In broad terms the parity principle states that if there is equality with respect to governing behaviour, between the causal contribution of certain internal elements and the causal contribution of certain external elements, then there is no good reason to count the internal elements concerned as proper parts of the cognitive system while denying that status to the external elements concerned. Parity of causal contribution mandates parity of cognitive status. (Wheeler, 2010, p. 30).Now, as I read this, it is somewhat ambiguous. "Equality with respect to governing behavior" can mean
a) Equal insofar as two things (processes?) both govern behavior.
b) Equal insofar as two things (processes?) both govern behavior in the same way.
Wheeler, et al., can advance whatever theory of equality they wish, but I think Wheeler intends the second reading. So, then, the issue becomes what is meant by "in the same way". That's what the very current debates regarding "coarseness of grain" are all (mostly?) about. More on that tomorrow....