Boolean logic is a mathematical symbol system. There is a population of symbols organized into a state space, a set of primitive function mappings, a logic expression specifying a progression of primitive function mappings, and a set of rules of behavior to coordinate the flow of symbols from the state space through the progression of function mappings to resolve the logic expression. This passive symbol system is enlivened by an active agent that can manipulate the symbols in accordance with the rules, traditionally a mathematician with a pencil.

When a logic expression such as Figure 1.1 is enlivened by a mathematician, the logic expression and the mathematician form a complete expression that properly resolves. The mathematician, understanding the rules of behavior, coordinates the behavior of the symbolic expression with her pencil. She animates the symbols moving them from function to function, instantiating functions in the proper order when their input symbols are available. This coordination behavior is embodied in the mathematician's understanding of the rules of interpretation and is not explicit in the logic expression itself.

A function mapping simply specifies a mapping from input symbols to output symbols. Nothing is expressed about the presentation ...

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