This essay continues my investigation of `syntactic semantics': the theory that, pace Searle's Chinese-Room Argument, syntax does suffice for semantics (in particular, for the semantics needed for a computational cognitive theory of natural-language understanding). Here, I argue that syntactic semantics (which is internal and first-person) is what has been called a conceptual-role semantics: The meaning of any expression is the role that it plays in the complete system of expressions. Such a `narrow', conceptual-role semantics is the appropriate sort of semantics to account (from an `internal', or first-person perspective) for how a cognitive agent understands language. Some have argued for the primacy of external, or `wide', semantics, while others have argued for a two-factor analysis. But, although two factors can be specified---one internal and first-person, the other only specifiable in an external, third-person way---only the internal, first-person one is needed for understanding how someone understands. A truth-conditional semantics can still be provided, but only from a third-person perspective.

What is the computational notion of "implementation"? It is not individuation, instantiation, reduction, or supervenience. It is, I suggest, semantic interpretation. This document is Technical Report 97-15 (Buffalo: SUNY Buffalo Department of Computer Science) and Technical Report 97-5 (Buffalo: SUNY Buffalo Center for Cognitive Science). 1 INTRODUCTION Consider the relationships among algorithms, computer programs, and the computers that execute them. An algorithm is (roughly) a procedure for computing a function (for more details, see Soare 1996; Rapaport, forthcoming). A program is a more specific and detailed textual expression of an algorithm, expressed in a programming language. Often, it is said that the program "implements" the algorithm. A computer process is an algorithm being executed (see Rapaport 1988, 1995; Smith 1997). It is a physical device (a computer) behaving in a certain way ; the way is described (or specified) by the program, and the physical device running the ...