In discussing Thomas Brown's Observations on the Nature and Tendency of the Doctrine of Mr. Hume, Concerning the Relation of Cause and Effect, Shepherd develops at greater length her contention that the foundation of causal inference is reason rather than custom (Hume) or instinct (Brown).

To represent the relation of Cause and Effect, as A followed by B, is a false view of the matter. Cause and Effect, might be represented rather by A x B = C, therefore C is INCLUDED in the MIXTURE OF THE OBJECTS called CAUSE. If C arises once from the junction of any two bodies; C must upon every other like conjunction, be the result; because there is no alteration in the proportions of the quantities to make a difference;—C is really included in the MIXTURE of A and B, although, to our own senses, we are forced to note down (as it were) the SUM arising from their union, after the observance of their coalescence. In like manner the results of all arithmetical combinations are included in their statements; yet we are obliged to take notice of them separately and subsequently, owing to the imperfection of our senses, in not observing them with sufficient quickness, and time being requisite to bring them out to full view and apparent in some DISTINCT shape. Indeed my whole notion, of the relation of Cause and Effect, is aptly imagined, by the nature of the necessary results, included in the juxta-position of quantities.

But as long as Cause shall be considered ONLY as an antecedent; the FUTURE can never be proved to be included in the PAST, which yet is truly the case.—For when it comes to be observed, that Cause means, and really is the creation of NEW QUALITIES, (from new conjunctions in matter or mind,) then it is perceived that the future is "involved in the past;" for when existing objects are the same, they must put on SIMILAR QUALITIES; otherwise contrary qualities or differences would arise of themselves; and "begin their own existences," which is impossible, and conveys a contradiction in terms*. All that experience has to do, is to show us, by what passes within ourselves, that there is a contradiction in the supposition of qualities beginning their own existence; and A CONTRADICTION is never admitted in the relation of any ideas that present themselves. The very act of reasoning consists, in such a a comparison of our ideas, as will not permit of inconsistent propositions†; which would be the case, if "like Causes could produce other than like Effects."

So then REASON does establish this beautiful and certain proposition, which is the foundation of all our knowledge;--That like Causes must ever produce like Effects.

* No mathematical reasoning can ever be driven further back, than by showing that the contrary of an asserted proposition is a contradiction in terms.

† The beginning of every quality is perceved to be only a change, upon some objects already in existence; and therefore cannot convey the same notion to the mind, as the beginning of a quality supposed to be independent of other objects and NOT to be a change. THE BEGINNING OF EXISTENCE, therefore, cannot appear otherwise than contrary to the idea of its independency of those objects of which it is a change.

Lady Mary Shepherd, An Essay upon the Relation of Cause and Effect. T. Hookham (London: 1824) 141-144.