5

Developing Understanding: Formulation

Properly, to abstract is to grasp the essential and disregard the incidental, to see what is significant and set aside the irrelevant, to recognize the important as important and the negligible as negligible.¹

(1) John can cultivate one acre in two hours. Michael can cultivate one acre in three hours. Working together how long does it take them to cultivate one acre?

(2)

1. How many swans must you see to justify saying, ‘All swans are white'?
2. How many humans must you see to justify saying, 'All men are mortal'?
3. How many corrupt politicians do you have to meet to conclude, ‘All politicians are corrupt’?

(3) Form one word from each of the following jumbles: [156]

• V I P T O
• D R N R B E A
• H T I G I N S
• R G O E A N N L

(4) Zeno, the Greek dialectician, wanted to prove that there was no such thing as space. He did this by reducing the opposing view to absurdity. This is how he argued. 'If there is space, then it is either something or nothing. But if it is nothing, then things cannot be in it. If however it is something, it will itself have to be in space, and that space will have to be in space, and so on indefinitely. But that is an absurdity. Therefore there is no such thing as space.

0. Is the logic of the argument valid?
1. What does he mean by space?
2. What does he mean by 'something'?

(5) Do you know the meaning of just and unjust? Can you define justice?

We have begun our appropriation of the activity of insight by identifying individual acts of understanding; we should now be familiar with the characteristics of an insight, the cooperation and coordination of activities of questioning, sensing, remembering, and imagining in reaching understanding. The purpose of this chapter is to reinforce our familiarity with all of these aspects as well as to extend our ability to deal with understanding as an ongoing process. Understanding is a dynamic process; individual insights tend to coalesce, to form a context, a system, a science. The initial act of discovering is one thing but the mode of demonstrating, presentation, formulation of the discovery is another; in between there is needed a stream of insights into the correct words to use, the extent of the discovery, correct expression in a formula or definition or theory or concept. We will now focus on the process from an insight to a correct formulation of that insight in a definition, or explanation. This requires many further acts of understanding both [157] into correct use of language and into the real extension of the intelligibility grasped in the insight.

We focus first on generalization, to show how the act of understanding pivots from the particular to the general: this is the very nature of understanding and hence of induction. Then we deal with the closely related topic of abstraction, to show how the act of understanding of its nature abstracts from the concrete; there is an enriching way of doing this as well as an impoverishing way. We then consider the contrast between conceptualism and intellectualism; we consider the role of the concept in understanding; is the concept that which we know, or that by which we know? We consider the relation between things and properties, discovering that there is a further pivoting involved in the development of understanding. Finally, we consider the dynamics of reaching a higher viewpoint and the infinite flexibility of human intelligence.

Our aim continues to be self-appropriation. It is a start to be able to isolate, identify and describe individual acts of understanding. Now we are appropriating, becoming aware, making explicit, the forward development of understanding as a process. We distinguish clearly between the initial act of understanding and the later formulation of that understanding in a theory. This chapter is important because certain philosophies and systems of logic attend to the formulation and not to the insights which made it possible. It is quite difficult to become aware of the subtle processes of the activity of understanding; it is easier and more tempting to take it that they do not exist and to consider the rules of grammar or logic or method as the rules of thought. The focus of this chapter is in showing that the act of understanding is the source of all philosophy, all empirical science, all human knowing, every human culture, and all systems of logic, methods and technologies. [158]

1. Generalization

1.1 Generalizing

We have found it to be an essential characteristic of individual acts of understanding that they pivot between the abstract and the concrete. One aspect or application of this characteristic is a pivoting between the general and the particular, the universal and the individual. We are continuing to describe simply and honestly what happens when we understand. We do not begin by saying what intelligence must do; we are looking at the activity of intelligence to discover what it is from what it does. The aspect we are now concentrating on is that it generalizes.

Animals do know particulars by way of their senses. They recognize individual persons, places, and objects. They can learn a limited amount by way of imagination and memory. They see the particular, individual, concrete sense objects. They know them at the level of sense knowing. There is a minimal generalizing based on sensible similarity evident in this activity of sensing.

In contrast, consider the insight of naming described by Helen Keller; she had an experience of something running over her left hand while at the same time her tutor was tracing the word w-a-t-e-r on the palm of her right hand. The insight was to see how they were connected; she realized that the shapes formed on one hand referred to the experience she was having on the other hand; the substance was water. It was an insight of naming, an insight into the correct use of words, grasping a relation between an arbitrary sign or sound and an experience. Naming is the beginning of the expression of understanding in words.

Crucially, the word did not only refer to this one particular experience of running water; it referred to past experiences dimly remembered and forward to future experiences. It referred to typical aspects of this experience, to the essentials not to the non-essentials, to the general and not to the particular. When she went to the house she was able to recognize that the liquid coming from the tap was the same as that in the garden; the liquid offered for drinking at table had the same name; the substance she washed with was also in the same [159] category. The insight was to see the sameness behind all these experiences. The same data are to be understood in the same way; once you have understood one set of data, then, any similar set of data will be understood in the same way. On the first occasion the insight is difficult, but to repeat it is a matter of habit; it becomes easier and easier until it becomes so habitual that it is hard to recognize as an act of understanding.

Helen did not have to be taught how to generalize; it is one essential aspect of the insight of naming that it does generalize; it does not refer exclusively to this particular, it puts this particular in a general category; it pivots between the particular and the general. If the name ‘water’ referred only to what was experienced in the garden, then, what was later experienced in the water for drinking would have another name. Insight automatically begins to classify, to divide into categories, to understand the particular in the light of the general. Further learning and later insights refine the first clumsy attempts at classification. Helen had still much to learn about liquids: alcohol, kerosene, ice, steam, etc. The limits of the categories had yet to be set; the basis for the insight to be made more explicit; the experience of water could be very varied as in steam or ice or snow, but yet it was the same substance. Naming is only the beginning of understanding but it is an essentially valid activity of generalizing.

1.2 Commonsense generalization

Commonsense generalizations tend to be made very easily, quickly and loosely. Listen carefully to any discussion and you will note the frequency with which we jump from the particular to the general. This politician is corrupt; therefore all politicians are corrupt. These Irishmen are drunk; therefore all Irishmen are drunks. These workers are lazy; therefore all the workers are lazy. The basic procedure is essentially valid, the work of intelligence, a sign of understanding at work. But that does not mean that every generalization is justified or correct; counter examples will often be invoked and so the argument proceeds. The activity of generalizing is ubiquitous: learning consists in understanding better the correct extension and application of words, i.e. to what particulars can these [160] terms be generalized. This is done in a loose way at the level of common sense but more precisely in the explanations of science.

There is a movement from the particular to the general, but there is also a reverse move from the general to the particular. Classifications are refined by reference back to concrete applications. A doctor can learn about malaria from a textbook in his training, but it may be twenty years before he is confronted by a particular patient with certain range of symptoms; it may take him a while to make the connection but then he gets it; the patient is suffering from malaria; so this is malaria. The general is applied to the particular. Diagnosis consists in recognizing the general category described in the textbook in this concrete particular.

We may see something coming down the road from a distance. It is something but we do not yet know what, so we put it in the most general category available: it is a 'something'. But as it comes nearer we can refine the category and assert, 'oh! It is a lorry.' This is a narrower classification but still very general; there are many lorries in the world. As it comes nearer we are able to recognize our neighbor coming with his lorry to collect sand, 'oh! It is John.' Finally we have reached the particular. But we can only talk about the particular lorry in terms of general categories, a something, a vehicle, a lorry, a Leyland, a tipper, etc. We can know particulars but only with a reference to the general category or classification of intelligence by which we name and categorize it.

A child visits a zoo with her father. 'What's that, daddy?' She asks. 'Oh! That's a giraffe, honey.' After a short silence the girl asks, 'What's a giraffe, daddy?' 'That is,' replies the patient father, pointing. The story of the child at the zoo illustrates how the process of understanding proceeds sometimes from the general to the particular and sometimes in the reverse. From the point of view of logic it seems to be a vicious circle, but it is an accurate depiction of the process of learning. The more we learn about the concrete, the more we need our names and categories; the more refined the categories the more we need to return to the data; it is a continual pivoting from the particular to the general and vice versa. As the child's understanding of animals develops she will learn to discriminate more precisely between giraffes, camels, zebras, and [161] horses. The process of generalizing correctly involves continual refinement of names and categories.

1.3 Scientific generalization

At a more refined level, the scientist is engaged in the same process of generalization. The first chemist to discover that combining hydrogen and oxygen through burning produces water, was very excited. He had made a monumental discovery; water was a combination of hydrogen and oxygen. Perhaps he repeated the experiment a few times to check; perhaps he sought to reverse the process to confirm his conclusions. What he did not do was to attempt to demonstrate that all water was a combination of hydrogen and oxygen. That was taken for granted. It was not necessary to prove that English water was the same as French water; that hot water was the same as cold; tap water the same as river water, etc. It was not necessary to repeat the experiment a month later to see if water was still made of hydrogen and oxygen. It was recognized that particular times and places were irrelevant to the correctness of the insight. The insight was precisely into an essential property of all water; to be water it must be a combination of hydrogen and oxygen. It was the establishment of a basic relation between the elements hydrogen and oxygen and the compound water. It was an insight involving generalization. The experiment was only performed on a limited number of samples. But the nature of the insight was such that the conclusions could be applied to all water, all hydrogen and all oxygen, regardless of time, place or circumstances.

1.4 Justification

The principle at work here is that similars are similarly understood. If one set of data is grasped by an insight, then another set of data similar to the first will be grasped by the same kind of insight. You do not need a different kind of insight for each particular instance of water. You do not need to compose or decompose every instance of water to prove that water is a combination of hydrogen and oxygen. It is the very nature of insights to generalize. [162]

Which data are similar to other data? Who decides that these data are similar to those? There is no simple set of rules that can be applied mechanically to give automatic, correct results. There is only the driving force of questions, understanding and the search for better and more perfect understanding. Mistakes will be made, but they can be corrected. What is similar and what is different? What are the significant similarities and what are the significant differences? What are descriptive similarities and what explanatory? It is matter of intelligence and insight to recognize significant similarities and differences. A real zebra in a zoo is different from a stuffed zebra, even though they do look alike. Ice, snow and steam seem to be very different and yet they are the same. A real man is different from a picture of the man, yet they do show resemblances. We are dealing with an immanent law of intelligence, which picks out the significant from the insignificant, the similar from the dissimilar, the real from the imitation; which grasps the general in the particular; which recognizes the particular in the light of the general.

1.5 Induction

Induction is a term used by logicians for a procedure that goes from a number of individual cases to a general conclusion. Question two of the preliminary exercises presents some examples of induction. The opposite procedure by which we start with a general statement and apply it to particular cases is called deduction. Logic concerns itself with the logical procedures and arguments involved in doing this correctly and identifying fallacies when incorrect procedures are used. Undoubtedly logic is of great value when it clarifies these procedures, reveals unstated premises, uncovers fallacious arguments or shows that conclusions do not follow from premises.

However, much contemporary logic is done in the context of an empiricist philosophy which holds, like Locke or Hume, that our ideas are simply 'less vivid images' and that the association of ideas in our minds is governed by the laws of imagination. They would not accept the possibility of insight grasping universals in particulars or pivoting between the abstract and the concrete: that inquiry operates [163] on what is given in the senses to grasp intelligible relations, laws, natures, solutions. Hence an empiricist philosophy would not recognize the ability of the human mind to generalize, to grasp a formula operating in a sequence and to apply that formula to produce and infinity of further individual cases. For us similars are similarly understood and it is human intelligence which works out significant similarities and differences.

For an empiricist philosopher then the human mind in itself cannot in principle grasp universals in particulars and so cannot generalize. Yet the hard fact is that people - including logicians - continue to generalize regardless and seem to do so successfully. Logic is then given the task of justifying this procedure and showing how generalization is possible. The laws of logic are being substituted for the laws of the mind; rules of correct procedures are put in the place of intelligence. It is in this context that the logic of induction has become an enormous, contentious, complicated issue today.²

If you ignore the generalizing nature of intelligence, as the empiricist logician does, you are impaled on the horns of a dilemma: you must justify induction either by way of a complete enumeration or by way of formulating rules for jumping from some particulars to the general. However, complete enumeration is neither an induction nor a generalization. Complete enumeration means counting each and every individual case: there is no going beyond the particular to the general; there is no going beyond the counting as the counting covers all the cases.

The alternative of formulating rules to negotiate the transition from a limited number of cases to all cases also breaks down. First, cases differ so much in common sense, science, philosophy, history, etc., that it is impossible to formulate rules to cover all cases. Are all politicians corrupt? Are all swans white? Are all men mortal? They are quite different cases and no one set of rules applies. Second, even if there were a set of rules there would be a need for intelligence to select the rules which apply to this particular case, to be able to recognize exceptions, to be able to decide what is similar and what is significantly different. But that is to invoke intelligence and once you invoke intelligence you are beyond an empiricist philosophy. [164] John Stuart Mill formulated five rules for an empirical scientific method: the method of agreement, of difference, of agreement and difference, of residues and of concomitant variation.³ These are a useful guide towards correct inductions in the field of empirical science; but they require intelligence in applying the laws to particular cases. They do not take the place of intelligence. They are not rules that if followed blindly automatically produce correct conclusions.

For us the fundamental principle for generalizing is the law immanent and operative in our activity of understanding: similars are similarly understood. To understand means to be able to classify, categorize, define and divide; to be able to assign the particular a place in the schema of things; to have a set of general categories in the light of which you can identify new particulars which are encountered for the first time. The advance of any science proceeds in this way. There was a time when only five sub-atomic particles were recognized and now there are over a hundred; research has revealed all sorts of new phenomena; the old categories are not sufficient; the new phenomena must be given a name; the name enables researchers to determine its properties. But that might well lead to still further subdivisions. Advancing understanding involves finding more refined, sophisticated, and accurate classifications and generalizations.

There is a legitimate and important function that the logic of induction has to perform. The generalizer tends to get out of control. The most common fallacy in ordinary conversation is jumping to generalizations from an insufficient number of cases. We do need Mill's rules as well as the fallacies and syllogisms of logic to keep things under control. We use the logic of induction to introduce formalization, consistency and coherence to our generalizations. But the crucial point is that induction helps us to generalize correctly; it cannot justify the process itself which is really intelligence at work.

1.6 Deduction

There is also a logic of deduction; in fact, most logic tends to be deductive i.e. arguing from given premises to specific conclusions. [165] We simply make the same point that we made as regards induction: the human mind works spontaneously by way of moving from the general to the particular and vice versa. That is how we understand; that is how scientists proceed; they do not need a course in logic to be able to do science. No one taught them logic; they did not need logic to work from mathematical principles to a particular conclusion.

The logic of deduction is after the fact of deduction and not before. The logic of deduction must presuppose the activity of intelligence proceeding from the general to the particular in order to develop its rules. As one geometrician put it, 'Now that we know this is true, how do we prove it?' The function of logic is to make explicit the formal structure of deductive arguments, but it does not justify deduction in itself. We can make mistakes in deduction, and so deductive logic identifies the procedures which are legitimate and those which are illegitimate. A formalist interpretation of Aristotle's logic seems to imply that we need the rules of logic to do any deductive thinking at all; that in order to do philosophy you must first learn logic. There is an implication there that the rules of logic determine the rules of thought, that deduction is then a matter of the application of rules to terms and propositions in syllogisms. Such an interpretation does not do justice to Aristotle nor does it do justice to the spontaneous procedures of the human mind.

2. Abstraction

Abstraction is a further process in the forward movement of the activity of understanding. We have already noted that the individual insight pivots between the concrete and the abstract. What are the implications of this pivoting in the long-term activity of insight? How does the concrete relate to the abstract and vice versa? What exactly happens in this pivoting? Many philosophical traditions have disputed about the meaning and mode of abstraction.⁴ It will further the process of intellectual self-appropriation if we can recognize this activity in our own thinking. At the same time we may find some guidelines as to correct and incorrect procedures of abstraction. [166]

As indicated in the caption of this chapter, abstraction is nothing more complicated that grasping the essential and putting aside the incidental; it is separating the important from the unimportant, the significant from the insignificant, the sense from the nonsense. We do this at the level of common sense; we do it in the sciences; we do it in mathematics and we do it in philosophy. It is a spontaneous activity of understanding; it is nothing more abstruse than pivoting between the abstract and the concrete, the idea and the image, the concept and sensible data.

There are degrees of abstraction. Traditional scholasticism distinguished three degrees of abstraction, grounding the distinction between science, mathematics and metaphysics. The sciences abstract from material individuality; science is not interested in this water, but in properties of water in general; it is not interested in this amoeba but in categories of amoeba. Science deals with sensible characteristics as the grounds for scientific generalization. Mathematics abstracts from all sensible qualities except number and quantity. The operations of numbering, dividing, multiplying, fractions, etc., can be applied to any material objects. Metaphysics abstracts even from quantity to focus on being as being.

Unfortunately, abstraction is often conceived in a negative sense as simply leaving out, not attending to, ignoring, prescinding from, certain aspects of the data. We are thought to be moving away from the concrete into the more rarified air of the world of abstractions. Sometimes the connection with the normal processes of understanding is not grasped and abstraction becomes a very strange magical activity indeed. In that sense abstraction becomes impoverishing rather than enriching.

2.1 Enriching Abstraction

The basic moments in the activity of abstraction are positive rather than negative. Abstraction is the addition of intelligibility to the data rather than some kind of subtraction. Understanding is enriching rather than impoverishing; the enriching involves the pivoting between the abstract and the concrete, the addition of the intelligible laws and relations to the concrete data. We distinguish [167] three moments in the unfolding of understanding and hence three moments in the activity of abstracting.

The first moment is the anticipation of the intelligibility to be grasped. We have data and we have questioning; we are looking for something further, a law, a correlation, an explanation, a cause, a solution. If we do not grasp that further something, we will not be able to solve the problem. Archimedes as he set out for the baths was in this state of mind. He was anticipating a method, a theory, a technique, an understanding by which he could answer the king. But what was it? He had the data, the question, the clues, the hints; but the laws, the theories, would not come. This stage can be called objective abstraction: there is already a preliminary sifting of the relevant from the irrelevant, a focusing on data which seem promising.

The second moment is the successful realization of these heuristic structures or anticipations in the liberating flash of insight. Archimedes grasped a technique for solving the problem and returning from the baths did the calculations and reported to the king. The data remained the same; the chalice was the same but he now approached it with a new understanding. He implicitly understood the idea of specific weight and flotation. These added to his understanding of the data; they emerge from the data by the action of questioning. They are not imposed arbitrarily from above; the ideas can be put into practice and verified; they do indeed apply to these data. The abstract adds intelligibility to the concrete. This can be called apprehensive abstraction; it is a grasp of the intelligible in the sensible.

A third moment is the formulation and expression of the idea in a concept. It may have taken Archimedes a few days to work out the implications of his insight and to define correctly the concepts of specific weight and flotation. To do this he had to reflect on his insight, work out the theory, define the scope of his concepts and their application. It is only here that there is a negative element to abstraction; it is here that we prescind from the concrete, leave behind the data that are not relevant and concentrate on the correct expression of abstract relations. Furthermore, it is only a temporary separation from the data; for verification, for further checking, and [168] for further refinements of concepts there will again be a return to the concrete so that the process of enriching understanding can continue. This stage can be called formative abstraction.

Enriching abstraction is a process by which the potentially intelligible becomes actually intelligible by the action of intellect on the data of sense. This is a classical formulation but seems to hit the mark. The concrete is not known as actually intelligible by just looking. If you want to understand the movement of the heavenly bodies you have to do more than look. When you look at the heavenly bodies for the first time it is just a chaos; you do not know what is moving or in which direction; you cannot distinguish a planet from a star; you do not know which movements are random and which are regular. But if you persevere in questioning, in further systematic and intelligent observation, it gradually begins to make sense. You do pick out the regularities; you distinguish fixed stars, falling stars, satellites, planets, comets, and galaxies. Insight is adding intelligibility; it is not an arbitrary addition but a grasping of an intelligibility immanent in the data. The amateur looking at the night sky sees chaos; the professional astronomer sees an extraordinary rich panorama of interrelated bodies moving according to well-defined laws.

An enriching abstraction does involve a moment of jumping to a theory, but always with a view to returning to the concrete. Any professional discipline like medicine, mechanics, economics involves theoretical definitions, concepts, formulations; these provide the explanatory framework that allows a return to the concrete with an enriched understanding. The person of common sense listens to his car and says it is working fine, but the professional mechanic can tell him one of his tappets is loose; they both hear the same sounds but the professional’s interpretative framework is so much more enriching. A farmer looks at his field with self-satisfied complacency; the agricultural extension officer will ask him what he is doing about the fungal infection of the grass. A person of common sense looks at a Picasso and sees some strange shapes and colors; an art expert sees the history, the allusions, the styles, the phases of development, similarities and differences all brought to bear on this picture. [169]

Similarly, philosophy should bring to bear an enriching abstraction. It does involve moving from description to explanation, from lower to higher viewpoints, from individual sciences to the unity of all human science, from knowledge of objects to knowledge of knowledge. It should bring an enriching framework to bear on individual ideas, controversies, books, or concepts. The withdrawal of the philosopher into the world of theory, explanation, interiority is only with a view to a return to the concrete, with the added enriched perspective of comprehensive theory.

1.3 Impoverishing Abstraction

More often in the history of philosophy abstraction has been taken in its negative meaning as leaving behind what is not considered relevant. This involves concentrating on what is common to many different instances. Impoverishing abstraction does not move in the direction of deeper understanding of our universe; it moves in the direction of emptiness, sterility and poverty of thought. It is the abstract separated from the concrete; the abstract becomes an end in itself; it neither arises from nor returns to the concrete.

In the opening of Book Gamma of the Metaphysics, Aristotle distinguished between first philosophy and the special sciences. In doing so he coined the phrase ‘being qua being.’ He was trying to establish the existence of a science of everything from the widest point of view possible, an enriching metaphysics. But in many instances the phrase 'being qua being' is taken from the point of view of an impoverishing abstraction: what does everything have in common? Eliminate all specific points of view. Leave behind all distinguishing features. Being then becomes what is neither substance or accident, what is neither material nor spiritual, what is neither finite nor infinite, neither changing nor unchanging. This becomes an abstract ontology of the transcendental properties of being which does little to help us to understand the real world in which we live.

This procedure is sometimes applied to the distinction between substance and accidents. What is the substance? Well, it is what is not accidental, so we leave out what is accidental and what is left [170] will be the substance. The procedure, then, is to abstract from the color, the shape, the weight, the chemical properties, the position, etc. But what is left when this procedure reaches its limit? It is like peeling an onion; you keep peeling off skin after skin, hoping to find a core or kernel. You are supposed to find the substance; what you find, in fact, is suspiciously close to nothingness.

Perhaps the logical notions of extension and intension will help us to understand this distinction between enriching and impoverishing abstraction. The extension of a term is the number of individuals to which it refers; the intension of a term is the minimum content which a thing must have to be covered by the term, its definition. Enriching abstraction moves in the direction of applying the definition to the diversity of concrete instances, somehow including them all; the abstract applied to the concrete. Impoverishing abstraction moves away from the data in the direction of the intension of the term, the minimum content necessary to fulfill the definition.

The activity of understanding is creative, positive, enriching; so also the process of abstraction should be adding to the intelligibility of the concrete. The speculations of a Newton or an Einstein are highly abstract; but when applied back to the concrete and verified in concrete instances of movements in space and time, they are enormously enriching. We have seen how this works when we considered the activity of classical and statistical laws and how the pivoting between the abstract and the concrete works in both cases.

3. Intellectualism versus Conceptualism

In Lonergan's formative years, the Scholastic philosophy and theology he was taught was largely conceptualist. Either in principle or in practice, the emphasis was on the concepts: how they were defined and divided, interrelated and subdivided. Much of his achievement was to retrieve and make respectable the intellectualism of Aquinas in philosophy and theology. Intellectualism and conceptualism are partly philosophical positions but mainly basic orientations or approaches to the whole business of doing philosophy. It is important for our work in self-appropriation to be able to recognize these orientations. Conceptualism heads in the direction of impoverishing abstraction, static concepts and propositional, permanent truths; intellectualism heads in the direction of creative search for understanding with the role of concepts as a means rather than an end. We will put together some of the principal characteristics of both trends.

3.1 Intellectualism

Firstly, intellectualism recognizes that intelligence is somehow ultimate; that it is the source of logic, of propositional truth, of culture, of language, of method, of technology, of social organization. The rules and the criteria formulated in logic are very useful and important, but they are not ultimate; you can have different systems of logic formulated by intelligence to objectify certain processes of arguing or reasoning. If you can have different kinds of logic, how are you to choose between them? There must be something more basic or ultimate.

Some philosophies regard language as the ultimate; beyond that you cannot go; philosophy is confined to elucidating the semantics of language. But where does language come from? How do meanings change? How do we communicate across language barriers? Why are there so many languages? The intellectualist would claim that languages are the creation of human intelligence and can only be understood as vehicles for human intelligent communication. We can, in fact, translate from one language to another, albeit imperfectly. We can understand the writings of civilizations and mentalities quite different from our own.

Others hold that cultures are somehow ultimate and absolute; that they should be preserved untouched and unchanged; that we cannot communicate across cultures because they are so different. This usually entails relativism where each culture has its own truth, its own values, its own customs and ways of doing things. In this view there is no truth across cultures, no possibility of one culture criticizing another; everyone must follow what his culture prescribes. The intellectualist would again point out that cultures are the creation of intelligence; that the one thing all human beings have in common is intelligence; the reason that we can in fact [172] communicate across cultures and learn to understand the customs of others is that we are intelligent. Human intelligence and creativity is the source of cultural diversity; we can study cultures, their development and decline; how they interrelate; the different kinds of cultures; the effect on culture of media of communication, etc. Cultures are products of human intelligence and can be studied in their development and decline.

Intelligence is the source and basis of truth; as we shall see, it has its own reflective criterion of truth; it is the only ultimate guarantee of reaching the truth. But there are some who want to substitute something more tangible, a verification principle: it is true if you can see the sensible meaning and consequences of a statement. But where did this come from? If it is true, does it itself satisfy the criterion?

A second characteristic of intellectualism is that it recognizes that we learn about intelligence by studying its activity. We know what intelligence is by becoming aware of the activities performed by intelligence in act. An old Latin tag had it that agitur sequitur esse, the being of a thing follows on how it acts. In other words we learn about the nature of something by studying how it moves or acts. Just as you cannot present a theory about the movement of the heavenly bodies without looking at them and collecting the relevant data, so you cannot propose a theory of knowledge without adverting to the activity of understanding in its various moments. The data about knowing are an experience; we can shift our awareness from external objects to the activities of sensing and understanding. Aristotle used this way implicitly; it is hard to see how he could have been so accurate about images and forms, active and passive aspects of understanding, and the intellectual virtues unless he attended to the data of consciousness. Aquinas explicitly states that intelligence reveals its nature by way of its activity; from objects to acts, to potencies, to faculties, was his procedure. Lonergan has elevated intellectual self-appropriation into an explicit, systematic and basic method for the first time. Some philosophers start out by laying down the necessary a priori conditions for the possibility of human knowing; this presumes that human knowing is necessarily how it is. Lonergan begins from the [173] position that human knowing could have been different; contingently, this is how it is; you only know that by experience of the activity of knowing. Fact proves possibility: instead of torturing ourselves trying to work out the a priori conditions for the possibility of human knowing, why not look at the facts of what human knowing can do and then you know that it is possible.

A third characteristic of intellectualism is that it pivots between the concrete and the abstract. We study the concrete in order to grasp the abstract; the verification of abstract formulations can only be done by reference back to the concrete. But in many systems the abstract becomes a domain all on its own; the abstract loses contact with the concrete; it becomes static and sterile. It is the concrete which changes; the abstract is static. Cut off from the source of change the abstract can remain in the illusion that it has attained permanent perennial truth. But it is an illusion: the onward march of understanding demands a constant reference back to the concrete from the abstract and vice versa.

Finally, we can say that intellectualism recognizes that concepts are a means rather than an end. The end of intellectualism is a better understanding of our universe, its source and purpose, human life and destiny. To that end we will formulate concepts; the concepts will be applied, sometimes verified, sometimes found to be wanting. We understand the concrete by means of ideas and concepts. But sometimes the concepts become an end in themselves; instead of being a means by which we know reality they become the object of knowing; what we know are the concepts. Philosophy is then a matter of the interrelation of concepts, their division and definition; it becomes removed from reality; it becomes more and more abstract, more and more unreal, and more and more useless.

3.2 Conceptualism

In contrast to intellectualism let us consider conceptualism. This can be an explicitly formulated doctrine or it can be simply a tendency as a matter of practice to emphasize the concept.

Conceptualism regards the concept as ultimate; it has no account of the origin of concepts in intelligence; the concept is the term or object of knowing. Scotus is an explicit conceptualist; he held that [174] the first act of the intellect is in knowing concepts and the second act of the mind, the judgment, is in knowing the nexus between concepts.⁵ But if judgment is affirming the relationship between concepts, then there is no need to refer back to the data to verify the judgments. This philosophy is explicitly concerned with the formulation of concepts and judging how concepts relate to one another. Here you have the basis for a philosophy of definitions and divisions, syllogisms and theses, propositions, premises and conclusions; a philosophy of words and how they are defined, in happy isolation from the real world.

In a conceptualist system, the concept is that which we know and not that by which we know. Explicitly we are cut off from the world of data, experience, the senses and change. If the concept is that which we know, how do we know the real world of concrete material things? There is no basis here for any empirical science or any inductive knowing. Usually conceptualists posit an intuition of the concrete to justify our knowledge of existence. There is no way of applying concepts; if they are what we know, how can we compare them to the real world to check if they are true?

In this kind of system concepts are derived by way of impoverishing abstraction. The concrete has been left behind, prescinded from, is unworthy of consideration. Because concepts are abstract they are immobile and permanent. Understanding formulates concepts in its purposive search for truth; concepts in themselves are mere suppositions of the mind; whether they are more than that is settled by way of judgment and verification. But in conceptualism there is no account of how concepts emerge from intelligence; it is an unconscious process like magic, not a rational process; concepts are the ultimate; there is no account of where they come from. The result is a static, sterile, system of the interrelation of concepts which enjoys the illusion of permanent truth because it is removed from any concrete data which would disprove its premises and propositions.

This approach dominated the Scholasticism of the nineteenth and early twentieth century, explicitly and in principle, in the schools which followed the Scotist tradition; implicitly and in practice even in the Thomist tradition where the emphasis and [175] presentation of philosophy was in terms of definitions and divisions, theses and corollaries, logic and deduction.

But the deficiencies of conceptualism are by no means confined to Scholasticism. Any philosophy which has been turned into a kind of dogma, which is not open, which does not criticize its own presuppositions, tends in that direction. Reading some of the discussions of linguistic analysts one gets the impression of a group of people living in a world of their own. Certain dogmas have been presumed about the limits of knowing, about the importance of language and the uselessness of talking about truth, God, the meaning of human life, or anything of real importance. Philosophy then consists of playing games with words; it is very clever, very sophisticated, invokes complicated procedures of symbolic logic. But it is not in the real world. It is extrinsic to anything of importance. It does not learn about understanding by observing the activity of intelligence; it has already predetermined the limits and activity of understanding. It has nothing to say to or to learn from the empirical sciences. It is cut off from the concrete.

Any tradition can become conceptualist if it becomes a kind of dogma. Dogma formalizes the basic tenets of a philosophy. Certain principles are beyond questioning; to belong to this group is to accept these dogmas, presuppositions and principles. Philosophy becomes a matter of repeating the words and forgetting the meaning. Even a Lonergan philosophy could become a formalist, conceptualist system; if it were to be reduced to a list of basic propositions, if you have to accept these basic propositions in order to belong to the school. If a philosophy is simplified in such a way as to dogmatize the essential principles to be adhered to, then, it is on the way to conceptualism. Once a great and original thinker has passed away, lesser minds take over; what was open becomes closed. They simplify and formalize the system; it can be reduced to its essentials and these can be learned off and repeated; it can become a set of propositions rather than a guide to the activity of understanding.

In teaching any discipline, it is usually easier to present conclusions, systems and rules rather than the problems and concerns that gave rise historically to the discovery embodied in the [176] system or the rules. Calculus can be taught in terms of learning off by rote the rules of integration and differentiation rather than understanding problem these are designed to solve. This encourages repetition and implementation, but it is unlikely that it will foster any originality or encourage new discoveries. An alternative approach is to learn about the process of discovery rather than the final results, to trace the discovery for oneself, to learn from history not particular answers to specific questions but general strategies for finding solutions to whole ranges of problems. Education can be, not in terms of learning off formulae and rules, but in terms of general heuristics, strategies for long-term discoveries and solutions; in other words, of understanding understanding. Conceptualism is a tendency to formalize, systematize, dogmatize; to substitute rules, systems, logic, techniques for the activity of understanding. Intellectualism focuses on the creativity of intelligence, the ultimate criterion of truth, the experience of the activity of understanding, the willingness to accept any valid technique or procedure if it promotes understanding.

4. Things and Properties

We have seen how developing understanding pivots between particular and universal, between concrete and abstract, between data and concept. Now we consider how developing insight pivots between things and properties, substances and accidents, terms and relations. The insight you get depends on the kind of question you ask. You can ask, What is the unity or identity of that thing? In which case you are seeking the name of the thing, its substance, what it is as a whole. But you can also ask, What are its properties? How does it relate to other things? We can focus on one aspect of the data and compare it with other data. The pivoting between these questions and answers illustrates again developing intelligence at work. It also throws some light on a problem at the heart of philosophy from the time of Aristotle to the present day.

4.1 Historical Background

In the Categories, Aristotle distinguished between substance and the nine other categories. He knew that a substance was unique but [177] he had great difficulty defining it. He noticed that the other categories cannot exist without that of substance; the other nine categories are all accidents and can only exist by inhering in a substance. A substance does not have contraries; the contrary of white is black, the contrary of healthy is unhealthy but what is the contrary of horse? Substance does not allow of degrees; one horse may be bigger or faster than another but is not more of a horse than another. A substance can sustain contraries; the same person can be healthy today and unhealthy tomorrow, sitting at one moment and standing at another. Contraries exist in a substance as in a subject.

In the Metaphysics, he returns to the attempt to define substance and explores the possibility that substance is the matter, the universal, and finally the essence. He clearly rejects matter and the universal and seems to settle for essence (Book 7 chapter 17). He uses the example of the syllable. If you juxtapose two letters, then you have two letters side by side; you have two things which happen to be side by side. What do you have to add to these letters to make them into a single syllable? It cannot be another material element, because then you would have a third element alongside the others. It cannot be nothing because a syllable is clearly different from two juxtaposed letters. What is added is the essence, the unity, the intelligibility, the identity of the new whole. For Aristotle the substance is the answer to the question, What is it? It is the whatness, the unity that integrates the accidents together, the essence. The substance was not something apart from, or under, or over and above the accidents. The substance is grasped by understanding the unity that exists between the accidents.

In the Middle Ages, the Scholastics formalized the teaching of Aristotle on substances and accidents, but began to lay the emphasis on the substance as that which 'lies under' the accidents, as the Latin term suggests, sub-stare, to stand under. This began to be taken in a rather literal sense and the original meaning and insight was slowly lost. The problem began to arise, how do we know the substance if it lies under the accidents?

In this context the English empiricists began to question the reality of substance. If you cannot see it, how can it be real? You can see the accidents, but you cannot see what lies behind them. John [178] Locke defined substance as "the supposed but unknown support of those qualities we find existing, which we imagine cannot exist sine re substante, without something to support them".⁶ He dubbed the substance the occult substratum standing under or upholding the accidents. David Hume abandoned, not just this fanciful notion of substance, but all notion of a nature or unity underlying sensible qualities. Descartes and the rationalists made their own contribution to the misunderstanding of substance. It is difficult to use the terminology of substance and accidents today without invoking one or other of these misunderstandings so Lonergan abandoned the terminology altogether substituting, thing and relation or central and conjugate form. Furthermore he used his unique strategy in approaching the definition of these terms.

4.2 Abstractive/Inclusive insights

Our approach is to identify the two different questions that are asked and the corresponding kinds of insights that arise. Most of our examples have been concerned with insights into properties. These have been what we might call abstractive insights; from the whole of the data we abstract a certain limited datum in which we are interested and ask about that; we prescind from the rest of the data and deliberately focus only on one aspect. We may focus on the movement, the color, the size, the chemical properties, its density, etc. If we are given an unknown substance in a chemistry lab and asked to identify it, then we enumerate its properties, how it reacts with other known substances; we test whether it is acid or alkaline, metal or non metal, crystalline or powder, soluble or insoluble, its taste, its color, etc. These are the properties; they will eventually lead to an identification of the whole but you have to start with the properties. Galileo was not interested in what the rolling balls were made of; he was only interested in time and distance; they could have been steel, or glass, or wood, or stone, it would have made no difference to him. He focused attention on what was important for his purposes and prescinded from the rest; time, velocity and distance were relevant to his purpose; what the balls were, or were made of, was irrelevant. [179]

The identity of a substance is grasped by a different kind of insight. It is an insight into the unity, identity, wholeness of the entirety of the data. Here all the data are relevant. You are asking a different kind of question, What is it? It is no use telling the chemistry professor that it is soluble, or that it is alkaline; he wants the identity of the substance not its individual properties. These properties belong to other substances also. The professor is looking for the identity of the whole. When you have a sufficient accumulation of properties you begin to suspect what it is, perform the decisive experiment and then conclude this is hydrochloric acid, or this is sulfur, or whatever. You have grasped an identity that grounds all the properties. All the properties are relevant; but the insight is not into the properties taken individually but taken as belonging to the one substance. Aristotle's example of the syllable was fairly accurate. This might be called an inclusive insight as it includes all the data as relevant to the identity of the substance or thing. This is in contrast to an abstractive insight which deliberately prescinds from much of the data to focus only on that which is relevant to some particular property.

Insights into the unity, identity, whole, are verifiable. The Greeks were happy enough with the four elements as it satisfied the data available to them. But this was found to be totally inadequate at the time of the Scientific Revolution and the periodic table of the hundred or so elements was constructed. Sub-atomic elements were first identified as four but have now been expanded to over a hundred. Substances are not hidden occult entities. They are the verified elements, different from one another, permanent over time, the basic unities, identities, things of scientific thought.

Properties can be attributed to a substance. A substance is the unity of the attributes. Attribution is not just a logical trick but is fundamental to the way we learn, the way we ask questions and the structure of our thinking. The more we learn about the properties the nearer we become to identifying the whole; the more we understand the whole, the more we grasp the properties. This is the way science proceeds; this is the way the human mind operates. In the developing of our understanding of any area, there is this constant oscillation from properties to things, from things to properties. [180]

The idea of thing and property go very much together. Without both of these together, we could not understand change. Change happens when something remains the same and something changes. If everything is changing, then you do not have change, you have chaos or complete flux. Heraclitus was involved in a deep contradiction when he said, everything is in flux. If that is so, then not only can you not step into the same river twice, but you can't step into it even once, because it is not a thing but a flux. If there is not something permanent then science cannot pin down what is changing. In accidental change, the substance remains the same while the accidents change, as a man is young or old, sick or healthy, awake or asleep, but still the same man. In substantial change, such as wood to ashes, you have to appeal to the original elements out of which wood is made as the basis for continuity. Understanding change involves grasping permanence and variation, things and properties.

The process of knowing, whether it is in building the periodic table, or studying sub-atomic particles, or exploring distant space, pivots from identifying properties to attributing them to things; things are given a name, their properties are explored. The more the properties are verified, the more we know the thing. The more we know the thing, the better we can predict further properties. This is a very fundamental aspect of how we think and learn and know. We can best deal with the old problem of substance and accidents by adverting to how the astronomer, the biologist, the atomic physicist, proceed. We can do the crucial experiment by adverting to the structure of our own thinking.

5. Higher Viewpoints

The process of human knowing is dynamic; the operating force behind this dynamism is questioning. We have outlined the heuristic structure from questions to correct answers. By this means we get an answer to one particular, limited, specific question, but automatically further questions arise. They might be questions seeking deeper understanding or they might be seeking more information about other topics. If they are aiming at a deeper understanding they are usually aimed at a higher viewpoint. Our [181] knowing is progressive and cumulative. Insights pass into the habitual texture of the mind but lay the basis for further insights at a higher level of generality.

A higher viewpoint presupposes a set of insights at a lower level of generality. We question, study and eventually correctly understand some particular matter or data; we move on to related matters; ideas accumulate, similarities are noted. Each individual insight unfolds according to the characteristics already identified. In its own way it is valid, answers the questions raised, passes into the habitual texture of the mind.

But at a certain point the further question will arise as to how this aggregate of insights relate together. Is there an organizing act of intelligence that can see how they fit together? At this stage the data for the further insight are precisely the set of earlier insights which have already occurred. What is sought is a principle of unification, which will establish what these insights have in common, and how they differ; what is sought is an insight into insight, or more precisely a higher viewpoint.

Finally, there is the emergence of the higher viewpoint. There is discovered a law, a principle, a new set of postulates, definitions and conclusions. The validity of the original individual insights remains intact; but they are swept up into a new unity, framework, or schema. The higher viewpoint is characterized by its generality, its simplicity, its greater exactitude and precision.

Let us look at a series of examples to see how this works. The transition from elementary arithmetic to algebra provides us with one example. The first painful steps in learning arithmetic are usually taken in counting. Each number has to be identified by its symbol and the symbol has to be associated with a sensible experience of quantity. So children learn to count from one to ten, write down the numbers from one to ten and are able to count out ten oranges or ten pencils. Each number and each operation successfully mastered is an individual insight, a breakthrough, a little flash of light. As familiarity increases with repetition, the operations of addition and subtraction are added. Mostly this is done in the context of sensible objects like oranges, cookies or pencils. But the operations can be generalized by learning the addition tables [182] and learning the rules for subtraction. Multiplication and division are another breakthrough, another intellectual triumph, not totally unrelated to the previous operations but going beyond them by generalizing. Multiplication is simply the addition of a certain number to itself so many times.

A crisis point might occur about this point when numbers appear in the operations that cannot be verified in a sensible experience. If you subtract a larger number from a smaller one you get a negative number. How can you represent a negative number sensibly? If you divide certain numbers you get fractions; they do not go in evenly. How do you add, multiply and divide fractions? How do you cope with square roots of minus quantities? Etc. Are these operations valid if you cannot provide a corresponding sensible experience with oranges or cookies?

The trick is to break free from the constraints of sensible experience. Let numbers be defined as the results of operations that are performed according to rules. Then mathematics is free to develop in all sorts of operations with strange kinds of numbers. These operations are generalized in algebra whose symbols allow further operations to be conceived and executed. Algebra is a higher viewpoint from arithmetic because it generalized the operations that are performed on sensible quantities; it goes beyond the limits imposed by immediate sensible quantities. It is a set of insights that presupposes the validity of all the different insights of arithmetic but systematizes, relates and generalizes these operations in a particularly expeditious way.

Perhaps learning to read can be taken as another example. The first stage in this process is to learn the alphabet. Each letter is a challenge; grasping correctly the corresponding sound is an insight. Each letter is understood and learned individually; the letters are 'what' is understood. But letters by themselves are not much use. Now they have to be put together into simple words, cat, man, mouse, mat. The individual insights into the letters must now be presupposed; we are going beyond the letters to a new reality, the unity or form of the word. You cannot understand the word without the letters; but understanding the letters is not enough to understand the word. The understanding of the unity of the word is a higher [183] viewpoint to the understanding of the letters. Similarly, sentences are wholes made out of individual words; the words are the individual insights which must be presupposed and transcended in order to grasp the meaning of the sentence. The sentence is another higher viewpoint. Helen Keller reports how a few months after her insight into 'water' she grasped her first sentence.

Physicists now talk about finding a 'theory of everything.' As I understand it, the physics of the microcosm, subatomic particles and forces, has developed in quite a different way from the physics of the macrocosm, the solar system, galaxies, black holes, etc. The theories, equations, principles of quantum physics works when applied to the microcosm but not to the macrocosm where quite different theories and equations are needed. Is there a unified theory - a simple set or principles, equations and techniques - which will apply equally validly to both? This is a search for a higher viewpoint: a unifying synthesis leaving previous partial theories intact but unifying them at a higher level of generality.

Perhaps another example can be seen in the relation between the empirical sciences and philosophy. Each of the individual sciences develops its own methods, theories, concepts and definitions. It progresses in understanding its own particular area of matter assigned to it. Each science has its domain, its territory, its limitations. But questions arise that go beyond the domain of the individual sciences; who laid down these domains? how are the sciences are related to one another? is there anything that they leave out? who criticizes and evaluates scientific method itself? is matter the ultimate reality of the universe?. There is a felt need for some higher principle of unification; an organization of the sciences, their methods, their conclusions; a total worldview which incorporates but goes beyond the individual sciences. Philosophy emerges as the needed higher viewpoint. It does not invalidate the conclusions of the sciences; but sweeps the multitude of conclusions into a higher unity and synthesis.

Finally, there are a multitude of philosophies. In history there have been a succession of philosophies which have contradicted one another, criticized one another, supplemented and complemented one another. These are all individual attempts to understand the [184] world, man, knowledge and truth. A question arises as to how all these attempts are to be related together? Is philosophy just going nowhere? Is it a waste of time? Or can all these efforts be used as the data for a new understanding of understanding, a philosophy of philosophies? Our effort to shift from the objects understood to the act of understanding itself is the basis for a new higher viewpoint in philosophy. If we can pin down an invariant structure of the knowing subject, then we will have pinned down indirectly all that is to be known by the knowing subject. If we can understand what it is to understand, then we will indirectly be able to understand any philosophy, any science and any branch of human knowing. If we can also understand the process of misunderstanding, then we can also grasp the secret of decline, of error, of falsehood. If we can grasp the dynamics of understanding and misunderstanding we will have the key, the fixed base, the invariant pattern opening on all further acts of understanding.

Higher viewpoints are not just new theories, or paradigm shifts, or revolutions in thinking. They are a special kind of insight which presuppose an aggregate of individual insights but sweeps them up into a new unity conferring a new significance. They represent a new unity, a deeper synthesis, a higher integration. The advantage of the higher viewpoint is its generality, its simplicity, the speed with which it gets to the point. It is part of the normal process of developing intelligence.

6. Infinite Flexibility of Intelligence

Aristotle defined human intellect as ‘potens omnia fieri et facere;’ the capacity to become and to make all things. This sounds strange to us but for him it meant the ability to make any form or definition and possess it in the mind; in that sense we become the things we know, we possess them, we are them. The crucial term is ‘all things;’ nothing is excluded; if it is intelligible it can be known. We would agree with this definition but express it in a different way: we can ask questions about anything and everything. There is nothing excluded in principle from the range of our questioning; we can question about quarks, about God, about other possible universes, about history, before the Big Bang, after the Final [185] Crunch; there is no end to our questions. Our desire to understand is unrestricted.

Our attainment reflects the limited capacity of our individual minds, the limited time we devote to study, the limits of data available, the horizon of our teachers or tradition. But we can name and intend to know everything. We can question beyond the tradition in which we were reared. We can go beyond the limits of our present language, to create new terminologies or learn foreign languages.

Contemporary philosophers often invoke the claim of incommensurability; that certain mentalities are totally incompatible and therefore mutually exclude one another, e.g. the mentality of the mythic culture is totally incommensurable with that of the theoretic or scientific culture. If this were so the two groups would not be able to communicate with one another and would be living not only in two universes of discourse but in two totally different universes altogether. The claim is that there are no rational criteria by which we can compare myth and science; no rational criteria which they share in common and by which they can communicate with one another. Sometimes this is extended to cultures and language groups, each culture representing one legitimate lifestyle and there is no cross-cultural communication or judgments.

What we have said about developing intelligence belies such claims. It is possible to understand, compare, contrast and evaluate the supposedly incommensurable mentalities of myth, science, theory and interiority. How do we know it is possible? Because we do it; this text is identifying the similarities and dissimilarities between these mentalities. It is possible because the principles of human intelligence are the common factor underlying all cultures, all mentalities, all description and explanation, all theory and concepts, all languages. There is the one desire to know, the one desire to be intelligent, to understand, to move from images to ideas, from data to facts, from the concrete to the abstract. Myth is descriptive knowing; it is limited by the symbols, the predominance of imagination and feeling, the confusion preceding clear distinction and definition. As the Greeks have shown, it is possible to move [186] from myth to theory by way of critical questioning. It is also possible to move from the world of theory to the world of interiority, the task which we are addressing in this text.

Not only can we intend knowledge of the universe, but we can also intend knowledge of the self, knowledge of the spark of the divine in us, knowledge of our own intelligence. This does require the special technique of self-appropriation by which we become aware of the activities of intelligence and thereby the infinite flexibility of our desire to know.

In conclusion, we have been appropriating aspects of developing intelligence in its movement towards fuller understanding and formal expression. We have seen how it generalizes, abstracts, oscillates from things to properties, reaches higher viewpoints, is always creative and open to further developments. One could go on and on examining the development of understanding but never exhaust its flexibility, inventiveness, and originality. It is understanding which devises the concepts, the methods, the logics, the strategies appropriate in each field. It is practical intelligence that devises the instruments, the measurements, the technologies, the research programs that reveal further relevant data. It is impossible to impose rules on creative intelligence or think that it can be controlled by a static logic or a specific methodology. We have only considered a few examples to illustrate certain basic properties of intelligence. Aristotle used the four causes as the basis for his method. Descartes used synthesis and analysis, the putting together and taking apart. Social scientists use structure and function, status and role, diacronic and syncronic. There is no end to the strategies of creative intelligence. The point here as elsewhere is to identify this source of creativity and discovery in yourself and let it be your guide and principle in whatever discipline you choose to specialize.

The process from insight to formulation is a step which tends to be overlooked. Yet its importance is stressed by the fact that it is this procession which is the precise analogy in the human mind of the divine procession of the Son from the Father. In the human mind this procession is not a single act, but a multitude of acts of understanding words, implications, applications, relations, things, a [187] process from confusion to clarity, from implicit to explicit. The processes we have examined in this chapter in abstraction, generalization, conceptualization seem to be types of the process from insight to formulation.

As we conclude the first part of our study on thinking, we have a better idea of what Kasparov was doing for those fifty-five minutes of physical immobility. The body was immobile but the mind was furiously active. Even though it was only a game we see how questioning, imagination, intelligence, hypotheses, relations, combinations, possibilities, whizzed through his mind. Without learning much about chess, we have learned much about your mind, its infinite potential and its actual limitations. We have seen and appropriated for ourselves how intellectual activities constitute a specific pattern of experience distinct from playing or art or getting things done. That underlying the infinite varieties of expression this pattern has a basic structure: questions applied to sensible experience result in the emergence of insights which are later formulated in a theory or concept. This process from individual insights to formulation includes a stream of further insights into the proper use of language, becoming explicit about what has been understood, clarifying the intension and extension of terms. We have concentrated on the activities of thinking; but thinking must eventually come to an end - even for Kasparov. We have been dealing with understanding leading to formulation; now we must move on to reasoning as it leads on to knowing.

Comments on Preliminary Exercises.

(1) This problem looks simple but can be deceptive. There are many ways of doing it. The danger is to add the two together and answer three hours. But a little reflection shows that the answer should be between an hour, and an hour and a half. But to get the exact time? In this case algebra does not help. What you need is some equation (relation) with both of them working together. We have them separately, how do you add them together? In two hours John will cultivate one acre. In [188] two hours Michael will cultivate two thirds of an acre. Add them together and the rest is technique.

(2) Generalizing and induction is not a matter of counting, it is a matter of understanding. If it were a matter of counting, then, you would either have a complete or an incomplete enumeration. But if there is a complete enumeration, induction would not be necessary; if there were an incomplete enumeration, you would not be entitled to go beyond that. But generalizing is grasping the essential and leaving aside the non-essential. It is the biologist who is competent to decide whether ‘whiteness’ belongs to the definition of a swan. He will not be counting all swans but noting that the basic species with which we are familiar are normally white. But there are species of black swan. Each case will give you a different degree of certitude. Each case will demand a different amount of evidence to establish the degrees of probability of the generalization. It is enough to understand one human being correctly to grasp that all human beings are mortal; because it is an essential characteristic of man that he be mortal. It is insight not counting that justifies generalization.

(3) This is partly a matter of luck but also method is involved. Compose syllables, do they fit together? Experiment with likely beginnings and endings. Imagination and memory are involved in throwing up possible solutions.

(4) The logic of Zeno's argument is correct but it all hangs on the ambiguity of the meaning of 'space' and of 'something'.

Does space mean emptiness, a void, a receptacle as something existing apart from and independent of material things in it? Or does it mean the verified relations of distance and time between material bodies?

Does 'something' refer only to horses, stones, men, etc. or can quantities, qualities, relations, positions, be a 'something'?. Is a relation real? Is it a something or pertaining to a something? [189]

Aristotle answered Zeno by saying that space was not a substance but a relation between substances. Even Newton did not get the correct answer, so do not be discouraged.

(5) Most of us claim to know the difference between just and unjust. However, it is very difficult to define it. This is the process of formulation; from individual cases we formulate a rule or definition to cover all cases.

End Notes