91�����

Audio

By
Professor of Philosophy
University of St. 91�����
St. Vincent de Paul Lecture and Concert Series
January 18, 2019

Accompanying handout (pdf)

 

Please consider the disciplines in a typical university, where physics, geology, chemistry, and biology are considered true �sciences,� and most other disciplines, let me name but a few: sociology, psychology, politics or political science, even education, have spent the time since the death of Auguste Comte in 1857, desperately trying to model themselves upon them. For it was Comte who founded the intellectual movement called �positivism,� which set what he called �positive science,� and we now simply call �science� at the head of all the disciplines. Educated at the Ecole polytechnique de Paris, but with a philosopher�s drive for comprehensive explanations, Comte held that progress in knowledge follows an iron �law of the three stages: the Theological, or fictitious,� because divinities provide the explanations, �the Metaphysical,� whose �abstract� laws are unverifiable, and �the Scientific, or positive,� whose laws are purely rational, empirical, and mathematically precise. While �positivism� is incoherent, since the supremacy of �positive� science cannot be demonstrated using its own method; and it was thoroughly refuted early in the twentieth century, by many, including Jacques Maritain and Etienne Gilson, who were educated at the Sorbonne during the high-tide of positivism; its cultural influence has been overwhelming, especially among the �educated� classes world-wide. It was not always so, and need not be again.

I�m afraid this is all the time I have to devote to �us.� The basis for this brief critique of what is currently popular is an alternative conception of �science,� based upon the thought of Plato and Aristotle, to whom I shall devote the remainder of my time. They developed a precise, technical conception of a kind of knowledge they called �science� (episteme, �i����, scientia). For them, �science� was one of a number of interconnected technical terms devised in order to explain how it is possible for humans to achieve true, universal, and necessary knowledge, this last having been almost completely abandoned on the current, Comtean conception of �science.� For Plato and Aristotle, the issue had become a pressing one, owing to that enigmatic man Socrates, who wrote nothing but changed the course of human history, not totally unlike another man who lived and died four centuries later. The earliest important Greek thinkers we know, such as Homer and Hesiod, Thales and Heraclitus and Parmenides, were called �sage� or �wise man� (sophos, sapiens). Their insights are arresting, but about how to become wise they said little more than Heraclitus: �listen to my logos.� With the advent of political democracy in the fifth C. BC, there arose a new style of teachers who updated their name by adding new ending, to sophist (sophistes), in order to match their updated wisdom. They downsized their claims to knowledge and invented the art (techne) of rhetoric for lawcourt and political assembly. In his Clouds Aristophanes ridiculed the sophists, in the person of Socrates. In defense of him, first Isocrates (436-338BC), himself a sophist, and then Socrates� student Plato (429-347BC) used �lover of wisdom� (philosophos), as a technical term, in order to separate Socrates from the sophists. But Isocrates thought philosophy should follow �the common opinions (doxa) of the Greeks,� while Plato devoted his life to devising a technique for achieving the old goal of true wisdom and necessary knowledge.

In the Platonic and Aristotelian traditions, then, �science� would maintain its intimate connection with �philosophy� for two millenia. And in the thirteenth century theologians like Aquinas even re-conceived theology as an Aristotelian �science,� so much so that the second question of his Summa theologiae begins with five philosophical arguments for the existence of God. And while many Renaissance humanists preferred rhetoric to logic, the leading lights of the so-called �scientific revolution� by no means threw over Aristotle�s conception of philosophical science. As evidence we might note that Isaac Newton did not include the word �science� but �philosophy� in the title of master scientific work, first published in 1686: Naturalis philosophiae principia mathematica, The Mathematical Principles of Natural Philosophy. Would that Comte had read more Newton and less of Voltaire and the Encyclopedia of Diderot and D�Alembert. If we look at the long march of intellectual history, then, this segregation, as we might call it, between the honorable �sciences� and the other disciplines, is actually very recent, and exceedingly dubious.

 

1. Plato�s Divided Line

As with most of Aristotle�s central philosophical doctrines, his conception of �science� (��辱����ê����) came from a critical reception of Plato�s thought, in this case, the divided line. In order to understand Aristotle on �science,� then, I�ll begin, and also end, with Plato. Now there are several versions of the divided line in Plato�s great �middle dialogues�: Republic, Symposium, and Phaedo. And the Republic contains three distinct versions, one each in Books 5, 6, and 7. Plato seems to have wanted us to compare these versions to get a full picture of the line, since different versions focus on different parts of his story. Knowledge always involves three factors, the things known or objects of knowledge, the techniques or methods we use to acquire knowledge, and the kind of knowledge they produce in our minds. So we should look at all three as we follow Plato�s thought in moving from the bottom (level 4) to the top (level 1) of the line.

After the competing definitions of justice in Bk. 1 of the Republic produce a stalemate, Socrates turns to a dialectical search for its true nature, with Plato�s brothers, Glaucon (whose name means �bright�) and Adeimantus (�confident�). They find humans are by nature political, discover that a good polis requires three classes of men, craftsmen, auxiliaries, and guardians, which classes respectively should exhibit the virtues of temperance, courage, and wisdom, with justice as the virtue of the whole polis (Bk. 2-3). Then they find the soul of an individual man has three correlative parts, appetite, emotion, and reason, which require the same four virtues (Bk. 4), and finally hear the shocking proposal of the philosopher-king (Bk. 5). At this point (Bk. 6), out of exasperation and exhaustion, Adeimantus asks Socrates �aren�t these virtues the most important things? Is anything else more important than justice?� To which Socrates gives the abrupt reply� �You�ve often heard it said �the idea of the good (tou agathou idea) is the most important thing� (505a2). Now the �many� say the good is pleasure, while the �cleverer� say knowledge. Both pleasure and knowledge, however, are subjective, they exist inside the human subject, but the good must be real, independent of us. So Socrates presents three great images to explain the good: the sun, which shows it is a reality, the highest reality; the divided line, which explains the hierarchy of knowledge that corresponds to the hierarchy found in reality; and the cave, to urge us to strive to achieve the good, not just know it. This is the context in which to understand the divided line, which sets up a hierarchy of states of knowledge described in relation to corresponding levels of reality, for we understand the knowledge found within our mind in terms of its objects and the methods which allow us to achieve it.

At the two lower Levels (4 and 3) are things known is the �visible� (horaton), so readers sometimes think they describe sensation. But this is wrong, since the term for the cognition covering both levels is �opinion� (doxa), which is intellectual, not sensory. I can see the sun, but I can think it revolves around the earth, which is an opinion, not a sensation. All four levels of the divided line describe four levels of intellectual cognition.

Intellectual thought arises when we recognize one individual in the changing �visible� realm is similar to another, its �image� (eikon), which Plato illustrates with these examples: the shadow of a tree (or in the cave) is its image, or its reflection in water is its image, or your reflection in a mirror is an image of you. The image is one thing, the thing imaged is another thing. This kind of thinking Plato calls eikasia, which has been variously mistranslated as �imagination� or �imaging� or �conjecture,� as though Plato were talking about something the thinker creates, which is how we think of imagination. But what Plato means is a kind of association or comparison of two real, individual, physical things. One thing leads us to another, which is exactly where our intellectual thought actually begins, with what I would translate as �image-thinking,� which we use all the time.

Plato then describes Level 3 in a single sentence: �In the next section put what this is an image of: the animals [in the plural] around us, and all plants [another plural], and the whole genus of man-made things. [yet a third plural]�[1] If �image thinking� consists in comparing one individual visible thing with another, here the object understood is what the individual is �like� or is �an image� of. Plato�s examples clarify the point by shifting our attention from individuals to classes: animals and plants and artifacts. So the difference is that the object of our mind is now what we can call a universal, or a genus, or a class of things. Plato does not tell us how our mind has moved from individual to group, but the method we employ is pretty clear, we have proceeded from individuals to what they have in common, using some sort of inductive generalization. Now this mental process is perilous, because we have generalized beyond our individual sense experiences; so Plato calls such Level 3 knowledge �trust� (pistis), and describes the two lower levels as �opinion� (doxa). Both of these terms indicate a want of necessity the sophists had recognized when they said opinion is the best cognition mere morals can attain, but which Plato rejects.

The transition to Levels 2 and 1 of the line Socrates sets up mathematically: �Would you be willing to say that the division between truth and untruth is in this ratio: the object of opinion is to the object of knowledge, as a likeness is to what it is like.� For knowledge to be necessary and universal requires our mental gaze to shift from individuals in the world of change that are like each other, to what they have in common. So while looking at this triangle the object of our intellect becomes �triangle itself,� which must exist in an unchanging and higher mode in order to support necessary and universal knowledge of it. Hence the world of �forms,� also called �exemplars� and immaterial �beings� or �substances� (ousiai). Such causes can produce true knowledge, in two ways.

Acquiring knowledge at Level 2 comes through �deductive reasoning� (dianoia), which moves from principles assumed, which are �suppositions� (hypotheseis) assumed, to objects of enquiry and then to conclusions deduced. Geometers, for example, �use visible figures and talk about them, but their thought is not directed to them but to those other things the figures are like.� Plato recognized that such dianoetic deduction depends upon forms that serve as �hypotheses� for such �downward� reasoning; but such principles cannot be proven through deduction, because deduction assumes such principles.

So at Level 1 of the divided line, reason (logos) must �reverse itself� and �travel up to a first principle,� using hypotheses not as principles from which deductions follow, but using hypotheses �as stepping stones from which to move upward and to reach the un-hypothetical first principle of all,� a process he calls �the science (��辱����ê����) of dialectic.� This principle is �the good� (to agathon); and it �is not a being (ousia), but is beyond being in rank and power.� For Plato, then, there is but one discipline, not many, an all-encompassing �wisdom� (sophia) sought by its �lover� (philosophos). Wisdom, also called �science,� is achieved in three stages: first, through dianoetic deduction, then followed by dialectical reasoning, which finally lifts the mind up to intuitive insight (�Դ�ê������) into �the good.�

2. Aristotle

In his �School of Athens,� Raphael portrayed Plato pointing upward, while Aristotle stretches his hand directly out to us, the earth-bound viewer, thereby illustrating how Aristotle had brought Plato�s heavenly forms down to earth. But far from completely abandoning his teacher�s thought, I am suggesting to you the best way to understand Aristotle is to view his innovations as ringing so many improvisations on Plato�s heavenly music. For both thinkers, �science� necessarily includes both dialectical argument, which allows us to understand principles, and dianoetic argument, which allows us to deduce conclusions from those principles.[2] If the center point of Platonic �science� is dialectical argument �from forms, to forms, via forms,� at Divided Line 1, the centerpiece of Aristotelian �science� is demonstrative deductive argument that proceeds downward �from things, to things, via principles, including forms, derived from things.� So Aristotle reverses Plato�s priority. Where for Plato dianoetic deduction from forms to conclusions served the further purpose of leading our mind higher to intuitive insight directly into the forms themselves, for Aristotle, the reverse is true. Insight into principles becomes a necessary preliminary to, and at the service of deductive demonstrations, because for Aristotle insight no longer comes from direct vision of separate beings (ousiai), the unchanging forms (�𾱻�ê). They no longer are needed, since we can come to know principles via inductive generalization from particulars, which is where forms actually and really exist.[3]

Aristotle emphasizes this general point from in the very first line of his Posterior Analytics: �All teaching and all learning through dianoetic deduction arises from pre-existing knowledge.� Learning is discovering truth by means of moving from potentially knowing something to actually knowing it, a point Aristotle makes through a critique of Meno�s paradox, which said that learning is impossible, because either we already know what is learned, which means we aren�t learning, or we have absolutely no idea of what to learn, so we don�t even know where to look. Now this paradox trades on thinking that knowledge is acquired by going from a state of absolute ignorance to one of full knowledge. But so, too, did Plato�s recollection theory in the Phaedo, which requires absolute but forgotten knowledge of forms, which are �remembered� on the occasion of some sense experience or other. So it was not Plato�s theory of recollection, but his dialectical theory moving up the divided line, in the Republic and Symposium, upon which Aristotle built.

This insight led Aristotle to embrace the plain fact that one can be a magnificent mathematician, but a horrid husband, a premier poet, but a coward in battle. So in a triumph of common sense and cognitive realism, over theoretical purity and unrealizable ideals, he found the need to recognize a multiplicity of �sciences,� each of which can be understood on its own. Consequently, Aristotle had to make several changes in the conception of a �science� he learned during his twenty years in Plato�s Academy, improvements he recorded in his Posterior Analytics. So let me begin by listing them; then we can consider each one more carefully, always focusing on how Aristotle re-worked Plato�s view to produce his own. In Aristotle�s conception of a �science� we see:

3. Many sciences, many subjects
4. The three parts of each science: subject, principles, and conclusions
5. Subject of a science
6. Scientific Reasoning: Using principles to deduce conclusions.
7. Scientific Principles 1: Three kinds of principles
8. Scientific Principles 2: Necessary principles can lead to necessary conclusions
9. Scientific Principles 3: How do we come to know scientific principles?

Let us now turn to each of these topics in turn.

3. Many sciences, many subjects:

The first, and arguably most important change Aristotle made, was to fracture Plato�s one all-encompassing �science� or �wisdom,� into many �sciences,� whose limited subjects make it possible for mere mortals to master one without another. The different sciences are distinguished from each other by each having its own �subject,� which delimits the area of knowledge it covers. This multitude is not just a convenient arrangement, but it also reflects the way in which humans learn, since we move from knowing something potentially to knowing it actually, in two distinct ways: First, sensing individuals provides potential for knowing them intellectually, through inductive generalization. Second, knowing premisses provides potential for proving a conclusion, when they are brought together in a deductive syllogism.

4. Three parts of each science: subject, principles, and conclusion

Each science has a structure consisting of three fundamental parts: its subject; the principles used in reasoning deductively; and the conclusions so proven. These three parts result from two steps Aristotle took. The first was his invention of the syllogism, in which he clearly distinguished the form of deductive reasoning, which makes it valid or invalid, from its content, which makes its conclusion true or false. �Science� requires both valid reasoning and necessarily true premisses, in order to achieve conclusions that are necessarily true. The second step was to use materials Plato himself provided in the divided line theory in the Republic, namely, noetic insight combined with dianoetic deduction.

If all learning is based upon pre-existing knowledge, we need to know what kind of knowledge of these three parts we must have to begin to learn a science. Aristotle answers by using the four kinds of questions we can ask in pursuing knowledge. When asking about a proposition, like �Is the sun eclipsed?� we first look for the fact, asking �whether the sun is eclipsed?� If it is, then we look for the cause or reason, asking �why is the sun eclipsed?� But when asking about a single term, such as �centaur or god,� two other questions arise: first, �Is there a god?� and then �what is a god?� So in beginning and pursuing a science, we are guided by these four kinds of questions: �Is it?� �What is it?� �Whether?� and �Why?�

5. Subject of a science:

The primary purpose of a science�s �subject� is to orient research by providing a horizon that determines its range. Aristotle uses two terms for this purpose: �subject-matter� fixes it in relation to the attributes (pathe) that will be demonstrated, on the model of matter perfected by form; and �genus� or �subject-genus� follow the model of a genus whose species are to be studied, such as in distinguishing various types of motion.[4] Describing the subject of a science with a succinct formula that covers its whole range does not come easily, because one must discover the �aspect� (logos) that separates the topics covered in that science from other sciences. Aristotle admitted about arithmetic that �nothing prevents some sciences from overlooking some of the [three parts], for example, not laying down that the genus exists when it is clear that it exists; for that number exists is not as clear as that hot and cold exist.�[5] For Plato there was no problem, because mathematics study a subset of the separate forms; but for Aristotle its subject must come from some �aspect� of the physical world. To solve this problem he had to invent his doctrine of �abstraction� (or �separation�). The subject of arithmetic is �one� or �ones� (monadas) in the plural, presumably because each counting number is generated by adding one, though we would be inclined to say number; and the subject of geometry is �magnitude� (megethos), though he also says �points and lines,� which are the principles of magnitude.

To get a firmer grasp on the �subject,� let us turn to the subjects of some other sciences, since for Aristotle, sciences are concerned with the real world as it actually exists, not possible worlds that might be, and compare Aristotle�s descriptions with a couple of the most famous Aristotelians, Avicenna and St. 91�����. Aristotle begins one of his numerous books about the physical world, On the Heavens, which actually covers both earthly and heavenly things, this way: �The science of nature clearly is mainly about bodies and magnitudes and their properties and motions; but it also is about the principles of this kind of substance, as many as they might be.�[6] Here we can see two different ways Aristotle describes the �subject� of a science. One is to focus on the kind of whole thing studied, in this case, bodily substance; the other is to use a fundamental principle of that kind of thing, here �nature,� defined as �a principle or cause of motion or rest in that to which it belongs primarily, through itself, and not accidentally.�[7] At the beginning of the first of his many books about material things, his Physics, Aristotle took this second approach, also calling it �the science of nature,� not nature in our sense of the whole physical world, but in his sense, a principle found within each and every natural thing. He wrote no Treatise on Man, but began his lengthy study of living things with On Soul, devoted not to whole things like animals, but to �the principle of animal life,� the soul.[8]

Faced with Aristotle�s different descriptions of the subject of physics, in the first of his eight treatises on the physical world, Avicenna chose to emphasize the whole thing studied: �the subject of physics is sensible body insofar as it is subject to change.� Here Avicenna modeled his description on the way of defining a species using genus, �sensible body,� and difference, �as subject to change.� Two centuries later, St. 91����� followed this model, but with an even more universal genus; for him the subject of physics is �mobile being� (ens mobile).

It would be wrong for me to pass over the most famous of Aristotle�s descriptions, of the subject of a science, that of the book called Metaphysics (ta meta ta physika), a title given it not by Aristotle but by an editor, to describe its contents: �the things after [or beyond] the physical.� What is strange is that the work contains two different descriptions of its �subject,� and it does not get to this issue until Bks. IV and VI. At IV.1 Aristotle contrasts metaphysics as a �universal� science, somehow covering the whole of reality, with �the so-called particular sciences,� which �cut off a part of being and investigate the attributes of this part, as do the mathematical sciences.� Since the notions of �being� (on) and �one� (hen) are absolutely universal, and broader than the ten categories, all of which divide being, metaphysics is �the science that investigates being as being (on hei on),� its subject, �and the attributes is has through itself (kath� hauto),� which are the conclusions metaphysics is to demonstrate, the third of the three parts of a science.

Here we meet two of the most important technical expressions Aristotle invented, �being as being� and �through itself,� so we should look at them. In �being as being,� the first being lets us know that the range of things metaphysics studies is as wide as possible, since everything real is a being. Then �as� (hei, qua) introduces the aspect that distinguishes metaphysics from the other sciences. It will not study beings �as� subject to motion, or quantified, or bodies, or in any other such respect. It will study them �as being,� that is, in their most fundamental features, the ones that make them beings in the first place. Now at this point you might be thinking: �this is all pretty abstract, what does it mean?�

So let�s think back to Plato, since he had a ready answer. For Plato, to study the beings in the lower world of change, �as being,� would be to look at them in relation to the forms in which they participate, since those forms or ousiai cause them to be the kinds of beings they are, and they the paradigms that fix the natural tendencies and motions they have, and so they allow us to understand them, to the extent we can. So if we approach Aristotle this way, we might not be surprised that he immediately narrows the scope of what is studied in metaphysics: �Now being is said in many ways, but with reference to one thing and to one certain nature, and not equivocally, but as healthy is said in reference to health,� which is properly found in the body, not in food, which causes health, or urine, which is a sign of health. Now the prime instance of being is ousia, not Plato�s separate ousia, but Aristotle�s, the first of the ten categories which, owing to Cicero, we now call �substance.� So the study of �being as being� turns out to be a study of substance; the other nine categories are treated hardly at all, and the reason is perfectly Platonic. We know the whole by knowing the prime instance, for Plato the separate forms, for Aristotle substances.

In Bk. VI, c. 1, Aristotle takes the next step down this road, offering his second description of the subject of metaphysics. Here he explains its subject by distinguishing it from the subjects of the physical and mathematical sciences. His criterion for comparing them is connection with matter; and he begins with a fond and memorable example. Socrates had a notably ugly face, with a �snub� or squashed-in nose. Now a snub nose is also a �concave� nose, but there is a difference. The notion �snub� necessarily includes �sensible matter,� whereas �concave,� a geometrical term, does not. So when we �search for and define what it is [the essence] of physical things,� we must include their physical matter, which enters into the very subject of the science. 91����� mathematics, Aristotle first bows in Plato�s direction, saying �whether it is about things unmoved and separate [from matter], is not clear now,� but then adds his own view, �but that we study some mathematical objects as unmoved and as separate [from matter], this is clear.� The things studied in mathematics are �abstracted� or �separated� by the mind from physical matter. Aristotle ends with the subject of metaphysics. �But if there is something eternal and unmovable and separate [from matter],� then �the first science will treat� such things. Such things are causes, and �these are causes of what we can discern about divine things.� So here he calls metaphysics �theology,� the study of the gods. This name raises a serious conundrum (aporia): �Is first philosophy a universal science� of being as being, or does it study �some definite [and limited] genus and some one nature.� Aristotle�s answer is Platonic:

If there is not some [Aristotelian] substance (ousia) in addition those composite by nature, then natural science will be the first science; but if there is a substance that is unmovable, this science will be prior [to the others] and first philosophy, and universal in this way, because it is first.[9]

As Plato said we know the whole of reality by knowing the highest part, the separate ousiai or forms, so Aristotle replies we know the whole of being by knowing the highest beings, the separate ousiai or substances.

Aristotle�s solution to this conundrum, however, has become itself a conundrum for Aristotelians down through the ages: Is metaphysics a universal study of all beings, or is it a theology? This problem bothered Avicenna so much that he tells us in his Autobiography, �I read the Metaphysics forty times but could not understand its overall scope and purpose (gharad).� But his mind was cleared when he read a small treatise by al-Farabi that showed him that �being as being� means being as a common feature of all things, is the �subject� of metaphysics, while a philosophical theology that demonstrates the existence and nature of the one God is its end and �perfection.� And later St. 91����� embraced this view of metaphysics. He said its subject is �common being� (ens commune), while its end and highest perfection is rationally proving the existence and nature of God. And this end of metaphysics leads to a science higher still.

Consequently, there are two kinds of theology or divine science. One treats of divine things (res divinae), not as the subject of this science, but as [ontological] principles of the subject. This kind is the theology the philosophers pursue, and also is called metaphysics. The other theology considers divine things in right, as the subject of this science. And this is the theology offered in Sacred Scripture.[10]

6. Scientific Reasoning: Using principles to deduce conclusions.

Plato renounced the sophists, and all their works and pomps. Now Aristotle, as much as he also rejected the content of what they said, recognized how valuable was their invention of rhetoric, because he distinguished the form or structure of discourse from its content. And this fundamental distinction made it possible for Aristotle to invent formal logic. His Analytics was originally one book, the first or �prior� part devoted to the formal logic of the deductive syllogism, and the second or �posterior� part devoted to what Plato called �dianoetic deduction� and Aristotle calls �demonstration,� which is �a syllogism producing scientific knowledge.�

Let us begin our look at principles and conclusions, the second and third parts of an Aristotelian science, with an example much beloved by Aristotelians over the centuries. I�ve put it down in two forms.

	A:	B:
	All rational animals are risible.	All risible things are rational animals.
	All humans are rational animals.	All humans are risible.
	Therefore, all humans are risible.	Therefore, all humans are rational animals.

Both syllogisms are valid, their conclusions follow necessarily from their premisses. And all six propositions are true. So both syllogisms are what logicians now call �sound,� meaning they combine validity of form and truth of premisses to yield a conclusion that must be true. Do we then have �scientific� knowledge of the conclusions? Not guaranteed, since the truths found in scientific knowledge must be necessary, not just in the formal sense that the conclusion follows necessarily from the premisses, but in what medieval Latin Aristotelians called the material sense, which considers their content. In these two arguments, the premisses contain propositions that are not just true but necessarily true, so the conclusions are necessarily true, as well.

 Now let me ask a question you might be asking yourself, if you haven�t already done this exercise in logic tutorial. How do we know that humans are risible, that is, have the capability to laugh, but �laughing� hyenas, who sound like they are laughing, don�t; laughter is just their call? The initial answer, of course, is that we see some people laughing about something. But that�s just one example, so we ask what is involved whenever humans laugh? Two things: we perceive an odd situation, which leads us to �animal�, and we recognize its oddity, which leads us to �rational.� So we laugh, or cry, which are two sides of the same coin, as the Greek dramatists recognized in following tragedy with a comic satyr play. So the risible thing must be a �rational animal�; this is what makes him �able to laugh.� How have we reasoned in this case? We start with a provisional conclusion; we have asked why it might be true; we have analyzed that provisional conclusion into its parts, its subject and predicate; we have searched for a �middle term� to unite the subject and predicate of the conclusion; we have then devised the major and minor premisses; and finally have drawn a conclusion. If the two premisses are not merely true but necessarily true, and our reasoning is valid, then our conclusion must be necessarily true, as well. Aristotle called his book Analysis, because he thought this is the way we search for demonstrations of necessary truths, at least most of the time.

One final but very important point about risible humans. When we compare syllogisms A and B we can see that their middle terms, rational animals and risible, are intrinsically related to each other: being a rational animal is the cause of being able to laugh. We saw this by seeing that the ability to laugh is built on being able to perceive events and also analyze them with our mind to determine how usual or unusual they are. So the reasoning in syllogism A moves from cause to effect, while the reasoning in syllogism B moves from effect to cause. So the heart of scientific reasoning, that is, demonstrative reasoning, is that the connection between premisses and conclusion is based on a causal connection; it is causal knowledge. Now Aristotle recognized that syllogism A is stronger than B, even though much of our causal reasoning is like B. So he gave them different names. Syllogism B shows us �that� (hoti, quia) humans are rational animals, based on an effect of being rational, namely, being able to laugh; the syllogism moves from effect to cause. So Aristotle called this kind a �demonstration that� or �demonstration of the fact� (apodeixis hoti, demonstratio quia). Syllogism A, by contrast, tells us both the fact and the reason (or cause) of the fact. It is a �demonstration of the reasoned fact� or �demonstration of the reason� (apodeixis dioti, demonstatio propter quid). So he opens Posterior Analytics 1.13, devoted to explaining this difference, by saying: �In the same science, scientific knowledge of the fact is different from scientific knowledge of the reasoned fact.�

Aristotle then goes on to illustrate this difference using two examples from astronomy, one showing the planets are closer to the earth than the stars, and the other showing the moon is a sphere. Here are the two syllogisms he lists about the twinkling case:

	T1	T2:
	All non-twinkling sources of light are near.	All near sources of light are non-twinkling.
	All the planets are non-twinkling sources of light.	All the planets are near.
	Therefore, all the planets are near.	All the planets are non-twinkling.

T1 is the way we actually reason to understand the planets are nearer the earth than the stars. We are aware the planets don�t twinkle empirically, but the stars do twinkle, by looking up at the night sky. I hope you have done this yourself, having left your cell phone behind. And then you ask yourself: Why is this true? Somehow Aristotle felt confident that non-twinkling sources of light are near. But how do you know this? By just staring for hours at the night sky. No! So here Aristotle gives us some advice: �We must take this truth as having been reached by induction or sensation.� Sensation of what? If you have gone out into the woods or fields to look at the stars, you probably saw different lights coming from sources on the earth, lights from a cabin, or a car, or perhaps a campfire. (Sorry, maybe I shouldn�t have mentioned fires here.) If you look carefully you will see that some lights twinkle, and some don�t; and you can measure the distances involved. If you generalize your finding inductively, you will find just what Aristotle says in the major premiss of T1. �Non-twinkling sources of light are near.� So what results is a syllogism moving from effect, non-twinkling, to its cause, being near, a �demonstration of the fact.� T2 simply exchanges cause and effect, producing what might appear to be a �demonstration of the reasoned fact,� because it moves from near, the cause, to non-twinkling, the effect. But this is only an appearance, because we have no means of determining �the planets are near,� apart from T1.

Now we can�t leave this point without asking about what modern science has to say. If you google �why stars twinkle� you�ll get a different answer from Aristotle�s, namely, that twinkling results from distortions caused by the earth�s atmosphere, not how far away the twinklers are. But what is more important for us is that modern science uses that same sort of reasoning that Aristotle set out centuries ago.

At this point we have to face a difficult fact. Aristotle himself thought he had demonstrated both that risibility is a necessary property of being a human, �all humans are able to laugh,� and that twinkling is necessarily a function of the distance between the light source and the observer, �the stars twinkle because they are farther away than the planets.� But the first is a necessary truth, the second, however, is not. But I don�t think Aristotle would be upset by this situation, because there is an important difference that leads us to understand more about the second part of a �science,� its principles. Proving humans are risible is based on a middle term, �rational animal,� that is more closely connected to the principles that govern our philosophical knowledge of humans, than is the case of knowing our distance from the stars. So we need to realize that the principles of an Aristotelian science usually are not the proximate middle terms of the syllogisms used in a science, but they are more universal and fundamental notions and propositions that give us knowledge of more fundamental ontological principles found in things.[11]

7. Scientific Principles 1: Three kinds of principles

Aristotle distinguishes three kinds of scientific principles. The first he calls axioms, because they are �worthy� of credence by all humans, since they are presupposed by all human thought and discourse. They derive from the very structure of reality, and as axioms they govern all thought and discourse. Absent these axioms, we could not know or even think anything. He has three favorite examples: First, what he calls �the first principle of syllogism� and we call the principle of non-contradiction, which is �the principle of all other axioms.� Second, the law of the excluded middle. Third, the subtraction axiom. While known to all, they do not normally enter into syllogisms, but make them possible.

The other kind of scientific principles are �proper� or limited to particular sciences or groups of sciences. There are two different kinds, because reasoning, the third act of the mind, presupposes both the first act of the mind, conceptualization which produces notions, and the second, assertion which produces propositions. Following Plato, Aristotle calls the fundamental notions �definitions� (horoismoi, horoi) and the fundamental propositions �suppositions� (hypotheseis). It is these �proper principles� that are the foundation of demonstrations.

Euclid followed Aristotle�s three-fold distinction of scientific principles when he set out the �definitions,� �postulates,� and �common understandings� (koina ennoia) of geometry, at the very beginning of his Elements. Aristotle, as he himself admits, was not so thorough in setting out the all the principles of his sciences. But he took care to set out the most important ones, and he focused on the primary notions that underlay study in the three major areas of theoretical science: physics, mathematics, and metaphysics. So let us take some examples. In distinguishing the three kinds of principles in Posterior Analytics 1.2, his example of a definition is that �the arithmetician lays it down that a unit (monas) is what is undivided in quantity.� This is why he also defined number, that is, counting number, as �discrete quantity.� He devoted the first two books of the Physics to setting out the principles which would guide all his physical sciences. In Bk. 1, after rescuing motion from the Eleatics, he identified matter and form as principles, along with privation as a subordinate principle, because a negative rather than a positive notion. And in Bk. 2, he rescued all four causes, matter, form, agent, and end, from Plato�s demotion of two of them, matter and agent, to being mere �conditions,� reserving the lofty term �cause� for form and end. He also introduced �nature,� as we have seen. Other principles, like potency and act, are clearly used, but are not put on a list. The first two books of the Metaphysics present these same four causes as the principles for metaphysical demonstrations. Again, not explicitly listed, but clearly used are: �one� the companion of �being�; the ten categories, especially substance; act and what we might call real potency, defined as �in general, the principle of change or motion in another thing,� exemplified by �the art of building ... which is not in the thing built.�[12]

Later Aristotelians added to this list. Avicenna followed Aristotle closely about the physical sciences, whose principles are the four causes.[13] But he offered significant innovations in metaphysics. �The first three notions that fall into the mind,� he said, �are the being, the thing, and the necessary.� And from these three notions, through dialectical argument, Avicenna drew three metaphysical principles: existence, quiddity, and ontological possibility, which produced a new kind of metaphysics. It required a single, creative God, quite different from Aristotle�s polytheism, one whose existence and nature are proven rationally, but only within metaphysical science.[14] And a God whose nature cannot properly be described using Aristotle�s categories or even narrower notions, but as the first, completely universal cause, must be described in the most universal terms, as �necessary existence� (necesse esse). 91����� Aquinas also accepted Avicenna�s separation of the principles of physics and metaphysics, and early in his writing career wrote two small philosophical explaining their scientific principles: On the Principles of Nature, which presented the four Aristotelian causes as the proper principles of the natural sciences, and On Being and Essence, which presented essence and existence (essentia et esse) as the proper principles of metaphysics. And he accepted Avicenna�s idea that the existence of God is proven rationally in metaphysics, using the metaphysical principles of essence and existence (esse). And most of all, he agreed that God�s nature cannot be properly described using limited notions like substance, but more universal terms are required, since God is �subsistent existence itself� (ipsum esse subsistens).

Now the most important feature of the principles of the sciences, for all Aristotelians, is that they make it possible to draw demonstrative conclusions that are not just universally true, but necessary. So arguably Aristotle�s most important achievements in the theory of a �science� were to explain how scientific principles are universally true and necessary, and also how we can come to know them to be so. Otherwise, necessary conclusions about the changing world in which we live would be impossible for us to achieve. Now Aristotle dealt with the issue of necessary knowledge at Posterior Analytics, 1.4, and of how we can achieve knowledge of universal and necessary principles at Posterior Analytics 2.19.

8. Scientific Principles 2: Necessary principles can lead to necessary conclusions

Let us now consider producing necessary knowledge. As we have seen, Plato�s brilliant answer is that the principles conveying this knowledge are not confined to our mind, but are real, unchanging, and necessary beings (ousiai) existing in the higher world of forms (eide), in which things in the lower world participate (methexis). And his explanation of how we come to know them is that our mind is directly illumined by such forms, because any intermediaries would dim our knowledge of them. As we have seen, one way Plato described a Form was to append the term �itself� (auto) to the term, as he has Socrates say in concluding the recollection argument in the Phaedo:

We knew before we were born, and when we were born, not only the equal and the greater and the less, but all such things. For our argument (logos) is not merely about the equal, but also about the beautiful itself (autou tou kalou) and the good itself and the just and the holy and of everything which we certify as �thing itself�.[15]

In �thing itself� (hauto ho), whose Latin equivalent would be id ipsum, Plato compacts several points. He focuses our attention on that kind of thing, as distinct from any other kind, on what makes it that kind, and most importantly on the highest level of perfection of that kind, which all things in our world can achieve but imperfectly, but which we can know through the influence of that �thing itself� or Form.

At the beginning of the last and most important argument in the Phaedo, where Socrates reasons from the true causes he has just isolated in his intellectual autobiography, he begins this way:

I take as my supposition (hypothemenos) that there is a beautiful itself through itself (kalon auto kath hauto) and a good, and a great, and all the others. If you grant me these I hope from these to discover and to show the reason why the soul is immortal.[16]

Socrates goes on to say the soul gives life to the body, so life is a necessary property of soul, as odd is necessary property of 3. But if we subtract 1 from 3, we get 2, which has the opposite property, even, and, more importantly, 3 has disappeared. So Socrates concludes conditionally. The soul is immortal, it cannot exist in a state of death, but only if the immortal is also indestructible, does the soul live on after death. Like all dianoetic arguments for Plato, this one is designed to lift our mind up to insight into its starting principle. Socrates has achieved this insight and so, in the face of his coming death, he is confident about immortality. We are not sure about Simmias and Cebes, since they are still seekers on their way to the vision of the Good.

Our purpose here, however, is to look at Plato�s formula: �the beautiful itself through itself (kalon auto kath hauto),� because this phrase was adapted, and adopted, by Aristotle, in order to describe what makes knowledge, and in particular a proposition, necessary, which is itself an absolute requirement for �science,� according to both Plato and Aristotle. Plato added the reflexive �through itself� to indicate the absolute independence of the Form �the beautiful� from any participant, and arguably from any other form, and its eternal existence, as well as the absolute and intrinsic dependence of beauty in any participant upon �the beautiful itself.� When Aristotle looked at things in the world of change, he recognized that whole beings, or substances in his sense, are subject to generation and corruption. But while they exist, they have features that are intrinsically, necessarily, and formally connected to each other, as in our example of �All rational animals are risible.� The formal feature �risible� intrinsically and necessarily flows as a property from �rational animal� as its cause. The phrase �through itself� (kath hauto, per se), then, for Aristotle, describes the necessary, unchanging, and even eternal relation of these two formal features, even though they exist in a composite being, a human, subject to birth and death. So it is the principles, like form and matter, existing within the whole being or substance that provide the causal basis for knowledge that can extend beyond that particular being.

I have spent this time try to explain the meaning of these arcane Greek phrases, and their Latin translations, not to convince you that the most literal translation of a philosophical text is always the best one. That isn�t true. �Essentially� or �in virtue of its own nature� are both decent translations of Aristotle�s kath hauto/per se, though I would draw the line at using the Latin per se in an English translation, as I found in one of the translations of Aristotle I used. Translation into Latin is not translation into English. But such freer translations do make it harder to see how Aristotle developed his own philosophy out of Plato�s, if you don�t develop a sense of asking �what�s under this translation?� So when you are reading a difficult text like Plato or Aristotle in translation, as we all do, please remember that your goal is to understand the thought lying underneath the words, first the words of the author, and then the words of the translator, and finally your own words.

So after this aside, let�s turn to Aristotle�s treatment of what is required for �scientific� knowledge, at Posterior Analytics, 1.4. Now �science� is attained through demonstrative syllogisms that deduce necessary conclusions. So what kind of premisses are required? Aristotle uses what has become a classic example: �All men are animals. Socrates is a man. Therefore, Socrates is an animal.� Everything depends upon how predicates is related to their subjects, so Aristotle sets out three requirements. A predicate must be (1) �said of all� or universal; (2) said �through itself� or �essentially�; and (3) the �appropriate universal.�

(1) The �said of all� universal is absolutely required for the conclusion to be true. But some truths are contingent, what we might call mere matters of fact, and not necessary truths. So this sense of �universal� isn�t strong enough to ensure a necessarily true conclusion; it ��DZ���ԙt progress beyond opinion to knowledge. A famous example is the �black swan problem.� For centuries Europeans thought all swans were white, until black swans were discovered in Australia in the seventeenth century.

(2) �Through itself� or �essential� predications are the most important, because they move arguments from mere truth to truth which is necessary because built on causality, not Plato�s Forms but Aristotle four causes. Aristotle distinguishes four �modes� or senses of �essential� (per se) premisses and conclusions.

(2a) The first mode he illustrates with two propositions: �triangles have lines� and �lines have points.� Line is part of the definition of triangle, as point is of line. So the connection between the predicate �line� and the subject �triangle� is �through itself,� that is, line is an essential and therefore necessary feature of a triangle. (2b) The second mode is the reverse of the second, since here the subject is part of the definition of the predicate. For example, lines are straight or curved. Straight and curved are properties of line, so if you want to define �straight,� you must include line in the definition. Again the relation between subject and predicate is �through itself� or essential, and therefore necessary. The opposite of �through itself� or �essential� is �accidental,� illustrated by �musical� (meaning educated, not able to sing or play an instrument) and �white� in relation to the subject animal. Here there is no intrinsic and necessary connection. The mathematical examples that Aristotle uses are designed to show that �through itself� or �essential� connections are causal connections, and that the kinds of causes involved include form and matter, though not necessarily physical matter, in the case of these examples.

(2c) The third mode is quite different, but exceedingly important, because here Aristotle brings �through itself � or �essential� down from the universal level to particular things. Aristotle�s examples are �walking� and �white.� These attributes are distinct from the being which is walking or white, which is an individual substance, and �through itself� in this sense, because not predicated of anything else. In this way, �essential� predications extend all the way to particular things, which means we can have necessary knowledge of them.

(2d) The fourth mode of �through itself,� which includes final and agent causes. They too can produce �essential� and necessary knowledge. Aristotle contrasts two cases. Consider a man walking down a path and suddenly there is lightening in the sky. Here there is no causal connection between the events, so their conjunction is �accidental.� On the other hand, in the cause of slaughtering a sheep causing it to die, so we can cook and eat it. In this case, the slaughtering and dying, and I would add the eating, are all �essentially� connected through agent and final causality.

(3) The final requirement for necessary knowledge is what Aristotle calls simply �universal,� but for clarity is normally the �appropriate� or �commensurate� level of a universal predicate. Aristotle again uses examples from mathematics. Consider the attribute �having its angles equal two right angles.� This can be true of �geometrical figure,� but ��DZ���ԙt have to be, figure is too broad a notion for an �essential� connection. An isoceles triangle always has its angles equal to two right angles, but this isn�t an �essential� connection either, because it does not depend on the triangle being isoceles. The figure that is the �appropriate universal� for the attribute �having its angles equal two right angles,� is, of course, �triangle.� So necessary knowledge must be developed through syllogistic connections stated at the right level of universality.

Now Aristotle might have set out the requirements for proving �scientific� conclusions through demonstrative syllogisms using some other language, but he didn�t. So in order to understand his own explanation of how �scientific� knowledge is developed, we need to understand the language he actually used, for which he was indebted to Plato.

9. Scientific Principles 3: How do we come to know scientific principles?

Let us end where we began. In the last chapter of his Posterior Analytics, 2.19, which has parallels in the first chapter of his Metaphysics, 1.1, Aristotle considers briefly, many would say too briefly, how we come to know scientific principles. I would suggest, however, that comparing his explanation with the ascent up Plato�s divided line helps us to understand Aristotle�s argument. After all, Aristotle could expect his audience to be quite familiar with Plato�s thought. So if we take Aristotle�s explanation as a succinct but not uncritical gloss on Plato, perhaps this will help us understand the views of both great philosophers. Both agree that we cannot draw necessary, true conclusions unless they are based on necessary principles, and that we can only understand those principles through non-discursive �intellectual insight� (noesis; nous; intellectus). The issue, then, is how to arrive at such insight: for Plato, it comes by moving up the divided line to arrive at direct insight into the separate eternal forms; for Aristotle, I suggest, it comes by moving up the divided line, but in his own way, which shows separate forms are not required, because the object of insight is the form present as a principle in individual things we sense. Even though those things come and go, the character (logos) of the forms never changes. Let us now turn to Aristotle�s ascent, not forgetting Plato. You might want to take out the handout again.

After having spent virtually all of the Posterior Analytics explaining how we can attain �science� through deductive and demonstrative arguments based on �first principles,� (A.1) Aristotle introduces his brief consideration of how we know those principles, at 2.19, by taking a swipe at recollection: �It would be odd if we already knew them, for then it would follow that we already had much better knowledge than demonstration, without knowing it.� So for Aristotle, as for Plato in the Republic and the Symposium and, I think, even in the Phaedo, we come to learn the principles of demonstration, since the intellect we are given begins life as a �scraped tablet.� Aristotle�s argument at PostA 2.19, I would suggest, has four steps, parallel to Plato�s divided line, if we divide what is usually presented as the first stage into two.

Aristotle begins by dividing the genus animal. All animals have sensation, some can remember what they sense, others not; and even fewer, only humans, from �repeated memories of the same thing,� can have �experience� (empeiria). And for the very few, not even all humans, from experience come �art� in the practical realm and �science� in the theoretical realm. Aristotle�s division is not just designed explain these attributes through a definition using genus and difference; he adds that acts at each level come from an interior �natural power� in the acting thing. And that power is his real focus, because it is a power for the �subject� to achieve a certain kind of cognition, in taking in a kind of �object,� using a particular �method.� (handout). So if we distinguish �sensation� and �memory,� on the one hand, from �experience,� which then is distinguished from �art and science� we can begin to see how Aristotle is offering a reply to Plato, by situating �experience� as the connecting link between sensation and full intellectual knowledge

Level 4

We have seen that the method of Platonic �image-thinking� is to compare different individual things, a comparison which is built squarely on sensation and memory. In such a comparison, the things (or objects) of our thinking are individual physical things. So here we have a point of agreement: for both philosophers �scientific� knowledge begins with sensation of individual �visible� things, and comparison of them using memory. So Aristotle begins his own explanation at Plato�s DL 4 (A4); he just focuses on the sensory basis of �image thinking� while Plato had focused on its intellectual character.

Level 3

At Level 3, Aristotle also uses Platonic language, but not that of the �divided line.� In his Gorgias, Plato had argued that the sophists did not have true knowledge, but they had what has been brilliantly translated as �a knack� for hitting on clever conclusions. �Knack� translates empeiria, which usually is rendered �experience,� and from which we get our word �empirical,� as in �empirical sciences,� a phrase that would be nonsense for Plato and Aristotle, since both said �science� and �experience� are not the same thing. When we say experience nowadays, we often mean an individual sensation of an individual thing. And I�m sorry to say that Plato and Aristotle often are translated this way. But this is not what they meant; for them �experience� is a habit that results from repeated sensations of individual things. And it connotes more than a series of sensations, as we mean when we say, approvingly, �a person of experience.� Now this is just what concerned Plato at DL 3, since �opinions� are universal cognitions we�re not sure about, and so we say �it�s my opinion� because we �trust in�, but are not sure of, our generalization.

To get a sense of how Aristotle understands �experience,� and why it undercuts the need for Platonic forms, let�s begin with the parallel text, Metaphysics 1.1, where he compares �experience� with the stronger knowledge found in practical �art� (techne) and theoretical �science� (episteme).

Art comes about when, from many things known in experience we derive the judgment (hypolepsis) of one universal. For to make the judgment that when Kallias suffered from this disease, that remedy benefitted him, and likewise for Socrates, and others, this just is experience (empeiria). But that it works to benefit all such people of one type (eidos, species) who suffer from this disease, such as phlegmatic or bilious people when they have a fever, this is art (techne).[17]

Experience, then, is a sort of mid-point between an individual sensation of an individual thing and a precise, universal and causal conception of a precise type of thing, a full universal. The example of healing a fever shows the difference. A new parent has no idea what to do when the baby has a fever; the experienced parent ��DZ���ԙt know medically why to choose a particular remedy, but does know a remedy that might work; and the contemporary physician tailors treatment to certain characteristics of the baby�s nature, which the Greek physician did based on a person�s predominant humor.

In the Metaphysics, Aristotle concentrates on what the person of experience ��DZ���ԙt have, in order to show the superiority of �art� and �science� to �experience,� but in Posterior Analytics 2.19 he concentrates on what experience does have, on how to move up to higher levels of knowledge, saying: �From sensation is generated memory, as we have said. And from repeated memory of the same thing is generated experience; for memories many in number are one experience.� So a multitude of memories are congealed, as it were, into one experience, which makes more general or universal knowledge, even if it is neither certain nor necessary. When Socrates and Kallias both have a fever, the person of experience will use cold water in both cases, which likely will not work equally well for both. So we achieve �experience� through inductive generalization, which has not reached the level of necessary knowledge, just as Plato said at DL2. In order to take the next step, from �experience� to �art� or �science,� Aristotle needs a definition of �experience,� and actually offers three. Experience is (1) �an all that remains in the soul, a universal; (2) a one over the many; (3) which is one and the same in all of them; the source (arche) of art and science, art for changing things and science for being (on).� Now these descriptions, except for the term �universal,� are set out in Platonic language, which seems to be an obstacle for Aristotle separating himself from Plato, a point Aristotle himself recognized. But at least we learn that �experience� includes some sort of �universal.� Perhaps we might call it an insecure universal, which is exactly how Aristotle, and Plato, and the sophists all thought of �opinion,� as distinct from necessary knowledge.

To firm up his argument, Aristotle then introduced what has become one of his most memorable images: �Art and science ... arise from sensation, just as after in battle a rout occurs, first one soldier makes a stand, and then another makes a stand, and then another, until the original position (archen) is restored.� The image is one of soldiers who were originally arrayed in a phalanx running helter-skelter in retreat and then reforming a phalanx; and the image is effective because a phalanx is far more effective in combat than an individual soldier. By analogy, the individual soldier making a stand is like a �sensation�; soldiers repeatedly making a stand and moving to lock arms and shields is like combining sensations to create �experience�; and the phalanx is like the full universals which that characterize necessary and �scientific� intellectual knowledge. The image helps us to understand the movement from sensation to experience to understanding scientific principles.

But an image is not the same as an abstract philosophical argument. So Aristotle, quite unusually for him, admits that the explanation we just considered is �not precise enough,� and offers a second try, starting again with sensation:

When one of the individuals [things sensed] has made a stand [is present in sensing or remembering], then there is the first universal in the soul. For though the individual is sensed, sensation is of the universal, for example, of man, but not of Kallias the man. Then among these [first universals] more stands are made, until [one arrives at] the universals without parts [= the categories or highest genera]. For example, [moving from] this kind of animal, then to animal, then repeating this process. So it is clear that we must come to know the first principles by induction, for in this way sensation produces the universal (to katholou empoiei).[18]

In this dense passage, Aristotle shows how inductive argument, moving from individual things sensed, all the way up to the highest principles, is the way we come to understand scientific principles. The key step in the argument is when Aristotle distinguishes the act of sensing, which is described using the verb �is sensed� and whose object is the individual thing sensed, from the content we receive in the act of sensing, which is described using the noun �sensation.� The same content, of course is found in sensing an individual, in having broader, more universal �experience,� and in understanding that content as a fully universal principle (or conclusion).

Thus far, Aristotle�s argument has shown that it is possible for induction to take us all the way from sensing an individual to the most universal knowledge, of the same content. The metaphysical reason this is possible is that Plato�s forms have now been securely placed within things in our world, as intrinsic principles. But are we still at the level DL3 and A3, at what we might call the insecure universals that can only produce �opinion�? The answer is that we must advance to the level of knowing the principles of �science� necessarily. And there is only one way to do so: to add onto what results from the inductive process non-discursive intellectual insight into the forms, here, Aristotle�s forms, not Plato�s, which is the very last point Aristotle covers in the final chapter of his Posterior Analytics. And how do we do so? He has already told us. The process of moving up to the highest principles, here the categories, is a dialectical process. In the course of discovering the arrangement of higher and lower notions, or propositions, our more all-encompassing vision is what makes possible an insight into the whole, and thereby insight into the �definitions� and �suppositions,� as well as the �axioms� of an Aristotelian science.

At this point there was only one thing left for Aristotle to do. After setting out the theory of demonstrative science in the Posterior Analytics, he could, and did, engage in the hard work of developing the �sciences.� That work is not over, and I hope some of you will engage in it, as a life�s work. But I would enjoin you to take your inspiration from two gigantic figures in the history of thought: from Aristotle, who set out a theory of science which still in its essentials is correct, it seems to me; and Isaac Newton, whose Mathematical Principles of Natural Philosophy took to the highest point I know of Aristotle�s own notion of studying the natural world using mathematical rather than ontological principles (in what is called a subordinate science).

Thank you and let me say I envy you for being able to study both Aristotle and Newton here.

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