franz Brentano
meant,
**(C1)**However,*none*of the following provide such a theory:**effective computability**;

—what can, can't, or is impractical to be done by abstract machine**execution of algorithms, or rule following**

(including recipes)**calculation of functions**

—behavior of taking I/P & producing O/P**digital state machines**

—automata with finite sets of states**information processing**

—storing, manipulating, displaying "information"**physical symbol systems**

—computer's interaction with symbols depends on physical implementation**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
- Computers get I/P from, & must act in (i.e., produce O/P to), the real world.
- 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.

- some
computer-

- i.e., the syntax and semantics of
real-world computational processes intersect

**(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.)]

- [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
- 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.]

- [Perhaps related to Simon's theory of how to
analyze complexity "hierarchically", i.e., recursively; see Simon, Herbert A. (1962),
"The Architecture of Complexity",

- anti-semantic

**(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

- [syntax concerns mark-manipulation;
**(C7)**A theory of computation needs a full theory of ontology- For a beginning, see Smith 1996.

**(C8)**- Computers are not natural kinds.
- There can be no theory of computation.

**(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!

(*) For a critique of Smith 2002, see: DeJohn, Jerry; & Dietrich, Eric (2003), "Editorial: Subvert the Dominant Paradigm! A Review of Computationalism: New Directions, edited by Matthias Scheutz",

Copyright © 2004–2010 by William J. Rapaport (rapaport@buffalo.edu)

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