By the end of the 19th century, scientists often identified mechanics with explanations in terms of local motion devoid of thermal, magnetic, electrical, or chemical factors. Thus, the main criticism addressed to mechanism was that it is much too abstract. Ernst Mach's Mechanics of 1883 was a clear expression of this criticism. Mechanics can be viewed as one physical discipline among others, and the mechanical reduction of phenomena has been considered a token of dogmatism. This is not the way mechanism should be seen when it is presented, as I do it here, as a unifying meta-model.

The identification of mechanism to a unique set of key concepts or parameters having constant or variable coefficients such as space, time, masse, material point, and force, would imply the imposition of some superfluous or excessive restrictions to mechanical explanation. Experience shows that modifications and additions can be introduced (consider the addition of the concept of field) without our having to abandon the ideals of mechanism. We are not to identify mechanism either to a unique kind of formalism, for instance, to second-order linear differential equations which exhibit the axioms of classical mechanics (Galileo, Newton). Such a restriction would leave out the equations describing motion required by the theory of general relativity, a set of explanations naturally treated as mechanical.

The observations just made suggest to us that it is convenient to view mechanism as a movement of ideas organized around a central nucleus and capable of evolution, of adapting itself to new situations. This is then my outline of the essence of mechanism:

• unity: there is one world, ruled by one rationality, apprehended by one great mechanical meta-theory;
• mathematization: nature is matter and form, entities and processes have continuous and discontinuous aspects. It is then reasonable to think that one of the basic strata of the world is mathematical in character and that we have much understanding to gain by using mathematics as extensively as possible;
• necessity: the best explanation is causal where it is shown that what happens, happens out of causal necessity, and that, what it is, cannot be otherwise;
• abstraction and verification; the mechanistic thinker begins by delimiting a phenomenology, that is, by picking up a system, a whole relatively stable and separable from its environment. Once the reason or necessity of the system adequately isolated is grasped, the mechanical thinker takes support from the conceptual resources of mathematics to have an idea of its evolution, a hypothesis he then verifies by observing the actual course of phenomena.

Having briefly described the nucleus of mechanism, let us examine the idea of necessity. In philosophy, this concept appears at least in two contexts, symbolically in logic and epistemology on the one hand, and in ontology on the other, that is to say, while describing reality. In the first case, it is said that a necessary proposition is such that its contradictory is known to be false a priori and without further reasoning. A necessary truth is a proposition that it cannot, in good faith, be called in question, and the logical consequences of a necessary proposition are also said to be necessary.

What is of interest for us here is, most of all, an ontological necessity. Is the universe ruled by necessity or do we have to add other principles to explain its development? Could the development of the world occur otherwise, and, if so, how could we know that? We have access only to a very small portion of it, and, anyway, we could not possibly vary the initial conditions of the world to know if everything follows from them by necessity, nor can we compare in a satisfactory, useful way, the evolution of our universe to the development of another world. Yet, typically, the mechanical thinker engages himself by assuming that the universe develops according to an internal logic or necessity. He knows that much knowledge is to be gained by assuming that necessity, not chance, rules over the universe.

Traditionally and from an ontological point of view, the necessary has, as a correlate, the possible, and is opposed, in all contexts, to the contingent. The necessary is that which cannot be or happen otherwise, the contingent, that which can be or happen otherwise. Contingency implies that in a given situation there is more than one solution, more than one situation coherent with the state of affairs. On the other hand, the necessary is the unique solution to a situation, the sole situation coherent with a given state of affairs. The absolutely necessary is that which cannot be or happen otherwise no matter what the circumstances are, whereas the hypothetically necessary requires that some conditions be previously fulfilled. The correlate of the necessary, the possible, can be conceived in a broad and logical way as the proposition which does not imply a contradiction. In a more narrow and physical sense, the possible is that which does not contradict the established knowledge in physics. And the potential, again from a traditional point of view, is an ontological notion conceived as that which is not in act but could be in act, or will be in act, given the metaphysical structure and conditions of the real.

Let us recall that according to what I have termed “the traditional position”, possibility, chance, contingency, and potentiality can, all of them, have a real status. Now contrary to this idea, my thesis is that all of them have only a symbolic existence: we can imagine them thanks to our systems of symbols. But, in fact, everything happens necessarily because nature is a tightly woven causal fabric, and so we can go beyond it only symbolically, guided by our usual language or by mathematics. Thus there are no potentialities that will never become real. If a potentiality symbolically imagined never becomes actual, it means that it was never an ontological, real possibility.

From the first Greek thinkers, we get the idea that the best explanation reveals a necessity. Explanation shows nature's depth. It is a matter of ontology since it has to do with the levels of reality. The best explanation is not merely an arrangement of premises and conclusions in a neatly, logically tied argument, but a demonstration in the practical sense in which a ballet dancer demonstrates what he can do, or in the sense in which an army demonstrates (deploys) its force. To know something, in the context of mechanism, means to know the necessary why of something, the articulation of its inward intelligibility or logos. Seen that way, the logos or reason of a thing is an essential part of its being, and this observation helps us to understand better the mechanical idea that nature is mathematically constituted.

To the determinism in the development of structures of mathematical physics corresponds natural necessity. Once this necessity or truth is apprehended, the generative power of mathematics can continue its way independently. Notice that it is not necessary that every single symbolic step be associated to a natural element. One can see how this procedure can be continued to the point of losing almost all contact with the system studied as long as, at the end of the process, predictions are verified.

To the most perfect form of necessity ruling a physical system corresponds a physico-mathematical determinism. In order for this kind of determinism to exist, the system has to be defined and delimited in space and time. Its state at a given instant, including eventually the memory of the preceding states, has to be adequately represented by the value of a reduced number of properties, the unknown quantities, which depend on a finite number of independent variables. Then the evolution of the system, the set of transformations, has to be described by a set of equations corresponding to the number of unknown quantities. Thus, the physico-mathematical determinism is the thesis that what is completely determined is the solution of the equations and the states of the system represented by those solutions, and this is valid for every future instant and in every point of its spatio-temporal domain. A difference between reversible and irreversible systems is that while in both cases the future states are determined, past states are determined only for reversible systems.

This clear case, the summit of determinism, allows us to have an idea of how the description of necessity can be degraded. For instance, the laws ruling the transformations undergone by a system may be unknown, or even if they are known, they may not be mathematizable. When systems are relatively complex, it is not unusual to appeal to statistics. If, in a mechanical explanation, mathematization is the only major difficulty, that is, if the system can be isolated, if the states of the system repeat themselves, if the initial conditions are discernible and remain stable, then one can speak of physical or experimental determinism. Things get much worse when the initial conditions are impossible to reproduce as happens with fluctuating systems; in that case, it is impossible to reproduce both the preceding states and the memory of the system.

It is implicit in this way of seeing necessity and determinism that natural or ontological necessity is one thing, epistemological determinism, another. From the fact that we -given our anchorage in the world, our way of perceiving and thinking- are unable to describe events in a way suitable to determinism, nothing follows concerning ontological determinism or indeterminism. Notice that some events can be described both statistically and geometrically. Since geometry implies a greater degree of determinism, we cannot say that one and the same event is really now determined in one way, now in another way, according to the different deterministic power of one or the other system of symbols we happen to employ. Another lesson to be drawn is that what is epistemologically determined is a historical fact, depending on the state of empirical and mathematical research at a given moment.

The contemporary mechanical thinker knows better than his predecessors: the mechanical explanation is not methodologically incompatible with the potentialities which will be actualised, nor is it incompatible with teleology, with the ancient Aristotelian final cause. We appreciate here the mechanical recognition of the idea that matter aspires to form and finality. There is an aim to be accomplished. The positive, evident, unavoidable fact which guarantees the metaphysical discourse about potentiality and finality is that there are entities or organisms where the action of the components is oriented by the whole, by an objective. Let us think, for instance, about the formation of the eye. In the case of an organism, the objective of the action of the components is to form a harmonious arrangement so that the organism can live.

Nature is intelligent, “it does nothing in vain” (Aristotle). In its selection of a way, a system is guided by a natural principle or final cause, which, in the mechanical outlook, is the metaphysical idea that nature follows the easiest, or the most simple, or the most economical ways, a rule such as the Principle of Least Action. This is perhaps the main natural principle given the quality and the quantity of the laws it has inspired and continues to inspire. Fermat’s principle of least time in classical optics is an excellent example: the path of a ray (e.g. light) from one point to another, including refraction and reflection, will be the one taking the least time.

“The mechanistic attitude, writes Théodore Vogel, continues to form the essential basis of part of our present knowledge, and the other parts have been built in opposition to it, i.e. in reference to the mechanical principles and methods… The mechanistic ideal was a noble ambition and a point of view whose principle remains valid… The secret hope of a unitary explanation of the world has probably not quite left us”.