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 ...

This essay explores the implications of the thesis that implementation is semantic interpretation. Implementation is (at least) a ternary relation: I is an implementation of an ‘Abstraction ’ A in some medium M. Examples are presented from the arts, from language, from computer science and from cognitive science, where both brains and computers can be understood as implementing a ‘mind Abstraction’. Implementations have side effects due to the implementing medium; these can account for several puzzles surrounding qualia. Finally, an argument for benign panpsychism is developed.