2~tC.

ALFRED NORTH WHITEHEAD

1861-1947

Alfred N orth W hitehead was bom on 15 February 1861, the son of the Reverend Alfred Whitehead, at that time the headmaster of a private school in Ramsgate, and later Vicar of St Peter’s, Isle of Thanet, and honorary Canon of Canterbury. Another son, Henry, became Superior of the Oxford Mission to Calcutta, and ultimately Bishop of Madras.

From Sherborne School Whitehead proceeded in 1880 to Trinity College Cambridge, where he remained for the next thirty years. In the Mathematical Tripos of 1883 he was bracketed third wrangler, the senior being G. B. Mathews, afterwards Fellow of St John’s, F.R.S., and a distinguished pure mathematician: in 1884 he was elected a Fellow of his college, and a few months afterwards was put on the staff as an assistant lecturer.

In 1890 he married Evelyn, daughter of Captain A. Wade of the Seaforth Highlanders, and niece of the famous Chinese scholar and diplomat Sir Thomas Wade.

In my undergraduate days at Trinity when he was the junior member of the mathematical staff, he had a place apart among our teachers, chiefly because his philosophic urge to grasp the nature of mathematics in its widest aspects led him to study what were at that time considered out-of-the-way branches of the subject: for instance, he offered a course of lectures on ‘Non-Euclidean Geometry’: this would not be thought remarkable nowadays, but the school­masters of that day had not prepared us for the existence of any alternative to Euclid: and we became much interested, particularly when we found that the lecturer could tell us also about algebras in which the commutative rule of multi­plication, ab=ba, was not obeyed. He was in fact at this time writing a book on such topics, which was published in 1898 under the title A Treatise on Universal Algebra, with Applications, the title being taken from a paper of Sylvester’s

which had appeared in 1884. ‘The purpose of this work’ he said in the preface, .‘is to present a thorough investigation of the various systems of symbolic reasoning allied to ordinary algebra. The chief examples of such systems are Hamilton’s Quaternions, Grassmann’s Calculus of Extension and Boole’s Symbolic Logic.’

A substantial portion of the volume was devoted to the Algebra of Symbolic Logic. The fundamental idea of this subject is due to Leibnitz. Leibnitz, in the course of his life as a diplomat, often found himself required to devise a formula for the settlement of a dispute, such that each of the contending parties could be induced to sign it, with the mental reservation that he was bound only

282by his own interpretation of its ambiguities. Equivocation, such as was practised in this connexion, was, as Leibnitz well knew, impossible in mathematics, where every symbol and every equation has a unique and definite meaning: and the contrast led him to speculate on the possibility of constructing a symbolism or ideography, like that of algebra, capable of doing what ordinary language cannot do, that is, to represent ideas and their connexions without introducing un­detected assumptions and ambiguities. He therefore conceived the idea of a logical calculus, in which the elementary' operations of the process of reasoning would be represented by symbols—an alphabet of thought, so to speak—and envisaged a distant future when philosophical and theological discussions would be conducted by its means and would reach conclusions as incontrovertible as those of mathematics. Perhaps this was too much to hope: but the actual achievements of mathematical logic, some of them brought about, as we shall see, by Whitehead, have been amazing. Logic, when its power has been augmented by the introduction of symbolic methods, is capable of leading from elementary premisses of extreme simplicity to conclusions far beyond the reach of the unaided reason.

The outstanding contribution to the subject previous to 1890 was made by George Boole, Professor at Queen’s College, Cork, whose Laws of Thought was published in 1854. It was the Boolean system which was described and extended in Whitehead’s book.

The volume contained much else, in particular expositions of the Theory of Matrices and other non-commutative algebras (Boole’s algebra is com­mutative) and of non-Euclidean geometry (the geometry of space of constant curvature in two and three dimensions). It is interesting to observe how White­head’s prophetic instinct impelled him to take up branches of mathematics which were at the time neglected, and unknown to most professional mathe­maticians, but which have since played a great part in the interpretation of nature. Matrix-theory first came into its kingdom in 1925, when Heisenberg, Born and Jordan showed that by its aid quantum-theory could be constituted as a complete logical structure. The non-Euclidean geometry of spaces of constant curvature has found its chief application in the cosmological investiga­tions of Eddington and others from 1930 onwards, though Euclidean space had been discredited fifteen years earlier by the theory of General Relativity. As to the original non-commutative algebra, namely quaternions, I remember discussing with Whitehead in 1900 what its future was likely to be; he remarked that hitherto it had been applied only to problems which had been solved previously by other methods, but that new fields might be created some day by advances in physics, for which quaternions would furnish the most natural and powerful method of treatment. This expectation was fulfilled only five years later by the discovery of the Special Theory of Relativity: for the Lorentz transformations, which are fundamental in that theory, are essentially rotations in four-dimensional quasi-Euclidean space, and these, as Cayley had shown long before, are most conveniently dealt with by quaternion analysis.

The Treatise on Universal Algebra was acclaimed on all sides as a splendid

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work of learning and research, and the reputation based on it led to the election of Whitehead as a Fellow of the Royal Society in 1903.

Of the scholars of Trinity who sat at his feet during the last decade of the nineteenth century, there was one who became a specially attached disciple, and played a great part in his subsequent life and work. This was Bertrand Russell, who entered the College in 1890, graduated as bracketed seventh wrangler in 1893 and was elected a Fellow in 1895. In 1897 he published an Essay on the Foundations of Geometry, and in 1900 a book on the Philosophy of Leibnitz. In the latter year he and Whitehead went to Paris to attend the Con­gresses in Mathematics and Philosophy which were being held in connexion with the International Exhibition: and at the Philosophical Congress they heard an account of the work of Guiseppe Peano, professor at the University of Turin, who in the years immediately preceding had invented a new ideography for use in symbolic logic.

The difference between this and the older Boolean system may be very simply explained. In Boole’s algebra, a letter x would represent a class, say the class of all graduates of Cambridge, and a letter y would represent another class, say the class of all women. Then x x y would represent those persons who belong to both classes, that is, all women graduates of Cambridge, while would represent those who belong to either class, that is, all graduates of Cambridge and all women. The rules of this algebra are different from those of ordinary algebra, since e.g. xxx, which represents those who have taken degrees at Cambridge and have also taken degrees at Cambridge, does not differ from x: that is, x 2= x.

Boole used only the ordinary algebraic symbols: the symbol x , which in ordinary algebra represents multiplication, may be said to correspond in Boolean algebra to the word and, while the symbol of addition, + , corresponds to or, and the symbol of a negative quantity, —, corresponds to not. What Peano did was to introduce new symbols to represent other logical notions, such as ‘is contained in’, ‘the aggregate of all x’s such that’, ‘there exists’, ‘is a’, ‘the only’, etc. Peano’s ideograms represent the constitutive elements of all the other notions in logic, just as the chemical atoms are the constitutive elements of all substances in chemistry: and they are capable of replacing ordinary language completely for the purposes of any deductive theory.

Russell had become interested in symbolic logic both from his study of Boolean algebra with Whitehead, and also through his work on Leibnitz. He and Whitehead now saw that Peano’s ideography was vastly superior to any­thing that had been known previously, and they resolved to devote themselves for years to come to its development, and in particular to attempt to settle by its means the vexed question of the foundations of mathematics.

The thesis which they now set out to examine, and if possible to prove, was that mathematics is a part of logic: it is, as they said, the science concerned with the logical deduction of consequences from the general premisses of all reasoning: so that a separate ‘philosophy of mathematics’ simply does not exist; this of course contradicts the Kantian doctrine that mathematical proofs depend on

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a priori forms of intuition. Whitehead and Russell soon succeeded in proving that the cardinal numbers 1, 2, 3, . can be defined in forms of conceptswhich belong to pure logic, and which can be represented by Peano ideograms. From this first success they advanced to the investigations published in the three colossal volumes of Principia Mathematica, which appeared in 1910-1913 and contain altogether just under 2,000 pages.

This great work was not conceived exclusively with questions relating to mathematics: it attacked and solved many problems of a general character, and in particular those presented by the paradoxes and contradictions which exhibit the defects of ordinary language. For instance, consider the simple statement ‘I am lying’. If while saying this I am actually lying, then obviously I am speak­ing the truth in saying it: that is, I am not lying. If, on the other hand, while uttering the words I am actually not lying, there is again a contradiction. Many other paradoxes were invented, and a theory known as the theory of types was developed in order to rule them out.

The growth of logic, which had been at a standstill for the two thousand years from Aristotle to Boole, has progressed with amazing vitality from Boole to the present day, the greatest single contribution being Principia Mathematica. It is very remarkable that some of the errors of Aristotle remained undetected until the recent developments: consider, for instance, his doctrine {Prior Analytics, I 2, 25a) that ‘in universal statement the affirmative premiss is necessarily convertible as a particular statement’, so that for example from the premiss: all dragons are winged creatures follows the consequence some winged creatures are dragons. The premiss is unquestioned: but Aristotle’s deduction from it asserts the existence of dragons. Now it is evident that the existence of dragons cannot be deduced by pure reason: and therefore Aristotle’s general principle must be wrong. Similarly, four of the nineteen moods of the syllogism, which the mediaeval schoolmen enumerated in the well-known mnemonic Barbara Celarent, are now recognized as actually invalid.

It must be said that many professional philosophers, while admitting the wonderful power of the new methods in logic, have found the Peano symbolism, with its complicated quasi-algebraic rules of operation, an uncongenial study, and have complained that the real result of Whitehead and Russell’s labours has been not to reduce mathematics to be a branch of logic, but to reduce logic to be a branch of mathematics.

While Principia Mathematica was Whitehead’s main occupation during the first decade of the present century, he wrote in 1905 a remarkable paper, ‘On mathematical concepts of the material world’, which occupied 61 pages of the Philosophical Transactions. ‘The object of this memoir’ he said in the preface, ‘is to initiate the mathematical investigation of various possible ways of con­ceiving the nature of the material world. In so far as its results are worked out in precise mathematical detail, the memoir is concerned with the possible relations to space of the ultimate entities which (in ordinary language) constitute the “stuff” in space. . . . The general problem is here discussed purely for the sake of its logical (i.e. mathematical) interest. It has an indirect bearing on

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philosophy by disentangling the essentials of the idea of a material world from the accidents of one particular concept.’ Whitehead was in fact feeling his way in this paper to a general philosophy of nature: as the ultimate existents he rejected particles of matter and points of space (thereby severing himself com­pletely from classical physics), and in their stead postulated what he called ‘linear objective reals’, which were something like Faraday’s lines of force. Some of the principles of his later philosophy appear here for the first time: thus the non-admission of Newtonian space is evidently a protest against exempt­ing any part of the universe from change. The paper is however extremely difficult reading, the propositions being established by aid of the Peano symbolism: and it fell completely flat so far as enlisting the attention of other writers was concerned.

For many years the Whiteheads lived at Grantchester, a village two miles higher up the river than Cambridge, which has been admired by many poets from Chaucer to Rupert Brooke. Their home, an old and romantic house beside the mill pool, was a centre of the intellectual life of the University.

As a consequence partly of his eminence in very remote regions of thought, partly of the affection that everybody bore him, and partly of some personal characteristics such as forgetfulness and inattention to correspondence, White- head became in College a legendary figure about whom st'ories were told (mostly invented). Perhaps I may be allowed to give one of them as a sample of the rest. Whitehead had promised to subscribe to the College Mission: but the cheque was not forthcoming, and the Treasurer of the Mission, after dunning him in vain, at last hit on a plan that promised success. Knowing that Whitehead and he kept their accounts at the same bank, he wrote a cheque from his own book payable to himself for the amount promised, and sent it to Whitehead for signature, with a stamped and addressed envelope for return. It reappeared, endorsed ‘A. N. Whitehead’ on the back, but not otherwise completed.

In 1910 he resigned the Trinity lectureship and removed to London. At first he had no teaching appointment, then in 1911—1914 he was on the staff of University College, and lastly, from 1914 to 1924 he held a chair of mathe­matics in the Imperial College, where he had as colleague his old friend A. R. Forsyth. In this period he underwent one of the great sorrows of his life, in the loss of his younger son Eric, of the Royal Flying Corps, who was shot down over the foret de Gobain in France in March 1918.

There was to have been a fourth volume of the Principia, written chiefly by Whitehead, and treating of geometry. In 1906-1907 he had made two preparatory studies in this field, which were published under the titles The Axioms of Pro­jective Geometry, and The Axioms of Descriptive Geometry', it was in the former of these that he gave his famous definition of geometry as ‘the science of cross­classification’. But as he now turned again to study the foundations of the subject, he found himself more and more involved in questions which really belonged to epistemology and metaphysics. For one thing, the discovery of the Special Theory of Relativity in 1904 had profoundly changed the relations between geometry and physics, and had opened up new prospects in the

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236 Obituary Noticesphilosophy of nature. He had always been interested in such matters: writing at the end of his life he said ‘By the time that I gained my Fellowship m 1884,I nearly knew by heart parts of Kant’s Critique Pure Reason' . He now returned to this domain and he ceased, for the time being, to develop Peano symbolism, the only notable contribution to it in his later life being an article published in Mind in 1934, which supplements the Principia in some important respects. The long and marvellously fruitful partnership with Bertrand Russell now began to dissolve: in Whitehead’s autobiographical notes he refers to this chai^H in the words ‘Our fundamental points of view philosophic and sociological^® diverged, and so with different interests our collaboration came to a natural

In 1915-1917 he published several papers of a definitely philosophical character. These were followed by two books, An Enquiry concerning the Principles of Natural Knowledge in 1919, and a volume of Tarner lectures on The Concept of Nature in 1920; in these he propounded a new type of natural philosophy, whose origins must now be indicated. Since his settlement in London he had formed a friendship with Herbert Wildon Carr, a disciple of Bergson who in 1914 published an account of the Bergsonian doctrine under the title The Philosophy of Change. The basis of this philosophy is that change is the primary reality: everything else is derived from it. The concept o f™ quantity of material with a definite spatial configuration at an instant of time is a very complex abstraction, and is by no means a fundamental datum, for t|j® purposes of metaphysics, that is, in order to discover the general ideas that are indispensable for the analysis of everything that happens, it is necessary to start from the truly primitive constituents of knowledge. This is the outlook of what are called process philosophies: and Whitehead fully accepted it. Accor™ ingly he began his exposition by rejecting the picture of Nature w h ic h ® commonly accepted as the starting-point of physics: namely, that space and tim || provide, so to speak, a stage, on which ponderable bodies, aether and electricity maintain an unending performance. In place of this, he put forward the doctrine that the ultimate components of reality are events. ‘I give the name “event he said, ‘to a spatio-temporal happening.’ For instance, a University lecture is an event: obviously it includes other events, e.g. the professor at his rostrum afl® the students listening at their desks: moreover, it may in its turn be regar e as part of a larger event, e.g. the aggregate of all the lectures delivered in the same building at the same hour. This property of extending over other events is characteristic of events, and is the fundamental relation on which W hiteheadf philosophy of the external world is based.

An event is never instantaneous, it always endures over a certain (thou™ perhaps very short) duration of time (this was a characteristic doctrine . Bergson’s): ‘the ultimate fact for observational knowledge’, as Whitehead said, ‘is perception through a duration’. The notions of an instant of time, an |M point of space, are not truly primitive notions: to obtain them, he introduc® what he called the method of extensive abstraction. The idea of this method is, t*| consider a set of events each of which includes all the subsequent members ot

the sequence, like a nest of boxes each slightly larger than the one next inside it: if the events ultimately diminish indefinitely (or, in more precise language, if no event is extended over by every event of the set), then they may be regarded as defining a limit: points of space and instants of time may be defined in this way: so that time and space are derivative concepts, they are abstractions which express relations between events.

One of the motives which led Whitehead to build metaphysics on this founda­tion was that it might now be found possible to abolish what he called the bifurcation of nature. More than two centuries before, the famous physicist Robert Boyle had introduced the terms primary and secondary qualities, and they had been discussed further by Locke in his Essay concerning the Human understanding. Primary qualities of matter are those qualities which are attributed to the objects themselves and occur in scientific theory, such as shape and motion, and spatio-temporal qualities in general: secondary qualities are those such as colour, smell and taste, which belong only to our senses and not to the things in themselves: they have been generally conceived as produced in some way by the impact on us of the primary qualities, so that the latter have been regarded as the more real. In a philosophy of process however, where material objects play only a subordinate and derivative part, the secondary qualities are as real as the primary—perhaps more so—and Whitehead’s hope was that he might be able to subsume both of these under a single category. ‘Natural philosophy’ he said, ‘should never ask what is in the mind and what is in nature’: ‘there is but one nature, namely the nature which is before us in perceptual knowledge’. It is clear however that whatever alterations in the metaphysical status of primary and secondary qualities may be effected by a new philosophy, the dis­tinction between the two is a useful one and can never be ignored entirely: and to that extent, something resembling a bifurcation cannot be avoided.

While Whitehead was engaged in his development of process metaphysics in 1914-1919, a cosmological discovery of profound philosophical importance was given to the world, namely Einstein’s Theory of General Relativity, in which the physical phenomenon of gravitation was expressed by a curvature of space- time, varying according to the physical situation from point to point over the whole universe. This first became known to men of science in this country by Eddington’s Report on the Relativity Theory of , which was pre­pared for the Physical Society in 1915. In 1920, Whitehead published in the Times Educational Supplement a criticism of it. ‘I doubt’ he said, ‘the possibility of measurement in space which is heterogeneous as to its properties in different parts. I do not understand how the fixed conditions for measurement are to be obtained.’ He followed up this idea by devising an alternative theory, which he set forth in a book The Principle of Relativity in 1922. ‘I maintain,’ he said, ‘the old-fashioned belief in the fundamental character of simultaneity. But I adapt it to the novel outlook by the qualification that the meaning of simultaneity may be different in different individual experiences.’ This statement is applicable to the Special Theory of Relativity, where the ‘instantaneous space’ or ‘domain of simultaneity’ of any particular observer is the infinite three-dimensional

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space which is orthogonal (in four-dimensional space-time) to the instantaneous element of his world-line: but it is not compatible with the General Theory of Relativity, in which an observer’s domain of simultaneity is usually confined to a small region in his immediate neighbourhood. Whitehead developed a theory of gravitational fields, alternative to Einstein’s, assuming uniform space-time as a basis. It has, however, never been favourably received by mathematical physicists generally: and the researches of Levi-Civita and others on the experi­mental observations which are required in order to determine the gravitation^^ potentials have been generally regarded as meeting Whitehead’s objections to Einstein’s theory.

In 1924 he resigned his chair at the Imperial College in order to accept a professorship in the Philosophical Department of Harvard University, which he occupied until his final retirement in 1937. In the session 1927-1928 he returned to this country for a time in order to deliver the Gifford lectures in Edinburgh University. These, which were published in 1929 under the title Process and Reality, an Essay in Cosmology, may be regarded as the definitive exposition^

of his mature philosophy, to which he gave the name Philosophy of Organism.

In his own words, ‘Speculative Philosophy is the endeavour to frame a coherent, logical, necessary system of general ideas in terms of which every element of our experience can be interpreted’. Comprehensive metaphysical systems are not much in favour with men of science generally: and there are even many professional philosophers who concentrate on particular well- defined domains and who renounce the search for a grandiose universal synthesis. Whitehead however believed that it was possible to construct such system, and he had now a clear idea of the method that should be employe^ and the aims that should be pursued. In the Symposium in honor of the Seventieth birthday of A . N . Whitehead, which was published in 1932, he states thenoi concisely. ‘The world is always becoming, and as it becomes it passes away and perishes. Almost all of Process and Reality can be read as an attempt to analyse perishing on the same level as Aristotle’s notion of becoming. The past is an element which perishes and thereby remains an element in the state beyond, and thus is objectified. That is the whole notion. If you get a general notion of what is meant by perishing, you will have accomplished an apprehension of what you mean by memory and causality, what you mean when you feel tha|jj what we are is of infinite importance, because as we perish we are immortal. That is the one key thought around which the whole development of Process and Reality is woven.’ ‘The creative advance of the world’ he said, ‘is the becom­ing, the perishing and the objective immortalities of those things which jointly constitute stubborn fact.’

Let us now see how the programme thus outlined was carried out.In regard to particular features, he was under obligations of one sort or another

to Descartes, Leibnitz, Locke, Berkeley and Hume, and among moderns to Bradley, Bergson and Alexander: but the main roots of his doctrine were to be found in Greek Philosophy: and it bore a relation to modern science which may

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be compared with that which Platonism bore to the Pythagorean conception of mathematics as the intelligible element in nature. In his view, the immense body of knowledge regarding the external world which has been gained by the labours of men of science must first be arranged and reflected on, so that cos­mology is exhibited as a scheme of broad conceptions held together by rational principles: and only when this scheme has been achieved should the philosopher try to extend it so as to take account of everything else in human experience and so to obtain formulations of the ultimate generalities. The foundations —the epistemological preparation for all that is to follow—must be a study of the concepts of physical science and an analysis and clarification of all that is known regarding the order of the external world: then the meaning of the ideas so acquired is to be developed by confrontation with the various types of experience: and finally a cosmology is to be elaborated in terms of which all particular topics find their interconnexions. The basis of philosophy is science criticizing itself.

Whitehead therefore turned his back on German idealist philosophy (Kant, Fichte, Schelling, Hegel). In spite of his early devotion to Kant, he tells us that he ‘had never been able to read Hegel’. His objection to them now was that they were concerned chiefly with mind, and had little interest in the study of nature by the methods of mathematical and experimental science. In this sense his philosophy is a recurrence to pre-Kantian modes of thought. It is indeed, as he says, ‘the inversion of Kant’s philosophy. The Critique of Pure Reason describes the process by which subjective data pass into the appearance of an objective world, so that for Kant, the world emerges from the subject: for the ‘philosophy of organism’, on the other hand, ‘the subject emerges from the world’. This however must not be understood as suggesting that a metaphysical system is to be reached by elaborate reasonings such as those of Principia Mathematica: ‘Philosophy’ he said, ‘is either self-evident, or it is not philosophy’.

In the Gifford lectures, as in the earlier works, the beginning is made with events. Those events which are ‘the final real things of which the world is made up’ are now called actual entities. ‘There is,’ he said, ‘no going behind actual entities to find anything more real: the final facts are, all alike, actual entities: and these actual entities are drops of experience.’ Thus the category of ‘actual entities’ plays the same fundamental part in the philosophy of organism that the category of ‘substance’ plays in many older philosophies: but the significa­tion of the two concepts is entirely different: the term ‘substance’ is associated with the notion of something that endures, and sustains qualities, and that remains numerically one amidst the changes of accidental relations: whereas a Whiteheadean ‘actual entity’ has no permanence. How it becomes constitutes what it is, so that its ‘being’ is composed of its ‘becoming’: it is the outcome of whatever may be ascribed to it in the way of quality or relationship. It cannot have any external adventures, but only the internal adventure of becoming: its birth is its end. Thus an actual entity perishes when it is complete, but in perish­ing it becomes immortal. In order to emphasize the difference between his philosophy and the philosophies of substance, Whitehead in many connexions

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described an actual entity not as a ‘subject’, but as a superject, a term designed to suggest its emergence from antecedent entities to itself.

As we have said, the philosophy of organism is in the first place a philosophy of Nature, or a cosmology. Now one famous philosophical cosmology has come down to us from the ancient world, namely that set forth in the Timaeus of Plato: and the resemblances between it and Whitehead are so many and so striking, that Process and Reality may be described, in a first rough approxima­tion, as the Timaeus brought up to date. In his attitude to the , Whiteheaddiffered profoundly from many of his contemporaries; Dr Charles Singer, the eminent historian of science, once described it as ‘a picture of the depth to which natural science can be degraded by a great mind’: and Whitehead’s old coadjutor Russell (who ultimately moved over to the philosophical doctrine known as ‘neutral monism’) said recently that it ‘contains more that is simply silly than is to be found in his [Plato’s] other writings’. ‘As philosophy,’ added Russell, ‘it is unimportant.’ Whitehead, on the other hand, admired it greatly: ‘What it lacks in superficial detail,’ he wrote, ‘it makes up for by its philosophic depth. If it is read as an allegory, it conveys profound truth.’

A fundamental idea with both Plato and Whitehead is the gradual evolution of order out of a primaeval chaos, by a process of divine achievement. In the Timaeus, a supernatural craftsman, who in some sense acts as God, and who is

called the demiourgos, is represented as operating on a confused aggregate ofpre-existent matter, and informing it with a quality of structure and harmony, in spite of obstacles arising from its refractory nature. Such a Being differs greatly from the omnipotent Creator of the monotheistic religions: but White- head found in the myth of the Timaeus the expression of a profound religious truth: for the Christian thinks of his Lord, both now and during His earthly life, as persuading men rather than compelling them: if the work of the demiourgos is interpreted as a picture not of creation but of the daily operation of divine grace, it is not out of keeping with orthodox Christianity.

Whitehead and Plato have the same essential conception, namely that Nature is in a state of continual flux, and that the aim of the seeker should be to find what is permanent and to discover its relation to the turmoil of changing appearance. In Plato’s case the solution was provided by his general philosophical principles: the things we perceive in the visible cosmos are imperfect and transient copies of eternal models. For example, we can draw triangles, but we can never succeed in making the sides accurately straight or devoid of breadth— indeed under the microscope the breadth would be seen to be completely irregular—and the sum of the angles, if we measured them, would never be precisely equal to two right angles. In Plato’s view, all the triangles perceived by the senses are defective repetitions of a triangle which has none of these shortcomings: it is one of a vast assemblage of eternal, immutable and faultless originals which are, so to speak, laid up in heaven, and are called Forms or Ideas. Whitehead’s doctrine in Process and Reality is not dissimilar: he accounts for the permanence that is discovered amidst the flux of events, by postulating what he calls eternal objects, which have a potentiality of ingression into the

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becoming of actual entities. The eternal objects, like the Platonic Forms, have not themselves any place in the world of impermanence, but they are exemplified in the things that do exist in it, the ‘actual entities’; and by their ingression they contribute definiteness or character to the actual entities, and thus make possible the recognition of permanences in events. The definition of an eternal object given in Process and Reality is: ‘Any entity whose conceptual recognition does not involve a necessary reference to any definite actual entities of the temporal world is called an eternal object’. ‘Actual entities and eternal objects’ said White- head, ‘start out with a certain extreme finality. The other types of existence have a certain intermediate character.’

Perhaps the chief difference between the conceptions of Plato and White- head as regards this feature of their philosophies is that Plato made the imper­fection of the copies a cardinal feature of his teachings: whereas Whitehead was well aware that a Form or Eternal Object such as for instance the number 2 is realized completely in every pair of shoes or couple of twins.

In the Timaeus, the primitive material or plastic substratum, out of which the copies of the Forms are made—the clay that is moulded by the into his sculptures—is named chora, a word for which perhaps the least unsatis­factory translation is space, though it is not the Newtonian space of modern physics: it is not created by the demiourgos, but is represented rather as something planless, indeterminate, perverse and intractable, over which he has partial but not complete control. In Whitehead’s philosophy there is a concept named creativity, .which corresponds more or less to Plato’s ch5ra, or to Aristotle’s

‘prime matter’ ( 7 TpcorrjvXrj), or to the ‘neutral stuff’ of the modern ‘neutral monists’. It is an ultimate, behind all forms, without a character of its own: but particular eternal objects can infuse their own character into it, thereby constituting actual entities. Thus it is by creativity that the actual world has its character of passage into novelty.

In both philosophies, time has a completely different status to space. For Plato, time is created by the demiourgos after the pattern of an eternal arche­type: as he says in the Timaeus, ‘At the same time that he imposed order on the heavens, he formed an image, proceeding according to number, on the model of the unchangeable eternity that abides in unity’. Whitehead’s doctrine of time is very similar: it is, he says, ‘the moving image of eternity’.

The Timaeus was one of the last of Plato’s works, composed when his philosophy had already attained its determinate form: so far as its physical side is concerned, however, he had little or no certain knowledge to rely on, and was compelled to draw on his imagination of what might be. Whitehead’s intellectual development, on the other hand, had been in the reverse direction: he had been a mathematician and physicist before he became a philosopher, and he had at his disposal the accumulated riches of modern science. Under these very different conditions, it is surprising that the two thinkers should have arrived at such parallel conclusions.

The audience at the Gifford lectures, in which Process and Reality was first communicated to the world, found them hard to understand. Halfway through

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the course, I had a visit from an earnest young philosopher, who begged me to throw some light on them. ‘They are about metaphysics, not mathematics’, I said, ‘surely you ought to ask X.’ ‘I have already been to him,’ was the reply, ‘and he referred me to you.’ The chief reason for the difficulty was the multitude of new words, and new senses of old words, in which the lectures abounded. This feature was made inevitable by its conviction that ordinary speech, which, as he had shown in Principia Mathematical is inadequate for the purposes of logic, is still more inadequate for the purposes of metaphysics: ‘most of the muddles of philosophy,’ he said, ‘are, I think, due to using a language which is developed from one point of view, to express a doctrine based upon entirely alien concepts’. It is fairly certain that many of Whitehead’s terms will be retained as a permanent enrichment of the philosophical vocabulary: in any case, some familiarity with them is necessary for a right understanding of his thought.

Some of his neologisms were introduced in order to guard against the tacit introduction of notions commonly associated with older and better-known words. For instance, a new term prehension enables him in many connexions to dispense with the use of the words ‘perception’ and ‘relation’. A ‘prehension’ signifies that one actual entity grasps other actual entities into a unity: (it does not necessarily involve consciousness). This word makes it possible to express the nature of an actual entity very simply. ‘The essence of an actual entity consists solely in the fact that it is a prehending thing.’ Thus the ultimate facts of immediate actual experience are actual entities, their prehensions, and the facts of togetherness, or nexus, among them. All else is, for our experience, derivative abstraction. ‘I have adopted the term “prehension” ’ said Whitehead, ‘to express the activity whereby an actual entity effects its own concretion of other things.’ This word concretion or concrescence, is another novelty: it means the together­ness or unity that comes to exist as a result of the prehension. Every event originates as a unity of concrescent prehensions: the process of concrescence

is Being.As each actual entity perishes, it is prehended by the succeeding member

of the nexus: and there may be a recurrence of character (the ingredience of an eternal object) through a series of actual entities. Groups of such series, in which character is simply reproduced without any development, constitute the ‘material bodies’ of physics. The solidarity of the world is explained by the fact that the concrescence of any one actual entity involves all the other actual entities among its components. The translation of familiar words into White - headean language is, in general, fairly straightforward: th of causationis simply an assertion of the derivation of actual entities from their antecedents. Time and space are expressions of certain extensive and cogredient properties of events: and geometry is the investigation of the morphology of nexus.

Metaphysical principles, in Whitehead’s view, are truths about the nature of God: and God is not to be treated as an exception to all metaphysical principles, involved to save their collapse: on the contrary, He is their chief exemplification. Let us then consider Whitehead’s doctrine regarding God,

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His religious opinions had undergone more than one change during his lifetime. His father, an Anglican of the Evangelical school, brought him up in an atmosphere of simple and even narrow piety. As an undergraduate, he talked openly and often to his friends about religion, and especially about his interest in Foreign Missions. There was (he said) some difficulty in compre­hending and following some of the divine commands, but the injunction to go out into all lands and spread the gospel was as plain as words could be. These convictions, however, lost their hold on him, and for a time he became an out­spoken and even polemical agnostic. This phase again did not endure, and in mature life there was a reflux towards spiritual belief: Process and Reality is theistic in the sense that a Being whom he calls God occupies a central position in it. But his God bears little or no resemblance to the Creator revealed in the Book of Genesis, or to the God indicated by the Ways of St Thomas Aquinas— the First Mover, the Ultimate Cause, the Necessary Existent. In St Thomas’s system these aspects of the divine nature are established by philosophy, that is to say, without the aid of revelation: in order to obtain the complete Christian doctrine of God, the pure reason of philosophy is insufficient, and it is necessary to have recourse to supernatural revelation: revelation contributes a new picture, that of a God who pleads with men, and whom, in the perversity of their wills, they can reject: a God in whom coercion is replaced by solicitation. Now it is precisely this latter aspect of God that is arrived at by Whitehead’s philosophy. Thus, as between St Thomas and Whitehead, there is a complete inversion of the parts respectively played by reason and by revelation: with St Thomas the omnipotent God is derived from reason and the persuasive God from revela­tion, while with Whitehead the persuasive God is derived from reason, and the omnipotent God cannot be arrived at except by recurring to revelation. White- head himself indeed refused to take this last step: and, while recognizing in God ‘the timeless source of all order’, he affirmed that the divine omnipotence, as conceived for instance by Calvinism, is definitely false. ‘The ascription of mere happiness, and of arbitary power, to the nature of God,’ he said, ‘is a profana­tion.’ Thus, in the philosophy of organism, God is presented as a non-temporal ‘actual entity’, Who is not the whole of reality, and Who is not the author of every decision that is made. His nature never reaches a static completion, but is always being completed by the creative passage of events: God and the world are instruments of novelty for each other. In Science and the Modern World He is called the ‘principle of concretion’ and the ‘ultimate limitation’: in Religion in the Making He is ‘wisdom’: and in Process and Reality He is ‘the lure for feeling, the eternal urge of desire’: which last is Aristotle’s original conception.

In an article on ‘Analysis of Meaning’, which appeared in the Philosophical Review of 1937 (reprinted in the Essays of 1947), Whitehead returned to his favourite study, symbolic logic. The development of mathematics and symbolic logic down to the present time represent, he said, only a minute fraction of the possibilities. When in the distant future the subject has expanded, so as to include a calculus of patterns depending on connexions other than those of space, number and quantity, then, he suggests, symbolic logic (that is to say,

Alfred North Whitehead 293

the symbolic examination of patterns with the use of real variables) will become the foundation of aesthetics: and from that stage he anticipates (as Leibnitz did) that it will proceed to conquer ethics and theology.

Whitehead’s last considerable effort was a lecture on ‘Immortality’, delivered after his eightieth birthday in the Harvard Divinity School, and printed in the Essays of 1947. The main thesis in this lecture is that we naturally simplify the complexity of the universe by considering it in the guise of two abstractions, namely the World of Activity and the World of Value. The World of Activity is the world that emphasizes the multiplicity of mortal things. It is the world of origination, the creative world: its prime characteristic is change. The World of Value is the world that emphasizes permanence: its prime characteristic is immortality. Each of these worlds is futile except in its function of embodying the other. Creation aims at value, whereas value is saved from the futility of abstraction by its impact upon the process of creation. But in the fusion, value preserves its immortality. In what sense does creative action derive immortality from value? That is the central topic of the lecture.

Either world can be described only in terms of factors which are common to both of them: such factors have a dual aspect, and each world emphasizes one of the two aspects: the factors are no other than the Platonic ‘Forms’. A key example for understanding the fusion of the World of Activity and the World of Value is the problem of ‘personal identity’: namely, a sequence of actual entities is such that each entity embodies in its own Being the antecedent members of the sequence, with an experience of the identity of the past in the immediacy of the present. There is an identity of primary character amid secondary changes of value. Personality is the extreme example of the sustained realization of a type of value: the immortality which belongs to value has entered into the changefulness which is the essential character of activity. The effective realization of value in the World of Change should find its counterpart in the World of Value: this means that temporal personality in one World involves immortal personality in the other.

The World of Value exhibits the essential oneness of the universe. Thus while it brings into view the immortal side of the many persons, it also involves the unification of personality. This unification derived from the World of Value is identified with the concept of God, who is the intangible fact at the base of finite existence, a unification founded on ideals of perfection, moral and aesthetic. Clearly this is not the God of the Christian theological tradition, nor is it the diffused God of the Hindu-Buddhistic tradition: the concept lies somewhere between the two.

Any attempt to form a general judgment on the Philosophy of Organism must, in the first place, take account of the principle, which Whitehead acknowledged, that a philosophy treating of the general notion of Being and covering the whole of experience can be attained best by enlarging the scope of a philosophy which is limited to the physical world, and that this in its turn must be based on the discoveries of theoretical and experimental science. This principle entails the consequence that philosophy, like physics, must be a pro­

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gressive subject: the conceptions of one generation will inevitably be transcended by those of the next: the day has gone by when systems framed a priori can be accepted as all-embracing and permanent solutions of the problems of meta­physics. The question may therefore be asked, how long is Whitehead’s philosophy likely to retain its position? One cannot feel sanguine on this point, for the tragic feature of Whitehead’s situation was that his labours were com­pleted just before it was possible to profit by the most remarkable and important of all modern discoveries in physical science: he assimilated relativity-theory, but he had not the opportunity of assimilating quantum-mechanics. The Gifford lectures, which embody the mature form of his philosophy, were delivered in the session 1927-1928, only two years after the successful reduction of quantum-theory to a rational form, and actually in the same year as the dis­covery of Heisenberg’s Principle of Uncertainty, which dominates all present- day ideas of the micro-world. As an example of the way in which his doctrines may be affected, it may be remarked that his ‘Method of Extensive Abstraction’ is endangered by the fact that molar conceptions are not applicable in the sub­atomic domain.

In his later years, Whitehead was acknowledged as the greatest living philosopher, and was the recipient of many distinctions from universities, learned societies and governments. He had honorary doctorates from Man­chester, St Andrews, Montreal, Harvard, Yale and Wisconsin: he was President of the Mathematical Association in 1915-1916, and of the Mathematical and Physical Section of the British Association in 1916. He was Sylvester Medallist of the Royal Society in 1925, and Butler Medallist of Columbia University in 1930. In 1931 he attained the very rare honour of combining Fellowship of the British Academy with Fellowship of the Royal Society and in 1945 he received the most honourable of all the distinctions in the gift of the British Crown, the Order of Merit.

Whitehead died at Cambridge, Massachusetts, on 30 December 1947. He was survived by Mrs Whitehead and by their son Mr Thomas North White- head and daughter Miss J. M. Whitehead, both of whom occupy positions on the staff of Harvard University, and by grandchildren and great-grandchildren.

Edmund T. W hittaker

Alfred North Whitehead 295

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