First, some quotes from Newell and Simon's paper "Computer Science as Empirical Inquiry: Symbols and Search" which define the essential ideas of the Physical Symbol System Hypothesis:

The hypotheses states:

"A physical symbol system has the necessary and sufficient means for intelligent action."

A physical symbol system "consists of a set of entities, called symbols, which are physical patterns that can occur as components of another type of entity called an expression (or symbol structure). Thus, a symbol structure is composed of a number of instances (or tokens) of symbols related in some physical way (such as one token being next to another). At any instant of time the system will contain a collection of these symbol structures. Besides these structures, the system also contains a collection of processes that operate on expressions to produce other expressions: processes of creation, modification, reproduction and destruction. A physical symbol system is a machine that produces through time an evolving collection of symbol structures. Such a system exists in a world of objects wider than just these symbolic expressions themselves."

"Two notions are central to this structure of expressions, symbols, and objects: designation and interpretation."

"Designation. An expression designates an object if, given the expression, the system can either affect the object itself or behave in ways dependent on the object. ... In either case, access to the object via the expression has been obtained, which is the essence of designation."

"Interpretation. The system can interpret an expression if the expression designates a process and if, given the expression, the system can carry out the process. ...Interpretation implies a special form of dependent action: given an expression the system can perform the indicated process, which is to say, it can evoke and execute its own processes from expressions that designate them."

"Additional requirements involve completeness and closure. (1) A symbol may be used to designate any expression whatsoever. That is, given a symbol, it is not prescribed a priori what expressions it can designate. This arbitrariness pertains only to symbols; the symbol tokens and their mutual relations determine what object is designated by a complex expression. (2) There exist expressions that designate every process of which the machine is capable. (3) There exist processes for creating any expression and for modifying any expression in arbitrary ways. (4) Expressions are stable; once created they will continue to exist until explicitly modified or deleted. (5) The number of expressions that the system can hold is essentially unbounded."

     A physical symbol system defined as above is in the class of computational models defined by a Turing Machine. That is, it has a finite set of symbols which can be composed to form a potentially infinite set of expressions. And, at any point in time the system contains a collection of such symbol structures (cf. the contents of the tape). Further, this collection of symbol structures can be modified over time (cf. the rewriting of the tape).

     However, Newell and Simon emphasize two additional ideas; those of designation and interpretation. Both of these notions are further specifications on the role that symbol structures or expressions play within a symbol system. Designation is the idea that expressions can refer to something else. That is, a symbol is just a symbol is just a symbol is just a symbol...alla Gertrude Stein unless there is some sense in which the symbol serves the function of reference. This is needed because the concern is not simply with a device that computes, but rather with a device that behaves with reference to a world that is external to itself. A symbolic expression designates some object if the system's behavior with respect to this outer world is dependent on the object which is referenced. Intuitively, the idea is that intelligent action is realized in relation to some external world. Thus, to reason about how to act in this world requires that the system of symbol structures in some sense represent aspects of this external world.

     Interpretation is a further extension of this idea of the representational power of symbol structures. Here the idea is that a symbol structure or expression can in fact refer to a computational process that the system can interpret and carry out. This idea is familiar to us in the guise of a computer program. Viewed statically, a computer program is just a collection of expressions. But, if it is a valid program, then this set of expressions can be read and "turned into" a process that carries out the instructions represented by the program. This gives the system the ability to compose a potentially infinite set of programs that yield a potentially infinite set of processes for computing results from its possible inputs.