Introduction
After writing this essay, I began to wonder as to its significance or its value. As will be seen, the essay shows that Lonergan has committed errors that make it impossible to affirm his conception of God obtained by reason alone. This raises the question of whether or not something of God can be known through natural reason. Having examined a number of arguments over the years, it seems to me that nature, life, reason, common sense, or however you approach the matter apart from revelation, can lead to all sorts of conceptions of God. Given massive human suffering, for example, and arguing from proximate causes to an ultimate cause, it would seem reasonable to affirm that God is the cause of suffering. Be that as it may, human beings are always working with intuition and logic to arrive at various conceptions of the Deity. Once these conceptions are in place, and if they are to retain some relevance for Christian faith, they cannot remain static when joined to Christian revelation. Rather, they must be denied in part, transformed, and augmented by the results of revelation. For example, the mind can rather easily arrive at a notion of a powerful and intelligent creator simply by looking at the universe and thinking about it. This process of thought, however, can also lead to God being the cause of suffering. When joined to revelation, God is not seen as the cause of suffering, although he obviously allows it, but his attributes of infinite wisdom and power are affirmed.
Perhaps some of what Lonergan believes about God as known by reason can be affirmed by revelation even if the reason is faulty. For example, revelation might affirm the simplicity of God. The communcatio idiomatum would appear to deny such a thing since God by incarnation knows particulars by means of multiple acts. That understanding of God, however, belongs to God the Son. God the Father creates effortlessly, his holy being is utterly transcendent, so perhaps, God as transcendent can know all things in one immediate flash of understanding. One thing does seem clear to me. It is problematical to approach God on the basis of reason. Better to know him through his divine acts, words, and appearings, given biblically and in life. My essay follows.
Modern Mathematics and Lonergan's Insight(1)
Lonergan has written extensively, but Insight is his most important work.(2) It was written after a sustained ten year encounter with the mind of Thomas, followed by an equally assiduous study of Western thought. It represents a creative appropriation of Thomas in light of the major scientific and philosophical developments since the medieval period.(3) Among theologians, his work is renown. David Tracy makes this claim: "That which Lonergan himself often refers to (as one trusts with some irony) as his 'little book' Insight is a major creative philosophical achievement is granted even by his most ardent critics."(4)
For those with logical and mathematical inclinations, Insight is especially attractive. It is self contained in that it starts with the simplest ideas and observations and develops logically and rationally toward an ever widening horizon that ends in God. Each logical step depends upon prior ones developed within the text itself. It is almost like the proof of a theorem. In comparison to many thinkers, Lonergan provides sufficient rigor to permit logical analysis. Rigor of this sort naturally arouses the mathematical passion, and I shall analyze one of his most important logical moves from a mathematical perspective.
I shall do three things. First, I shall show that mathematics plays a significant role in Bernard Lonergan's thought as developed in Insight. Secondly, I shall show that Lonergan's move toward transcendence makes use of a mathematical concept, and that mathematics, far from fortifying this move, shows it to be irrational. And finally, I shall show that Lonergan's concept of God cannot be intelligently grasped and reasonably affirmed.
Before investigating the significance of mathematics for Lonergan's thought, I will give a very brief overview of his thinking as context for what follows.
The first part of Lonergan's Insight addresses the question, What is happening when we are knowing? The second part addresses, What is known when that is happening?(5) In the first part Lonergan investigates how the mind knows. He does so by analyzing how the mind knows in the fields of science, mathematics, and common sense.(6) He discovers that knowing consists of three components, experiencing through sense impressions, understanding, and judgment.(7) Being is defined as the objective of the pure desire to know. (8) The human desire to know never arrives at the fullness of being. Nevertheless, human beings do know, and what they know, grasped in sense impressions, enriched by understanding, and terminated in judgment, is called proportionate being. Proportionate being is whatever is known by human experience, intelligent grasp, and reasonable affirmation.(9) Then, at a transition point, Lonergan claims there is an isomorphism between the structure of knowing and the structure of the known which is being.(10) Corresponding to experience, understanding, judgment, there is within being, potency, form, act, the three Aristotelian Thomistic categories.(11) Although human knowing is restricted, the desire for knowing is unrestricted, i.e., the mind constantly drives toward an ever widening horizon of knowing.(12) This leads to the notion of the unrestricted act of understanding which, for Lonergan, is God.(13)
This is the bare bones framework of Insight. Our next step is to assess the relevance of mathematics for Lonergan's thought.
Lonergan uses mathematics in a variety of ways. First, he uses examples from mathematics to show how the mind knows. His first specific example of understanding is to imagine a person looking at a cart wheel and asking themselves why it is round.(14) He then analyzes how the mind might resolve this question, and in the process describes how the rim of the wheel might give rise to the concept of circumference, the hub to the idea of a central point, the spokes lead to the concept of radii. These concepts can be related to each other. Finally, the mind may decide that the cart wheel is round because it approximates a circle with all points on its circumference being of equal distance from a single point.
In this example, the mind does three things.(15) First, the mind disregards the accidental properties of a specific cart wheel. It focuses on qualities that are common to all cart wheels, or even all wheels their roundness, their center, the distance from the center to the rim, and so forth. The remainder of the cart wheel's characteristics, size, exact shape, number of spokes, are ignored. This latter information is positive empirical data, but has no relevance to the question of the cart wheel's roundness. Lonergan calls the ignored data the empirical residue.(16) Then the mind formulates concepts and relates them to each other, thereby enriching its experience of the given object. This act of the mind is understanding, and it consists of the formation of concepts and their relatedness, in this case, center, circumference, radii, and their relations. Finally, the mind decides, makes a judgment. For example, the knower decides that the cart wheel is round because it roughly corresponds to a set of points of equal distance from a center. By this and many examples from mathematics, science, and common sense, Lonergan shows that the mind experiences empirically, understands, and decides that something is so.
Not only does Lonergan use mathematics to discover how the mind works, but specifically, he associates mathematics with the second component of knowing, that is, with understanding. "Thus, the precise nature of the act of understanding is to be seen most clearly in mathematical examples."(17) In understanding, the mind forms concepts and relates them. This gives understanding a formal quality. Mathematics investigates these forms. He describes the formal pursuit of mathematics with these words: "Again, there is a formal element in mathematical thought, and it tends toward a general, complete, and ideal account of the manners in which enriching abstraction can add intelligibility and order to the material element."(18) In other words, mathematics seeks to discover and formalize the totality of formal systems. As a partisan of Aristotle and Thomas, Lonergan is not a Platonist. He believes mathematics begins with sense experience, or at least, mathematicians derive their initial images from sense experiences. "For it is quite clear that mathematical thought in pursuit of the general and complete and ideal reveals a profound unconcern for the existent. Still it does seem to be true that the empirical reside does supply mathematics with samples of the type of stuff on which mathematical ideas confer intelligibility and order."(19) Nevertheless, Lonergan's is aware of the fact that mathematics can develop without regard to the existent, and further, mathematics gives rise to formal systems which have no model in the real world.(20) In summary, mathematics seeks to elaborate all the formal systems pertinent to understanding. Some of these systems, thought not all, are applicable to the material universe.
For Lonergan, mathematics provides examples of how the mind works, it is especially relevant for the act of understanding, and finally, mathematics supplies the primary concept Lonergan uses to enable the reader to grasp the intelligibility of his concept of God. Before discussing this intelligibility, I first need to introduce a few mathematical ideas which will be important for our discussion.
Mathematics is in a crisis, only the third in its more that 2500 years of existence.(21) Essentially, mathematicians have discovered that absurdities and paradoxes occur if any one of the following are accepted: a) impredicative definitions or propositions, statements that define set membership in terms of the set itself, or statements which refer to themselves, or b) allowing sets to be members of themselves, or c) unrestricted use of sets or infinities.(22) The crisis exists because portions of mathematics involve these procedures.
Some of these paradoxes and absurdities are very easy to state. For example, consider this sentence: "This sentence is true iff Santa Claus exists." This is an impredicative proposition because it refers to itself as a sentence. When it is subject to the laws of propositional logic, it will turn out that Santa Claus must exist.(23) Or again, if we admit the concept of sets being members of themselves, consider the set of all sets not members of themselves. If this set is not a member of itself, then it is, and vice versa. Or, there is a simple theorem in mathematics which states that the cardinality of a set is always less than the cardinality of its set of subsets.(24) Admit unrestricted sets and consider the set of all sets. As the set of all sets, its cardinality is maximal, yet, by the theorem, its cardinality is less than that of the set of its subsets.
Although these paradoxes are simple, their effects have been profound. Certain portions of mathematics were found to involve constructions of the type just given, and, as yet, no way has been found to regain all the mathematics that was lost. For example, Bertrand Russell communicated one of the above paradoxes to the German mathematician G. Frege just as Frege completed his two volume work on the foundations of arithmetic. In spite of the simplicity of the paradox, it had been implicit in some of Frege's formulations and Frege's work collapsed beneath his feet. In Frege's words, "A scientist can hardly meet with anything more undesirable than to have the foundation give way just as the work is finished. In this position I was put by the letter of Mr. Bertrand Russell as the work was nearly through the press."(25) In short, mathematics is an extremely rigorous investigation into valid forms of logical thought, and it will not accept conclusions or methods which lead to absurdities and paradoxes.
At this point, we need to discuss the relevance of mathematics for Lonergan's concept of God. My first step will be to introduces some paradoxes that can be generally applied to a notion of God arrived at by reason. Secondly, I shall show that Lonergan's notion of God exemplifies these paradoxes or absurdities.
A key concept for Lonergan is the simplicity of God. God is simple iff God knows everything it knows in one act.(26) Let God be simple and know several things. Let N be the set of things God knows. Then, being simple, God knows all the elements of N in one act, which is to say, God knows the set N and N is a member of itself. Mathematicians have shown, however, that it is not reasonable to posit a set that is a member of itself. One might say, at this point, that Lonergan's God might be beyond reason. However, as will be shown, Lonergan affirms a concept of God that requires understanding and reasonable affirmation at the level of finite reasoning.
Or, again, let God be simple and omniscient. Let N be the set of things God knows. Let N* be the set of subsets of N. Being omniscient, God knows N*, and therefore, N* is contained in N which is impossible since no set contains all its subsets.
For Lonergan, God is simple, omniscient, eternal, timeless, the primary cause, and much more.(27) These same paradoxes can be rephrased using some of the other of God's characteristics. For example, if God is timeless and knows all in one instantaneous eternal moment, both of the above arguments apply.(28)
We now have to assess whether the paradoxes just given have any relevance for Lonergan's idea of God. Perhaps they are simply formal arguments, having no relation to the substance of Lonergan's thought. I will show that Lonergan's thought is concerned with the formal characteristics of God in ways that make these paradoxes directly relevant.
To begin with, we need some sense of how Lonergan develops his concept of God. For Lonergan, God is the primary component in the idea of being.(29) The idea of being is the act and content of unrestricted understanding. I shall make these notions clearer as we proceed, but for the moment, consider that we understand things partially with our restricted understanding. For example, we observe wheels through sense impressions. As we reflect on what we have observed, we can arrive at understanding. We can formulate such things as the center of a circle, its radii, and its circumstance. We can then reflect on our understanding of these concepts, and as we do so, we understand the formal characteristics of wheels that we have observed through sense impressions. In other words, we can understand things we have observed by understanding ourselves. Our understanding, however, is restricted, there are many things beyond our intellectual grasp. Imagine, however, an unrestricted act of understanding. It would understand all things, and then by understanding itself, understand all things. The primary component is God understanding himself, and the secondary component is God understanding everything else by understanding himself. How does Lonergan make this intelligible?
Lonergan makes this concept of God intelligible in two steps. First he extrapolates from the idea of proportionate being to the unrestricted idea of being, and then he shows that it possesses a primary and secondary component. At every step, mathematics plays a key role. The concept he uses is that of the integers, understood as individual integers, and also understood as the entire set of integers generated by consecutively adding one. As one reads his use of this image, it becomes apparent that this is the critical concept which governs Lonergan's though as he develops his idea of God. With one minor exception, this is the only explanatory example used in the sections introducing the transcendent idea which leads to God.(30)
Before going further, it might be helpful to make one further observation. For Lonergan, the idea of being is the object of unrestricted understanding. The objects of understanding are ideas, and normally, we do not conceive of ideas as themselves understanding. Lonergan will affirm, however, that some intelligibles are also intelligent. "A distinction was drawn between the intelligible that is also intelligent and the intelligible that is not."(31) Therefore, when thinking of the idea of being, the primary component, which is God, is both the act and content of unrestricted understanding. In this way God can understand himself as act, and know all things by knowing himself as content. We can see these two ideas related in these words which introduce Lonergan's notion of God,
But by asking what being is, already we have been led to the conclusion that the idea of being would be the content of an unrestricted act of understanding that primarily understood itself and consequently grasped every other intelligibility. Now, as will appear, our concept of an unrestricted act of understanding has a number of implications and, when they are worked out, it becomes manifest that it is one and the same thing to understand what being is and to understand what God is.(32)
As indicated, the mathematical image of the integers provides the insight Lonergan uses to arrive at his conception of God. Lonergan develops his idea of God in two steps, and the example of the integers is critical for both. First, the mathematical example provides the insight that enables Lonergan to go from proportionate being and restricted understanding to unrestricted understanding and the idea of being. Secondly, once Lonergan has developed the idea of being, the example provides the insight that enables Lonergan to distinguish between the primary and secondary components in the idea of being. We will begin with the first, the extrapolation from proportionate being to the idea of being. This is an important move, and I will quote Lonergan at length.
The nature of the extrapolation may best be illustrated by comparing it with mathematics. For the mathematician differs both from the logician and from the scientist. He differs from the logician inasmuch as he cannot grant all the terms and relations he employs to be mere objects of thought. He differs from the scientists inasmuch as he is not bound to repudiate every object of thought that lacks verification. In somewhat similar fashion, the present effort to conceive the transcendent idea is concerned simply with concepts, with objects of supposing, defining, considering, and therefore no question of existence or occurrence arises. None the less, the extrapolation to the transcendent, though conceptual, operates from the real basis of proportionate being, so that some elements in the transcendent idea will be verifiable just as some of the positive integers are verifiable."(33)
At this point, Lonergan is going to argue from a knowledge of proportionate being to the transcendent. For this to happen, his ideas of proportionate being must be sound, and this includes his grasp of mathematics. In terms of a mathematical insight taken from proportionate being, the image of the integers as individuals and the set of integers guides Lonergan's thinking at this point. Human knowledge of proportionate being is like knowing a few of the integers as individuals. In seeking to understand the intelligibility of the integers, one notices that 1+1=2, 2+1=3, 3+1=4, etc. As the mind formulates the integers, one by one, an insight occurs, represented by the "etc." The insight is into the totality of the set, the set of all integers. In the same way, the intellect grasps the intelligibility of proportionate being, and driven by the pure desire to know, it always raises further questions which cannot be answered by restricted human understanding. Nevertheless, the mind can grasp at once the possibility of moving beyond restricted understanding to an unrestricted act which grasps all intelligibility. This move toward the transcendent idea is similar to moving from a few integers to grasping the entire set. As conceived by Lonergan, the integers represent proportionate being which can be verified, the entire set represents the total intelligibility of the idea of being.
Furthermore, Lonergan is not concerned at this point to prove the existence of the idea of transcendent being. He is simply presenting the concept as intelligible, and showing how the mind will move in that direction as one moves from the integers to the set of integers which transcends all of them. The intelligibility of the idea of being will be like the intelligibility of mathematics. Mathematics is an object of understanding, and therefore exemplifies the formal character of understanding. It is not surprising that Lonergan uses mathematics at this point, for he has already affirmed mathematics as the discipline that elaborates all formal possibilities.
Once he indicates how the extrapolation is to take place, he then develops the object of the extrapolation which is the idea of being.(34) The idea of being is the content and act of unrestricted understanding. "Therefore, the idea of being is the content of an act of understanding that grasps everything about everything."(35) Lonergan's next step is to deduce the characteristics of the idea of being. Here are two of the key deductions,
Again the unrestricted act of understanding is one act. Otherwise, it would be an aggregate or a succession of acts. If none of these acts was the understanding of everything about everything, then the denial of unity would be the denial of unrestricted understanding. If any of these acts was the understanding of everything about everything, then at least that unrestricted act would be a single act. Again the idea of being is one idea. For if it were many, then either the many would be related intelligently or not. If they were related intelligibly, the alleged many would be intelligibly one, and so there would be one idea. If they were not related intelligibly, then either there would not be the one act, or the one act would not be an act of understanding.(36)
This one act, or one idea, has a certain property that is directly relevant to our purpose. It understands everything in all their details in one act as one idea. "For it has been shown that the idea is one, yet it is the content of an unrestricted act that understands at least the many beings that there are in all their aspects and details."(37) Lonergan then asks how this can be, and offers his standard mathematical example as the key to this possibility.
For what is possible in the content of restricted acts of understanding is not beyond the attainment of unrestricted understanding. But our understanding is one yet of many, for in one single act we understand the whole series of positive integers.(38)
We may make several observations. Regardless of whether one accepts Lonergan's logic at this point, the relevant fact for our purposes is that Lonergan argues logically and conceptually. He has a notion of the unrestricted act of understanding and he draws out its consequences formally and conceptually. His thinking unwinds with exactly the type of reasoning just given, deducing steadily the characteristics of the unrestricted act, timeless, eternal, simple, non material and so forth.
Furthermore, no effort is being made at this point to assert whether or not this unrestricted act exists. That affirmation comes later after Lonergan has completely developed the idea of being or the notion of God.(39) Then he will define God as the primary component or primary content of the unrestricted act in the idea of being, since act and content give rise to each other. At this point, however, Lonergan is doing nothing more than logically developing the idea of being, discerning the formal, intelligible, characteristics of being. To do so, he gives logic free reign, allowing the mind to go forward, discerning one intelligible conclusion after another. In other words, his thinking is mathematical. It is simply the consideration of formal relations between objects of thought, deducing conclusions from premises.
Further, he imagines that the unrestricted understanding "understands" mathematically. Its understanding is like our thinking as we move from specific integers to the set of integers and back again. In this way it knows the many in one act as restricted understanding knows the set of integers. Further, he imagines the unrestricted act grasping a series of things partially. He asks what happens in this case, and concludes that this cannot occur because the series would not be intelligibly unified and therefore understanding would be partial and not unrestricted. In other words, he denies certain objects of thought to unrestricted understanding because their "existence" as objects of thought lead to contradiction.
In light of the foregoing, we may present two alternatives. Either the unrestricted act of understanding understands or grasps one individual thing only, and no other individual thing, or it understands everything about everything in a multitude of acts. Or again, either the idea of being is one idea, and one idea of one individual thing, or it is many ideas. The one thing it cannot do, if mathematics has any bearing, is to understand many things as individuals in one act, or be many ideas and one idea simultaneously. We shall show this by discussing the matter from a mathematical perspective.
One result of the attempt to build mathematics out of logic, represented in Russell and Whitehead's Principia Mathematica, was the recognition that sets and propositions can correspond to each other.(40) A set is the set of all objects which satisfy a certain proposition. Conversely, a proposition can be defined in terms of the set of all objects for which the proposition is true. In order to avoid the sorts of mathematical contradictions that have precipitated a crisis in mathematics, a theory of types was developed, both for sets and propositions.(41) For sets, the theory begins with individuals, type zero, and then type one, sets of those individuals. Type two sets are sets whose members are type one, type three sets are sets whose members are type two, and so on. The rule is stipulated that each set can only draw its members from the type just before it. In this way, sets can never become members of themselves and the absurdities can be avoided. Similarly, propositions can only have as their possible subjects elements of the previous type and cannot make use of elements of other levels.(42) For example, if we define the proposition M by "mortality," and let M(x) be the proposition, "x is mortal," the range of values for "x" can go over the set of human beings as individuals, but we will not allow the range to include sets of or the set of individuals. In other words, M(x) cannot be allowed to say, "the human race is mortal." By maintaining this convention, impredicative propositions are eliminated.
Returning to the example of the integers, and Lonergan's argument that the unrestricted act is one act, we have the following. First, the act knows individuals. Keeping in mind the extrapolation from proportionate being, the unrestricted act understands the formal individual characteristics of proportionate beings. This is type zero. Then the act grasps the intelligibility of the set of all individual characteristics, just as the mind knows the set of integers. This is type one. Then the unrestricted act does both in one act. As claimed by Lonergan and just quoted, "Again the unrestricted act of understanding is one act." This is an absurdity since the unrestricted act has as its range of objects, or values for R(x) where R is "the unrestricted act understands," elements of type zero and one. Actually, Lonergan allows unrestricted understanding to know all types whatsoever in one act. In other words, when Lonergan says this unrestricted act understands "everything about everything," in one act, he includes individuals, sets, sets of sets, propositions, propositions about propositions, and so forth, all in one blinding flash which fuses and confuses sets and their elements, propositions and the acceptable range of objects to which they refer.(43)
Similarly, the theory of types does not allow the one idea of the many, which corresponds to type two, to be conflated with the ideas of the many, type one. Either there is one idea at level two, or, if level one is being considered, there are many ideas. The idea of a set is not simultaneously the ideas pertinent to each of its members. Therefore the idea of being is either one idea, an idea of one individual thing, or many ideas of many things. It is never one idea of many things, although the one object of the one idea may be composed of many things.
Perhaps it could be said at this point that God's understanding, or unrestricted understanding, is distinct from restricted human understanding and as a consequence the results of mathematics are not directly relevant. For Lonergan, however, the unrestricted act of understanding grounds and includes finite human understanding. This is because the unrestricted act is extrapolated from proportionate being and its intelligibility. The extrapolation preserves correct distinctions made at the level of proportionate being. Consequently, it preserves the correct insights of mathematics. Therefore, the unrestricted understanding cannot understand a set and its members in one conceptual act, since restricted understanding, at least if mathematics is our guide, does not confuse types.(44)
A further word might be helpful here. Lonergan's argument does not depend upon mathematics. He could easily have advanced his arguments apart from mathematics. Mathematics is relevant, however, in that mathematics belongs to proportionate being. It describes aspects of the formal relations that can hold between finite beings. As such, the unrestricted act of understanding will understand mathematics, and do so correctly, according to how mathematics is understood for finite beings. But mathematics does not allow individuals and sets to be understood as subject of one proposition, and therefore, the unrestricted act of understanding will not understand itself and all things in one act as well.
Further, before Lonergan deduces that the unrestricted act is one act or one idea, he speaks of it as grasping "everything about everything," beginning with the singulars of proportionate being, or type one, and from there, to the unrestricted act understanding everything which includes all types.(45) Then, and only then, does he assert that the act is one act. Therefore, as developed by Lonergan, the one act is presented as grasping all types, and then, subsequently, it is argued that it is one act. This is impossible, or if possible, irrational.
Lonergan's second major logical step is to distinguish between primary and secondary intelligibilities in the idea of being.(46) Since the act of unrestricted understanding is unrestricted, it understands itself, and further, understands all things through understanding himself. Primary intelligibility is the idea of being understanding itself, and through understanding itself, understanding all other things which is the secondary intelligibility. In moving from restricted understanding to unrestricted, Lonergan went from a few given integers to the entire set. In moving from primary intelligibility to the secondary, Lonergan goes in the opposite direction, from understanding the set in one act of insight, to grasping the individual integers by understanding the set.
The idea of being has been defined as the content of an unrestricted act of understanding; and in that content a distinction has been made between a primary and a secondary component. Naturally one asks just what is the primary component, and the answer will be that the primary component is identical with the unrestricted act. It will follow that, as the primary component consists in the unrestricted act's understanding of itself, so the secondary component consists in the unrestricted act's understanding of everything else because it understands itself." (47)
Once again, the positive integers are the explanatory insight that illumines this concept.
There must be, then, a primary component grasped inasmuch as there is a single act of understanding, and a secondary component that is understood inasmuch as the primary component is grasped. For just as the infinite series of positive integers is understood inasmuch as the generative principle of the series is grasped, so the total range of beings is understood inasmuch as the one idea of being is grasped.(48)
Or again,
Finally, the secondary intelligibles may be mere objects of thought. For they are grasped as distinct from the primary intelligible, yet they need not be distinct realities. Thus, the infinity of positive integers is grasped by us in the insight that is the generative principle of the relations and the terms of the series.(49)
Intuitively, Lonergan is conceiving of an archetypal idea, or primary insight, which generates or grasps all other ideas and insights including itself. In this sense there is, within the idea of being, a root, or basis, or generative principle as in knowing the integers in one insight, which also understands, and understanding itself, understands all things. This root is the primary intelligibility; the secondary are the particular intelligibilities of proportionate being. "More profoundly, it denotes the primary component in an idea; it is what is grasped inasmuch as one is understanding; it is the intelligible ground or root or key from which results intelligibility in the ordinary sense."(50)
Let us develop this idea a bit. Lonergan begins with proportionate being, objects given to sense impressions. Aspects of these objects, aspects not neglected in the empirical residue, are ordered by an insight. We may, for example, think of circumference, radii, and center seen in a cart wheel, and ordered by an equation between them. In other words, to each set of ordered objects there correspond an insight that orders them. Then there are higher insights, insights upon insights, with higher insights ordering sets of lower ones. Each set of higher insights correspond to the insight which grasps it, so that there is a natural map from sets of ordered objects or insights into the set of insights. In this map, each insight in the range of the map represents a set, the set of objects ordered by the insight, and the archetypal insight, the primary intelligibility, or the primary component in the idea of being, corresponds to a "set of all sets," which leads to an absurdity.(51)
Or, let us look at this in another way. Let us call the primary intelligibility PI, and the secondary intelligibilities, SI. Consider the set: {PI, SI}. PI and SI are related, the latter known through the former, and therefore, the set {PI, SI} admits of a higher insight which generates it. Let us call this higher insight, PI*. According to Lonergan, all realities which have some positive intelligible relation are generated or understood by a higher insight. Otherwise, there would not be unity.(52) This insight, PI*, must be PI, for if not, the PI which is a member of {PI, SI} is subsumed under a higher insight and is therefore not primary. But it was assumed that PI is the primary insight which generates all other insights. Therefore, PI* equals PI. Therefore, we have an idea, PI, which corresponds to the set {PI,SI}, and yet PI is an element of that same set. Logically, this is what is happening when Lonergan says the primary intelligibility understands itself and by understands itself understand all things. Within that statement PI corresponds to or generates the set and is a member of itself. Mathematically, however, allowing sets to be members of themselves leads to absurdities.
The same structure is seen in the sentence, "This sentence is true iff Santa Claus exists." PI corresponds to "This sentences is true," while SI corresponds to "Santa Clause exists." Yet "This sentence is true" or PI, also refers to the entire sentence or set {PI, SI}.
The matter can be phrased in a slightly different form. Consider all the intelligibilities understood by unrestricted understanding. These are grasped in one insight, PI. PI represents the set of all grasped intelligibilities. It is the set of all intelligibles, just as N={1, 1+1=2, 1+1+1=3, . . . } is the set of integers. Unrestricted understanding also understands itself, and therefore, PI is a member of PI.
Or, we may look at it another way. Let I be the set of all correct partial insights. PI generates I, it is the insight that grounds all partial insights. Let O be an arbitrary subset of I not equal to I. O is a collection of correct partial insights, and can be understood as ordered by a higher insight just as one goes from individual integers to the entire set. Even if members of O have no intelligible relation, insight can grasp this and understand why.(53) Therefore, corresponding to O there is an insight, call it OI. Further, if O and O' are two distinct subsets of I, OI and O'I are distinct insights since they refer to distinct sets, they order different partial insights. For example, the insight that grasps {1,3,4,5,6,7,8, . . . } is different from the one that grasps {2,4,6,8,10,12, . . . }, and both of these are different from the insight that grasps {1,3,5,7,9,11, . . . .}. Further, OI and O'I are partial, since they do not order all of I, only PI does that. For example, the insight that grasps {1,3,5,7,9, . . . } is not the insight that generates all the integers since the positive integers are missing from the set of odd integers and insight into the odd integers must grasp this. Therefore, for any arbitrary subset O, OI is a partial insight, and further, if O and O' are distinct, OI and O'I are distinct. Furthermore, I contains both OI and O'I since I contains all partial insights. Therefore, I contains as many elements as it has subsets which is impossible.
The flaw in this argument is that I began with all partial insights, which is the same absurdity as beginning with a set of all sets. But unrestricted understanding leads us to exactly that. PI understands "everything about everything," and therefore, it has insight into all partial insights, and, at the same time, insight into sets of all partial insights, which means the one object of its understanding possesses at least two distinct types and two distinct cardinalities.
We may put this matter in another form. If Lonergan claims, and he does, that there is an isomorphism between the acts of the mind and the thing known, then to subsume a set N and each of its elements under one act, is to identify elements of a set with the set itself.(54) This is impossible. The same can be said for the primary intelligibility. If it understands itself and the secondary intelligibility in one act, then its object is one thing, not two. Or again, if the act understands "everything about everything," they are one, that is, they are, in the one act of understanding, one thing, not many.(55)
Or again, mathematicians have discovered that absurdities occur if one allows defining elements in terms of the set to which they belong. As a mathematician would say it: "No set S is allowed to have members m definable only in terms of S, or members involving or presupposing S."(56) The secondary intelligibility is a subset of the primary, and is, to use a Lonergan phrase, "grounded" by the primary. "For the primary being would be imperfect if it could ground all possible universes as objects of thought but not as realities; . . . . But the primary being and primary good is without any imperfection; and so it can ground any possible universe and originate any other instance of the good."(57) In other words, although Lonergan begins conceptually with the secondary intelligibilities, and then goes toward primary intelligibility, once there, he grounds, defines, and establishes the secondary through the primary, i.e., the elements of the set are defined by the master set to which they belong as members. In fact, Lonergan's aim is to ground limited human understanding in unrestricted understanding.
In sum, if primary intelligibility is an archetypal insight, and if insights, as Lonergan suggests, grasps sets of restricted insights, then a absurdity will occur because the ultimate insight is similar to the set of sets. Or, in the end, it will have to be a member of itself in order to terminate an eternal regression. If the primary intelligibility is some form of a proposition, then similarly, we would derive a paradox since it is hard to imagine a proposition that explains everything about everything. As used by Lonergan, its range of propositional values would include itself which makes it impredicative.
Lonergan's major weakness is that he seems unaware of the fact that mathematics places certain limits on formal understanding. Above all, mathematics does not allow sets and their subsets to be the object of a single conceptual act, nor can there by any unification between sets and their elements since these belong to different types. This leaves Lonergan with only two alternatives, either introduce a multitude of acts into the transcendent idea, or, have the transcendent idea grasp only one individual thing and no other individual thing.
Once Lonergan has introduced the idea of being, primary and secondary intelligibility, he then discusses causality.(58) In this section, he does not further explicate the intelligibility of the idea of God, but rather, advances reasons for affirming the idea of God. I will not discuss this section in detail, since my main interest is the intelligibility of his notion of God. Nevertheless, a few observations can be advanced.
In essence, his argument runs as follows. First, being is intelligible, and if something is not intelligible, it has no being. This follows from prior definitions and observations since being entailed intelligibility. Secondly, proportionate being is conditioned being, it is conditioned by efficient causes. Further, it is riddled with contingency. By this he means that its intelligible causes are ultimately unknown. We know proximate causes, and can infer the existence of more remote causes, and can even infer an infinite regress of explanations and causes, or a circle of them. But this is not explanatory, for what gave rise to the infinite regress or the circle? If there is no ultimate intelligible ground, then the presumed being, in so far as we know it, is not real in that it does not possess final intelligibility.
However, the real requirement is that, if conditioned being is being, it has to be intelligible; it cannot be or exist or occur merely as a matter of fact for which no explanation is to be asked or expected, for the non intelligible is apart from being. Now both the infinite regress and the circle are simply aggregates of mere matters of fact; they fail to provide for the intelligibility of conditioned being; and so they do not succeed in assigning an efficient cause for being that is intelligible yet conditioned. Nor can an efficient cause be assigned until one affirms a being that both is itself without any condition and can ground the fulfillment of conditions for anything else than can be.(59)
Implicitly, this argument contains the same absurdities encountered above. The infinite regress can only terminate at a point where the intelligibility or the being grounds both itself and the previous series in one act, otherwise, another term in the series arises. Formally, this type of reasoning leads to absurdities.
In the next section, Lonergan explicates his notion of God. These are the Thomistic characteristics of the God of reason, timeless, immutable, perfect, and so forth. These characteristics depend logically upon God being the unrestricted act understanding itself and all particular things in one act. For example, the primary intelligibility is self explanatory, for if not, its understanding would not be unrestricted.(60) Or, there is only one primary being, and this follows from the unrestricted act being only one act.(61)
In short, Lonergan's notion of God depends upon the credibility of his extrapolation from proportionate being to the idea of being, his concept of the idea of being, and upon his distinction between primary and secondary intelligibility. All lives or dies in that ditch.
Lonergan's final step in developing the concept of God is to ask the reader to reasonably affirm God's existence.(62) Before discussing the validity of this affirmation, we must investigate what Lonergan means by "reasonably affirm." That is our next step, and then we will evaluate Lonergan's invitation that we affirm the God he has brought before our understanding.
When Lonergan asks his readers to affirm his idea of God, he is not asking us to accept a rigorous logical proof. He is asking us to make a judgment. Knowing comprises three elements, sense impressions, understanding, judgment. Sense impressions and understanding lead to judgment, and this judgment is a decision on the basis of what he calls the "virtually unconditioned."(63) By this he means that the human process of knowing entails a sense of what conditions must hold if a certain judgment is made. To say this is a typewriter, or that my house is on fire, requires a knowledge of the conditions that must hold if something is called a typewriter, or what conditions must be satisfied if something is on fire. The mind, and this is the critical point, makes judgments. Lonergan is not arguing abstractly. His epistemology, like his metaphysic, is derived from understanding how the mind works.(64) Spontaneously and naturally, the mind judges. The knower reaches the point where further questions are deemed irrelevant. A decision is made.(65) Of course, error is possible. There is no overwhelming evidence that can guarantee the validity of any given judgment. Further questions and reflection may uncover error, but then, that judgment could be mistaken. In other words, there is no truth that can exclude judgment, and further, as all know, there are correct judgments. And that conclusion itself is a judgment.(66)
In the case of God, Lonergan presents his case in two steps. First, he presents the idea or notion of God as something that can be intelligibly grasped. In other words, with respect to God, the virtually unconditioned must include as one of its conditions the intelligibility of Lonergan's concept of God. Only after the notion of God has been intelligibly presented, does he ask his reader to reasonably affirm the God which corresponds to the intelligible notion. Lonergan begins his section on the notion of God with these words, "If God is a being, he is to be known by intelligent grasp and reasonable affirmation."(67) In short, Lonergan is not proving God's existence He is asking his readers to affirm themselves as knowers, and on the basis of what they judge to be adequate conditions for intelligibility, to judge whether or not his idea of God can indeed be intelligently grasped and reasonably affirmed. In continuation, I will review Lonergan's final arguments for God's existence, and leave it to the reader to terminate this matter in judgment, or, return to mathematics, philosophy, and Lonergan in search of further insight.
Lonergan rejects the ontological arguments for God's existence, and advances a cosmological argument in which the partial intelligibility of proportionate being calls for a ground of complete intelligibility.(68) He states the essence of his argument in these words,
If the real is completely intelligible, then complete intelligibility exists. If complete intelligibility exists, the idea of being exists. If the idea of being exists, God exists. Therefore, if the real is completely intelligible, God exists.(69)
Let us consider these four statements.
To begin with, statement four is a logical result of the first three. If they are true, four is true. Therefore, let us focus on the first three statements. The third statement is simply a definition. God has been defined as the primary component in the idea of being. Now, consider the other two statements without the words "completely" or "complete." With these modifications, the first two statements are simply definitions coupled with observations in reference to proportionate being. Lonergan has defined the real as that which is sensed, intelligently grasped, and reasonable affirmed.(70) Therefore the real is intelligible and intelligibility exists. The idea of being is this intelligibility insofar as it refers to proportionate being. In other words, the only content in the statements beyond proportionate being is given in the words "complete" or "completely."
The words "complete," or "completely" refer, of course, to the unrestricted act and its content in the act of understanding itself and thereby understanding all things. Lonergan concludes his argument for God's existence with these words,
It follows that the only possibility of complete intelligibility lies in a spiritual intelligibility that cannot inquire because it understands everything about everything. And such unrestricted understanding is the idea of being. . . . . For if the idea of being exists, at least its primary component exists. But the primary component has been shown to possess all the attributes of God. Therefore, if the idea of being exists, God exists.(71)
We may draw the following conclusions. First, I have shown that the idea of God as developed by Lonergan is based on invalid logical procedures. The divine characteristics that Lonergan lists in the section on the notion of God, a section whose content follows logically from the idea of being, depended upon God being a complete intelligibility which understands all things by understanding itself in one blinding act. We have shown this to be an irrational concept that cannot be intelligibly grasped for proportionate being, and therefore it cannot be extrapolated to transcendent Being, that is, to God. Therefore, it cannot be reasonably affirmed.(72)
Endnotes
1. Bernard Lonergan, Insight, New York: Philosophical Library, 1973. All quotations of Lonergan given in this essay are from his book Insight.
2. See the bibliography, pp. 271-78, of David Tracy, The Achievement of Bernard Lonergan, New York: Herder and Herder, 1970.
3. Ibid., pp. 82-3.
4. Ibid., p. 1
5. Lonergan, p. xxii.
6. Introduced on the first page of Insight, p. ix, and developed throughout the book.
7. Ibid., p. xviii, and developed throughout the book.
8. This definition is fundamental. See Chapter XII, "The Notion of Being," p. 348. He begins with a definition: "Being, then, is the objective of the pure desire to know." p. 348.
9. Ibid., pp. 391, 400, 483.
10. Ibid., p. 399. This affirmation of the isomorphism is an analytic statement. I thought about this for a long time and could see no reason to deny it.
11. Ibid., p. 432.
12. Ibid., pp. 637-9. "Man's unrestricted desire to know is mated to a limited capacity to attain knowledge." p. 639.
13. Ibid., pp. 657f.
14. Ibid., p. 7. Lonergan's realist assumption is present from the beginning. A mathematician might well admit that the sight of the cart wheel gave rise to the concept of roundness. But his question would not be, "Why is the cart wheel round?" but rather, "What is round?"
15. Lonergan uses this example for only the first two of the mind's acts since he has not yet introduced the concept of judgment which come later.
16. For the exact definition of empirical residue, see pp. 25-26.
17. Ibid., p. 10.
18. Ibid., pp. 313-4.
19. Ibid., p. 312.
20. Ibid., pp. 314-5.
21. Eves and Newsom, The Foundations and Fundamental Concepts of Mathematics, (New York: Holt, Rinehart, and Winston, 1961), p. 281.
22. See the discussion, Eves and Newsom, pp. 281-5. See also Raymond Wilder, The Foundations of Mathematics, (New York: John Wiley and Sons, 1952), pp. 55-7, 124, 224-5.
23. The sentence is of the form (A iff B) where A is "This sentence is true" and B is "Santa Claus exists." For logical propositions, (A iff B) is true iff A and B are both true or both false. (A iff B) is false iff A is true and B false or vice versa. Referring to the proposition, we have the following: If (A iff B) is true, then A is true and B is true. If (A iff B) is false, the A is false and B is true. Hence B is always true and Santa Claus exists.
24. Two sets are said to have the same cardinality if they can be put in a one to one correspondence. A is of lesser cardinality than B if A can be mapped one to one into but not onto B. If F is any one to one map from A into or onto B, where B is the set of subsets of A, then define C by all elements a in A such that a is not an element of F(a). It is easy to see that C is a subset of A and element of B and not in the range of the map F from A to B.
25. Eves and Newsom, p. 283.
26. Lonergan, p. 659. Lonergan states God's simplicity in terms of understanding, not knowing. The paradox holds whether one uses the term "understanding" or "knowing." As discussed in footnote 72, Lonergan is not logically consistent in working out his notions of knowing and understanding.
For Aquinas, and Lonergan follows him in this, God is simple or non composite. See, for example, Thomas Aquinas, On the Truth of the Catholic Faith Summa Contra Gentiles Book One God, (Garden City: Doubleday and Company, Inc. 1955, translated by Anton C. Pegis), pp. 103-4. Further quotations of Aquinas will be from this volume.
27. See Lonergan's descriptions given in the section on the notion of God, pp. 657-669.
28. Ibid., pp. 651, 660.
29. Ibid., p. 674, as well as the entire development of ideas beginning with his move to the transcendent, p. 641, and ending with his section on the affirmation of God, p. 677.
30. The first of these sections is section 4, p. 641, entitled "Preliminaries to Conceiving the Transcendent Idea." He begins the section with the example of the integers, 641-2, and ends with a comment that appears to refer to the same analogy, along with a comment on absolute zero being the same sort of limit for the physicist, p. 644. The next section, the critical one, entitled, "The Idea of Being," pp. 644-646, gives the integers twice in two pages as his only example. The next section, pp. 646-8, entitled "The Primary Component in the Idea of Being," describes how the positive integers and their existence as a set provide the example for understanding how God knows all things through knowing himself, p. 647. Furthermore, in the section entitled, "The Notion of God," he returns to the concept of the integers in distinguishing between the primary intelligible and the secondary ones, p. 660.
31. Ibid., p. 647. See also p. 516.
32. Ibid., pp. 657-8.
33. Ibid., pp. 641-2. Apparently, Lonergan has this image in mind from the very beginning of his treatise. Shortly after the example of the cart wheel, he introduces the concept of higher viewpoints. His example is that of the integers, pp. 13-4. Do mathematicians, unlike the logicians, claim that their concepts are more than "mere objects of thought?" One school of mathematics has sought to reduce all of mathematics to logic. See Eves and Newsom, pp. 286-7. Their logistic program has not, however, been universally accepted. Nevertheless, mathematicians feel no need to affirm their conceptions as more than "mere objects of thought." The standard practice is to begin with axiom sets with no consideration as to its existence beyond being intelligible. Of course, many proofs will contain the phrase, "there exists," but this is defined in terms of the initial axiom set and subsequent definitions and theorems. In practice, it has nothing to do with the "real" world. Philosophically, of course, there are a variety of opinions. See, for example, Raymond Wilder, pp. 283-4, for one view.
34. Lonergan, the section, "The Idea of Being," pp. 644-6.
35. Ibid., p. 644.
36. Ibid., p. 645.
37. Ibid.
38. Ibid., p. 645.
39. First Lonergan develops the idea of being, pp. 644-646, then its primary and secondary components, pp. 646-651, its causality, pp. 651-7, and then the notion of God, pp. 657-669. Then, once the intelligible form of God has been explicated, Lonergan asks the reader to affirm God in the section entitled "The Affirmation of God," pp. 669-677.
40. Wilder, p. 224.
41. To avoid contradictions involving sets and their members, Russell and Whitehead developed a theory of types in which sets and their elements are carefully distinguished by belonging to distinct levels of a hierarchy. See Eves and Newsom, pp. 287, and Wilder, 224-28.
42. Wilder, p. 225.
43. According to Aquinas, "It is, furthermore, impossible to understand a multitude primarily and essentially, since one operation cannot be terminated by many." Aquinas, p. 178. Thomas is referring to intellectual operations. Subsequently, Thomas argues that the divine mind can know singulars while remaining one act. The argumentation involves Aristotle and is beyond the scope of this essay. One does get the feeling, however, that Thomas may have been a bit on the defensive. See footnote to Thomas by Pegis, pp. 209-10.
44. See Lonergan, the section, "Preliminaries to Conceiving the Transcendent Idea," pp. 641-4.
45. Ibid., pp. 644-5.
46. Ibid., pp. 646-651, for the two sections on the primary and secondary components in the idea of being.
47. Ibid., p. 646. "If we put together these two conclusions, it appears that God knows Himself as primarily and essentially known, whereas he knows other things as seen in his essence." Aquinas, p. 181.
48. Lonergan, p. 646.
49. Ibid., p. 660.
50. Ibid., p. 647.
51. Lonergan's discussion on explanatory genera and species, pp. 437-44, introduces notions that have some relation to the ideas of this paragraph. He discusses the idea of building insights upon insights, and thereby unifying the various fields of knowledge. He does not carry the matter to the point of unrestricted insight, although he hold out the possibility that the unrelated sciences could be unified, p. 440 The mathematical theory of types could shed light on his discussion of genera and species, but he makes no use of this contribution.
From an explanatory point of view, a succession of higher viewpoints would seem to lead toward a single upper viewpoint if one started with a finite number of elements of type one. Then, unification will eventually lead to a final explanation. We have already shown, however, that his cannot be done in one act, and the knowledge it brings, the highest and final explanatory system, cannot know all in one act. Further, the process will lead toward simplification if the explanatory hierarchies do not introduce new elements for consideration. For example, even if the secondary intelligibility started with only a finite number of facts, sets of those facts run rapidly toward the infinite.
In mathematics, for example, the formation of higher insights, as in the advancement from the positive integers to both positive and negative integers closed under addition, to rationals closed under multiplication, to reals closed under limits, to complex variables closed under roots of negative numbers, does not introduce simplifications, but rather, a proliferation of elements since higher insights involve sets of objects illumined by lower insights. For example, in passing from the rationals to the reals, one can define the reals by what are called "Dedekind Cuts," which involve subsets of the rationals. Eves and Newsom, pp. 210f.
52. Lonergan, p. 645.
53. Lonergan calls this type of insight, "reverse insight." See pp. 19f.
54. The isomorphism is introduced, pp. 399-400, and using the isomorphism, he introduces the metaphysic, in Chapter XV, p. 431. The metaphysic depends upon the isomorphism. Lonergan used the isomorphism for knowing, the know corresponds to the character of the act of knowing. But the same principle holds for understanding, the structure of the understood reflects the structure of understanding.
55. For Aquinas, if I understand him correctly, God, who is one, cannot be the formal being of things. "If, therefore, God were the formal being of all things, all things would have to be absolutely one." Aquinas, p. 129. For Lonergan, the one idea, the primary intelligible, contains the secondary intelligibles, and further, the primary intelligible is one idea, Lonergan, p. 660.
56. Eves and Newsom, p. 284.
57. Lonergan, p. 661.
58. Ibid., pp. 651-7.
59. Ibid., p. 656.
60. Ibid., p. 659.
61. Ibid.
62. See section 10, "the Affirmation of God," pp. 669f. It is interesting that Lonergan includes a prior chapter entitled the "Self Affirmation of the Knower," pp. 319f. The book is an experiment which "will consist in one's own rational self consciousness clearly and distinctly taking possession of itself as a rational self consciousness. Up to that decisive achievement, all leads. From it, all follows." p. xviii. See also the section, "Method in Metaphysics, pp. 396-401, especially the comments p. 397. In other words, one benefit of Lonergan's tutelage will be that his readers will be able to take possession of themselves as knowers, and thereby have the courage to affirm their own intelligent grasp of his arguments for the existence of God.
63. Ibid., initial discussion pp. 280-1.
64. It is difficult for me to understand how Lonergan can claim that his metaphysic is stable and permanent, pp. xxviii, 393, 512, 735-6. Due to the isomorphism between knowing and being, the metaphysic reflects the structure of knowing, with the result that all metaphysical problems are reduced to an analysis of cognitive behavior. This is his philosophical methodology. "It will be methodical because it transposes the statements of philosophers and metaphysicians to their origin in cognitional activity and it settles whether that activity is or is not aberrant by appealing, not to philosophers, not to metaphysicians, but to the insights, methods, and procedures of mathematicians, scientists, and men of common sense." p. xii. See also p. 423.
But how can an analysis of knowing lead to stable results? Lonergan argues that the heuristic notions of sensing, understanding, and judging, underlie all cognitive acts, and, constituting an upper limit, admit of no higher viewpoint as do the data of science. Or, the domain of science is an object of thought, whereas, the presuppositions or forms of thought are not objects in the same way and therefore do not admit of modification, pp. 393-4.
It is difficult to understand these arguments. Virtually the whole of Lonergan's work prior to his claim of metaphysical permanence entailed taking cognitive activity as an object of experience, and from there, formulating concepts that intelligibly order its being. His own descriptions of scientific method tallies perfectly with his own approach to analyzing cognitive activity. If there is a revolution in our understanding of cognition, there will be a revolution in his metaphysic because the latter is isomorphic to and dependent upon the former. Since Kuhn, it has been widely recognized that science is subject to revolutionary changes. It would be surprising if the intense interest taken by contemporary science in the nature of the brain, sense perception, and cognitive activity, did not revolutionize our understanding of how the mind knows. It may well be that sensing, understanding and judgment will continue to have experiential validity, just as our perception that the sun goes around the earth still corresponds to daily experience. But, as new data accumulates, those three concepts may not be the ones used to describe the full range of the mind's ability to know.
65. Lonergan contrasts his position with relativism, pp. 342-7, and for the modern reader, this probably gives the best insight into the nature of his position. See also his section on probable judgments, pp. 299f.
66. Ibid., especially the concluding remarks, pp. 346-7.
67. Ibid., p. 657.
68. Ibid., pp. 677-8.
69. Ibid., p. 673.
70. The real and being are the same thing, and both are the object of experience, understanding, and judgment See pp. 252, 669. See similar identifications p. 553.
71. Ibid., p. 674.
72. In my view, there is another major logical error in Lonergan's concept of God. For Lonergan, being is the object of knowing, the idea of being the object of understanding (p. 644). Knowing involves sensing, understanding, judging. Yet Lonergan, after defining God as primary intelligibility, suddenly claims that God is primary being. As he puts it, "Thirdly, what is known by correct understanding is being; so the primary intelligibility would also be the primary being; . . . " (p. 658) This cannot be. Being and the idea of being are not the same. The former is the object of sensing, understanding, and judging, the latter, the object of understanding alone. The primary intelligibility is only the formal conceptual aspect of primary being. If God is primary being, then God must be the ultimate object of sensing, understanding, and judging, and not simply the object of understanding alone. The problem can be solved if Lonergan would allow the world to be God's body. If he defines human knowing by sense impressions, understanding, and judgment, and if he defines proportionate being as the object of human knowing, and if the transcendent being is extrapolated from proportionate being (p. 641), then he must define transcendent being as the object of unrestricted knowing and not unrestricted understanding alone. Unrestricted knowing would then include unrestricted sensing, and that is a bodily activity. If his God included the material universe, then God could materially sense all things by sensing itself, just as it understands all things by understanding itself. Further, this God could determine all things, including matters of physical fact, by determining itself. In this way, and only in this way, could God truly know himself or be known, for knowing involves sensing, understanding, and judgment. For the sake of logical elegance and reasonable affirmation, Lonergan's God should include the material universe. This, of course, would still not solve the problem of simplicity.
The Rev. Robert J. Sanders, Ph.D.
January, 2002
