An Inquiry into the Question of Inertia

You will notice that there is much in this article that was taken from my previous post on the definition of motion. I decided to re-direct my ideas and focus on method, more than the actual question of motion and inertia.

St. Thomas Aquinas makes a bold claim concerning Aristotle’s definition of motion saying, “And therefore it is wholly impossible to otherwise define motion through what is prior and more known, but as the philosopher has here defined it.”i Such a claim, from such a mind, warrants a careful look as to the reasons behind a claim of this force. The significance of this inquiry is great. Aristotle's definition of motion is challenged by a fundamental principle of modern day physics, inertia. How to reconcile these ideas or change them is, therefore, an important question for those who do not wish to simply abandon Aristotle and St. Thomas.
We are left then with the quandary of what to do. Modern day thought on the whole encourages us to scorn ancient thought and embrace the current understanding of things. After all, modern science has taken us to the moon. Even so, there is a puzzle. When Aquinas made his bold claim, was he merely stuck in the world of own limited science? Did he make this claim based upon the poor and limited scientific data available at the time? It is interesting to note, that neither he nor Aristotle bring up the importance of accumulating more “data” at all in their explanations. Probably most striking to our modern sensibilities is that neither of them even mentions the idea of force or anything like it in their accounts.
The differences between the present day approach to the physical world and in particular to motion, and the ancient and medieval approach explains many of these difficulties. The modern day physicist proceeds according to what is commonly known as the scientific method. I here define it as a systematic method of inquiry proceeding according to hypothesis and experiment. Consequently, modern scientists establish various models to explain what they experience and then abandon them for another, better model when one should come along.
Aristotle and St. Thomas were engaged in a much different enterprise as can be clearly seen in their works. The classical approach was one that sought, first of all knowledge, or as St. Thomas would have said scientia. This cognate is obviously related to our modern day word for science, but its meaning is much different. Aristotle defines such knowledge in his Posterior Analytics,
“We think we know each [thing] without qualification, but not in the sophistical manner with respect to an attribute, when we think that we know the cause through which the thing exists as being the cause of that thing and that the thing cannot be other than what it is.”ii
As he will later show in his De Anima this knowledge comes from the abstraction of the forms of things by the agent intellect, so that the mind truly knows things.iii
As is clear, the two approaches to understanding the physical world are vastly different. While the differences between these two approaches are such that it seems impossible to say whether one is better than the other, it does seem that we may argue for one being prior to the other. This brings us to the purpose of this paper. While it would be a great task to once and for all settle the question about inertia and the classical definition of motion, at least we can here argue for where we ought to begin looking. My thesis is two-fold: Aristotle's definition of motion is prior to the account of inertia in the order of knowing in that it is self-evident. Consequently, any account of inertia must be able to keep this definition if it is to be taken as true.
To proceed I will first argue that the only valid way to proceed in any inquiry is as Aristotle states in the beginning of the Physics “The natural path is to go from things which are more known and certain towards us toward things which are more certain and more knowable by nature.”iv I will then address some preliminary concerns to the definition of motion. After this, I will examine Aristotle's definition of motion and how he argues that it is true showing that it is in fact self-evident, given Aristotle’s principles of nature. This being shown, I will conclude by claiming that this definition must be held if one is to investigate the physical world, in particular in examining the principle of inertia.

Beginning
In every inquiry in which there are principles or causes or elements, understanding and science occur from knowing these. For we think we know each thing when we know the first causes and first principles and have reached the elements. It is clear, then, that in natural science as well one must try to determine first what concerns the principles.v

So Aristotle opens the physics and directs us to examine the principles of natural philosophy. It is then that he enunciates the principle which will be our primary concern in this essay, “The natural path is to go from the things which are more known and certain to us toward things which are more certain and more knowable by nature.” There are some questions that the formulation of this principle brings up. In particular, the distinction between what is more known to us and what is more known by nature, for this is the principle by which Aristotle justifies this mode of proceeding. In this section I will argue that there is no other way to proceed with certainty and scientia except by this path that Aristotle lays forth. While such an inquiry belongs properly to epistemology, we will be able to touch on this matter briefly.
It is sufficient here to see that there are some things that we are able to see more immediately than others. For instance, I know that the whole is greater than the part, or that equals added to equals are equal. Such axioms are certain and clear to our minds. Further claims, such as the interior angles of a triangle equal two right angles, are true, but certainly cannot be grasped with the immediacy of the afore mentioned axioms. In fact, following Euclid's Elements there are various definitions, axioms and postulates, let alone propositions that I must comprehend before I can see that the interior angles of a triangle are equal to two right angles.vi
The movement in mathematics, however, is simpler than that of Aristotle’s Physics. Aristotle, since he is dealing with physical and therefore sensible realities, must move from his experience of things to the principles, and then from principles to demonstrations. The greater part of the Physics is dedicated to the discussion of principles. It is not until the sixth book (of eight) that Aristotle even begins to do demonstrations, properly so called. Therefore we see that the philosopher of nature must spend time examining his experience, moving from the more known to the less known.
He gives three analogies by which to understand this method. The first: “For the whole is more known according to sensation, and the universal is a certain whole. For the universal embraces many things within it as parts.”vii This analogy allows us to consider our experience in a way like the universal and particular. In our experience of things, say a tree, we realize that this is a kind of whole that is composed of other things which are themselves able to be known. We must be attentive to our experience to see what things might be contained therein.
This idea is further elaborated when Aristotle gives the second analogy, “In a way the same thing happens in the relation of a name to its account. For the name signifies indistinctly some whole, as circle, but the definition of this divides into the single parts.”viii Therefore, given that sensible whole, with its various parts, we see that the whole is grasped by the intellect as something indistinct. To better understand this whole we name and define the parts which are less obvious to us, but simpler and clear ideas in themselves. So in the case of the circle, we see that its principles are the point and the line, and these are more simply intelligible in themselves, but we first know the circle.
Aristotle then gives his final analogy, “And children at first call all men “fathers” and all women “mothers” but later they distinguish each of them.”ix Children take time to distinguish between adult males and adult males with offspring. So also we need time to distinguish those things that look the same to us, so that we must see their differences. As we are defining and seeing parts we will come to distinguish some things that were confused before.
Using these three examples Aristotle establishes that the confused whole that we first grasp, is in fact confused. It is what we know better, but it is not as intelligible on its own as the parts. We must grasp the parts and define and distinguish them in order to understand our experience. We must wade through the various sensations that we have received, and Aristotle gives us an ordered means by which to do so. Start with what we know, and then move forward. To abandon what we knew at first leaves us lost and adrift in the wild ocean of natural philosophy. We see therefore, that the “natural path” is the only path on which we can proceed with certainty. Therefore, it is the only path by which we can proceed scientifically.

Preliminary Considerations
It is well that we should first make a note regarding the most jarring part of my claim about motion that it is self-evident. Something can be self-evident in many ways. There are principles which the mind grasps immediately, and as obvious, such as “the whole is greater than the part.” There are also principles which St. Thomas calls “self-evident to the wise.”x What is characteristic of such principles is that they are not obvious to everyone. However, both kinds share in common that the mind immediately grasps them. What this means is that there is no middle term showing that they are the case, but rather, through sufficient reflection on experience one sees that it is true. This is to say, there is no proper demonstration of the definition of motion.xi (ref.)
It is nonetheless true that Aristotle's definition of motion, “the actuality of what exists in potency, as such,”xii provides challenges. Prima facie, this definition seems incomprehensible. This is because he is defining motion by what is prior to motion. While it seems reasonable enough that we must define motion in terms of something prior to motion, it challenges us, because there does not seem to be motion in the definition. This difficulty can be surmounted, only if we are able to understand how act and potency are prior to motion.
One final note about Aristotle's definition of motion before we proceed: he is not only defining locomotion, that is, motion from place to place. He certainly sees this as the paradigm of motion and will even say that it is at the base of all other kinds of motion, but he will consider growth and diminution, alteration, and locomotion as kinds of motion. Therefore he will speak of motion in very general terms, which is at once an excellence of his account, and a challenge to we who would understand him.
There are certain principles Aristotle assumes that his readers have at this point grasped and understood. I will not here argue to these principles, but take them as given. First of all we should know that there is such a thing as change and what a change is. If one denies that there is change then natural philosophy can have nothing more to say to him. Such an objection is for metaphysics. According to Aristotle, we must understand change to be, generally speaking, the loss or reception of a substantial or accidental form by some substance. Likewise, we must accept that there is such a thing as a nature. Again, the denial of this brings us to metaphysics. Aristotle defines nature as “a certain principle and cause of moving and of resting in that which it is, primarily, in virtue of itself, and not accidentally.”xiii
Aristotle comes to the principles of nature and change and calls these matter, form and privation. These again are taken as given. It is worthwhile here to point out though that these are indeed principles. There is no demonstration that these are true; they are manifested by reflections upon experience. Finally, Aristotle expects us to have some idea of potency and act. While these are likewise principles and therefore indemonstrable, we will pause briefly to see how Aristotle is able to come to the ideas of potency and act.
Aristotle first mentions the ideas of actuality and potentiality as a proper consideration of natural philosophy in Book II chapter 1. Here we are introduced first to potentiality when he says, “We would not yet claim, in the former case, that the bed has anything according to art if it is only a bed potentially and had not yet the species of a bed.”xiv He is here setting up an analogy between nature and art. The timber is potentially a bed just as matter is potentially flesh. This analogy is very similar to the one he uses to show that there is prime matter. There he argues that as the timber is to the bed, so is there some underlying principle that stands to formxv. He thus moves from matter to see that there is potency, a more general idea that something can be something, but is not. The idea of actuality immediately follows as a correlative. Therefore, when the timber is, the bed, it is no longer the bed potentially but actually.

Definition of Motion
When beginning his inquiry into the definition of motion Aristotle lays out those things that are concomitant to motion.xvi This should make us realize that a complete understanding of what motion is, will be impossible until we have considered the continuous, the infinite, place, void, and time. Having given us this context Aristotle makes a division between potency and act. “There is, then, something which is only in actuality and something in potency and actuality.”xvii This is the first of three divisions that he makes in his search for the definition of motion. As Glen Coughlin points out in his appendix on the definition of motion, it is important to note what is meant by potential.xviii He is dividing act from potency and for this division to be helpful, and then there must be things that stand in opposition to one another. For instance, it does not aid our inquiry to say that I have the potency to stand because I am standing. Therefore, we must understand potency together with privation of some act. However, we cannot confuse potency and privation.
Aristotle proceeds to explain the basis for relations as excess and defect, action and passion, the mover and the mobile. He leaves this aside at this time, but he will return to this consideration when discussing the relation between the mover and the moved. We shall also take this up below.
The second distinction is made when Aristotle states, “motion is not beyond things.”xix That is to say, that it is not beyond any of the categories. The final distinction points out that in every genus there is a being and privation of that being.
We see from the first division that motion must belong to what can be in potency and act. This is clear if we consider that motion is a kind of change, which is obvious from experience. What does not have potency (and this is potency understood with privation, as was said) is unable to change, for there is, as it were, nowhere for it to go. Therefore, motion must pertain to what can be in potency and act.
The second distinction, that motion belongs to the categories, must be understood in two ways. First, that motion cannot be some super genus since “one can grasp nothing common.”xx Second, we must understand that motion is not some eleventh category since there is “nothing beyond the things named.”xxi We may therefore conclude from this that motion is going to be understood in the context of a genus.
The third distinction concerning the being and privation in each genus indicates where to look for motion in a genus. That is, it is going to be somewhere between the being and privation, the white and the black or the perfect and imperfect, etc. It must be clear that when Aristotle says that “the species of motion and change are as many as are those of being,”xxii it does not mean that there is motion in every genus, as he will later deny, but he is claiming that as many categories as admit of motion, so many will the species of motion be. There will not be one kind of motion for multiple categories.
From the above we may conclude that motion belongs to those things that are in act and potency in some genus, according to the mode of that genus. We must take this together with our common experience of motion. We know motion as that which is between its two ends, “that from which” and “that towards which.” For we see the apple moving from green to red, or the child growing to his full height when a man, or the cup being here, and then being there. Such is out experience of motion.
What we know about motion at this point is its ends. For I know that the mobile is here or there, but when it is here or there I do not say that it is in motion. Therefore, since we know the ends of motion and we must always proceed from what is more known to the less known, then we must define motion in terms of its ends. For the sake of generality we will names these ends, “that from which” and “that towards which”
The end “from which” is what the mobile posses now, before it has gone somewhere. It is the end that is held in act. The end towards which is what is held in potency, the mobile is not there. We also see that there are any number of points in between these two at which the mobile could be said to be if its motion did not continue on. The mobile has no intrinsic order away or towards either end if it comes to rest at one of these points. If I get up and walk to the doorway and stop, I do not belong to either room more than the other. It is only in motion that I have an order towards or away from some point.xxiii
From these considerations we see that motion is a kind of potency, since it does not possess its end. We see also that there is a kind of actuality to motion. The points at which the motion could stop are closer to the end, so long as we take the order provided by the motion, than the point from which the motion began. Therefore, as long as it is moving it is becoming the end towards which.
Now, the end that towards which is what the mobile holds in potency, before and during the motion. Once the mobile holds the end towards which in act the motion is completed. However, we may still define this in terms of the end from which as the end from which. In order to do this in the language of act and potency, we say that mobile at the end “towards which” is the actuality of the potency. Or in a parallel formulation to Aristotle's definition, it is the actuality of what existed in potency.
So far, we are still speaking of the ends and not of what lies between them. We therefore want to understand the end “towards which” as it exists in potency, not as it existed. Therefore we must understand that potency insofar as it is still in potency. This is our definition: the actuality of what exists in potency, as it is in potency. As Aristotle phrases it, “the actuality of what exists in potency, as such, is motion.”
We see therefore, that Aristotle proceeds by starting with what is prior and more known, namely potency and act. We then consider what is “in between” these and this is what gives us motion. The argument works by the mode of manifestation. If something is in potency it is not moving, and if it is in act it is done moving, we therefore must look to what is between. There is however, no cause of this definition given. We do not see why motion is this way; we see only that it must be this way. This is what is proper to a principle, that there is no cause of it that the mind can grasp; we see only that it is.
Inertia
Sir Isaac Newton first introduced the world to the idea of inertia in his treatise Natural Philosophy’s Mathematical Principles. Right away we see that his conception of natural philosophy is different that Aristotle’s, given that he is searching for its mathematical principles. For Aristotle, mathematics and philosophy of nature were two very different things. We will discuss more of these differences below. In this section I will argue that Newton’s approach to natural philosophy is positivist in nature and that he proceeds as a mathematician.
Newton introduces us to the idea of inertia in the third definition. “Innate force of matter is the power of resisting, by which and body whatever, as much as is in it, perseveres in its state either of resting or of moving uniformly in a directed line.”xxiv By innate force of matter I am understanding inertia. This understanding seems to hold weight given the first sentence of the explanation of his definition, “This force is always proportional to its body, and does not differ in anything from the inactivity {inertia} of the mass except in the mode of conceiving it.”xxv At this point, there is not much to say regarding his method, only that he has proposed definitions of things that may or may not exist and that these definitions bring up questions them.
After his definitions Newton expounds the philosophical framework in which theses definitions are to be understood. In his Scholium Newton explains his understanding of “Time, space, place, and motion.”xxvi There is much that can be questioned in his accounts but to do so would divert us from our purpose. We will here only note what he does.
After his Scholium Newton introduces us to his “axioms or laws of motion.”xxvii The first law is that which interests us, as it is the law of inertia. “Every body perseveres in its state of resting or moving uniformly in a directed line, except insofar as it is compelled to change its state by impressed forces.” immediately there seem to be difficulties. First of all questions arise such as “What does it mean for a body to be in a state of motion?” and “What is force?” These questions should then lead us to wonder what Newton could mean by calling these axioms. This law seems to be a far cry from “The whole is greater than its parts.”
We see that this proceeds very much like Euclid’s Elements. Euclid first lays down his definitions postulates and common notions and then proceeds. There is no discussion of these principles. This seems to be more acceptable since most of these seem fairly straightforward.However, when Newton begins a study of natural philosophy thus, it seems to beg many questions that are not here addressed. What Newton has effectively done is proposed a model by which to understand the phenomena. The certainty that we have in his explanation comes from seeing how effectively it explains the phenomena. This is what has become known as positivism.
In his highly influential work The Structure of Scientific Revolutions, Thomas Kuhn undertakes to describe the process of scientific revolutions and points out that they are essentially changes of what he calls “paradigms”xxviii That is, someone posits another model by which to understand the phenomena and the majority take hold of it. This is essentially what Newton has done. He has put forth a way of understanding the world. This includes the definitions and the Scholium which we mentioned earlier. This world view and the laws by which he describes it are far from axiomatic. This is not to say that they are false, merely that are not immediately grasped by the mind, and that a great amount of discussion should be gone through before accepting these ideas as true. We must work through our experience to see these as principles.
It seems right that Einstein has improved on Newton and his theories have taken precedence.xxix We will not, however, go on to discuss Einstein, because it is beyond our purpose. It is of concern here to put forth the way in which modern empirical science ought to proceed, not to describe how it has proceeded. What is more, I am not here going to criticize the principle of inertia, but only provide certain requirements which adherents to this principle must meet. This is the subject of the final section.
Conclusion
Newton's method fails to proceed according to the natural path as laid down by Aristotle. The language he uses seems to indicate that he is, but on a closer examination, we see that there are significant gaps. The difficulties with Newton's method are that he treats physical objects mathematically and that he does not proceed from what is more known to us, to what is more known by nature. What follows is that his method is not scientific in the classical sense.
The argument about treating physical objects mathematically has hitherto only been implied in this paper. A further discussion of this question would belong to a different study that would examine the various degrees of abstraction, and to what extent certainty can be had in these various degrees and whether there can be any overlap. Since this would take us beyond our primary purpose, we will leave this discussion aside and attend to the second difficulty raised, namely, Newton's invalid mode of proceeding.
Given that Newton is discussing natural philosophy he should proceed in the manner the Aristotle did, moving from the confused whole to principles, and from principles to demonstrations. As we saw above, Newton instead posits his principles, much like the mathematician. The difficulty here is that these principles are not axiomatic as we saw. There needs to be arguments to manifest that these are in fact principles.
There are two ways to go from here, one is to supply the missing dialectic of Newton’s Principia, and try to manifest his principles, or to say that Newton's project is wholly other than that of Aristotle's and that we ought not to hold him to the same standards. It is a different method. Given that Einstein does improve on Newton and effectively throw out Newton's world view, I will take the harder case, that Newton is undertaking a wholly different project.
This position is lent credence by examining the very title of the work, where it speaks of mathematical principles. Throughout his work Newton will express phenomena in a mathematical way. This seems to be vastly different than the way Aristotle speaks of motion and comes to his definition. If this is the case, as it seems that it is, then the question resolves back to the first difficulty raised regarding Newton's method, namely treating physical objects mathematically.
What can be said here is that this may in fact be a valid means of proceeding. The modern scientific hypothetical-deductive method has seemingly accomplished much and we should be loath to abandon it simply because it does not seem to conform so precisely to Aristotle's “natural path.” However, despite the great ability of this method to accomplish things, we must also be wary not to throw out the method of Aristotle. To use contemporary terminology, Aristotle is doing philosophy and Newton is doing science. Aristotle's method provides certainty, while Newton's does not seem to do so. If then we are to proceed effectively and with knowledge, then any account of inertia and inertial motion should be informed by what is held with certainty by following Aristotle. Aristotle's definition of motion is therefore prior in the order of knowing, as it is held with certainty and to further understand inertia and the world about us, we must hold on to what we know and proceed to into the unknown.

NOTES
i Thomas Aquinas In Pysicam bk. 3, lectio 2
ii Aristotle, Posterior Analytics, 1.2.71b10-2
iii Aristotle, De Anima, 2.5.
iv Aristotle Physics 1.1.184a17-19
v Ibid., 184a9-16
vi Euclid, Elements bk.1
vii Aristotle, Physics 1.1.184a25-27
viii Ibid., 184b9-11
ix Ibid., 184b12-13
x Thomas Aquinas, Summa Theologiae, I, Q.1, a1
xi Thomas Aquinas, In Physicam, bk.III, lectio 2
xii Aristotle Physics 3.1.201a11-12
xiii Ibid., 2.1.192b21-23
xiv Ibid., 193a34-36
xv Ibid., 1.7.191a9-11
xvi Ibid., 3.1.200b16-26
xvii Ibid., 200b26-27
xviii Aristotle. Physics Or On Natural Hearing, ed. and trans. Glen Coughlin, William of Moerbeke Translation Series, (South Bend IN :St. Augustine’s Press, 2005), App. 6, 246.
xix Aristotle Physics 3.1.200b33
xx Ibid., 200b34-35
xxi Ibid., 201a3
xxii Ibid., 201a9
xxiii Aristotle. Physics Or On Natural Hearing, ed. and trans. Glen Coughlin, William of Moerbeke Translation Series, (South Bend IN :St. Augustine’s Press, 2005), App. 6, 248.
xxiv Isaac Newton Natural Philosophy’s Mathematical Principles, ed. Chris Decaen, trans Ronald Richard , (Thomas Aquinas College, 1996) 3.
xxv Ibid.
xxvi Ibid., 6.
xxvii Ibid., 11.
xxiii Thomas Kuhn, The Structure of Scientific Revolutions 3rd ed., 10
xxix Antonio Moreno, “The Law of Inertia and the Principle Quidquid Movetur ab Alio Movetur,” Thomist 38 (1974) 313-316.