Comment by MarkusQ

This paper annoyed my when it first came out, and still does. Harnad sets arbitrarily high standards for what constitutes a symbol system by I) requiring that the rules must also be fully symbolic, II) everything must be "semantically interpretable", III) omitting _relations_ between symbols from the domain of discourse.

In doing so, he rules out much of mathematics (e.g. matrix multiplication, in which the elements have no meaning in isolation, geometry, where points, lines and lines are explicitly left undefined, formal logic, etc.). This "turtles all the way down" stricture largely creates the problem that he then addresses.