Don't blame the tool

procedural semantics I have been concerned for some time with the question of how to overcome the limitations of a purely Tarskian seman’The old woman’s theory was that the world rested on the back of a giant turtle. When the sage asked what the tunle stood on, she replied that it stood on the back of an even larger tunle. When asked what that tunle stood on, she replied, “Ah Ha! It’s turtles all the way down!” tics in order to obtain a theory of meaning that could in principle be connected to the world in a way that a machine (or for that matter, a person) could use. Even in its most generous interpretation i.e., when the elements of the model are taken to be real world entities and the predicates are real world relations a Tarskian model theory gives an automaton nc; means for accessing or recognizing the real world instances and relationships that correspond to its internal symbols. This has led some to conclude that it is not necessary for the automaton to have a semantics for its notations that the meaning lies not in the observed system but in the observer. While this is probably the right characterization of the representational states of a mollusc or a thermostat, this posture, of course, still leaves us with no foundation for the semantics of our own symbols. I have argued elsewhere (Woods 1983) that any automaton with sufficient learning ability has a need for meanings that it can itself exploit. Specifically, it has.an advantage in its ability to learn if it has access to the meaning criteria of its terms. Procedural semantics, as I have used the term, refers to an evolving theory of meaning that extends the predicate calculus to meet the needs of a language-using or knowledge-learning automaton by identifying the semantics of its operators with abstract procedures (Woods 1981, 19866). The essence of the argument is that the logical operators and the quantifiers are already abstract procedures for assigning truth values toprocedures (Woods 1981, 19866). The essence of the argument is that the logical operators and the quantifiers are already abstract procedures for assigning truth values to expressions as a function of the truth values of their constituents. Procedural semantics extends these operations with additional abstract procedures for reasoning, calculation, and sensory-motor operations that can interact with concrete referents in the real world. This machinery permits one to characterize the meanings of symbols via abstract reasoning procedures that can ultimately connect them to the world through operations of reasoning and perception. Such a theory must include abstract procedures for various operations of attending, perceiving, and hypothetical reasoning and for initiating genuine sensory-motor actions in the real world (Woods 19866). A key component of a successful theory of procedural semantics is the notion of an abstract procedure. If we are to use procedures as a basis for meaning, then we do not want every syntactic detail of a low-level procedural definition to count as part of the meaning. The issue is similar to the motivation that led to Carnap’s concept of intension if we take extensional equivalence to define the meaning of a proposition, then there can be no difference in meaning between “the moon is made of green cheese or it isn’t” and “Sir Walter Scott is Sir Walter Scott.” Although these two sentences intuitively mean different things, both necessarily have the same extension, i.e., both are necessarily true. On the other hand. if we take the superficial syntactic form as tlie essence of the proposition then we have to consider the proposition “John likes Mary and Mary likes John” to have a different meaning from the proposition “Mary likes John and John likes Mary.” What is needed is a level of abstraction that lies between the two extremes. In the case of logical propositions, Carnap called such an entity an “intension.” In procedural semantics, an abstract procedure represents a similar intermediate level of abstraction between mere input-output equivalence and a detailed syntactic identity. Formally, an abstract procedure is an equivalence class of procedures, characterizing a level of abstraction at which any two members of the class are considered the same. Such a class can be identified by specifying one member of the class