On Newton's Third Rule of Reasoning in Philosophy, “the Universal Qualities of All Bodies Whatsoever," and the Speciation of Physical Systems

Erik Curiel

Ludwig-Maximilians-Universität München

Abstract: 
At the beginning of Book Three of Principia, Newton proposes his “Rules of Reasoning in Philosophy”. Rules I, II and IV are incisively brief, both in the statement of the rules themselves and in their attendant scholia. Rule III, by contrast, is considerably more com- plex in its statement, and bears a scholium more than 6 times the length of the scholia of the other three rules combined. Clearly, something rich is in the offing. I quote the rule in full: The qualities of bodies, which admit neither intensification nor remission of degree, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever. In order to understand the Rule, we must get straight on three predicates possibly at- tributable to qualities of bodies, namely, ‘admits neither intensification nor remission of degree', `belongs to all bodies within the reach of our experiments', and `is universal', and, in particular, we must get straight on why a quality's satisfaction of the first two predicates implies its satisfaction of the third. Grasping the meaning of the latter two predicates prima facie poses no serious problem (though I shall argue that there are in fact serious subtleties involved in working out their full purport). The first predicate, to the contrary, has no trivial, obvious significance, much more one with obvious application to the question of the universality of a quality that may or may not satisfy the predicate. I claim that a proper interpretation and explication of the Rule, with particular attention to the meaning of those three predicates and the relations among them, points the way to important insights about the way that physical theories allow for the speciation of physical systems - why it is, e.g., that we think the physical system occupying that region of spacetime is a Navier-Stokes fluid and not a Maxwell field, and in particular why it is a given species of Navier-Stokes fluid rather than another (e.g., liquid water rather than gaseous Nitrogen). (In more traditional terms, this is to ask how physical theories allow one to categorize systems as instances of a “natural kind”.) The Third Rule, I argue, expresses in concise yet exhaustive terms (albeit, after slight emendation) the fundamental notions on which a proper understanding of such speciation ought to be founded. In particular, the notion of universal quality that Newton characterizes is most properly understood, in contemporary terms, as that of a kinematic quantity in the context of a theory of mathematical physics, those, in other words, one assumes for the sake of the investigation at hand to remain constant throughout and the same across all the system's dynamical evolutions (as opposed to its dynamic quantities, which in general vary over the course of its dynamical evolutions). One way to see this is to note that the kinematic quantities of a physical system accrue to its representative space of states as a whole in a theoretical representation of it, and not to any individual state (as the dynamic quantities do)|the kinematic quantities serve to differentiate otherwise formally isomorphic spaces of states (and the spaces of states, e.g., of all Navier-Stokes fluids are indeed formally isomorphic, water's the same as Nitrogen's). In other words, the kinematic quantities are precisely those that “admit neither intensification nor remission of degree" relative to a particular species of physical system. The emendation to Newton's Rule required to defend this interpretation turns, I argue, on a proper comprehension of the predicate ‘belongs to all bodies within the reach of our experiments': one must restrict attention to those experiments that can appropriately and adequately be modeled using the theory relevant to the investigation at hand.