University of Alberta Dictionary of Cognitive Science: Componentiality

The complex patterns produced by Jacquard’s loom are produced by processes that are mechanical, simple, repetitive – and local (Essinger, 2004). The entire pattern is defined by a sequence of punch cards. With each pass of the loom’s shuttle, weaving a set of threads together into a row, the only function of a punch card was to manipulate rods that controlled individual threads. In other words, each punch card only controlled small components of the overall pattern. While the entire set of punch cards represented the total pattern to be produced, this total pattern was neither contained in, nor required by, an individual punch card as it manipulated the loom’s rods. The finished product was a global pattern that emerged from a long sequence of simple, local operations on the pattern’s components.

In the Jacquard loom, punch cards control processes that operate on local components of the “expression” being weaved. The same is true of the physical symbol systems. Physical symbol systems are finite devices that are capable of producing an infinite variety of potential behavior. This is possible because the operations of a physical symbol system are recursive. However, this explanation is not complete. In addition, the rules of a physical symbol system are local or componential, in the sense that they act on local components of an expression, not on the expression as a whole.

For instance, one definition of a language is the set of all of its grammatical expressions (Chomsky, 1957). Given this definition, it is logically possible to treat each expression in the set as an unanalyzed whole to which some operation could be applied. This is one way to interpret a behaviorist theory of language (Skinner, 1957): each expression in the set is a holistic verbal behavior whose likelihood of being produced is a result of reinforcement and stimulus control of the expression as a whole. However, physical symbol systems do not treat expressions as unanalyzed wholes. Instead, the recursive rules of a physical symbol system are sensitive to the atomic symbols from which expressions are composed. The advantage of operating on symbolic components, and not on whole expressions, is that one can use a sequence of very basic operations (writing, changing, erasing, or copying a symbol) to create an overall effect of far greater scope than might be expected. As Henry Ford said, nothing is particularly hard if you divide it into small jobs. The power of physical symbol systems arises from their inherent componentiality. Some have argued that connectionist networks are less powerful because they are not componential (Fodor & Pylyshyn, 1988).

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