Abstract
We consider the answer to this question to be the central problem of the interpretation of Descartes’ scientific work. Schuster declared Descartes’ physics, because of its verbal character, to be natural philosophy, and excluded it from the tradition of mathematical physics, which he associates with Galileo and Newton. This assessment is mistaken, and the reason for the mistake is the vagueness of the concept of mathematical physics. Galileo’s physics, which completely lacks any description of interaction, which attributes to bodies a natural tendency to accelerate in free fall, and which considers circular motion as inertial, is automatically taken to be mathematical physics. On the other hand Descartes who introduced the notion of interaction into physics, who clearly saw that the acceleration of falling bodies must be the result of interaction, and who regarded only uniform rectilinear motion to be inertial, is not included in mathematical physics. My aim is to correct this obvious error.
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Notes
- 1.
This requirement is only necessary, not sufficient. Astrological texts, for example, are often full of numbers, but we would probably consider them pseudo-mathematical rather than truly mathematical.
- 2.
Newton’s system is mathematical in both of the above senses of the word ‘mathematical’, and this is misleading because it does not force us to realize that besides having a mathematical language it is also mathematical in the ontological sense. If we use only the ordinary sense of the word ‘mathematical’ and say that Newton’s system is mathematical, we have seemingly succeeded in characterizing Newtonian physics, but only seemingly: in fact we have only characterized a part of it. Newton created a language that made it possible to link the two meanings (the common and the ontological) of the word ‘mathematical’ and it linked them in a mathematical way. Thus, Newton’s system is triply mathematical: it uses a mathematical description of phenomena (like Galileo), it has a mathematical ontology (like Descartes), and it has a mathematical connection between the description of phenomena and the ontology (in the form of the law of universal gravitation, which expresses forces as functions of the positions of the interacting bodies).
- 3.
In Štoll et al. (2017, p. 98) the formula for the terminal velocity of free fall in a resisting medium is given.
- 4.
A first sign of something resembling physical compositional synthesis can be found in Galileo’s discussion of the motion of a body in the cabin of a moving ship. Here, in a sense, two motions are combined, but the very point being made by Galileo is that they do not influence each other. Thus, this cannot be taken as an example of a system composed of two interacting bodies. Even though Galileo combines the two motions, this combination does not require the use of any tool for expressing physical compositional synthesis.
- 5.
Peter Machamer and James Edward McGuire wrote in this context that “Descartes takes bodies to be fully geometrical in nature and isolated from their past” (Machamer and McGuire 2009, p. 153). This is an accurate characterization of an important aspect of the notion of state. One of the reasons for the introduction of the notion of state in physics is precisely to cut the system off from its past. The entire future behavior of a system is determined by its current state, and so all systems that are in the same state, by whatever means they got there, will behave the same way in future. This distinguishes physical from biological systems, which carry with them a record of their entire history in the form of DNA. However, Machamer and McGuire add immediately after the quoted sentence that this “leaves no room for laws to describe their motion”. This is an incomprehensible sentence when we take into consideration that it is the notion of state, i.e., the cutting off of a system from its past, that allows motion to be described by laws of motion. The state of a system gives, mathematically speaking, the initial conditions of the equations of motion. It is the supply of the initial conditions for the equations of motion that allows the motion of the system to be described. The future of biological systems cannot be described by laws of motion because such laws do not have access to the information hidden in the DNA, but only to the physical state of the system.
- 6.
Here we see the limits of ancient science. The Greeks knew only one exact discipline—mathematics—whose ideal objects were timeless and immutable. Therefore, they identified perfection with timelessness and immutability, and could not imagine how something perfect (i.e., absolute and ideal) could be subject to change. Descartes was able to imagine it, and that is the key to his mathematical physics (see Kvasz 2019).
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Kvasz, L. (2024). What is Mathematical Physics?. In: Descartes on Mathematics, Method and Motion. SpringerBriefs in Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-031-57061-2_5
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