Cartesianism in the form of occasionalism does involve miracle, for though God is said by it to act according to laws in conforming body and mind to one another, he thereby causes them to act beyond their natural capacities.

3.  On the problem, how can the simple act otherwise than uniformly?

Leibniz distinguishes:  some uniform action is monotonous, but some is not.  A point moves uniformly in describing a parabola, for it constantly fulfils the formula of the curve.  But it does not move monotonously, for the curve constantly varies.  Such is the uniformity of the action of simple substances.

Bayle read this reply, and was pleased but not satisfied with it.  In the second edition of the dictionary, under the same article ‘Rorarius’, he added the following note: 

’I declare first of all that I am very glad I have proposed some small difficulties against the system of that great philosopher, since they [38] have occasioned some answers whereby that subject has been made clearer to me, and which have given me a more distinct notion of what is most to be admired in it.  I look now upon that new system as an important conquest, which enlarges the bounds of philosophy.  We had only two hypotheses, that of the Schools and that of the Cartesians:  the one was a way of influence of the body upon the soul and of the soul upon the body; the other was a way of assistance or occasional causality.  But here is a new acquisition, a new hypothesis, which may be called, as Fr. Lami styles it, a way of pre-established harmony.  We are beholden for it to M. Leibniz, and it is impossible to conceive anything that gives us a nobler idea of the power and wisdom of the Author of all things.  This, together with the advantage of setting aside all notions of a miraculous conduct, would engage me to prefer this new system to that of the Cartesians, if I could conceive any possibility in the way of pre-established harmony.

’I desire the reader to take notice that though I confess that this way removes all notions of a miraculous conduct, yet I do not retract what I have said formerly, that the system of occasional causes does not bring in God acting miraculously. (See M. Leibniz’s article in Histoire des Ouvrages des Savants, July 1698.) I am as much persuaded as ever I was that an action cannot be said to be miraculous, unless God produces it as an exception to the general laws; and that everything of which he is immediately the author according to those laws is distinct from a miracle properly so called.  But being willing to cut off from this dispute as many things as I possibly can, I consent it should be said that the surest way of removing all notions that include a miracle is to suppose that all created substances are actively the immediate causes of the effects of nature.  I will therefore lay aside what I might reply to that part of M. Leibniz’s answer.