Green offers us two options: either connectionist models are literal models of brain activity or they are mere instruments, with little or no ontological significance. According to Green, only the first option renders connectionist models genuinely explanatory. I think there is a third possibility. Connectionist models are not literal models of brain activity, but neither are they mere instruments. They are abstract, IDEALISED models of the brain that are capable of providing genuine explanations of cognitive phenomena.
2. Given all this, one might think it reasonable to claim, as Green does, that "at present the only way of interpreting connectionist networks as serious candidates for theories of cognition, would be as literal models of the brain activity that underpins cognition" (1998, para. 20). However, while this claim is right in spirit, I think it seriously misleads, because it suggests that a connectionist network can only teach us about cognitive phenomena if it precisely models the brain circuits involved in those phenomena. And THIS suggests that connectionist research can only be productive if it proceeds at the same pace as detailed neural mapping. In my view, these suggestions do not amount to good methodological advice, not least because they ignore what the history of science teaches us.
3. Consider the development of Newton's programme for a planetary system. Lakatos (1978, pp.50-1) informs us that Newton first worked out his programme for a planetary system containing only a single point-like planet orbiting a fixed point-like sun. He then introduced the complication that, according to his own third law of dynamics, orbiting masses actually revolve around a common centre of gravity. Next he added further planets without including any interplanetary forces. Later he began treating planets and sun as mass-balls rather than mass-points. Later still he added spin, interplanetary forces, and non-spherical planets. (See Chalmers 1982, Chap.7, for further discussion.) Lakatos makes the point that despite early falsifications Newton continued to pursue his programme, and that it was rational to do so. Green correctly identifies one moral of all this (although he is dubious about its merits): that "new research programs need a grace period in the beginning to get themselves established" (1998, para.21). But there is another significant message here, which I don't think Green has fully taken on board: a theoretical model can produce useful causal explanations even when it only partially reflects the structure of the system we seek to understand. For example, Newton's simplest (and therefore least realistic) model of our planetary system -- a fixed point-like sun with a single point-like planet subject to an inverse square law of gravitation -- explains the elliptical nature of planetary orbits.
4. Consequently, it is an oversimplification to suppose that we have only two options regarding the interpretation of theoretical models: instrumentalism or out and out realism. Realism is not an all or nothing affair, as Dennett (1991) has pointed out. One can regard some features of a model realistically, and others as useful approximations or simplifications. When, for instance, Newton treats the sun and planets as point masses, he clearly does not intend this literally; but the other geometric property he ascribes to the solar system, namely, that the planets orbit the sun, is meant to reflect actual spatial relationships. This model is therefore not best interpreted as a mere instrument, with no purpose other than to corral a range of astronomical observations. But neither is it best interpreted in a completely realistic fashion. It corresponds with reality in some respects, and not in others.
5. What we see here is the significance of IDEALISATION in science. Idealisation occurs when some of the properties we ascribe to objects in a theoretical model are not genuine features of the objects modelled, but are introduced merely to "bring the objects modelled into the range of the mathematical theory" (Cartwright 1983, p.153). These properties are often limiting cases of real properties (e.g., frictionless surfaces, perfectly spherical planets), but sometimes they are pure fictions. The point to emphasise is that engaging in idealisation is NOT equivalent to adopting an instrumentalist attitude towards one's model. A certain amount of idealisation is consistent with a generally realist attitude towards a model, because there will typically be properties of the objects in the model that are intended as genuine features of the situation being modelled.
6. Applying these insights to connectionism has all sorts of payoffs. To begin with, there is at the heart of connectionism a kind of idealisation that strips away many of the known details of brain morphology and physiology to leave a rich but skeletal model of real neural networks. This model is the basis of the PDP computational framework: a distillation of key structural and functional features of neural networks, together with conjectures about the nature of representation and processing in the brain. Clearly, PDP does not engage a microstructurally realistic model of the brain, but rather a model that captures certain high-level characteristics of neural networks (those described in terms of units, connections, connection weights, activation patterns, and so forth), while ignoring lower level details. Strictly speaking, this is not idealisation as I have characterised it above, but an ABSTRACTION, whereby only the level of structure that is most plausibly associated with the brain's information processing capacities is modelled. The process of abstraction is not inconsistent with a realist interpretation of connectionist models. Connectionist models are best understood, in my view, as realistic treatments of certain (high-level) structural features of the brain.
7. Having said this, when one examines some of the prominent examples of connectionist models in the literature one is immediately struck by how implausible they are from the perspective of brain architecture. NETtalk (Sejnowski & Rosenberg 1987), for example, does not begin to model the structures responsible for grapheme-to-phoneme conversion in the brain, which presumably involves multiple networks scattered across a number of distinct systems (at least visual and motor, but probably auditory too). However, NETtalk was never intended as a serious model of a human competence. From the perspective of cognitive science, it is what we might call a TOY NETWORK: not a model of the brain, but a demonstration of what can be accomplished by a small network of neuron-like elements. Toy networks are very useful, because they allow us to explore a class of computational systems that are structurally isomorphic with the brain at a certain level of description. They illuminate the STYLE of computation in the brain, even if they fail to model any specific neural system (O'Brien 1998).
8. When connectionists turn from examining toy networks, and take up the serious business of modelling the brain as a complex, multi-network PDP system, a number of strategies are available to them: (1) accurately model small sections of cortex that have been mapped in detail; (2) produce architecturally faithful, but stripped down models of larger sections of cortex; (3) develop conjectural models of roughly or incompletely mapped brain regions. The first strategy generates what I'll call NEURAL MODELS. These preserve, or closely approximate, the neuron numbers and patterns of connectivity within real (but tiny) segments of neural tissue. Neural models enable one to investigate the processing characteristics of small networks in the brain, and, with a view to their systemic context, develop hypotheses about the information processing tasks they perform. The second and third strategies generate what I'll call SCALE MODELS. A connectionist scale model preserves the architectural details of cortical tissue -- for example, how many networks are involved, the broad features of inter-network connectivity, perhaps the rough intra-network layer structure -- without achieving a one-to-one match between units and neurons.
9. This set of connectionist modelling strategies is by no means exhaustive, but it highlights the important fact that the degree of realism we ought to accord a connectionist model varies enormously from case to case. When it comes to neural models, the aim is to achieve a high degree of realism at the level of description of units and connections. Scale models are not realistic at this level -- they idealise as regards neuron population sizes and the details of inter-neuron connectivity. An illustrative example is the stereoscopic vision network described by Churchland (1995, pp.71-9). Churchland's network may be treated as a tentative hypothesis about the neural structures responsible for human stereopsis. It coheres with what we know about these structures; and in tests on random-dot stereograms it has an impressive capacity (which we share) to recover figures that are hidden in the stereo pair (pp.74-7). There is no one-to-one match-up between units and neurons here. Churchland's model is not only scaled down, having too few units (by orders of magnitude), but it also contains fewer intra-network layers than the corresponding part of the brain. Even so, this model is nothing less than a tentative EXPLANATION of stereopsis, and one that may well be borne out by further investigation of the brain. Consequently, while I agree with the spirit of Green's claim that to be explanatory connectionist models must be "literal models of the brain activity that underpins cognition" (1998, par.20), I think we ought to treat the "literal" cautiously. Connectionist models are NOT literal models of brain activity. But neither are they mere instruments. They are abstract, idealised models of the brain that are capable of providing genuine explanations of cognitive phenomena.
 The historical order of events is the derivation of the inverse square law on the assumption that planets trace out Kepler's ellipse. (Lakatos 1978, p.50)
 As such it is open to revision in the light of new conjectures about the computationally salient features of neural networks (see O'Brien 1998). Moreover, precisely because the PDP framework employs an ABSTRACT structural model of the brain, it is capable of being applied to all sorts of information processing problems in AI where its neural origins are quite incidental to its usefulness and interest. Nevertheless, from the perspective of connectionism, I think the neural heritage is crucial, because if connectionism is not in the business of modelling the brain, then it is hard to take it seriously as a source of COGNITIVE theory.
 Admittedly, even here certain simplifications come into play. Connectionist models generally allow both inhibitory (negative weight) and excitatory (positive weight) connections to emanate from a single unit. Neurons are not like this; but this simplification is easily made good by introducing inhibitory interneurons that are actually seen in the brain (see Churchland 1995, pp.71-9 for a discussion in the context of his connectionist model of stereo vision).
 It also generates false correspondences and ignores equal luminance colour variations, both quirks of human stereo vision.
Cartwright, N. (1983) How the Laws of Physics Lie. Oxford University Press.
Chalmers, A. (1982) What is this thing called science? 2nd ed. University of Queensland Press.
Churchland, P.M. (1995) The Engine of Reason, the Seat of the Soul. MIT Press.
Dennett, D.C. (1991) Real patterns. Journal of Philosophy 88:27-51
Green, C.D. (1998) Are Connectionist Models Theories of Cognition? PSYCOLOQUY 9 (4) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/psyc.98.9.04.connectionist-explanation.1.green
Lakatos, I. (1978) The methodology of scientific research programmes. J. Worrall & G. Currie (eds.). Cambridge University Press.
O'Brien, G. (1998) The role of implementation in connectionist explanation. PSYCOLOQUY 9(6) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/psyc.98.9.06.connectionist-explanation.3.obrien
Sejnowski, T.J. & Rosenberg, C. (1987) Parallel networks that learn to pronounce English text,. Complex Systems 1:145-68.