Lonergan Wittgenstein Lindbeck Rules Insight

Wittgenstein's notion of cultural phenomena as so many ‘language games’ embedded in ‘forms of life’ has exerted an influence on theologians. For example, George A. Lindbeck has criticised Bernard Lonergan's methodology from such a perspective. Thus, in The Nature of Doctrine Lindbeck is suspicious of the idea that ‘different religions are diverse expressions or objectifications of a common core experience.’Footnote ¹ Lonergan appears to prejudice the scholarly study of religious phenomena in favour of ‘the affirmation of a basic unity,’ but the common core that he identifies is ‘hard to specify,’ and seems ‘vacuous’ or ‘logically odd.’Footnote ² Here the context is an ecumenically conceived introduction to religion in which Lonergan is reconceiving sanctifying grace in terms of the experience of ‘falling in love with God,’ but Lindbeck clearly has general concerns with Lonergan's methodology. He faults those such as Lonergan who ‘seem to maintain a kind of privacy in the origins of experience and language that, if Wittgenstein is right, is more than doubtful.’Footnote ³ Lindbeck then cites a section from Lonergan's Method In Theology entitled ‘The Dialectic of Methods: Part One.’ There Lonergan had addressed ‘certain contentions of linguistic analysis’ that would imply that his own procedures ‘are mistaken and even wrongheaded.’Footnote ⁴

Lonergan went on to cite a ‘helpful basis for discussion’ from Edward MacKinnon referring to a growing consensus since the publication of the Philosophical Investigations that ‘the meaningfulness of language is essentially public and only derivatively private.’ One consequence of this view is that meanings are ‘primarily in concepts’ and that ‘the meaning of a word is not explicable by a reduction to private mental acts.’ Lonergan responded by drawing a distinction between ordinary and original meaningfulness. Lonergan agreed that mental acts occurred within sustaining flows of expression and had no doubt that ordinary meaningfulness was ‘essentially public and only derivatively private.’ Ordinarily, language is not the decision of some private individual, but it is what is commonly held by the group. However, Lonergan pointed out that language grows; words have origins. ‘New developments consist in discovering new uses for existing words, in inventing new words, and in diffusing the discoveries and inventions. The discovery of a new usage is a mental act expressed by the new usage. The invention of a new word is a mental act expressed by a new word.’ This was highly significant, for Lonergan held that the source of philosophical problems is ‘not only in linguistic expression but also in mental acts.’Footnote ⁵ No wonder, then, that Lonergan began Insight by examining simple examples of mathematical understanding in what was to be an ‘essay in aid of self‐appropriation.’

Here it is possible to regard Lonergan's procedure as similar to Wittgenstein's. Like Lonergan, Wittgenstein paid close attention to the phenomenon of the ‘flash’ of understanding,Footnote ⁶ often making use of pictures in his presentation (especially in his Remarks on the Foundations of Mathematics) in an attempt to gain a perspicuous view—an insight into insight we might say. The differences between the two procedures, it seems, were pinpointed by Lonergan in speaking of originality. Whereas Wittgenstein was interested in the practices we do not originate—no one gives birth to their mother tongue, for example—Lonergan was interested in the sources of development— a young child does not need to be taught to ask questions. Thus, in The Remarks on the Foundations of Mathematics Wittgenstein claimed that he was interested in the phenomenon of immediate insight (Einsehen), ‘not indeed as a special mental phenomenon, but as one of human action.’Footnote ⁷ Moreover he pointed out the heterogeneous nature of mathematical practices and referred to the ‘motley’ of mathematical techniques of proof.Footnote ⁸ Wittgenstein considers the phenomenon of insight in the context of rules and conventions.

Arguably, then, the two procedures are complementary. Still, the two philosophies that Wittgenstein and Lonergan originated appear to diverge on the question of foundations which Wittgenstein rejects and Lonergan embraces. Here some light may be afforded by the mistakes that children make. So as to get to the root of their differences, then, we may turn to a thought experiment discussed by Wittgenstein, in which a boy fails to follow a rule. Just as Wittgenstein's concern was not in empirical psychology, but rather the relations between rules and insights, so our concern is whether Wittgenstein's reflections cast doubt on Lonergan's method.

From the Mouths of Babes: Public Criteria

In his Philosophical Investigations Wittgenstein discusses the following ‘language game.’Footnote ⁹ A student is being taught about number sequences, and is meant to add two. That is to say, the child is to generate the sequence 2, 4, 6, 8 and so on. Wittgenstein is very interested in the ‘and so on.’ His interlocutor suggests the explanatory value of the insight—as might a student of Lonergan. Wittgenstein, however, warns against the temptation to think of understanding as akin to a mental process—like a pain, for example—and breaks off to discuss a series of remarks on reading, that is to say, the phenomenon in which a child makes sense of some text that has been produced by an author. After making this digression Wittgenstein then returns to develop a scenario in which a child makes a bizarre mistake. When the child reaches 1000 he continues 1004, 1008, 1012, and so on. That is, he goes up in fours, not twos as he had done at first.

What are we to make of this thought experiment? Six points can be made briefly. In the first place, the example is artificial. Wittgenstein would have known that the example was scarcely true to life—still, he believes that it is instructive nonetheless. Secondly, the boy does indeed originate a new way of constructing the sequence, but does so bizarrely. Thirdly, however, the boy is deemed intelligent. True, he does not understand what he was meant to do, but he knows that he has done something intelligent by his own lights, and it may be assumed that what Lonergan would call an insight has taken place, for within the multiplicity of the natural numbers the boy has grasped a pattern, that is to say, he has grasped an intelligible unity, or equivalently, a set of relations in some data. Fourthly, the boy is aware of the need to meet norms—indeed, he thinks that he has already done so. Fifthly, in this scenario there are indeed norms, but these are not private, but public—we are telling the boy what to do. Sixthly, such public norms set up an exigence which, despite the boy's ingenuity, he fails to meet. The boy was wrong.

Here it might be worth using Lonergan's cognitional theory to consider why the example is artificial. The boy certainly did obtain an insight. Wittgenstein does not tell us whether this insight came as a release to the tension of inquiry—perhaps the boy was thinking too much! But, presumably, an intelligibility has been grasped. Lonergan is at pains to distinguish the images of say, a teacher's diagram, and the point that such diagrams are meant to teach. When the instance provided by the teacher truly becomes an example, then the data fall into some unity, or some relation is found that connects the various aspects of the image—the significant parts at least—or else some necessity is found to obtain in what has been presented. The object of insight (the intelligibility) just is this unity, relation, or necessity.

However, Lonergan's interest in insight was to explore the way they accumulate, indeed, combine and coalesce (for example, in different patterns of experience such as science or common sense). We can acquire many insights, and Lonergan explains how they coalesce into higher viewpoints. By way of example, Lonergan cites the transition from operations performed on the natural numbers to ‘the same’ operations performed on the integers.Footnote ¹¹ In fact, whilst we are preserving some elements (positive twelve take positive five is still positive seven) we are also going beyond the old system. Whereas previously we could not take twelve from five, the introduction of negative numbers makes this move possible. Or again, Lonergan suggests the transition from arithmetic to algebra. Because we perform certain processes in arithmetic, and can reflect on such operations, we may then act analogously in accord with more abstract rules. Thus, in attaining higher viewpoints we develop. This is not simply a case of assimilating more examples to schemata that we already possess, but rather, of acquiring new schemata. Such adjustments may be awkward, precisely because we were accustomed to looking at things in the old way. Knowledge, as Lonergan was inclined to say, makes its bloody entrance.

The point here is that when we develop we gain a new facility without losing the old, but if we have not yet developed, then we are unable to cope. In Wittgenstein's example, the boy is presented as leaping to the higher insight, but for some reason stumbling over easier tasks. That is to say, the example prescinds from any realistic account of development. Here, the development in question is of the child—not simply of the child's curriculum. The point of a curriculum is to organise a child's learning so as to respect the child's development, moving forward gradually where appropriate. For example, mathematical exercises might be set in sequence so that what the fictitious boy was not able to solve are presented before those that the boy was able to solve. In this way, although a (girl, for example) does not originate her learning in the sense that she devises her own curriculum, at least her natural intelligence is encouraged to grow, and the girl might feel that her teaching is helping her to make progress in the way. The inner life of the child does not have to clash with public norms as it seems to with the boy who wants to go up in fours. So by ignoring such development, Wittgenstein presents us an utterly contrived example.

Why does he do so? Here the following is suggested. Wittgenstein's concern is with what Lonergan called ‘ordinary’ rather than ‘original’ meaningfulness. He addresses the question of normativity and does so in the context of teaching rather than learning. Social norms are being handed on; the boy is being taught what we do. Wittgenstein is drawing attention to the role of public norms, hinting, perhaps, that private norms are beside the point. Suppose that an intelligent boy, indeed, a boy capable of authentic, ‘higher’ insights, was to originate a new way of doing things, what of it? We would still teach him our way of doing things, and this is just what is happening in ‘our’ sequence that goes up in twos. “But our way really is more natural than the boy's innovation!” To such a protest it can be countered, that it seems natural for those brought up like us—even as those who speak French feel that their language orders the words in the way that we naturally think them.Footnote ¹² In this way Wittgenstein can minimise the significance of any private mental acts, of intuition, say. For example,

It is not that the existence of such acts is denied, but rather, a deflationary attitude is taken to the alleged normativity of such ‘mental processes.’ Instead, attention is drawn to the exigence of public norms.

From the Mouths of Babes: Intellectual Development

At this juncture, it might be worth considering some more realistic mistakes that children make, for they testify to, rather than detract from, the child's intelligence. After all, when chief examiners analyse the performance of candidates taking a public examination and report back to teachers, they often include a section entitled ‘Common Errors’ in which the most common mistakes are collated. These are useful to teachers precisely because they give some insight into the (albeit faulty) intelligence of the child who tries but fails to make sense of the demands of the examination. They highlight just where adjustments need to be made. Again, our interest is not to offer an empirically rigorous account of educational psychology, but to continue reflecting on rules and insights.

We might consider: 1) a child who says, “I catched the ball.” 2) A child who thinks that negative five plus negative seven makes positive twelve. 3) A child who thinks that the year 5 B.C. came 12 years before the year 7 A.D. 4) A child who thinks that the decimals, 0.8, 0.16, 0.234 are in ascending order. 5) A child who thinks that when there are d days, and w weeks to Christmas, then, w = 7d. In each case we can detect some faulty intelligence at work.

First, the child who says ‘catched’ has generalised the rule for forming past participles by adding the suffix ‘‐ed’ to verbs but he or she transgresses the convention that makes an exception for this irregular verb. Presumably the child will be corrected much as the boy who went up in fours was, and so this example aptly illustrates the arbitrariness of convention. There is no reason why the participle should be formed in this way and the child must recognise that this is what we do. On learning that we say ‘caught,’ the child may at first be puzzled, but the child will come to accept the fact. The child may understand that there is nothing to understand, and so must rely on the community as the origin of such rules—the way we speak does not depend on a private insight. The child may appreciate that potentially, any verb might break the rules—perhaps ‘matched’ and ‘hatched’ are wrong too. Still, although in each case there is the possibility of irregularity, it does not follow that there is the possibility of irregularity in every case, for if so, then there would be no regular verbs, and language would be unintelligible. To draw on Lonergan's terminology, we could say that understanding conventions is a matter of inverse insights,Footnote ¹⁴ but still, these do not rule out direct insights, indeed, inverse insights depend on direct.

In the second case, the child has misapplied a rule that he or she has been taught. He or she relies on the short‐cut: two negatives make a positive. Such slavish reliance on rules can be regarded as a vice and perhaps efforts will be made that encourage a more questioning attitude to rules. We are inclined to think that the child has little insight into directed numbers (negatives), and that a new teaching strategy is in order, for example:

A child is introduced to a series of red and black cards. The number ‘three’ is to be represented by three black cards. The child is to think of the number ‘negative four’ as representing four red cards. Black and red are like credit and debit. The child is to think of zero as the absence of cards and then taught to add and subtract in cases where what we take away is never more than what we have in the first place. So, if we have five black cards we can remove three of them, but not eight and so on. Now the child is to think of borrowing money so that one has to pay back one's debts and taught to think of a black and red as pairing off so that they cancel out. In this manner the child is taught a way of seeing ‘3+⁻4’ as three blacks and four reds, which after combination and cancellation leaves us with one red, that is, ‘⁻1.’ Checking that the child really understands may be time‐consuming but hopefully, the reward will be that the child can see that negative five and negative seven corresponds to five and seven red cards, something that is obviously twelve red cards. How, starting with red, and adding more red, could we ever end up with a great deal of black? The strategy will be to make the rules intelligible, including the case where taking away a negative is equivalent to a positive. Though greatly dependent on the teacher at first, the child will gradually acquire independence.

At this point the asymmetry between two mistakes can be noted. The first is almost opposite to the second. The child who misspeaks breaks the rules because he or she already has an insight; the child who gets the sum wrong does so because he or she follows the rules without having an insight. The one needs to learn a new convention; the other needs to grasp a pattern anew. Whereas the first merely has to accept an inverse insight, the second has to adjust to a higher insight. If and when each child is suitably corrected, only the latter is likely to exclaim: aha!

In the third case, the child has made a mistake in applying mathematics to the Christian calendar. The child has not grasped that we assign a number to a whole year so that although we can think of organising time on a number line, years will correspond to intervals rather than points. Even though we do this as a matter of convention, still, the rationale can come to be appreciated. In fact, learning how this works may afford pleasure: it is nice.

The fourth case is that of a child who does not understand decimals, probably because he or she does not appreciate the place value system. He or she mistakes the decimal point as a separator between natural numbers, much as when we tell the time. Here the melange of conventions that the child has to negotiate may aptly be compared to an ancient city.Footnote ¹⁵ No wonder that children can, and regularly do get confused about mathematics. The teacher faced with such misapprehensions may despair of telling the child that they have gone wrong. What is needed is some restructuring whereby the dissonance of the child's confusion is brought, without too much distress, into the open.

Similarly, in the fifth case, discussion may bring enlightenment. It may happen that presented with the option of agreeing or disagreeing with the equation, the class may be equally divided so that an argument may be generated, and young people will have to rely upon their wits to defend what they believe to be the case. Such a teaching strategy may help bring about a change of mind. Perhaps some members of the class will attempt to descend from abstractions by substituting values into the variables, and so by reasoning come to understand the conventions of algebra. From such dialectics, perhaps, insights may emerge.

To sum up, whereas Wittgenstein could reflect upon the phenomenon of a child making an intelligent mistake so as to illustrate what can be called ‘ordinary’ (that is, non‐originary) meaningfulness, several examples may also be supplied that highlight Lonergan's concern with the development of understanding. Wittgenstein, it is true, makes some welcome contributions to the idea of understanding as habit, “Now I can go on.”Footnote ¹⁶ Lonergan, however, does not conceive of intellectual habits in opposition to development:

Not Merely a Desire, But an Exigence Too

Unlike Wittgenstein, Lonergan may be thought of as a foundationalist, finding philosophic foundations in the ‘pure desire to know’ manifest in such questions as, What is it? Is it really so? Lonergan regards this desire as the ‘core of meaning,’Footnote ¹⁸ which explains the significance for Lonergan of not obscuring originary meaningfulness. Lonergan holds that such wonder constitutes a nature in the Aristotelian sense of ‘an immanent principle of movement and rest.’Footnote ¹⁹ Intelligence in potency brings itself to act as our questions receive answers. Thus Lonergan conceives of our intelligence as dynamic. By no means does Lonergan think of our insights as normative—they are ‘a dime a dozen.’ If in response to the first type of question we obtain an insight which we then express in concepts, we still need to reflect and ask the second type of question to make sure that our insight is better than a hunch.

These foundations are termed ‘transcendental notions,’—our sense of the intelligible, the true, of value. They ‘both enable us and require us to advance in understanding, to judge truthfully, to respond to values.’Footnote ²⁰ They ‘are our capacity for seeking and, when found, for recognizing instances of the intelligible, the true, the real, the good … they are relevant to every object that we come to know by asking and answering questions.’Footnote ²¹

One comment may be advanced. For Lonergan, the desire to understand is also conceived as an exigence,Footnote ²³—it is a desire that sets standards. We are to understand correctly.

We may lack knowledge, and become aware of this lack, and so be discontented with our ignorance, and thus want knowledge, and so intend, or aim at knowledge. Such intention is not yet attainment, and indeed, we can be aware that we are merely intending without yet attaining. This awareness that we have not yet attained, and that certain conditions must be fulfilled if we are to attain, constitutes a demand on us. In this connection, Lonergan will also speak of transcendental precepts: be attentive, be intelligent, be reasonable.

Wittgenstein's many philosophical investigations clearly manifest the desire to understand, correctly, and after all, he has given us a highly original philosophy, but he almost deflates the significance of the desire—the philosopher is to treat the question as if it were an illness.Footnote ²⁴ Thus, in the Remarks on the Foundations of Mathematics, Wittgenstein will consider a puzzle for children in which four triangles are to be fitted together to make a triangle.Footnote ²⁵ For Lonergan, the act of understanding is characterised as a response to such puzzlement. Wittgenstein, however, goes on to by present a picture of a rectangle with three lines drawn on it so as to display the completed solution to the puzzleFootnote ²⁶ and so invites us to see the solution almost as if it was a triviality, and this minimises the significance of the desire to understand.

Here, perhaps, a metaphor captures Wittgenstein's attitude. If it is proposed that we think of the solution to a puzzle like an arrow meeting the target, the Wittgensteinian counters by asking how it would appear if the arrow had been fired into the air, and the target had subsequently been painted around the place where the arrow lands. Here, there is a meeting of desire and fulfilment, but it no longer appears as though the fulfilment meets standards that the desire had set. For in the comparison of aiming an arrow at the target, the target sets demands on the archer but in thinking the target as painted around the fallen arrow obscures these demands. This seems to be the import of Wittgenstein's example. Thus, it seems, Wittgenstein deemphasises private criteria and finds normativity only in public criteria. What for Lonergan is foundational becomes almost trite for Wittgenstein.

A Rock on Which to Build

Was Wittgenstein right? Was Lindbeck's judgement sound in finding Lonergan's method dubious? If we wonder about such things then the dialectic of methods has arisen. But how can we decide? Lindbeck finds the ‘complicated gymnastics’ offered by Lonergan as unpersuasive.Footnote ²⁷

Although he was more concerned with self‐appropriation than other‐persuasion, still Lonergan regarded his transcendental method is a rock on which to build. Those who want to understand correctly will find it difficult to disagree with Lonergan on ‘wanting to understand correctly.’ For in the first place, if the disputant finds the desire operative within themselves, then that fact constitutes a fulfilling of the conditions for the judgement that the desire is indeed operative. And in the second place, any inclination to disagree would seem to imply that Lonergan's account is deficient to some extent, for example, because the requisite conditions for judgement do not exist. But such a critical stance is precisely what is entailed in regarding the desire in question as an exigence, and this is what Lonergan's position on the ‘desire to understand correctly’ means. Thus, the counter‐position invites its own reversal.

With some justice Lindbeck detects a prior theological commitment as underpinning Lonergan's conviction that in the many religions there is evidence for a core experience of falling in love with God. It is indeed an optimistic view, and Lonergan appreciated the need for dialectics, but he presented an ideal partly because he was interested in understanding the case in which religion comes alive for the believer. Lonergan regards this experience as the fulfilment of the transcendental notions which constitute, as it were, our capacity for grace. In this way Lonergan was able to show how religion was relevant to the deepest needs of our spirits. Thus he had an answer to a question once posed by Wittgenstein: What is thinking for?