Symbolism & Connectionism. An overview by Erik Borra For the course Philosophy of Mind 2003. What this talk is about. What is symbolism? The first computer metaphor. What is connectionism? The second computer metaphor. I’ll show you how they relate to the cognitive sciences
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At its core, the serial digital computer is a machine that manipulates symbols.
It takes individual symbols (or strings of symbols) as its input, applies a set of stored algorithms (a program) to that input, and produces more symbols (or strings of symbols) as its output.
These steps are performed one at a time (albeit very quickly) by a central processor. Because of this serial constraint, problems to be solved by the First Computer Metaphor must be broken down into a hierarchical structure that permits the machine to reach solutions with maximum efficiency.
a) there is difference between structurally atomic and structurally molecular representations (bv A or (A & B) )
b) structurally molecular expressions have syntactic constituents that are themselves either structurally molecular or are structurally atomic (hierarchical)
c) the semantic content of a (molecular) representation is a function of the semantic contents of its syntactic parts, together with its constituent structure. This is the same as saying symbolism is committed to ‘complex’ mental representations or ‘symbol structures’
Because classical mental representations have a combinatorial structure, it is possible for classical mental operations to apply to them by reference to their form. The result is that a paradigmatic classical mental process operates upon any mental representation that satisfies a given structural description and transforms it into a mental representation that satisfies another structural description.
Red(X) & Round(X) …
Color(X) -> Red(X) or Orange(X) Shape(X) -> Round(X) or …
Symbolism: graphical explanation
input = symbol(s) -> algorithms who work on input -> output = more symbol(s)
if (Orange(X) & Round(X) … ) then Orange(X)
if (Red(X) & Round(X) …) then Apple(X)
Mental relations have a combinatorial syntax and semantics
Structure sensitivity of processes
that there are absolute primitive simple elements (context-free) and logical relations in a subject who mirror the primitive elements and their relations of the world.
GOFAI made this an empirical claim. GOFAI would find these elements and relations.
The symbols that are manipulated by a serial digital computer are discrete entities. They either are or are not present in the input
the program also consists of discrete rules
discrete decisions, all that really counts is already there from the beginning
(functionalism; Frued, Gesell, Baldwin, Piaget …)
After a lot of years and a lot of effort it still doesn’t work well
Think about the red apple
There were philosophical objections against the theories on which symbolism was founded (Late Wittgenstein, Heidegger, …)
Maybe we would be better of if we could find a computational model (or class of models) in which it would be easier to organize and study the mutual constraints that hold between mental and neural development.
Connectionism: systems that can exhibit intelligent behavior without storing, retrieving, or otherwise operating on structured symbolic expressions
Connectionist networks are networks consisting of very large numbers of simple but highly interconnected “units “.
Certain assumptions are generally made both about the units and the connections: Each unit is assumed to receive real-valued activity (either excitatory or inhibitory or both) along its input lines. Typically the units do little more than sum this activity and change their state as a function (usually a threshold function) of this sum. Each connection is allowed to modulate the activity it transmits as a function of an intrinsic (but modifiable) property called its “weight”. Hence the activity on an input line is typically some non-linear function of the state of activity of its sources.
The behavior of the network as a whole is a function of the initial state of activation of the units and of the weights on its connections, which serve as its only form of memory.
The network is a dynamical system which, once supplied with initial input, spreads excitations and inhibitions among its units. In some types of network, this process does not stop until a stable state is achieved. To understand a connectionist system as performing a cognitive task, it is necessary to supply an interpretation. This is typically done by viewing the initial activations supplied to the system as specifying a problem, and the resulting stable configuration as the system’s solution to the problem.
Connectionist systems can be constructivist
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