Curt Ducasse, Philosophy as a Science, 1941

CHAPTER THREE

Philosophy as Poetic Literature about the Cosmos




THE problem of philosophical method has aroused the interest of many philosophers, but most of those who have discussed it have done so only incidentally. Some years ago, however, the late R. G. Collingwood devoted to it, and to the question of the nature of philosophy, an entire volume.{1} The attempt he makes to differentiate philosophy from science, and to vindicate philosophy of the charges of looseness and confusion so often brought against it, is noteworthy for its unusual elaboration, its systematic character, and its high literary quality. But, as I shall try to show, the attempt nevertheless completely fails of its purpose. Indeed, it serves only to provide in itself one more example of the very manner of philosophizing against which those charges are brought. Moreover, the conception of philosophical method Collingwood sets forth is no more defensible than the untenable positions upon which he rests it.

I. Collingwood's Vindication of Traditional Philosophy. -- Collingwood attempts to define for philosophy a procedure distinct from that of science, and allegedly grounded in the very nature of philosophical concepts. An understanding of this procedure, he believes, will vindicate philosophy of the charge that it is loose and confused as compared with science. Before examining that procedure, let us briefly note the nature of the supposed vindication. It is set forth in the following passage:

To a person who does not understand what philosophy is, or by what processes it moves, the history of those sixty generations [of European philosophical thought] appears as a chaos. . . . . But this appearance of irrationality, I make bold to say, cannot survive the discovery that philosophical thought has a structure of its own, and the hypothesis that in its changes it is obeying the laws of that structure.{2}

Now, even without agreeing with Collingwood that philosophical tradition (except on the assumption he puts forward) is "only a chaos of discordant ravings,"{3} one may nevertheless insist that ravings may well be systematic without ceasing to be ravings. To discover that the thought of the insane has (to apply to it the words he applies to that of philosophers), "a structure of its own, and . . . . that in its changes it is obeying the laws of that structure," is not to discover that it is after all not insane thought. It is only to discover the laws of the psychology of the insane.

Hence, even if it could be granted that philosophers have typically thought in the way Collingwood describes, no light would thereby be thrown on the merits of that way of thinking. What the nature of that way is, and whether the results it produces are themselves good, are distinct questions. Collingwood's "vindication" of traditional philosophy in effect consists in telling us that the philosophical pudding tastes very bad, unless one knows the recipe by which it was cooked! Yet that it is the taste of the pudding which really decides the merits of the recipe, is his implicit admission when in the end he rests his case on the question whether we are willing to believe "that in sixty generations of continuous thought, philosophers have been exerting themselves wholly in vain ."{4}

2. Differentiation of Philosophical and Scientific Concepts. -- Although Collingwood's pages are throughout haunted by the assumption that the question quid facti somehow decides the question quid juris much the major portion of his essay consists of an attempt to show chat, where philosophical concepts are concerned, the manner in which he alleges philosophers have typically thought is also the manner essentially right. It is this attempt that we must now examine in some detail, for this, if successful, would constitute a genuine vindication of the kind of philosophizing he wishes to defend and of the precepts of philosophical method he lays down. Let us first outline his argument.

Collingwood contends that the difference between the procedures of traditional philosophy and those of science is not evidence of defectiveness in the former, but arises from certain differences between the logical properties of philosophical and of scientific concepts. One of these alleged differences in particular is of such fundamental character that he rests the whole structure as well as the conclusions of his essay upon it. It is, namely, that whereas in scientific concepts the species of a genus are mutually exclusive, in philosophical concepts the species of a genus on the contrary overlap. Collingwood further contends that the species of a philosophical genus constitute a "scale of forms," and, as a result of the alleged overlapping, a scale of a peculiar sort.

A scale of forms arises when differences in degree are combined with differences of kind. For example, in the realm of science, differences in the degree of heat of H(2)0 are accompanied, at certain critical points, by the several kinds of phenomena called ice, water, steam. But in philosophical as distinguished from any scientific scales of forms, the differences of degree are, Collingwood contends, essentially unmeasurable because they are not simply correlated with, but identical with, differences of kind. Every increase, for instance, in heat as we feel it, is, he asserts, also a change in the kind of feeling we experience:

From a faint warmth through a decided warmth it passes to a definite heat, first pleasant, then dully painful, then sharply painful. . . . . I can detect as many differences in kind as I can detect differences in degree; and these are nor two sets of differences but one single set. . . . . In a philosophical scale there is only one set of differences having this peculiar double character [viz., degree and kind].{5}

This itself is due, he asserts, to the fact that

Differences in degree and differences in kind are two species of the genus difference, and in the case of philosophical concepts they must accordingly overlap to form a type of difference partaking of the nature of both . . . . a difference in degree, but nor measurable, and a difference in kind, but not susceptible of arrangement in ungraded species; a difference, that is, between various forms in which the generic essence is embodied, which is also a difference in the degree to which these forms embody it.{6}

In philosophical scales of forms, moreover, the two species of relations called distinction and opposition are (again because of the alleged overlapping of philosophical species) asserted by Collingwood to be fused. into a single relation. Opposition, in non-philosophical concepts

is a relation subsisting between a positive term and its own mere negation or absence. Cold, as understood by the physicist, is the lack of heat. . . . . But cold as we feel it is nor mere lack of heat as we feel it, but another feeling with a positive character of its own; yet these are not two distinct feelings merely, but two opposite feelings.{7}

3. Collingwood's Precepts of Philosophical Method. -- From such premises Collingwood draws his methodological conclusions. Because in philosophy

the species of a genus are not mutually exclusive, no concept can ever come to us as an absolute novelty; we can only come to know better what to some extent we knew already. We therefore never need an absolutely new word for an absolutely new thing. But we do constantly need relatively new words for relatively new things. This demand cannot be satisfied by technical terms.{8}

On the contrary, technical terms, which Collingwood claims are subjects of verbal as distinct from real definition, thwart that demand because of their rigidity and artificiality:

In order to satisfy it, a vocabulary needs two things: groups of words nearly but not quite synonymous, differentiated by shades of meaning which for some purposes can be ignored and for others become important; and single words which, without being definitely equivocal, have various senses distinguished according to the ways in which they are used.{9}

Formal definitions, accordingly, are taboo in philosophy:

Wherever a philosopher uses a term requiring formal definition . . . . the intrusion of a nonliterary element into his language corresponds with the intrusion of a non-philosophical element into his thought..Thee duty of the philosopher as a writer is therefore to avoid the technical vocabulary proper to science, and to choose his words according to the rules of literature. His terminology must have chat expressiveness that flexibility, that dependence upon context, which are the hallmarks of a literary use of words as opposed to a technical use of symbols.{10}

4. Do the Co-ordinate Species of a Philosophical Genus Overlap? -- What we must now first examine with particular care is the startling contention upon which Collingwood founds his argument at every point, namely, that in the case of philosophical concepts the species of a genus overlap. It is not necessary, however, to consider all the examples which he adduces in the effort to establish it. One or two will serve as a sample of the rest and will show how precarious is philosophizing which in effect proceeds on the doctrine that precision, because it introduces technicality, is a philosophical sin. Collingwood writes:

Logic distinguishes within the genus thought two species, judgment or proposition and inference. These, as subject matter of separate parts of logical treatises, seem at first sight to be related much as the triangle and the circle are related in elementary geometry; and in that case they would, like the triangle and the circle, be mutually exclusive classes. But they are nor mutually exclusive. That it is raining is a judgment; that it is raining because I can hear it is an inference. Of these two statements one includes the other; and it is therefore clear that the specific classes overlap: a judgment may also be an inference, an inference may also be a judgment.{11}

Now, the only point essential to note here is that even if the example did beyond question show that an inference may be a judgment and a judgment an inference, Collingwood's basic contention that overlapping of the species of a genus is what distinguishes philosophical from scientific concepts would not in the least be established thereby. To establish it, he would need to show not merely that judgment and inference overlap and are both of them species of the genus "'thought," but in addition that they are co-ordinate species of it. For the overlapping of species that are not co-ordinate is a ubiquitous fact, in no way distinctive of philosophical concepts. Polygon and triangle, for instance, overlap, and both are species, although not co-ordinate species, of geometrical figures. Again, red and scarlet, conifer and pine, rodent and rat respectively overlap, and in each case both are species although not co-ordinate species of, respectively, color, tree, animal. Yet the concepts of geometrical figure, color, tree, animal, are not philosophical concepts.

Co-ordinateness of overlapping species of a philosophical genus is thus the only thing that, if it were a fact, would be distinctive. It is therefore the only thing that needed demonstration, and without demonstration of this Collingwood's examples contribute exactly nothing to show that philosophical concepts have logical properties different from those of scientific concepts. That, in a way, he realizes the crucial importance of co-ordinateness, and that the overlapping concepts he instances (although he almost everywhere refers to them only, indefinitely, as species of a philosophical genus) are tacitly claimed to be in all cases co-ordinate species, is indicated by at least one passage, where he says that when a concept is philosophical "the class of its instances overlaps those of its co-ordinate species ."{12} Yet in none of the examples he adduces to prove that overlapping of the species of a genus is what distinguishes philosophical from scientific concepts doff he even attempt to show that the species he mentions are co-ordinate.

5. Another Alleged Example of Overlapping Species. -- One more case, this one from the field of ethics, will suffice as sample of the sort of evidence upon which the basic contention of Collingwood's essay rests. He writes:

Actions are commonly divided into classes according as they are done from motives of different kinds: desire, self-interest, duty. . . . . If it could be held that acts done from these different motives fall into separate and mutually exclusive class", this would greatly ease the task of assigning to each act its true moral worth. sum . . . moral philosophers have always recognized that in fact our motives are often mixed, so that one and the same act may fall into two or even into all three classes. These and similar considerations make it clear that in our ordinary thought about moral questions, whether we call this thought philosophy or common sense, we habitually think in terms of concepts whose specific classes, instead of excluding one another, overlap.{13}

Now it is perfectly true that we may select from the class of actions in general those where desire is a motive, those where self-interest is a motive, those where duty is a motive. It is also true that these selections of actions overlap. It is also true that each of these three selections would commonly be referred to as a class or a species of actions. But the only question that has any bearing here on what the example is intended to establish is whether they are co-ordinate species of actions. As to this, literary language, which according to Collingwood is what the philosopher must use, unfortunately tells us nothing, for "co-ordinate species" is a technical term belonging to logic. Logic, however, tells us that when a class is being divided on the basis of three principles of dichotomy at once the number of co-ordinate species obtained is eight. They would here be: actions done from desire, self-interest, and duty; actions done from desire and self-interest, but not from duty; actions done from desire, but not from self-interest or from duty; etc.

Indeed, by introducing degrees of each of the three motives (assuming them to be measurable), we could divide the class of actions into a much larger number of co-ordinate species, but these species still would not overlap. They would on the contrary be mutually exclusive and together exhaustive of the class of actions. Or has Collingwood perhaps a definition of his own, other than the ordinary one, for co-ordinateness? If he has, it is to be regretted that he did not introduce it even despite his own taboo of formal definitions in philosophy. For so long as we adhere to the ordinary meanings of terms, the contention that the co-ordinate species of a philosophical genus overlap is simply the contention that the co-ordinate species of a philosophical genus are not coordinate !

Rejection of a contention which essentially consists of this contradiction does not, as he claims, in the least commit us to "throw overboard the whole conception of genus and species";{14} nor does it involve us in "thinking that every concept must have a group of instances to itself."{15} Nor, again, does our division above of actions into mutually exclusive, co-ordinate species, on the basis of the three determining motives, in any way entail that we "must give up thinking at all about" that particular topic of ethical philosophy."{16} On the contrary, it enables us to think about it without confusion.{17}

6. Collingwood's Basic Contention either Contradictory or False. -- The very foundation of Collingwood's entire theory of philosophy and philosophical method is now seen to consist either of the contradiction that the co-ordinate species of a genus are not mutually exclusive, or of the false proposition that overlapping of non-co-ordinate species of a genus is something to be found only in the case of concepts that are philosophical. This means that the whole ingenious edifice he erects on that foundation collapses; and the case against his view of philosophy and philosophical method might therefore be rested here. Since, however, falsity of premises does not necessarily imply falsity of conclusion, some of his secondary contentions, and the methodological precepts he finally lays down, might nevertheless happen to be sound. It is therefore necessary to examine at least the more important of these secondary contentions.

This will at the same time furnish an a posteriori test of the merits of the methodological principles which Collingwood recommends. For if these are sound, any errors our examination may reveal should be traceable to violations of them. Since, however, his own obedience to them is unquestionably faithful, any errors we find will constitute evidence of the unsoundness of the principles.

7. Nonaddibility of "Philosophical" Degrees No Evidence of Essential Unmeasurability. -- The vice which has now been exposed in Collingwood's initial and most fundamental contention is the first and most remarkable of the fruits of the use of those principles. For it is directly traceable to the lack of precision which Collingwood regards as a requisite of literary quality, and to the consequent ambiguity of language which he dignifies by describing as expressiveness and flexibility. Other fruits of the same sort are to be found at many other points.

Let us first turn to the contention that what distinguishes the scale of forms allegedly constituted by the species of a philosophical genus is that the differences of degree on which a philosophical scale is based are essentially nonmeasurable. Collingwood bases this contention on the fact that these differences of degree cannot be added together to produce a greater, and on the assumption that nonaddibility implies nonmeasurability. This assumption, however, is erroneous.

An example of nonaddible quantities which are nevertheless measurable is that of temperatures. They are measurable, and universally measured, by means of a thermometer, but, although the figures which measure the temperatures of two rooms, say 60 degrees and 70 degrees, can be added, the temperatures themselves cannot in any way be added to yield a third actual temperature which would be measured as 130 degrees.

As concerns Collingwood's own example, viz., feelings of warmth, their nonmeasurability is not, as he assumes, an implication of their nonaddibility, but is due only to the empirical difficulty of correlating them with some fixed scale, whether a scale consisting of some of them (as the scale for measuring length consists of a set of lengths) or one consisting of units of some other sort of quantity (as the scale-for measuring temperatures consists of a set of heights of the mercury column in the thermometer tube). Collingwood's other assertion, that observation of the intensity of some bodily function that happened to vary concomitantly with the intensity of pleasure (or, similarly, of the feeling of warmth) would not constitute measurement of it, is explicable only as based on the false assumption that the scale used to measure something needs to be homogeneous with (instead of only correlated with) the thing measured. The falsity of that assumption is sufficiently shown by the fact that temperatures are admittedly measured by heights of mercury, which are nevertheless something heterogeneous to them.{18}

From these considerations, it is evident that the nonmeasurability of something that observably admits of more and less is never known to us to be an intrinsic character of it. The most we can ever say about such a thing is that we do not at the time know any way of measuring it.

8. Differences of Kind, even in Philosophy, Not Identical with Differences of Degree. -- Let us next turn to Collingwood's contention that in "philosophical" scales of forms differences of kind are not correlated with but somehow "fused" or identical with differences of degree. None of the examples by which he attempts to establish the existence of differences of this sort in fact illustrates any such difference, and any appearance these examples may have of doing so is due only to the lack of precision in statement which, according to the methodological precepts Collingwood lays down, would constitute a philosophical virtue.

The fact he mentions, for instance,{19} that the feeling of warmth at a given intensity is pleasant and soothing, at another dully painful or exciting, and at another sharply painful, does not mean, as he asserts, that every increase in the heat I feel is (rather than is merely accompanied by) a change in the kind of feeling I experience. For to say that at any intensity the feeling of warmth becomes different m kind from itself would be to say that the intensity at which this occurs is an intensity not of the feeling of warmth, but of some other. That the feeling of warmth at certain intensities is accompanied, e.g., by pleasure, and at other intensities by pain, shows that other feelings, connected with the feeling of warmth, change at certain intensities of the feeling of warmth, but it does not in the least show that the feeling of warmth itself, at any intensity, becomes qualitatively different from itself; nor, as Collingwood would have us believe, that at slight intensities it is only slightly of its own kind! The case of the allegedly "philosophical" feeling of warmth is thus in no relevant respect different from the case of, let us say, the physical substance iron which, at no matter what temperature or pressure, etc., completely remains iron, notwithstanding the diversity of the attributes it exhibits at various temperatures, pressures, etc.

9. Species of a Genus Never Species of it in Various Degrees. -- Nowhere, in spite of all his efforts, does Collingwood give any evidence whatever that the species of a genus (whether co-ordinate or not) may be species of it in various degrees. What is possible - and, if stated with sufficient lack of precision, might be mistaken for this - is that the individual entities which belong co a given species of a genus should possess the generic character only in a degree too small for some stated purpose. But that degree is never too small, if greater than zero, for the purpose of insuring that the entities of the given species belong as fully as any others to its genus. In the case of academic degrees, for instance, which Collingwood offers as an example, it would obviously be false to say that the lowest, viz., the bachelor's, is only slightly an academic degree. What is true is that the degree of scholarly attainment (not of academic-degree-ness) which this species of academic degree represents is lower than that represented by the other degrees, and is possibly too low for certain purposes.

10. Distinction and Opposition, even in Philosophy, Not Fused into a Single Relation. -- Let us finally consider Collingwood's contention that, in philosophical concepts, distinction and opposition are "fused into a single relation." One example he uses is that of the feeling of cold and the distinct but allegedly opposed feeling of warmth. Yet he not only fails to show that the feelings of warmth and of cold are "opposed" to each other, but he even omits to say what would constitute opposition of the "philosophical" sort, as distinguished from the "nonphilosophical" relation "subsisting between a positive term and its own mere negation or absence." He merely asserts that the two feelings, although not opposed in this sense, are yet "opposed." The fact is, however, that the feeling of warmth and the feeling of cold are opposed only each to its own psychological zero. This zero happens, for both, to correspond to a physical temperature about that of the blood, and therefore when a temperature moderately higher or lower than this is applied to one area of the skin - i.e. to one group of cutaneous organs consisting both of organs for warmth and of organs for cold - only one of the two feelings can be experienced: if one is, the other ceases to be, and vice versa. But that the two feelings are nevertheless not opposed to each other is shown by the fact that if a warm stimulus and a cold stimulus are at the same time applied, respectively, to one of the cutaneous organs for warmth and to one of those for cold, both feelings are experienced together. The things that are mutually exclusive and lie on one scale of opposition instead of two are not the two feelings, but the physical temperatures that serve as stimuli to them respectively.

What perhaps leads Collingwood to believe that there is opposition of a sort other than opposition to a zero is the sort of situation we should have in a case where two things, each capable of existing in various degrees, happened to be distinct in the sense that no contradiction was involved in the supposition that either should exist or not exist, whether the other did or not; while at the same time, although each was opposed only to its own zero, the zero of each always in fact turned out to coexist with the maximum of the other (and analogously for the other degrees). No examples of two such things occur to me, and perhaps there are none; but even if any exist in philosophy or elsewhere, they do not illustrate a "fusion" of distinctness and opposition, nor a new sense of either of these terms.

11. Three Easy Confusions Accounting for the Surface Plausibility of Collingwood's Methodological Precepts. -- Many other of Collingwood's contentions are equally questionable, but those already criticized are the ones on which his theories of the nature of philosophy and of the processes and structure distinctive of philosophical thought essentially depend, and with which they stand or fall. So likewise with the methodological precepts he lays down for philosophers. We may therefore here rest the case against all these, and conclude with a brief account of the reasons for such prima facie plausibility as the precepts themselves may have in spite of their unsoundness. Three easy confusions adequately account for it.

The first has to do with the kind of value philosophy essentially seeks to have. Collingwood, rightly, never doubts that the imposing systems constructed in the past by the great philosophers are achievements of high human value. What he seems to neglect, however, is that what these philosophers were striving to reach was knowledge, properly so called, concerning the matters they considered; that they very largely failed in this; and that the high value their constructions nevertheless have had is of a kind other than that peculiar to knowledge. As already pointed out, the value they have had has been chiefly as articles for possibly helpful faiths, or as more or less fanciful pictures representing beautiful or reasonable worlds chat could serve as pleasant imaginative escapes from facts too often tragically stupid. This is to say that philosophy, in spite of the failure, in such large part, of its own search for knowledge, has been a good deal of a success in terms of the demands of persons who took it as nonrevealed religion or as poetic literature about man and the cosmos. And, for success of this sort, a "literary" as contrasted with a precise use of words is nor only permissible but of great aid; while any errors or confusions that may result from it hinder little or not at all.

Collingwood's belief that traditional philosophy has been what philosophy ought to be, and his injunction upon the philosopher to make a literary and not a technical use of words, mean that the theory of philosophy which consciously or unconsciously he actually is defending, is that philosophy is essentially poetic literature about the world and man's relation to it, and therefore that philosophy is good when it has the characteristics which would make literature of this kind good.

This brings us to the second of the confusions referred to above. The eulogistic connotation of the word "literary" evidently compels us to reject any suggestion that philosophy should use words in an unliterary manner. This makes the assertion that it should use them in a literary manna plausible without regard toe its ambiguity. But if by that assertion is meant that in the search for philosophical truth we should use words in the manner appropriate to "literary" purposes, then the assertion ceases to be plausible as soon as we realize that literary purposes are such things as aesthetic enjoyment, imaginative stimulation, expression and communication of feelings, moods, and attitudes. For although, these purposes are quite as worthy as any, they are yet quite other than the purpose of discovering truth. What the latter requires is a use of words which, instead of being literary in the sense just indicated, is on the contrary "rational" in the sense that it makes dependable reasonings possible. And this means a use of words which is consistent, unambiguous, and precise even when this requires it co become technical. Just that is what constitutes a literary use of words in such writing as philosophical and scientific literature, which essentially aims to be not poetic, dramatic, imaginative, or biographical, but heuristic.

With this we come, third, to technical terms. Whenever, in any field, knowledge beyond what is common begins to be won, the introduction of technical terms quickly becomes indispensable; for a technical cam, far from being, as Collingwood assets, an arbitrary innovation in vocabulary created by verbal definition, on the contrary represents, in highly compressed form, genuine knowledge previously won, or a definite hypothesis about to be tested. Therefore, as Whewell has abundantly shown, technical terms are the products of, or the programs for, always "real" and never merely "verbal" definitions. For merely verbal definitions are bi-verbal definitions, and create not a technical terminology, but only a jargon new, esoteric language into which, for the convenience of condensation, it is sometimes desirable to translate portions of the old, the mere translation, however, constituting no addition to knowledge. A technical term, on the contrary, aims to express an addition to knowledge, i.e., to be the name of something real: of a theory that has been or can be verified of a distinction corresponding to a difference that exists, etc.

Collingwood's assertion that in philosophy we only come to know better what we already to some extent knew before is true only in the sense in which it is also true that in theoretical physics we only come to know better the nature, already to some extent known to us, of the material objects around us. Such a situation, than, is in no way peculiar to philosophy. Rather, it is of the very essence of analysis, no matter what the subject. That it does not relieve us of the need of technical terms is evident enough in the case of physics. The reason why it does not relieve us of that need is that analysis, although indeed only making us know better what we in a way already knew, is often itself possible only in terms of entities (whether physical or other), which, although they were implicit all along in what we already knew, are nevertheless completely novel to us, and therefore call for novel names exactly as do newly discovered chemical elements or prehistoric animals.


Notes

{1} Philosophical Method (1933). [Back]

{2} Philosophical Method, p. 224. [Back]

{3} Philosophical Method, p. 225. [Back]

{4} Philosophical Method, p. 225. [Back]

{5} Philosophical Method, p. 72 f. [Back]

{6} Philosophical Method, p. 74. [Back]

{7} Philosophical Method, p. 75. [Back]

{8} Philosophical Method, p. 205 f. [Back]

{9} Philosophical Method, p. 206. [Back]

{10} Philosophical Method, p. 207. [Back]

{11} Philosophical Method, p. 36. [Back]

{12} Philosophical Method, p. 35. [Back]

{13} Philosophical Method, pp. 42 f. [Back]

{14} Philosophical Method, p. 37. [Back]

{15} Philosophical Method, p. 48. [Back]

{16} Philosophical Method, p. 44. [Back]

{17} Partial mutual overlapping of two species of a genus (vs. total overlapping of one by the other) is a character indeed absent from classifications which are scientific in form, i.e., logically useful (whether their subject matter be philosophical or natural-scientific). But presence of that character is not something distinctive of any particular kind of concepts. (Consider, for instance, "aquatic animals" and "mammalian animals.") Presence of partial mutual overlapping of species is only a logical defect, to which any purely empirical classification is exposed. It constitutes a logical defect, whether the subject matter be philosophical or not, because knowledge that a given thing does, or does not, fall under one concept furnishes no basis for inference as to whether or not it falls under the other of the two. [Back]

{18} That is to say, Collingwood simply ignores the distinction between "fundamental" and "derived" measurement, and writes as if all measurement were of the fundamental sort. Cf. N. Campbell, Measurement and Calculations (1928). [Back]

{19} Philosophical Method, p. 72. [Back]


[Table of Contents] [Chapter 4]