International Catholic University
Let me begin by introducing myself. I am William Augustine Wallace of the Order of Preachers, the Dominican Order, and I will be giving six introductory lectures on the philosophy of nature. I first learned philosophy of nature during my early studies in the Dominican Order, when I was then close to thirty years of age. That was after a naval career during World War II in which my main work was in science and engineering.
Now, it is common for people who study philosophy as their main interest to begin with a course on the philosophy of nature. This is a difficult beginning, particularly for those who already have the mind-set of modern science, as I know from experience. But I shall try to minimize that difficulty by showing the harmony that can exist between the philosophy of nature and modern science. I will also be using examples drawn from science wherever this is possible.
The main text I shall use is my own, The Modeling of Nature: Philosophy of Science and Philosophy of Nature in Synthesis. It was published by Catholic University Press in 1996. To supplement this I will draw on one of my earlier books, The Elements of Philosophy, published by Alba House in 1977. This is essentially a compendium of all the philosophy articles in the New Catholic Encyclopedia, of which I was the editor for philosophy. It would be desirable to have access to the fifteen-odd volumes of the New Catholic Encyclopedia, but this is not necessary for the course.
Philosophy of nature can make claim to being the oldest branch of philosophy. Perhaps that is a reason why students of philosophy start with that discipline. It began in the fifth century before Christ when Ionian philosophers, notably Thales of Miletus, speculated about the basic stuff of the universe -- matter in its most primitive form -- which the Ionians identified with the nature of things. A different approach was that of the Greek philosopher Plato, who saw form as distinctive of various natures. Plato postulated ideal forms -- existing in some heaven apart from earth -- in which he thought earthly forms somehow participated. It was Plato's student Aristotle who, in the fourth century before Christ, took Plato's forms from the heavens and put them into things, maintaining that that is where forms really exist. For Aristotle, both matter and form satisfied his idea of nature. He explained this teaching in a work called the Physics (Phusika in Greek, Physica in Latin). This gets its name from the Greek word phusis, translated into Latin as natura, which is the origin of our English word "nature."
Aristotle's Physics is one of the most durable works in the history of philosophy. It occupied the attention of the Greeks until the sixth century of the Christian era, and then was studied by the Muslims until the twelfth century. It took on new life in the thirteenth century, in the universities of the Middle Ages and the Renaissance, where it was required of all students. Indeed, this requirement lasted well into the seventeenth century. Not surprisingly Aristotle's Physics provides the core teachings I shall be explaining in these lectures. They do, of course, require development and exemplification in terms of discoveries made since the seventeenth century, with the rise of modern science.
To show the correspondence between the titles of my lectures and the matters treated in the eight books of Aristotle's Physics I employ my first schema. I shall be using graphical aids such as this throughout my lectures to illustrate the points I am making. These are available as diagrams to those taking the course for credit. Many of these figures are from The Modeling of Nature, though generally with numbers different from those in the lecture series. This is Fig. 1.1, not found in Modeling:
| Lecture Title | Aristotle's Physics |
|---|---|
| 1. Fundamental Concepts | Book I |
| 2. Nature: The Inner Dimension | Book II |
| 3. Nature's Powers and Natural Kinds | Book II (plus De anima, etc.) |
| 4. Nature's Property: Motion or Change | Book III |
| 5. Nature's Measures: Place and Time | Books IV through VI |
| 6. Nature's First Unmoved Mover | Books VII and VIII |
Reading Aristotle's text, even in English translation, is difficult. But if you have the time and energy I would suggest that you try to read along in his text as we progress through the lectures. I would recommend the translation with commentary of Hippocrates Apostle, published by the Peripatetic Press of Grinnell, Iowa.
Aristotle begins the Physics with the cryptic statement that in natural philosophy we must proceed from what is more known to us to what is more known to nature or is more knowable in itself. Unpacking that statement will enable us to explain a few concepts relating to the theory of knowledge that are indispensable for our enterprise.
What Aristotle means by this statement is that we gain knowledge of nature from our senses or from sense experience, the type of knowing that is more obvious to us. But a deeper knowledge is also possible for us through our minds or our intellects, which enable us to transcend the knowledge of individuals provided by our senses. Our intellects are capable of grasping the natures of things as they are in themselves, through universals. Universals are less obvious to us, but with their aid we can go beyond the surface appearances of things as presented by our senses.
In Aristotle's theory of knowledge we attain intellectual knowledge through sense experience, for with him nothing is in the intellect that was not first in the senses. But sense knowledge for Aristotle was not as simple as it might first appear. Actually it is attained in two stages. The first stage is provided by our sense organs -- the eye, the ear, the nose, the mouth, the skin -- called outer senses because they are on the periphery of our bodies. When properly stimulated, each of these organs produces within us a sensation proper to the particular sense. These are the sensations of sight, hearing, touch, taste, and smell. The second stage then complements our outer senses by other senses we have in the interior of our bodies, called inner senses to distinguish them from the outer senses. The organs for these senses were not easily identified by the Greeks, but we now know that they are lodged in our brain and nervous system.
In a simplified view, the inner senses may be seen as made up of three components, the central sense, the imagination, and the memory. What is common to all three is that they are concerned not with a sensation, as are the outer senses, but with what I shall call a percept. A percept is nothing more than a unified sense image, a composite of the sensations produced by the outer senses. It is generated by the first of the inner senses, the central or unifying sense. This receives sensations and integrates them into a singular composite representation. In doing this it forms the percept, and the process by which it does so is known as perception.
For example, in sense experience I perceive an apple. This is an individual large, red, cold apple. All of these sensations, and possibly many others, are incorporated into the single percept whereby I perceive the particular apple.
Two other inner senses are imagination and memory. Once I have perceived an apple it is possible for me to reconstitute the elements that entered into its percept and, in the apple's absence to imagine the apple. I may imagine it as it actually was, or I may embellish it in fanciful ways, imagining it, for example, as a gold apple. Alternatively, I can recall the particular percept as it was in a past time, doing so through my memory, and in this way remember the apple.
As we use these three inner senses we build up what is called sense experience. This is nothing more than the accumulated memory of all the percepts we have experienced in our lifetime -- a huge storehouse of information on which we may draw with our intellects.
Intellectual knowledge is quite different from sense knowledge, whether this derives from the outer senses or the inner senses. What the intellect does is work on our sense experience and extracts from it various intelligible aspects of things, telling us, in effect what things are. Put simply, it does so by focusing on the percept and extracting from it a universal that is called the concept. The intellect does this in two stages: first, by illuminating the percept in a particular way, and second, under this light, by abstracting from the percept its intelligible content. A percept, as already explained, is a concrete and singular image of the thing perceived. The concept, as opposed to this, is an abstract and universal representation that furnishes us with an idea of what we have perceived.
To return to our example of the apple, the percept of a particular apple is a composite image incorporating many sensations, such as would be found in a large, red, cold apple. Under the illumination it itself provides, the intellect considers the percept of that apple and leaves aside its particular size, color, temperature, etc. From what is left it forms a universal concept of apple. This is what we might call "appleness," whatever it is that that object has in common with other apples. The concept of apple is abstract because it is abstracted from the particulars of sense knowledge. It is universal because it grasps the nature of apple, essentially what we mean when we call the object perceived an apple.
Once we have grasped a concept -- and we do it all the time throughout our lives -- we are able to apply that concept to all objects we may perceive that share the same nature, in this case to all apples. This is what it means to say that the concept is a universal, it is a "unit" related to many "others" (a unum versus alia) that share the same meaning or intelligible content.
We may summarize what we have covered thus far by reference to our next schema, Fig. 1.2 (p. 133 of Modeling). This is a much simplified diagram that illustrates the process of concept formation. On the far left is the external object, the real apple as it exists by itself independently of my knowing it. When properly illuminated and situated the apple affects my sense organs, identified in the first box on the left as "Outer Senses," and produces one or more sensations in them. These stimuli are then transmitted to my "Inner Senses," as shown in the next box, by signals sent to the brain through the central nervous system. There the central sense integrates the sensations received from the outer senses into a composite image known as a percept. Through this percept I perceive the object as "this large, red, cold apple."
Finally, my mind, shown in the last box on the right as the intellect, works on this percept to generate the concept. It does so in two stages. First it illuminates the percept to render it intelligible to my mind in a particular way. Second, under this illumination it extracts the intelligible content from the percept and gives birth to the concept. The first stage of the process, illumination, is produced by the natural light of the intellect when attending to percepts. The second stage, abstraction, is the way the intellect naturally effects a transition from singulars to universals. The percept, as we have already said, is "concrete and singular." The concept, by way of opposition, is "abstract and universal." Other terms for a concept are an idea or a meaning. In general we have in our minds as many concepts as we know words whose meaning, or the idea they convey, we correctly comprehend.
The process we have just sketched is an over-simplified explanation of how concepts are generated by the human mind. By the time students come to study the philosophy of nature they have obviously attained considerable experience of nature. Their minds, one might say, are chock full of concepts. I refer now to every-day experiences, where conceptualization is done naturally and effortlessly, just as easily, for example, as other natural processes such as breathing and digesting one's food. (Admittedly there are some abstruse matters that are difficult to conceptualize, such things as "entropy" and "geodesics," for example, but we are not concerned for the present with conceptualizations of this type.)
Let me make a start here, however, at classifying concepts, and begin with the types that can be understood simply on the basis of ordinary experience of the real world. A basic way of classifying concepts is in terms of the two processes whereby they are formed, already identified as illumination and abstraction.
We begin with the process of abstraction. To abstract is to pull out, or to extract, one or other intelligible content or meaning latent in a percept, leaving aside everything else that may be present in it. This abstractive process can yield various degrees of abstractness, depending on how the percept is illuminated by the intellect so as to leave aside various material aspects imbedded in the percept. Three orders or degrees of abstraction are generally enumerated. These suffice to differentiate concepts into three basic types, namely, natural concepts, mathematical concepts, and metaphysical concepts. Each of them we now consider in turn.
Natural concepts are important for us, since these are the type that are studied in the philosophy of nature. Natural concepts are associated with the first order or degree of abstraction. In this type of abstraction the intellect leaves aside only the individual and concrete aspect of the percept, that associated with the "this" of the percept. Up to now we have been considering "this red apple" as a percept. Here let me add a different percept, "this lead ball," assuming that we have perceived a little ball made of lead just as we have perceived a red apple. When we leave aside the "this" in these two cases, we come to the universals of "apple" and "lead," and are no longer tied to the particular apple or lead before us. "Apple" is the fruit of an apple tree, any and every apple, not merely the one we are perceiving. Lead is a metal, the eighty-second element in the periodic table, and again, any and every lead, not merely the lead we are considering.
What happens in this type of abstraction is that we grasp a meaning that is common to all classes of objects that share the properties of apple and lead. The concepts formed all imply some reference to sensible matter, that is, to matter that falls under our senses, but they abstract from individual matter, they leave aside all individual and distinctive attributes. The resulting abstraction is called natural or physical abstraction. It is employed in our ordinary discourse as well as in natural philosophy.
Mathematical concepts are more abstract than natural concepts for the simple reason that more matter is left aside when they are conceptualized. Consider, for example, the perceptual basis for expressions like "three apples" and a "lead ball," and then the concepts of "three" and "sphere" that may be abstracted from the apples and the ball respectively. "Three" and "sphere" are mathematical concepts. They do not refer exclusively to any group of three or any individual sphere, but rather to all classes of objects that share that number or geometrical shape. Nor do they contain any reference to sensible matter. The "three" we conceptualize contains no reference to the apples, the sensible objects from which it is abstracted. It merely indicates a group of units that are only imaginable. Similarly "sphere" does not connote that the object known is composed of lead or wood or rubber. It merely indicates a body composed of continuous quantity, an imaginable or intelligible matter. Its matter, if you will, is made of pure extension, not matter that exhibits sensible qualities associated with lead or wood or rubber.
Metaphysical concepts, finally, have more in common with mathematical concepts than with natural concepts. They are, in fact, the most abstract of all. They are separated from matter entirely, for they include in their understanding no reference whatever to individual, sensible, or intelligible matter. Examples of such concepts would be "being" and "existent." The concepts of "being" and "existent" express an intelligible content that is found in apples, lead, and mathematical objects, since all of these are beings and existents in some sense. So characterized, metaphysical concepts are very general and apply to being as such, not merely to objects that exist in sensible or intelligible matter. They apply to whatever "is" in any way whatever, including things that are completely immaterial and incorporeal, such as God and spiritual substances.
When concepts are distinguished on the basis of their abstractness or degree of separation from matter, it is relatively easy to identify the objects studied in the philosophy of nature. A natural philosopher is not concerned with the entire range of being as such, as is the metaphysician. Nor is the natural philosopher concerned with quantified being as this is studied by the mathematician. The natural philosopher is concerned with the objects of ordinary experience, objects that exist in matter as it is perceived by our senses, what we call sensible matter.
One of the characteristics of such matter, as we shall see, is that it is always capable of undergoing change. Thus we can say that the natural philosopher studies changeable being, not quantified being or being as such -- the proper concerns of mathematicians and metaphysicians. And since motion is a kind of change, we can also say that natural philosophy is the science of moveable being, the type of being that can be changed and that undergo motions or mutations of various types.
At this point let me summarize what we have covered so far by sketching a preliminary typology of concepts as shown in Fig. 1.3 (p. 140 of Modeling). The entries to the left of the double line pertain to the perceptual order. They designate extramental objects as they are perceived by the senses, basically through sensations and then through perceptions, as schematized in the two boxes to the left of the diagram on Fig. 1.2. The entries to the right of the double line, on the other hand, represent concepts. Thus they refer to the contents of the intellect box on the right of the diagram. In the middle column concepts are arranged vertically according to their order or degree of abstraction. A description of the kind of abstraction involved is then found in the column on the right.
I have already mentioned the term "science," so let me make some preliminary remarks about science and how it relates to philosophy. Before the seventeenth century, for one studying nature the expressions natural science (Lat. scientia naturalis) and natural philosophy (Lat. philosophia naturalis) had exactly the same meaning. What science meant in those days was certain and unrevisable knowledge of objects, based on the causes that make the objects be what they are. The same definition applied to philosophy, for it too was regarded as certain knowledge of things based on their causes. In the case of metaphysics, the causes that are investigated turn out to be ultimate causes, and so this most generalized branch of philosophy seeks the deepest causes or explanations of everything that exists. But other branches of philosophy are more restrictive in their concerns, and that is why natural philosophy is concerned only with the causes of material substances, not of being as such.
Since the seventeenth century this concept of science has gradually eroded, so that few scientists of the present day would say that their science was certain knowledge through causes. This does not mean that scientists have given up their search for causes. One of their most frequently asked questions is "why" a particular phenomenon occurs. But science has now become so complex that it is rarely possible to give a definitive answer to that question.
Again, modern science has changed its emphasis because of two features that are now its dominant characteristics. One is its use of mathematics and measurement, the other is its extensive use of experiment. The first, the use of measurement, means that modern science focuses almost exclusively on the quantitative aspects of things and neglects many qualitative characteristics that are revealing of their natures. The second, the use of experiment, means that modern science makes extensive use of hypothetical reasoning, and such reasoning rarely yields conclusive results.
At the end of the twentieth century, therefore, the mind-set of the modern scientist is not the same as that of the natural philosopher. Obviously they have different concerns and different methods of investigation. This does not mean that their two disciplines are incompatible, or that a person trained in both disciplines would not be able to coordinate their findings into a meaningful synthesis. But one cannot presume at the outset that the modern scientist and the philosopher of nature have similar objectives in mind in their reasoning processes.
Thus far we have discussed three kinds of concepts -- natural concepts, mathematical concepts, and metaphysical concepts. These are all concepts drawn from the real world by various degrees of abstraction and so we refer to them as real concepts. Real concepts are formed in our intellects, but they are concepts of things that exist outside our intellects and they enable us to grasp the natures of such things.
Not all of our concepts, it turns out, are real concepts. Many of the concepts that exist in our intellects are not concepts of things but are concepts of concepts. Since logic is the science that studies "concepts of concepts" we call them logical concepts. Our primary focus, of course, is on the study nature, but to study nature we also have to acquire some knowledge of how our minds work when handling concepts. So we must now make a brief detour into logic.
Our first contact with logical concepts probably came when we studied grammar. Grammatical concepts are a special type of logical concept. Let us assume that we have grasped the concepts of apple and red, and then form from them the proposition or sentence, "The apple is red." Now let us reflect on that sentence from the viewpoint of the grammarian, and formulate two additional sentences: "Apple is the subject" and "Red is the predicate," indicating by these new words the place of "apple" and "red" in the sentence "The apple is red." In doing this we have formulated two new concepts, "subject" and "predicate." What we mean by this is that, in the sentence "The apple is red," the words "apple" and "red" stand in different relationships to each other, that, namely, of being the subject and the predicate of the sentence. The apple and the redness exist outside my mind as real objects. Subjects and predicates, of course, do not. They exist in my mind when I reflect on the structure of the sentence I have formulated, but apart from that they have no independent existence in the way that the apple and the red do without the sentence.
Logical concepts, like real concepts, are universals, but they are universals of a special kind. The most important logical concepts are of two types: predicables and categories. Predicables are referred to as modes of predication, whereas categories are referred to as modes of being. Each of these types requires fuller explanation. You might wish to refere here to my The Elements of Philosophy for greater detail.
The predicables are five in number, usually enumerated as genus, species, differentia, property, and accident. Genus is the universal said of many things that differ in species, in answer to the question "What is it?" For example, one might say of human beings and brutes that they belong to the same genus, since all of these species fall under the genus of "animal." Species is the universal said of many things that differ only in number, in answer to the question "What is it?" For example, "man" or "human" are the species in which Plato and Socrates belong. This is the species of all humankind, containing as it does all individuals that share in human nature. (You will notice right away that the logician's use of genus and species is different from that of the biologist. Taxonomy in modern science requires many more groupings of natural kinds than those of genus and species, but these suffice in a general way for logical purposes.)
The next predicable, differentia, is predicated as the qualitative part of the nature of things that differ in number but also in species. Thus we say that a human being is "rational," for rationality is what differentiates the human species from all the species of brute animal. The final two predicables, property and accident, then indicate further specifications with regard to species themselves. Property in the strictest sense is the universal said of a species as belonging exclusively, necessarily, and always to that species and its individuals. An example would be "scientifically teachable," since only humans are capable of learning a science or other intellectual discipline. (Property is also used in looser ways, particularly in ordinary speech, but here we focus on the strictest meaning.) Lastly, accident is the universal said of a species as belonging contingently to the species and its individuals. "White" as said of humans is a predicable accident, since it does not pertain to the essence of being human to belong to the white race.
Reflecting on the five predicables, we might see that they reflect different aspects of the notion of universality. Universality is found more properly in essential predicates than in those that do not indicate the essence of the subject. Of the essential predicates, the genus is more universal than the species, and so these predicates are given first as substantial predicates. After them comes differentia as a qualitative predicate. And finally we have property and accident as predicates that are yet more distant from the essence of the subjects to which they are being attributed.
The categories differ from the predicables, as already said, as designating modes of being rather than modes of predication. There are ten basic modes of real being, which were called categories by Aristotle. The first of these is substance, and other nine are quantity, quality, relation, location, time, situation, vestition, action, and reception. These are the basic or ultimate genera into which real entities may be classified.
As modes of real being the categories are not merely logical entities. They have a direct connection to reality in the sense that what they categorize is real. On the other hand, when something is so categorized it takes on a logical relation, and in this way takes on the character of a universal. There is nothing merely logical about an individual's being a substance, but to say of substance that it is a category is to say that we conceptualize it as a universal. On this basis philosophers distinguish between first substance and second substance. First substance is the individual being as it exists in itself; second substance is substance as it exists in the mind as a universal. The same idea could be applied to the remaining categories.
Substance, then, is the first category, and substance is unique in that it exists in itself. The remaining nine categories share in common that they are predicamental accidents and exist in another, that is, not by themselves but in a substance. Thus substance is what is most basic and independent in existence. It "stands under" (sub-stans) and sustains accidents in their being and itself is a source of activity.
The first idea we gain of a substance is our very self. Each of us is a substance. I am aware that I now am, and have been, the same being over the entire course of my life. All of my accidents have changed, and yet I have remained the same. And I easily recognize that you are substances too, and so are plants and animals, and stones and minerals, and the various chemical elements.
Of the remaining categories for the time being I shall mention only three, quantity, quality, and location, for these are most important for the study of motion. Quantity is the accident by which a substance is said to be large or small, or to have part outside of part, or to be divisible into parts. It answers the question "How much?" (quantum). There are two kinds of quantity, discrete quantity, as in number, and continuous quantity, as in magnitude or size and extension.
Quality is the accident by which a substance is said to be of a certain kind (quale). The question "What kind?" can be answered in many ways, and so there are various species of quality. Now I focus attention on only two: sensible qualities and powers. Sensible qualities modify a substance insofar as it is capable of affecting the senses. On their basis we can identify sensible matter, that is, matter discerned through its color, heat, sound, taste, and odor. Powers are the abilities and capacities of substances to initiate activities of various types. These are distinctive of various natures, as we will see in our next lecture. A nutritive power is found in plants, for example, motive powers in animals, reasoning power in humans, and so on.
As accidents, quantity and quality are absolute and intrinsic to a substance. The remaining accidents are said to be relative and extrinsic because they indicate a way in which a substance is related to something outside it. Location is one of these relative and extrinsic accidents. It answers the question "Where?," telling how a particular substance is related to place or space. Change of place is called "local motion." When I go from "here" to "there" I change my place, and this is one of the most obvious motions I can undergo.
With this we have now completed our exposition of concepts. Let us return to our earlier typology of concepts and update the diagram by presenting a fuller typology of concepts. This is given in Fig. 1.4 (see p. 255 of Modeling). Again, all the entries on the left of the vertical double line pertain to the perceptual order and so designate extramental objects that are perceived by the senses. The entries to the right of the double line, on the other hand, represent concepts. These are now shown as being of two types, real concepts and logical concepts. The real concepts, as before, are arranged vertically according to the three degrees of abstraction. The logical concepts are also arranged vertically into three groups: grammatical concepts, predicables, and categories. Their vertical ordering does not match that of the degrees of abstraction. It indicates only that these are logical universals formed by the mind in its attempt to put order into its real concepts.
With these tools in hand we can now proceed to a final topic that is important for a philosophy of nature, that of scientific reasoning in the strict sense. By this I mean reasoning that is able to attain certain and irrefutable knowledge. This is the type of knowledge Aristotle called science (Gr. episteme, Lat. scientia), and which he sought in a work closely related to his Physics, namely, his Posterior Analytics. In that work he named the process through which science is attained demonstration, and this in turn was for him a special type of syllogism. So we have to explain the notions of syllogism, demonstration, and science if we are to have a grasp of what Aristotle meant by scientific reasoning.
We begin with a brief overview of methodology in the science of nature as this was viewed by Aristotle. The science he was seeking was causal knowledge, but he recognized that causes in nature are frequently hidden from us. Natural science is thus different from mathematics. Mathematics can begin with causes and principles that are easily grasped -- the definition of a triangle, for example. Not so in the study of nature. Normally in nature we are presented with effects that are grasped by our senses, and our intellects are challenged to discover the causes of these effects.
In reality, of course, causes come first and effects follow from them. So we say that the cause is prior and the effect is posterior. These two words, prior and posterior, are used to describe the two types of reasoning that are used in the science of nature. One is reasoning that proceeds a priori, that is, it starts from what is prior, the cause, and reasons to its effect. The other is reasoning that proceeds a posteriori, that is, it starts with what is posterior, the effect, and reasons back to its cause. And what Aristotle was saying is that in the science of nature, the order of knowing is usually the reverse of what happens in reality. We must begin with a posteriori reasoning to discover causes from their effects, and only when we have uncovered the causes can we reverse the procedure and later reason a priori to explain their effects.
Thus scientific method in the science of nature normally proceeds in two stages, the first involving a posteriori reasoning and the second a priori reasoning. Some philosophers would describe the first stage as a process of induction and the second stage as a process of deduction. There are also other ways of characterizing this twofold movement of the mind, and these are indicated on my next schema, Fig. 1.5. This shows the two processes, on the top the first going from effect to cause, below it the second regressing or going back from the cause, when it has been determined, and using it to explain the effect. In view of this regressing, the twofold reasoning process is called by Aristotelians the demonstrative regress.
Note on the left of the figure that the starting point is effects. These are usually observations, and they begin with singulars that are perceived by the senses. The first process employs a posteriori reasoning and it concludes with the discovery of causes or explanatory principles. These, we shall see, are not singulars but universals, and they are grasped not by the senses but by the intellect. Basically they are what we shall call natures or definitions. When we have grasped these, and this requires some additional work, we can embark on the second process. This employs a priori reasoning or deduction and it uses the causes or natures or definitions we have arrived at, all universals, to return to the observations we now fully recognize as effects, and understand them in terms of the factors that make them be what they are.
The work that intervenes between the ending of the first process and the beginning of the second process is what I call an intermediate stage. Aristotelians refer to this as a "work of the intellect" (Lat. negotiatio intellectus) or one of "mental examination" (Lat. examen mentale). This activity is difficult to explain in the abstract and is best seen through the use of an example. I shall use one given by Aristotle himself in the Posterior Analytics (I,13).
His example is the proof that the moon is a sphere from the obvious fact that it exhibits phases. The basic argument is that the moon (the Subject) is a sphere (the Predicate) because it exhibits phases (the Middle term). We may write the argument in the form of a syllogism:
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A body that exhibits phases (M) is a sphere (P) | M is P |
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The moon (S) is a body that exhibits phases (M) | S is M |
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Therefore, the moon (S) is a sphere (P) | S is P |
Now, for Aristotle, this is an a posteriori argument and a demonstration. Then, if one is sure that the moon's spherical shape is really the cause of its exhibiting phases, one can turn the demonstration he has given into an a priori demonstration simply by interchanging its middle term and its predicate. If we do interchange these terms we obtain the following syllogism:
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A sphere (M) exhibits phases (P) | M is P |
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The moon (S) is a sphere (M) | S is M |
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Therefore, the moon (S) exhibits phases (P) | S is P |
This entire argument may be formulated as the demonstrative regress, which is diagramed in Fig. 1.6 (pp. 304-305 of Modeling). A person who grasps the force of this demonstration can be said to have scientific knowledge of the moon's having phases. One who does not will have only probable knowledge or opinion about this particular phenomenon.
Fig. 1.1 The Lectures as Related to Aristotle's
Physics
Fig. 1.2 The Process of Concept Formation
Fig. 1.3 A Basic Typology of Concepts
Fig. 1.4 A Fuller Typology of Concepts
Fig. 1.5 Methodology in the Science of
Nature