Final causes. The principle of final causes consists in finding the causes of the effects of nature through the end that its author must have set for himself by producing such effects. We might say, in other words, that the principle of final causes consists in finding the laws of phenomena through metaphysical principles.

This word was much used in ancient philosophy to explain several phenomena (both good and evil) through metaphysical principles (both good and bad). For example, it was argued that water rises in pumps because matter has an aversion for the void. Such is the absurd metaphysical principle through which this phenomenon was explained. And it is for this reason that Bacon, that sublime genius, does not defend the principle of final causes in physics. Causarum finalium , he says, investigatio sterilis est, et tanquam virgo Deo consecrata, nil parit. [Research into final causes is sterile, and like a virgin dedicated to God, brings forth nothing. [1]]( De augm. scient.lib. III.c.v ). When this great genius spoke these words, he undoubtedly had in mind the principle of final causes , which he discusses in a more reasonable manner than the scholastics. However, a great modern philosopher, Leibniz, tried to rescussitate final causes , in a published work, Act. erud. 1682, possessing the title Unicum Opticae, Catoptricae, & Dioptricae principium . In this work, Leibniz declares himself for this manner of philosophizing according to final causes , and he devotes to it an essay on the laws of light.

Nature, he says, always follows the simplest and shortest paths; it is for this reason that a ray of light will always follow a straight line so long as it does not encounter an obstacle. If it encounters a solid surface, it must reflect in such a way that its angles of incidence and reflection are equal. This is because the ray is obliged to reflect itself, and as such, travels from one point to another via the shortest route possible. This has already been proven . See Mirror and Refraction. Finally if a luminous globule encounters a transparent surface, it must break in such a way that the sinus of incidence and refraction be in direct correlation to the speed of both environments; this is because, in this case, it moves from one point to another, in the shortest possible time.

Before Leibniz, M. de Fermat had recourse to this same principle to determine the laws of refraction; and perhaps, what I have described earlier is all that we need to demonstrate just how dangerous the use of final causes is.

Indeed, it is true that in the reflection of the light on plane and convex mirrors, the path of the ray is as short as possible; but it is not the same for concave mirrors. In this case, it would be easy to demonstrate that the ray takes the longest, instead of the shortest, path. I admit that Father Taquet, who presented in his Catoptrique the principle of the shortest path in order to explain reflection, is not embarassed by the difficulty posed by concave mirrors. When nature, he states, cannot take the shortest path, it takes the longest one; this is because the longest path is singular and determined, just like the shortest path. We can apply here Cicero's maxim: Nihil tam absurdam excogitari potest, quod dicture non sit ab aliquo philosophirum. [Nothing so ridiculous can be thought up, that it hasn't been said by some philosopher. [2]]

The principle of final causes thus fails to explain reflection. It is even worse in the case of refraction, for, in the first place, why is it that in the case of reflection nature follows the shortest path in the shortest possible time, while in that of refraction, nature takes only the shortest possible time, but not the shortest path? Perhaps a choice was required, for in the case of refraction, the shortest time and the shortest path cannot be achieved simultaneously. All in good time. But why does nature, in this case, prefer time to space? And in the second place, in keeping with M. Fermat and Leibniz, the sinus is in direct correlation with the speed, instead of them being in inverse correlation. See Refraction and Action [Action (Ethics), Action]. Let us thus recognize the abuse of final causes in the phenomena that partisans of the concept seek to explain with the aid of this very principle.

But if it is dangerous to have recourse to final causes a priori in order to discover the laws of phenomena, it nonetheless has its uses. It might seem less strange to discern how the principle of final causes fits with the laws of phenomena, if we first establish such laws according to clear and incontestable mechanical principles. This is precisely what M. de Maupertuis has suggested we do with regard to the question of refraction in a Mémoire imprimé parmi ceux de l' Academie des Sciences (1744). We have had occasion to speak about this in Action [Action (Ethics), Action]. He provides at the end and beginning of this treatise some judicious and philosophical reflections on final causes . He has since extended his reflections on this question in his Mémoires de l'Académie de Berlin (1746) and in his Cosmologie . In these works, he shows the abuses that have been made of the principle of final causes in order to provide proof of the existence of God via the least important effects of nature, instead of looking at its entirety for proof of this incontestable truth . See the article Cosmology. Understanding the wisdom of the Creator, says M. de Fontenelle, is limited more by our weak grasp than by his power. See his Eloge de M. Leibniz . See also the sound reflections of M. de Mairan on the principle of final causes in his Mem.acad. 1723.

Notes

1. [Translation from the Latin courtesy of Ruth Scodel.]

2. [Translation from the Latin courtesy of Ruth Scodel.]