One of Shepherd's key complaints against Hume has to do with his attempt to make causal reasoning entirely a matter of custom rather than reason, in the sense that the basic causal principle (for every beginning of existence there must be a cause) is not due to reason but to custom. She attempts to show, contrary to this, that the basic causal principle is due to reason, in combination with what she calls an experimentum crucis. Her analysis of our causal reasoning goes something like this:
1. A new quality appears to my senses.
2. New qualities are differences; and thus the appearance of a new quality is the introduction of a difference; the introduction of a difference is causation.
3. This new quality could not be caused by itself (it would not then be an introduced difference).
4. In the environment of this new quality there are not any surrounding objects except such-and-such object(s) that could affect it.
5. Therefore such-and-such occasioned it, because there is nothing else to make a difference and a difference cannot begin of itself (3 and 4).
This is a rough characterization, although it is very close (see Cause and Effect pp. 43-44); it is one of the many things in Shepherd scholarship that has not yet been adequately examined.
She says of her analysis (p. 44):
This is an argument, which all persons, however illiterate, feel the force of. It is the only foundation for the demonstrations of the laboratory of the chymist; which all life resembles, and so closely, in many instances, that the philosopher, and the vulgar, are equally sure of what cause is absolutely necessary to the production of certain effects; for instance, each knows that in certain given circumstances, the closing of the Eye will eclipse the prospect of nature; and the slight motion of reopening it, will restore all the objects to view. Therefore, the Eye (in these circumstances,) is the Cause or Producer of vision.
She is insistent that, in general, only one trial is necessary. It is because of this that she uses the term 'experimentum crucis', which is used also by Boyle and Newton, and indicates a single experiment sufficient to decide an issue. Because only one trial is necessary, our causal reasoning cannot be based on custom. On the basis of this 'reasoning upon experiment' we derive the notion of 'power'.
(3) is a significant move in the analysis, so it is worthwhile to look more closely at her reasoning on this point. Suppose we have an object that 'begins its existence of itself', i.e., just begins, uncaused. This beginning of an object is "an action, which is a quality of an object not yet in being, and so not possible to have its qualities determined, nevertheless exhibiting its qualities" (p. 35). In other words, she thinks "beginning to be, uncaused" involves a contradiction; beginning to be is necessarily an introduction of a difference, and therefore requires something from which it may be introduced. As she puts it elsewhere, objects cannot begin their existences except as having the nature of effects.
One of the criticisms Shepherd makes of Hume is that he attempts to distract from this conclusion by shifting suddenly from the question of the existence of the causes to the question of how the nature of the causes may be determined. It is this sort of sophistry, she thinks, that enables him to pretend that "whatever begins to exist has a cause" is not a necessary truth.
The above analysis connects with her account of causation as mixture of qualities through her conception of what is involved in introducing a difference (p. 63):
A Cause, therefore, is such an object, as shall enable it, in conjunction with another, to form a new nature, capable of exhibiting qualities varying from those of either of the objects unconjoined. This is really to be a producer of new being....An Effect is the produced quality exhibited to the senses, as the essential property of natures so conjoined....An object may be defined, a combined mass of qualities; the result of proportional unknown circumstances in nature, meeting with the human senses.
(I'm not sure whether these are to be taken as definitions in strict generality, or as accurate descriptions under normal conditions. Yet one more thing that needs to be studied.)