The heading of this chapter requires further explanation: The title of the Paris edition of 1740 does not correspond to the title of the Amsterdam edition of 1742. The title of the Amsterdam edition is as follows: “From the Shape, Porosity and Solidity of the Bodies, and from the Causes of Cohesion, from the Hardness, Fluidity and Softness.” The paragraphs of both editions do not exactly match, too. The order is partly changed. Some of the paragraphs are missing in one or the other edition. Some paragraphs can be found in other chapters. In any case, the chapter opens with the statement that shape is a necessary attribute of bodies. Because every body is extended and has some boundaries, and all limited extension necessarily has a shape (InstPhy, § 184):

A figure est un attribut nécessaire du Corps; car on entend par Corps une étendue qui a bornes: or toute étendue terminée a nécessairement une Figure. (Amsterdam 1742)

Shape is a necessary attribute of Body; for one understands by Body extension that has some boundaries: now all limited extension necessarily has a Shape. (Copyright © 2018 KB)

[ Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ]

The Amsterdam edition of 1742, § 184 has the addendum: We cannot recognize the shapes of the small bodies that elude our senses. But our mind is no less certain that they are really there. Empty space, which seems to separate the parts of the bodies when we look at them through the microscope, might be filled with an infinite amount of matter which we cannot observe. At least, we have a priori reasons for rejecting such entities, which contradict the principle of sufficient reason, such as absolute empty space.

The following paragraphs deal with porosity. Many experiments would show the porosity of bodies: mercury penetrates gold, water penetrates the membranes of animals and plants, gold itself gives passage through its substance to water, fluids penetrate one another, the phenomena of electricity, magnetism, and light prove the porosity of bodies, etc.

Another important property of bodies is solidity. Du Châtelet suggests that it is touch that gives us the idea of solidity. To support this thesis, she cites the following thought experiment (InstPhy, § 191):

Un Etre privé de toute faculté tactile, & qui n’auroit de sens que celui des oreilles, é-prouveroit à la vérité une espèce de douleur, en entendant un bruit trop aigu; mais quoique cette douleur ne fût causée que par la façon trop forte dont les nerfs de fon oreille auroient été frappés par l’air, cependant l’espèce de douleur qu’il ressentiroit par cet ébranlement, ne lui donneroit aucune des idées que nous avons lorsque quelque Corps nous résiste, ou nous frappe; ainsi quoique la source de nos sensations soit commune, quoique nos sens semblent se tenir , cependant rien n’est plus séparé que leurs objets, la main ne jugera jamais des sons, ni l’oreille des couleurs, & l’on peut leur appliquer ce beau Vers de Mr. Pope sur les différens Etres.

Toujours près l’un de l’autre, & toujours séparés. (Amsterdam 1742)

Being deprived of any tactile faculty and who would have only the sense of hearing, would in truth experience a type of pain in hearing a noise that was too shrill; but although this pain is caused only by the too strong shaking of the eardrum, it would, however, not give this Being any idea of what caused this shaking; for the feeling of pain does not give us any idea of the cause. Thus, although the source of our sensations is the same in each case, and although our senses seem to be reliable [setenir], nothing, however, is more distinct than their objects: the hand will never judge sounds, nor the ear colors, and we can apply to them this beautiful Verse of Mr. Pope on the different Beings.

For ever near, and for ever separate. (Copyright © 2018 KB)

[ Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ]

The quote is taken from Alexander Pope’s Essay on Man (1733–1734), which gained a great popularity in France and elsewhere on the Continent, as well as in England. Appearing first in English during the years 1733 and 1734, it was translated into French several times during the 18th century. Voltaire received Pope’s poem (presumably only the first two epistles) as early as May, 1733. In Cirey, the philosophic optimism of Pope had won the adherence of Du Châtelet, who certainly knew about Voltaire’s marginal comments upon his copy on Man.

“For ever near, and for ever separate”  in the paragraph quoted above: The tactile sense and the visual sense are two different sensory modalities to which two different sensory tools (objects) can be assigned: the hand and the eye. The background of this thought experiment is the famous Molyneux’s problem concerning immediate recovery from blindness. It was first formulated by William Molyneux, and notably referred to in John Locke’s An Essay Concerning Human Understanding (1689). The problem can be stated in brief, “if a man born blind can feel the differences between shapes such as spheres and cubes, could he, if given the ability to see, distinguish those objects by sight alone, in reference to the tactile schemata he already possessed?”

Du Châtelet’s assumption that the visual and tactual sensations of an object differ from each other is interrelated with her idea of solidity that we receive by our touch. In order to understand this interdependence it is helpful to remember that Locke put solidity under the heading of primary qualities. He argued that, unlike the primary qualities, secondary qualities, like taste, smell, feel and color, exist in our perception and are not a part of the object in the same way. Solidity, according to Locke, fullfils two roles: We receive solidity by touch and solidity arises from the resistance of a body.  And bodies resists through their inertial force. This force is the cause of the solidity of bodies (InstPhy, § 203).

Du Châtelet criticizes Nicholas Malebranche, who misjudged the role of inertia (InstPhy, § 203), and Nicolaas Hartsoeker, who claimed that there are two types of matter, absolutely hard atoms on the one hand and a perfectly fluid on the other hand. Du Châtelet was well aware that Leibniz’s mature theory of the cohesion of material bodies was forged in polemical engagement with the views of Locke and Hartsoeker. In his letter, dated on 6 February 1711 (Journal de Trévoux, March 1712, 498), Leibniz clarified his view, explaining the solidity of bodies by their conspiring motion. Du Châtelet concludes that cohesion of Bodies comes from the conspiring motions of their parts (InstPhy, § 201):

Puisque la cohésion des parties des Corps vient des mouvemens conspirans de conspirans de leurs parties, les Corps feront plus ou moins cohérens, selon que leurs parties feront plus ou moins éxaćtement appliquées l’une contre l’autre, c’est-à dire selon qu’elles se toucheront en plus ou moins de points, & que leurs mouvemens conspireront plus ou moins. (Amsterdam 1742)

The cohesion of Bodies comes from the conspiring motions of their parts. They are more or less hard, depending on whether the surfaces of their parts are more or less exactly applied one on the other, and on whether their motions conspire more or less. (Copyright © 2018 KB)

[ Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ]

In § 209 of the Amsterdam edition of 1742 (which corresponds to § 182 of the Paris edition of 1740) Du Châtelet explicitly refers to Leibniz who made Hartsoeker see that his “two matters” are nothing but a fiction and that there is no such thing than a perfectly fluid or an absolutely hard atom, opposing at the same time the view that cohesion is caused by attractive forces, or action at a distance. “I will tell you in Chapter 16,” to quote Du Châtelet, “how the Newtonians explain by attraction these same Phenomena of cohesion, hardness, softness, and fluidity; for according to some among them, it is in these details that the necessity of admitting attraction is most manifest” (Amsterdam 1742, § 205, corresponding to § 210 of the Paris edition of 1740).

Whereas most seventeenth-century atomists accounted for rarefaction, condensation and density in terms of the intrusion of tiny void spaces within the particles of a body, Du Châtelet defines these terms in agreement with her analysis of solidity and cohesion. The Amsterdam edition of 1742 ends with § 210, which is missing in the Paris edition of 1740 (and in the manuscript).  It argues that the existence of simple things should be presupposed in order to avoid the dilemma between an infinitum regressum and the arbitrary will of the Creator :

ainsi les êtres simples, dont je vous ai prouvé l’éxistence a priori dans le Chapitre 7, le sont encore a posteriori, par le besoin qu’on a de ces élémens, pour éviter les difficultés insolubles dans lesquelles on s’embarasse dans les autres Systêmes, lorsqu’on veut trouver la source prémière des effets qui nous entourent. (Amsterdam 1742)

Thus, there are simple things, as I proved in the 7th cap. a priori, as well as a posteriori, because one has to presuppose elements in order to avoid insoluble difficulties, to which one gets involved in other systems when one seeks the first source of the effects that we perceive. (my own translation)

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