Representationalism in cognitive science holds that semantic meaning should
be explained by representations in the mind or brain. In this paper it is
argued that semantic meaning should instead be explained by an abstract the
ory of semantic machines - machines with predicative capability. The concep
t of a semantic machine (like that of a Turing machine or of Dennett's "int
entional systems'') is not a physical concept - although it has physical im
plementations. The predicative competence of semantic machines is defined i
n terms of independent agreement alone (cf. independent, and yet synchronis
ed, clocks). Abstract theories are analysed as systems of quasi-apriori rul
es for abstract predicates. A relatively limited number of such theories an
d a few fundamental dimensions (space, time, mass, etc.) are today assumed
to exhaust physical reality. However, that assumption need not be in confli
ct with predicates that cannot be defined in physical terms - for instance
the functional and intentional terms that are crucial for cognitive science
.