Mandeville is probably the most influential, yet recently least read thinker of the last few centuries. Even pretended scholars (aka yours truly) are remarkably ignorant of his writings. This despite the fact that we can reliably guess that his works were open on the table when some of the most important passages in Hume, Berkeley, Hutcheson, Rousseau, Smith, Helvetius, and Reid were written. Hayek's (1966) endorsement of Mandeville (as a great psychological thinker) probably doomed Mandeville's reputation. Here I want to focus on Mandeville's non-trivial role in reviving a Spinozistic suspicion about applying mathematics after the success of Newton had seemed to settle the issue.
A crucial passage in Spinoza's writings occurs in his so-called "Letter on the Infinite," written to Lodewijk Meyer (Rhijnsburg, 20 April, 1663):
“from the fact that we can limit duration and quantity at our pleasure, when we conceive the latter abstractedly as apart from substance, and separate the former from the manner whereby it flows from things eternal, there arise time and measure; time for the purpose of limiting duration, measure for the purpose of limiting quantity, so that we may, as far as is possible, the more readily imagine them. Further, inasmuch as we separate the modifications of substance from substance itself, and reduce them to classes, so that we may, as far as is possible, the more readily imagine them, there arises number, whereby we limit them. Whence it is clearly to be seen , that measure, time, and number, are merely modes of thinking, or, rather, of imagining. It is not to be wondered at, therefore, that all, who have endeavoured to understand the course of nature by means of such notions, and without fully understanding even them, have entangled themselves so wondrously, that they have at last only been able to extricate themselves by breaking through every rule and admitting absurdities even of the grossest kind. For there are many things which cannot be conceived through the imagination but only through the understanding, for instance, substance, eternity, and the like; thus, if anyone tries to explain such things by means of conceptions which are mere aids to the imagination, he is simply assisting his imagination to run away with him.”
There is, of course, a lot to say about this passage, which presupposes a Spinozistic distinction of knowing things by way of the epistemically inferior imagination (or confusedly, abstraction) and the epistemically privileged intellect. Somewhat surprising to modern readers (who think of Spinoza as infatuated with mathematical tools), perhaps, Spinoza insists that when we conceive nature with mathematical concepts, in particular in order to measure things, we are in the realm of the imagination. This line of argument made Spinoza an easy target for triumphant Newtonians. Even so, as late as the end of 1730s that supposedly most Newtonian of philosophers, David Hume, reinvents a version of the argument (Treatise, 184.108.40.206-31) in order to argue for the superior security and utility of the human sciences. As we know, Hume overplayed his hand here. As I remarked last week, the great naturalist, Buffon, conceded that the "union of mathematics and physics can be accomplished" in "astronomy and optic" as well as a few other, less useful subjects. Buffon cleverly uses Newton's insistence that the mathematization of nature proceeds in the first instance by way of abstraction from the senses as an argument against the utility of mathematics in most of the terrestrial sciences.
Last week I emphasized the possibility that Adam Smith also endorsed this line of argument. Mikko Tolonen (a very creative young, Finnish historian) called my attention to the third (1730) edition of one of Mandeville's bestsellers: A Treatise of the Hypochondriack and Hysterick Diseases, in Three Dialogues. [Note the link is to a reproduction of an earlier edition, where "Diseases" are "Passions."] Like Locke, Mandeville was a practicing physician; the work is a mixture of personal PR, public health, moral psychology, and philosophy.
Mandeville, grants that in mechanics and hydrostatics mathematics is very useful. And he grants that in (what we may label) fundamental research mathematical treatments are indispensable (178-9). But he denies that they are of any use in medical treatment at the time because "we are unacquainted with the figure and magnitude of innumerable particles that the causes of things are made of." (A variant of the argument is in Spinoza E2p24, but in context Mandeville offers an unspecified reference to Sydenham.) [I'll spare you a summary of the very amusing treatment of the dangers of fake exactitude in scientific purging and emetics!]
Moreover, Mandeville, offers a positive argument for the enduring popularity of mathematics in the human sciences: "The reason, therefore, why the mathematics are so highly recommended to all young students in general, is not so much the utility they are of in their studies, and to understand the business they are to follow, as that they are a modish science, the knowledge of which thought to be a fine accomplishment." (176)In particular, "to ingratiate themselves with the Publick; and that they hope from it to be sooner trusted with sick People, than they would be, if it was known that thy had never applied themselves to that science." (178) Mathematical skill is status enhancing among a public that seeks reassurance. Mandeville has not lost any relevance, despite our progress in sub-atomic knowledge.