Christopher Hitchcock
California Institute of Technology
It is a familiar moral from the philosophy of science that the tools that are available to represent various phenomena can shape the ways that we think about those phenomena. Newton believed that he needed an absolute rest frame in order to permit absolute acceleration, in part because he lacked the mathematical resources to represent affine connections on a spacetime manifold. The notion of a superposition in quantum mechanics became intelligible, in part, because superpositions can be represented as vectors in a Hilbert space.
In this paper, I consider a mode of representation that has been widely used by philosophers to represent systems of causal relations: neuron diagrams. These diagrams depict 'neurons' connected by stimulatory and inhibitory connections. I argue that this mode of representation has impeded progress in the study of causation for a number of reasons:
I. The role of neuron diagrams is ambiguous. Sometimes they are used to depict particular causal networks (perhaps not real neurons, but something like them), which are then used to test our intuitions about causation. At other times, they are used as an abstract form of representation for more general causal networks.
II. The diagrams are characterized in causally loaded terms — 'stimulatory' and 'inhibitory' connections — and so cannot be used to solicit pre-theoretic intuitions about what causes what.
III. 'Standard' neuron diagrams can represent only a limited variety of causal networks; those consisting of binary variables with 'or' or 'nand' gates. Additional conventions are easily adopted ad hoc (e.g. 'thick' neurons which must be stimulated twice before firing). However, it does not take many ad hoc additions of this sort before neuron diagrams completely lose their utility as perspicuous representations of causal systems.
IV. Since new types of causal connections require ad hoc modifications to the representational conventions, neuron diagrams are of no heuristic value in suggesting unforeseen possibilities.
V. The construction of neuron diagrams seems to be guided by implicit metaphysical assumptions. For example, in no neuron diagram is the following ever seen: a neuron that has arrows into it fires, even though none of its 'input' neurons does. This seems to embody a kind of principle of sufficient reason. But this principle is never stated explicitly, let alone defended.
VI.
The convention that one node in the diagram corresponds to one neuron and also
to one event is invidious. How do we represent a case in which the same neuron
fires (or might fire) on two different occasions?