As I understand it, the disjunction problem is how could a causal theory of inner representation account for mistaken identification of external objects or object types. For example, if I see a fox and mistakenly take it to be a dog (my internal representation of dog is activated) how is this possible? My internal representation of dog is created and henceforth activated by dogs, and a fox is not a dog. The conclusion seems to be that the inner representation is not of a dog but rather represents the disjunction fox-or-dog.
The suggested solution has two parts. First, an inner representation of a, say, dog, is not a unitary atom but is composed of a bunch of property representations, each a representation in its own right. In poor lighting condition, at a distance, when occluded (etc.) when I see a fox, it activates the property representations that are a subset of the property representations that collectively mean dog. So at this point what is activated is a subset of the property representations that mean either fox or dog (is a disjunction). But it is not a distinction between fox and dog. Fox and dog are represented by further – and between each other different - property representations that are not activated on this occasion (due to poor light, distance, occlusion etc).
Secondly, The activation of the dog representation may not be a causal consequence only of looking at the fox. What if I recently saw a film about dogs? What if have a pathological fear of dogs and tend to jump to conclusions about things that look like dogs but aren't? What I've just read a book about dogs? In other words, the causal antecedents of the activation of the dog representation might not be only current sensory input.
The errors of the disjunction problem being (1) inner representations of external object types are atomic when in fact they are actually a collection of property representations only a subset of which might be activated, and (2) the activation of an inner representation of an external object type may not be purely a result of a causal chain from the current environment to the brain.