[1]
There is a terminological issue that needs to be raised at the outset to avoid confusion. Craver & Bechtel (2007; Craver 2008) usually, but not always, use S to refer to a mechanism. In contrast, I will always use S to refer to the system or entity exhibiting the explanandum phenomenon ψ, and I introduce the symbol M to refer to the responsible mechanism. I do this because M and S are clearly not identical. Moreover, they are (or at least appear to me) to be distinguished in this passage, at least on one reading. I think it is unfortunate that neither Craver nor Bechtel formally and consistently distinguish the system S and the mechanism M in their analysis, for reasons that will become clear at the end of this section. Here I’ll attempt to faithfully capture the essence of the Craver–Bechtel mechanistic framework, were it to have included this important distinction.
[2]
Note that within this framework “componential mechanism”, “constitutive mechanism”, and “compositional mechanism” are synonymous.
[3]
On my reading, the framework developed in (Craver 2008) implicitly assumes the weaker condition, although most likely not the stronger one. But for my purposes here it is not crucial to pin this down. If the framework does assume the weaker condition, what follows should be read as arguing (contra this model) that there are systems for which functional and spatial levels in fact dissociate. If it does not, then what follows should be read simply as offering an account of some of the possible functional relationships between mechanisms and systems, an issue not explored in the original analysis. Either path leads to the same recommended modification of the original model.
[4]
In the case of the action potential, one might mount the argument that the system that ψs is strictly speaking S + {the nominally non-S parts of M}, including the surrounding extracellular fluid. That would make M part of S in this case, but it is not clear to me that this move will be equally attractive in every such case, nor do I think the mechanist is forced to adopt this strategy.
[5]
In fact there are two classes of bipolar cells, “on” and “off”, functionally differentiated by their disposition to respond to stimulus onset vs. stimulus offset—i.e., one responds to light and the other to dark—and anatomically distinguished by whether they synapse onto the “on” or “off” level of the inner synaptic layer (Figure 4). As the mechanisms for direction selectivity in SAC dendrites are the same regardless, I’ll ignore this detail in what follows.
[6]
Thanks to an anonymous reviewer for pointing out this way of expressing the matter.
[7]
For instance, what explains why a neuron has a particular functional property cannot be an event involving the transmission of some property, power or conserved quantity from the parts of the neuron to the whole, because if causes must precede their effects, this would appear require that there be a time prior to which the neuron did not have the functional property conferred by its parts. Interlevel functional relationships do not generally appear to be temporal in this way.  Rather, for Craver and Bechtel, what explains the functional property of the neuron is the way it is constituted by its parts. Enabling constraints are also synchronic in the relevant way, and so the view I am advocating here is also able to accommodate such cases of interlevel functional relationships.