This is mostly for my own purposes; I wanted a more readable format than in Shepherd's own nineteenth century publication, and putting it here makes it easily accessible. This is from An Essay upon the Relation of Cause and Effect, pp. 131-135. The second, fourth, and sixth play some important roles in Shepherd's attack on Hume's account of causation; but, interestingly, none of these failings are Shepherd's primary point of attack -- it's the development of Shepherd's own account of causation that does most of the work in her criticism.
I appeal to those who are acquainted with Mr. Hume's Essays, if this statement be not the sum of the argument—and I also appeal to every man capable of logical accuracy, if it doth not involve every species of illogical sophistry; for,
1st.—There is drawn a general negative conclusion; from an examination of particular instances only. If the adversary may not draw from particular experience the general affirmative conclusion, that there is a necessary connexion; neither can Mr. Hume infer a general negative position, that there is not a necessary connexion between Cause and Effect. He also deduces a general affirmative conclusion, viz. "that the future shall invariably resemble the past; from particular instances only.
2dly.—The mind is directed to infer a conclusion against the general relation of Cause and Effect, by the demonstration of a proposition in nowise inconsistent with it; namely, that like sensible qualities, NOT being like Causes, might be followed by DIFFERENT Effects.
3dly.—A general negative conclusion is in fact drawn from negative premises, merely;—(however the illogical method may be disguised both as to manner and diction), for it is concluded there is no proof for the existence of the general relation of Cause and Effect between objects ;— because experience shows that like sensible qualities are not like Causes; and are therefore not necessarily connected with like Effects!
4thly.—The question is shifted from the examination of the general relation of Cause and Effect, to that of the criterion for ascertaining the presence of like Causes.
5thly.—The very proposition is admitted, which is in dispute; in order to serve the purpose of his argument;—first, in the statement that impressions are the productive Causes of ideas;—secondly, in supposing the secret powers of an object to be alone the real productive Causes of its future properties;—thirdly, in conceiving Nature may alter her course for the express purpose of changing the secret powers; and that they are changed by such alteration; —and lastly, in alleging custom to be the sole Cause (i. e. producing generating principle) of the IDEA of causation.
6thly.—The proposition that the course of nature may be supposed to change, is used ambiguously, signifying indifferently either an uncaused alteration of the SUBSEQUENT sensible qualities or of the ANTECEDENT secret powers.
7thly, and lastly.—The two chief propositions of the argument are in opposition to each other; for Mr. Hume attempts to establish, that CUSTOM not reason is the principal of causation, whilst he allows Reason to be the sole ground and necessary Cause of this belief.
In presenting the foregoing observations to the reader's attention, I have endeavoured, I hope, without presumption, to show that Mr. Hume's reputation for logical correctness has been overrated. The effect of his work is to astonish by its boldness and novelty;—to allure us by its grace and lightness; his propositions are arranged so artfully, that their illogical connexion is not perceived, and the understanding, without being satisfied, is gradually drawn into inferences from which it would gladly but cannot readily escape.