There is a long standing debate in cognitive science regarding how best to understand computational capacities of connectionist systems and the brain.  One side of this debate advocates an approach to understanding the computational capacities of the brain would treat these systems as Turing-equivalent computers.  The other side of this debate urges that researchers treat these systems dynamically.  To treat connectionist systems dynamically, is to treat them as computing devices that are fundamentally different from Turing Equivalent computers.  Specifically, it involves, as Smolenski (1988) has suggested, treating these systems as ones in which computation occurs according to differential equations describing the numerical evolution of the activation patterns--not by means of the recursive application of a finite set of read/write rules for manipulating symbols.  (I ignore a third position, dynamic systems theory as it is non-computational in approach.)  In this paper I review in principle arguments found in the philosophical literature against treating connectionist systems as dynamic systems.  I suggest that these arguments fail to establish their intended conclusion.  My overridding theme in reviewing these arguments is that they conflate issues concerning theoretical characterizations of computing with issues concerning finite instantiations of theoretically decribed systems.  I then explore two arguments for treating connectionist systems dynamically.  One of these arguments settles decisively the question of theoretic non-equivalence between connectionist systems and Turing-equivalent systems.  The second argument speaks decsively for treating connectionist systems as finite instantiations of dynamically described systems.