Mechanics, science and principles. An interpretation from Polo

Author: Santiago Collado González
Published in: Studia Poliana, nº 9, pp. 215-231.
Date of publication: 2007

summaryPhysics, which was born in the 17th century, soon established itself as a scientific paradigm. The core topic of its success was Newton's use of mathematics. I argue that the analysis of Newtonian mechanics contained the reasons for the crisis it underwent in the 19th century, and also the resources to overcome it. In this article we study the epistemological reasons that explain these vicissitudes from the perspective of Polian gnoseology.

Palabras core topic: Leonardo Polo, mechanics, Newton, epistemology, gnoseology, philosophy of mathematics, philosophy of science, philosophy of nature, theory of knowledge.

Summary: Modern physics was born in the XVII century and soon became the principal scientific paradigm. The key to its success was the use that Newton made of mathematics. I hold that Newton's analysis of mechanics contained flaws which led to its crisis at the end of XIX century and at the same time had resources to overcome this crisis. I study in this paper the epistemological reasons for these vicissitudes using Polo's theory of knowledge.

Key words: Leonardo Polo, mechanic, Newton, epistemology, philosophy of mathematics, philosophy of science, philosophy of nature, gnoseology, theory of knowledge.

Introduction

The current state of science in general, and of physics in particular, is far from being the quiet, undisturbed place, the fully explored and familiar landscape, that the scientists and thinkers of the 19th century expected. The birth of quantum mechanics and the theory of relativity came to solve problems that were then born within science itself, but they also opened up new and hitherto completely unknown territories, raised new questions and shattered the expectations of tranquillity that rested on the consolidated Newtonian physics.

Today no one dares to put dates, as was once done, on the achievement of the ancient ideal of the unification of knowledge, which is now called unified theory, or theory of everything. We have learned the lesson of the advent of the 20th century. Today science certainly constitutes the most prestigious subject of rationality. Arguably, it alone holds many in hope for a better future. But the predominance of scientific thought cannot hide the great shadows that are cast over the future, against the backdrop of the experiences that humanity has lived through during the 20th century and which have been made possible by the advances of science.

It is logical that the changes that the new century brought with it pushed philosophy to fix its gaze on science. It can be said that in those years a new branch of philosophy was born and has since been concerned with understanding it: where lies the amazing power of this mode of knowledge born in the 17th century and which has not stopped progressing until today, what products can carry the label of scientist, what is its scope, how far we can trust it,... are some of the many questions that have been raised and which are still largely unanswered. There are many who think that philosophy itself is mortally wounded by science, as the former is cornered by science into a corner that will become increasingly narrower.

In reading Polo's work I have found numerous important indications that allow us to understand science itself, its success and its limitations, or how it has had to do with the very course of history since its emergence. financial aid It seems to me that Polo's contribution constitutes an invaluable contribution to the task that the philosophy of science has set itself since its beginnings. His theory of knowledge contains a philosophy of science of great depth that I would dare to describe as innovative.

When Polo explains the various operations of the intelligence, he looks to history for support for his ideas. It is very interesting to see how his statements on abstraction, and on the rest of the operations of the intellect, allow us to see what is happening at the dawn of philosophy as if from a balcony. I think that it is also possible to look out with great fruit on the balcony of the history of science from the light projected on it by Polian epistemology. It is not, of course, a matter of explaining history by placing it in the narrow moulds of a theory. This is not what he does when he illuminates the birth of philosophy with his findings on the inception of thought. What he offers are arguments that allow us to see the coherence and timeliness of his proposals. If the indications he offers us in his epistemology are true, they would also have to be contrastable with the history of thought that is involved in the development, consolidation and crisis of science.

What I am trying to do in this paper is to trace those indications that seem to me to be key to a better understanding of science and its history. The length of this work obliges me to approach this task from the brevity of a few pages. This will undoubtedly condition the structure of the work. I believe that what Polo has already written on these questions will allow much more extensive and in-depth studies to be undertaken. What follows is my own interpretation in which the source source of inspiration is Polo's writings. It is to him, therefore, that I owe the successes that may be written here. The interpretative shortcomings, both in the history of science and in Polo's philosophy, that I have exposed in this work are my sole responsibility.

1. Newton defeats Aristotle

There seems to be agreement to point out that experimental science begins its journey in its proper sense in the 17th century. Newton's mechanics is the scientific theory that gave science the prestige it has enjoyed ever since. It is true that Newton himself acknowledged that he reached so high because he stood "on the shoulders of giants" who preceded him (Copernicus, Kepler, Descartes, Galileo, etc.), but Newton cannot be denied that he managed to formulate and set up the instructions of what science (and not only physics) is today. Although his most important work, The Mathematical Principles of Natural Philosophy, contains in its title the name of philosophy, his way of thinking moves in a quite different orbit and can already be considered strictly science in the modern sense of the word, which was soon endorsed by the successes and progress that accompanied it up to the present day.

At the beginning of modernity there was a widespread feeling among the leading thinkers of the time that they were ushering in a new way of thinking. Greek philosophy had explored a vast expanse of the world of ideas and discovered many of the problems that have recurred throughout the history of thought, but it did not initiate science, although some of its representatives thought in scientific terms. It can be said that the Greeks exercised most of the methods *(1), however, the Greek thinkers did not give rise to science as we understand it today, although they did exercise intellectual acts proper to science. In fact, it is more just to science if it is understood as an activity rather than only as a method. And it is, moreover, an activity of extraordinary complexity, which demands the exercise of a plurality of intellectual acts, which has its own characteristics and also demands a particular attitude in those who practice and develop it *(2).

With the maturity of science represented by Newton, Aristotle's thought seemed definitively displaced. Certainly, the elements of Aristotle's work that could be called scientific had been largely superseded, in particular his vision of the universe or worldview. Aristotle's thought was supported, to a large extent, by the knowledge that could be provided by the senses stripped of instruments and lacking the baggage of experimentation that had already accumulated at the beginning of modernity. But Aristotle's ability to read into that experience is hard to surpass. In Aristotle, elements that we now consider scientific (representations of an observational nature, for example) and elements that can be considered purely philosophical went hand in hand. Aristotelian philosophy is not a subject of rationality that starts from a level completely separate from common experience or, with the limitations of the time, from experience of a scientific nature, but was firmly grounded in the body of knowledge available at the time. Its philosophical conclusions may be fully valid today, even if their scientific elements are outdated, outmoded or even false. In any case, it does not seem sensible to reject his philosophy a priori just because his science is outdated. But the thinkers who initiated modernity rejected Aristotelian thought as a whole*(3), which I think has had consequences from that time to the present day: we will try to highlight some of them.

Although the beginning of the revolution that led to the replacement of Aristotelian science by modern science may bear the name of Copernicus, it can also be said that it was Newton who brought it to its definitive triumph. The change that took place in thinking at that moment in history was to condition its future drastically and already contained, in germ, the crises it had to face, such as the aforementioned one at the end of the 19th century. I think that it is also in those years that we can trace the cause of the strange mixture of feelings that we can experience when we consider the extraordinary effectiveness of science together with its, so often questioned since the beginning of the 20th century, relationship with truth. Paradoxically, it seems to me that we could say that the power and efficacy of science and its strange relationship to truth are linked, in a way, to relativism.

2. The achievements of mechanics

Newtonian mechanics made important achievements, as is evident from the fact of its effective use and application up to the present day. Its triumph was so important that it also induced a way of looking at material reality as a whole, a world view, which was dominant for almost three centuries *(4). Its achievements could be summarised under the following two headings:

1. Unification of the stellar world with the Aristotelian sublunar world. From then on it was no longer necessary the resource to a fifth element, the ether, which made possible the peculiar and more perfect circular motion of the astral bodies. Although, paradoxically, it was then necessary to resort again to the hypothesis of the existence of another subject of "ether" to save the coherence of the mechanical theory in the face of the phenomena of the propagation of light. It was no longer necessary to resort to the existence of two worlds with different motions. The barriers separating the harmonious celestial region from that of our world, the scene of continuous "violent" movements, had been broken down.

2. Unification of ordinary experience with mathematics. In other words, he succeeded in quantifying the material reality with which we have to deal on a daily basis. Interestingly, the greatest mathematical achievements among Greek thinkers had been driven by the aspiration for a description of astral motions. It was precisely this complex description that centuries later led to the collapse of the Ptolemaic edifice. With Newton, not only was it possible to describe and calculate astral motions, but the same mathematical principles were used to calculate, for example, the trajectories of projectiles. It was logical that the Aristotelian worldview was shattered by the new mechanics.

The positive consequences of these achievements were, on the one hand, to reach a general and coherent understanding of the whole of material reality. Simplicity in the formulation of theories, especially if it increases their descriptive power, has always been an aspiration and a clear indication of correctness. The second unification mentioned above gave the possibility of exercising effective experimental control over the movements occurring around us. The latter was, in my opinion, what made the real beginning of experimental science possible. The core topic of the new science lies in the effective possibility of experimentation. But this possibility is based on the high Degree of knowledge of mathematics. Mathematics was therefore the real core topic of the change.

In Newton there is a real choice for mathematics, for what in reality we can describe mathematically. What things are in themselves is less important than the mathematical description that can be made of them. This is already evident in the title of his most important work: Mathematical Principles of Natural Philosophy. The title really corresponds to its content in which, when he refers to the terms that are supposedly known to all such as time, space, place, and motion, he points out that the vulgar conceive of these magnitudes with respect to the sensible and that this entails certain prejudices that need to be destroyed by distinguishing them into "absolute and relative, true and apparent, mathematical and vulgar" *(5).

It can certainly be said that the novelty brought by the new science comes from its hypothetical deductive method culminating in experimental contrastation. But this is only possible because of the peculiar unification achieved between mathematics and ordinary experience *(6). The importance of experiment can be emphasised, but experiment achieves its value, it is realisable in the modern sense, because a way of experimenting is found in which recourse is made, directly or indirectly, to number. By virtue of the new tools of calculation, it is possible to experiment in the world that interests me from a practical point of view, not in the distant world of the celestial spheres, but in the world in which we can construct artefacts. The new physics will also eventually make it possible to build artefacts that can be used to exercise our control in the celestial world as well. But the core topic of experiment is in numbers. Experimental verification in the science that was born with Newton, directly or indirectly, is solved in an adjustment of numbers. This new approach gives rise to an authentic scientific revolution *(7) but, curiously, in this union of number and experience is already implicit the crisis that will come a few centuries later and, at the same time, in Newton's net option for mathematics is the resource so that this crisis can be, at least in part, overcome.

The achievements of mechanics rest on the basis of a new method in which mathematics is the cornerstone and experiment the confirmation that our hypotheses are correct. According to Polo, together with the above, the success of mechanics rests on two postulates which, strictly speaking, are not verifiable: the isotropy of space and the isochrony of time. Neither of these postulates is mathematical in nature, but their assumption is necessary for the mathematical principles formulated by Newton to be applicable and for the experiment to make sense.

Where Newton stakes the efficacy of the theoretical ensemble he puts forward is in his analysis of reality, that is, in the simplifications he introduces and through which he is going to understand material reality and its movements, which are the ones he intends to control. The main notions resulting from his analysis are mass, force, space and time. These objectivations are for Newton fundamental magnitudes. That is to say, in them the description of reality is resolved subject *(8) - they are fundamental - and, moreover, they are magnitudes because he has succeeded in quantifying them, in assigning them numbers. In this way he has achieved a way of quantifying the totality of material reality and its movements. The success of the analysis will depend on the experiments confirming the different hypotheses formulated about physical reality. Newton has made a kind of "sketch" of reality, but when we compare the sketch with the model it represents (the experiment) the result is strikingly similar: the numbers proved Newton right.

3. Understanding change from within the hierarchy

In any simplification or analysis there is a part of the reality under analysis that is retained, and another part that is omitted because it is not considered relevant to the objectives pursued. The analysis achieved by Newton constituted an effective method for dealing with the motion of physical reality as it is presented to our ordinary experience. The development experienced by physics since then and the accuracy of the predictions made regarding the then observable motions of celestial bodies, and also of those closer to us, turned mechanics into a paradigm of science: an example to be imitated by any discipline aspiring to be scientific and, in time, an aspiration of any subject of rationality. The ideal of being able to verify with certainty the truth of what is claimed seemed to have been achieved by physics. Mastery over the material world would then be guaranteed and, with it, progress. In this context, in the 19th century, many voices predicted the exhaustion of what remained to be discovered in the physical world. This sort of scientific euphoria began to fade at the end of the 19th century and seemed to dissipate completely during the 20th century. During the last century, despite the many questions raised by the crisis of Newtonian physics and its replacement, or rather correction, by quantum and relativistic physics, empirical science has not ceased to progress until the present day. At the same time, questions about the truth of what we come to know from physical science have not diminished *(9). Paradoxically, it could be said that these questions and issues opened up to thought by physics grow at the same pace as its progress and achievements.

How to explain the changes alluded to in the preceding paragraphs? I refer to the one in the seventeenth century, with the boom period that followed, and the storms that arose on the sea of science and philosophy of science in the nineteenth and twentieth centuries, the turbulence of which continues today and in some respects may even be said to have increased. To try to answer this question we now turn to Polian gnoseology. As we mentioned at the beginning, the coherence of his theory of knowledge with the facts presented would mean a certain confirmation of the correctness of his proposals.

I consider that one of Polo's most original contributions is the distinction of a plurality of operations which, as anyone who has worked on his gnoseology knows, are distributed in two operational lines (rational and generalising) *(10), each of which constitutes a distinct operational hierarchy. The thematic explanation of the different operations, as well as of the double operative line, not only does not break with the gnoseological tradition of classical philosophy, but constitutes an extension B which brings important novelties. We will only make use of it insofar as it serves the purpose of this article.

4. Mathematics and imagination face to face

Newton's commitment to mathematics is the core topic of the success of the analysis proposed in his mechanics. Why? Mathematics corresponds to a subject of operations of the understanding that Polo calls logos *(11). These cognitive acts succeed in gradually unifying - according to the hierarchy of the two operative lines - by means of operative intellectual acts, the objects of the two indicated lines. Although we shall not go into the details, we can summarise the characteristics of this subject of objects by saying that they are objects which Polo calls "pure objects" or relational properties *(12), their subject of intentionality is hypothetical *(13) and, most importantly for us at this point, they are the only mental objects which are directly concerned, though still intentional objects, with the physical real. The latter requires a somewhat more extensive explanation.

For Polo there really are physical numbers. Material reality has numbers which Polo calls physical numbers. These numbers are the way in which the physical principles (the four causes discovered by Aristotle) concause each other, which is why we can say that reality "has" numbers. Polo states that "physical number is the success of concausality"*(14). But the way we know the physical number is through the thought number, which deals with the physical number with a subject of intentionality which is precisely the hypothesis. We do not know numbers as we know principles. The latter, for Polo, are not known intentionally, that is, through operative acts, but through acts that are habits. The knowledge of physical principles, of causes, is a knowledge of the physical real, but it is not effective in order to control it. A knowledge which is operative or intentional and which also deals with the physical does allow us to exercise control over material reality, since the operations of the logos do not intentionally deal with the abstract, as happens with the other objects of intelligence, but with what reality has, that is to say, with the numbers of reality. But it is worth insisting that the numbers thought of are not the physical numbers: there are more physical numbers than we can think of. The way in which we refer the thought number to the physical number is precisely, for Polo, the hypothesis. This is possible as a hypothesis precisely because there are more physical numbers than thought. Hypotheses, therefore, are thought numbers, but they are about, they are intentions, about physical numbers which they do not exhaust *(15).

Among other things, what Polo is doing at this point, from the perspective of his gnoseology, is to show why mathematical objects seem to be pure inventions or novelties that occur in our mind and are "a priori" with respect to the physical world: in fact not a few mathematicians or physicists, even some very important ones, consider themselves Platonists*(16). Mathematical objects are so "pure", or purely thought, that they seem to have a life of their own independent of physical reality, a life that is only discovered by our intellect. But on the other hand, Polo accounts for the efficacy of number without departing from Aristotelian realism, without having to admit a kind of harmony pre-established by God, who would be the creator of both the world of ideas and the complex reality of physical changes. Mathematical objects are intentional, not ideas per se, but their intentionality is hypothetical in the sense mentioned above.

This approach to mathematics also sheds light on the problem of verification and falsification of hypotheses. A new hypothesis does not falsify a previous hypothesis, since each hypothesis has its own coherence. One hypothesis can replace another, but without the first one being falsified. Simply with some numbers we can manage to think better or worse about the numbers that reality has, and the effective control that we exercise over it will depend on this. To put it simply: five does not replace three because one is as much a number as the other. The problem is whether the reality we want to describe has three or five: by thinking three or five we make a hypothesis about the tenure of reality.

It seems clear that Newton's analysis was right to think of the numbers by which we can describe the motion of the physical that we get to know in our ordinary experience, that which we know directly with our senses, for example. Newton's success, and the boom period in science that followed, can be said to have been due to the harmony between what mathematics told us and what ordinary experience showed us. The numbers seemed to be an endorsement, a confirmation of observable and experimental physical reality. This was Newton's unification of mathematics and reality.

I am not going to try here to justify Newton's success because his own success justifies it. What we have done is to indicate, from Polo onwards, why this success is possible; we have tried to show that it is the commitment to mathematics, together with the analysis of reality that allows its use at that time, that makes Newton's triumph possible by managing to control movement. The problem is that the movement that mechanics manages to capture does not seem to be the only movement that we can know in the natural world and, on the other hand, all analysis entails a simplification. The objectivations resulting from this analysis allow us to contemplate reality, in this case, with the aim - albeit not the only one - of control. The vision of reality that we have through the previous analysis does not allow us to see the whole of reality: there are areas that have been left out. If we constitute this analysis as a paradigm for knowledge and we have no experience or knowledge of the areas that have been left out, we will not encounter problems. We will stumble upon them when we get to experience those regions that the analysis had excluded. In the inadequacy of Newtonian analysis was hidden, as we have said, the seed of the crisis that broke out at the end of the 19th century.

The Michelson-Morley experiment, the problems of explaining the nature of light, the theory of relativity and, above all, the experiments that led to the birth of quantum mechanics caused a break in the tranquillity and optimism in which scientists, particularly physicists, had lived for the last few centuries. What caused disquiet at the turn of the century, and still does for many, what led to the questioning of certain well-established philosophical principles that seemed to be beginning to waver (the principle of non-contradiction, for example), was the rupture between what mathematics tells us, increasingly sophisticated and difficult to "understand" but allowing for experimental contrast, and what the senses present to us at the level of the ordinary knowledge , i.e. what many ascribe to the so-called common sense *(17). This cognitive level of the physical world is the one that corresponds most directly to what the imagination makes known to us. The adjustment between the level of knowledge at which the logos moves - it is on a purely intellectual plane - and the level at which the objects of the imagination move is the one that fails to account for what happens in the new experiments. There is a rupture or lack of adjustment that can no longer be bridged as a consequence of the enormous hierarchical distance between the objects of one cognitive level and the other.

Physicists and mathematicians can go on "inventing" numbers. These numbers are hypotheses about real numbers whose correspondence with them is checked by experiments. The development of physics is a confirmation of the timeliness of this approach and of the effectiveness of opting for mathematics, as Newton did, when one wants to control movement. The challenge for the scientist is to invent new hypotheses, new numbers that provide us with knowledge - certainly intellectual in this case - about the possession of the physical real: about physical numbers. The difficulty is that the imagination is at a level of sensitive knowledge and, consequently, inferior to that of logos, which is purely intellectual, that is, the objects of logos do not deal with abstract objects, nor are they the elevation of a phantasm to the level of the intellect, as happens with abstraction. This is why we can properly speak of invention when referring to numbers. Imagination does not make known to us the possession of the physical but it is, as with the non-mathematical knowledge goal , a knowledge which Polo calls aspectual. Moreover, imagination only offers us knowledge of sensible formalities of reality, however elaborate they may be. These formalities are the aspects that make up, for the most part, our ordinary knowledge of the physical world *(18). The experience of what has happened and is happening with physics shows that, indeed, our knowledge of material reality seems to deviate more and more from what we admit as belonging to common sense. This is why we find ourselves in the strange situation of realising that we are gaining more and more effective control over the physical and, at the same time, we seem to be further and further away from understanding the reality we control.

We said that Newtonian analysis already contained the crisis that would have to be faced sooner or later, and also the resources to get out of it. The crisis comes from the inadequacy of the analysis. The resources lie in the option for the mathematization of reality. To get out of the crisis actually means the acceptance that what mathematics tells us we cannot represent imaginatively and, therefore, that we have to leave behind in certain areas of physics the "common sense" that is provided by the cognitive level of the imagination.

5. The inadequacy of Newtonian analysis

Where is the inadequacy of Newtonian analysis? In reality, it is a great inadequacy because it introduces simplifications that lead to capturing a very reduced sphere of movement. A subject of movement which it is doubtful that it is even physically real *(19). The movement objectified by Newton corresponds precisely to the time that is objectified at the level of the imagination. It is therefore not even physical time in the strict sense, nor is it time objectified by the external senses. It is a time that already has a high degree of formality Degree but it is not time understood on the intellectual level either. It is time itself, and also space, which corresponds to Kant's a priori forms. Simplification certainly allows mathematization: the formulation of hypotheses about physical reality. But the objectification of time and space employee belongs to the knowledge that the imagination gives us of them. This makes it possible to account for the success of Newton's mechanics in relation to ordinary experience and, also, for the rupture that later occurs between that experience and physics.

Another very important notion in Newtonian mechanics is that of mass, which is closely related to the notion of force because they are objectified at the same level. Polo points out that at the first level of objectification of Newtonian physics - in which the principle of inertia is formulated - what is inertial is the movement itself. At a second level - that of Newton's 2nd law: f=m.a - what is properly inertial is mass, i.e. mass drives acceleration out of itself and thus makes possible the quantification of force - the other notion core topic of mechanics - and its relation to time. Mass is also the notion that serves to link time with space, since in the law of universal gravitation mass refers to distances and also includes force. Mass therefore plays a role core topic in unifying and putting into operation the different elements of Newtonian analysis: space, time, force. Its constancy - its inertia - is the core topic to achieve the synthesis that allows the system to function. It is also crucial, in order to achieve this unification, to remove mass from space, thus reducing it to a point. That is, the relation between bodies depends exclusively on their masses and their distance. But now bodies are not extensive and what the consideration of spatiality or extension assumes is pure distance. Mass captures the materiality of physical reality, of physical bodies, but in a peculiarly reductive way: on the one hand it expels movement from itself and, on the other, also extension. The quantification of experience has taken a heavy toll.

We could summarise very briefly the implications of Newton's objectification or analysis of the physical by saying the following:

1. There is a separation between subject and motion achieved through the notion of mass. The subject is inert or inertial, a constant factor that makes it possible to unite space, time and force. This will later force the adoption of a dynamic principle, which will be energy. But energy will also be external to the subject which maintains its constancy in any case.

2. There is a separation between space and time. Time does not pass through space and time flows apart from space, which receives a consideration, like time, that is absolute *(20). It can be said that there is a substantialisation of space and time. This mutual exclusion is what allows space and time to be unified with the material, through mass, in a mathematically simple way. But this is an a posteriori unification. We could say that it is a unification that comes very late in relation to the strictly physical consideration of space and time.

A unified and closed vision of physical reality has been achieved. The objectification of the material and, in particular, of movement, bore important fruits, while the experienced remained in the realm where the cognitive weight falls on the imagination. The fractures resulting from this analysis were those that would later become invoice at the end of the 19th century and which would have to be remedied by other objectivisations that went beyond those of mechanical analysis.

We might now ask what does the objectification of Newtonian motion leave out of consideration? To begin with, it forgets vital motion. Although we are not discussing this now, it is clear that life does not allow itself to be enclosed in the narrow analysis devised by Newton. To want to approach the study of living beings with a method that is heir to mechanical approaches would be a serious obstacle to the understanding of life. Such an approach would be to consider living beings as Structures which are sites of energy exchange, or in other words systems of energy optimisation and utilisation, for example *(21).

Consideration of the Aristotelian final cause is also completely excluded. Strictly speaking, Newton's inertial motion is uncaused. The objectification of mass together with the other simplifications introduce important reductions in the understanding of causes: finality, for example, is completely eliminated. The core topic of this suppression, as already pointed out, is in the notion of mass and the reduction in the consideration of the types of motions that this suppression introduces. Paradoxically, leaving no room for the consideration of final cause leads to the determinism that is characteristic of Newtonian physics.

Newtonian mechanics substantially modifies the understanding of the causes discovered by Aristotle. In the Aristotelian outline the elimination of any of the causes significantly alters the understanding of the others and their relationships. Newton's analysis makes it impossible to understand the final cause as the physical cause of the world. Within mechanics, if finality is maintained, it is as something external to the world. It is impossible to understand, from Newton's point of view, the final cause in a way other than intentional finality, i.e. without anthropomorphising it.

Along with this important elimination, the understanding of the rest of the causes is also modified in a way B. In the Aristotelian tradition, material and formal causes are regarded as causes intrinsic to the substance. The efficient cause is, on the other hand, extrinsic in transitive physical motions. Another important alteration introduced by the Newtonian analysis is to make the formal cause an extrinsic cause to the substance and, at the same time, to understand the material and efficient causes as intrinsic causes *(22).

Concluding remarks

One problem that emerges from what has been said so far is what we accept as an understanding of physical reality. The Aristotelian approach extended by Polo financial aid also confronts us with this problem. To understand physical reality is to understand its principles, but an accurate knowledge of the principles cannot be reached by means of a knowledge goal . On the other hand, we can objectively know something that physical reality has: it is a hypothetical knowledge (thought numbers) of the way in which causes are related to each other, that is, of the concausalities (physical number). This subject of knowledge allows the control of the movement. But the knowledge of the physical principles (causes) is neither goal nor, consequently, is it useful for the control of nature, but only for its contemplation. Herein lies for Polo the difference between mathematical physics and philosophical physics (or philosophy of nature).

Scientific Platonism, problems in the demarcation of science, difficulties in the interpretation of the results of quantum mechanics, the aspiration for a unified theory that explains everything, understanding science as a kind of hermeneutics of nature, physicalist tendencies in biology, etc., are some of the problems that would be clarified if they were seen in the light of the distinctions we have approached in this paper.

The coherence between what the history of science presents us with and the proposals of what we could call Polian epistemology indicates that these proposals can constitute a very valuable contribution to understanding science today and being able to frame it in the context of knowledge as a whole: the way to control science itself.

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Notes

1. On this occasion I use the notion of method in the sense in which Polo puts it: "Método es una noción equivalente a la de acto intelectual", Curso de teoría, II, Eunsa, Pamplona 1989, 216. "Método equivale a acto intelectual", Antropología, I, Eunsa, Pamplona, 2003, 103.

2. A systematic and detailed study of what scientific activity entails with all its demands and characteristics can be found in: M. Artigas, Filosofía de la Ciencia Experimental, Eunsa, Pamplona, 1999 (3rd ed.). The first page of this volume states the following: "In 1687, Isaac Newton published his Mathematical Principles of Natural Philosophy, which contains the first physical theory in the modern sense".

3. Cfr. J. M. Posada, La física de causas en Leonardo Polo, Eunsa, Pamplona, 1996, 57-64.

4. This worldview is known as mechanicism, which establishes mechanics as the paradigm of knowledge in the physical world, giving it a dogmatic formulation. One of the architects of the establishment of a mechanistic worldview is the late 18th century mathematical physicist Pierre Simon Laplace (1749-1827). The mechanistic worldview had few rivals until the end of the 19th century. I maintain that, in its core aspects, we have not yet rid ourselves of it.

5. I. Newton, Mathematical principles of natural philosophy. In On the Shoulders of Giants. The great works of physics and astronomy. Annotated edition by Stephen Hawking, Crítica, Barcelona, 2003, 655.

6. Polo also seems to think so when he says: "Leibniz (...) thought that if he discovered a relation defined in a very small interval of a curve, he would know what the whole curve was like. This gave rise to the differential calculus, a great advance in the mathematics of his time that allowed Newton's physics", Introducción, Eunsa, Pamplona, 1995, 208.

7. There are authors who do not so readily admit the existence of a genuine scientific revolution in the 17th century. For example, Steven Shapin begins his book The Scientific Revolution. An alternative interpretation by saying "The scientific revolution never existed, and this book is about it", 16. What in any case cannot be denied is the consolidation of this new subject of rationality of which Newton represents its mature expression.

8. Strictly fundamental there are only three. Any one of the four could be derived from the other three.

9. development It is well known that one of the scientists who contributed most to quantum physics in the 20th century, Richard P. Feynman (1918-1988), award Nobel Prize in Physics in 1965, said: "I think I can safely say that no one understands quantum mechanics".

10.  "I propose the following thesis: operative pursuit follows a double line. There are two types of pursuit: generalisation by negation, and reason. These two types are distinct in that they diverge (starting from the inchoative operation) and their objects deal in different ways with abstract objects. On the other hand, they do not deal with each other", Course of Theory, II, 307-308.

11. "I call logos the unification of the objects of the prosective operations, which is achieved according to their different modes of compensation. According to agreement , reason refers, not before the explication of the causes, but from their compensations, to the general ideas and their determinations. The peculiar nature of mathematical objects is thus explained", Curso de teoría, IV, Eunsa, Pamplona, 2004, 53.

12.  "Mathematics is the science of forms which are pure objects. Pure forms are relational properties", Course of Theory, IV, 480.

13. Here the hypothetical does not refer to the probable, to a postulate, or to an opinion or conjecture, but to the precise way in which number intentionally refers to physical reality. This subject of intentionality is a cognitive novelty that can only be discovered by exercising it, which happens when thinking, for example, of any three objects.

14. Theoretical Course, IV, 487.

15. "In short, the numbers thought of are intentions about the way in which the causes in the concausalities are held among themselves. I call such a holding (which in no way entails consolidation of concausality) physical number. Physical numbers are intentionally discovered in a hypothetical way, because as they belong to concausalities, they are discovered rather than known: what is known are the thought numbers, intentionally hypothetical about physical numbers. With a play on words I will say that the hypothesis makes it possible to establish the thesis of causal content, which is known only hypothetically insofar as it is a finding", Curso de teoría, IV, 486.

16. This is considered, for example, by Heisenberg, who sees in the mathematization of quantum mechanics the victory of Platonism over the materialism of Democritus and Leucippus. Cf. W. Heisenberg, The Structure of the subject, Folia Humanistica, Vol. VII, No. 82; October 1969. An important testimony is also the following: "The Platonic conception is the only sustainable one. By this I mean the conception that mathematics describes a non-sensible reality, which exists independently of both the acts and the dispositions of the human mind, and which is only perceived by it, though probably incompletely. This conception is rather unpopular among mathematicians, although some of the great ones have adopted it, for example Hermite, who once wrote the following: "There is, if I am not mistaken, a whole world which is the whole of mathematical truths, to which we have access only by intelligence, just as there is the world of physical realities; both are independent of us and of divine creation", K. Gödel, Ensayos inéditos, edition at position by F. Rodríguez Consuegra, Mondadori, Madrid, 1994, 169.

17. Here we do not, of course, refer to the specific meaning that the expression "common sense" has in Aristotelian-Thomistic philosophy. In Aristotelian-Thomistic philosophy it is the second level of knowledge , which corresponds to perception. Here we refer, as has been said, to what in common language means to have common sense.

18. It is illustrative in this context what Heisenberg says in the following sentence: "After all, science too must rely on ordinary language, because it is the only language in which we can be sure of really understanding phenomena", Heisenberg, W. "The Structure of the subject", Document accessed online athttp://www.arvo.net/pdf/la%20estructura%20de%20la%20materia(1).htm [enquiry: 18/11/2006].

19. "In my proposal, Newton's limitations are dealt with by admitting different types of movement and, therefore, of time, different from those that Newton objectifies", L. Polo, Nietzsche, 249. "The same [as with space] must be said of Newton's time: it is not physical either", Curso de teoría, IV, 424. Polo places this correspondence on the formal level of the imagination.

20.  "Absolute time, true and mathematical in itself and by its nature, and without relation to anything external, flows uniformly (...) Absolute space, by its nature and without relation to anything external, always remains the same and motionless", I. Newton, Mathematical Principles of Natural Philosophy, 655.

21. This way of conceiving life is not so alien to how some people understand it today. An example might be the following text: "This flow of energy is the essence of life. A cell can best be understood as a complex of systems for transforming energy. At the other end of the biological scale, the structure of the biosphere, i.e. the whole of the living world, is determined by the energy exchanges that occur between the groups of organisms within it. Similarly, evolution can be seen as a skill between organisms for the most efficient use of energy resources", H. Curtis ; N. Sue Barnes, Biología, publishing house Médica Panamericana, Buenos Aires, 1993 (5th edition), 38.

22. "The efficient cause (...) in double concausality with the subject is the notion of force". (...) "To think that the subject can be animated by efficiency, be concausal with it, without formal concausality is mechanistic", L. Polo, El orden, 150-151.