rapaport@cs.Buffalo.EDU (William J. Rapaport) (10/20/88)
UNIVERSITY AT BUFFALO
STATE UNIVERSITY OF NEW YORK
BUFFALO LOGIC COLLOQUIUM
GRADUATE GROUP IN COGNITIVE SCIENCE
and
GRADUATE RESEARCH INITIATIVE IN COGNITIVE AND LINGUISTIC SCIENCES
PRESENT
RAYMOND J. NELSON
Truman Handy Professor of Philosophy
Case Western Reserve University
CHURCH'S THESIS, CONNECTIONISM, AND COGNITIVE SCIENCE
Wednesday, November 16, 1988
4:00 P.M.
684 Baldy Hall, Amherst Campus
The Church-Turing Thesis (CT) is a central principle of contemporary
logic and computability theory as well as of cognitive science (which
includes philosophy of mind). As a mathematical principle, CT states
that any effectively computable function of non-negative integers is
general recursive; in computer and cognitive-science terms, it states
that any effectively algorithmic symbolic processing is Turing comput-
able, i.e., can be carried out by an idealized stored-program digital
computer (one with infinite memory that never fails or makes mistakes).
In this form, CT is essentially an empirical principle.
Many cognitive scientists have adopted the working hypothesis that the
mind/brain (as a cognitive organ) is some sort of algorithmic symbol-
processor. By CT, it follows that the mind/brain is (or realizes) a
system of recursive rules. This may be interpreted in two ways, depend-
ing on two types of algorithm, free or embodied. A free algorithm is
represented by any program; an embodied algorithm is one built into a
network (such as an ALU unit or a neuronal group).
CT is being challenged by connectionism, which asserts that many cogni-
tive processes, including perception in particular, are not symbol
processes, but rather subsymbol processes of entities that have no
literal semantic interpretation. These are parallel, distributed, asso-
ciative memory processes totally unlike serial, executive-driven, von
Neumann computers. CT is also being challenged by evolutionism, which
is a form of connectionism that denies that phylogenesis produces a
mind/brain adapted to fixed categories or distal stimuli (even fuzzy
ones). Computers deal only with fixed categories (either in machine
language, codes such as ASCII, or declarations in higher-level
languages). So, if connectionists are right, CT is false: there are
processes that are provably (I will suggest a proof) effective and algo-
rithmic but are not Turing-computable.
However, if CT in empirical form is true, and if the processes involved
are effective, then connectionism or, in general, anti-computationalism
is false.
A direct argument that does not appeal to CT but that tends to confirm
it is that embodied algorithm networks as a matter of fact are parallel,
distributed, associative, and subsymbolic even in von Neumann computers,
not to say super-multiprocessors. Finally, I claim that the embodied
algorithm network models are not only _not_ antithetical to evolutionism
but dovetail nicely with the theory that the mind/brain evolves through
the life of the individual.
REFERENCES
Edelman, G. (1987), _Neural Darwinism_ (Basic Books).
Nelson R. J. (1988), ``Connections among Connections,'' _Behavioral &
Brain Sci._ 11.
Smolensky, P. (1988), ``On the Proper Treatment of Connectionism,''
_Behavioral & Brain Sci._ 11.
There will be an evening discussion at a time and place to be announced.
Contact John Corcoran, Department of Philosophy, 636-2444 for further
information.