THE THOMIST A SPECULATIVE QUARTERLY REVIEW OF THEOLOGY AND PHILOSOPHY EDITORS: THE DoMINICAN FATHERS oF THE PROVINCE oF ST. JosEPH Publishers: The Thomist Press, Washington, D. C. VoL. XXXVI APRIL, 1972 No.2 CAUSALITY AND EVOLUTION The Search for a Proportionate Cause of Evolutionary Processes I WILL ASSUME in the following that the principle of causality which states that " nothing which comes to be, comes to be without a proportionate cause" cannot be eliminated from empirical science, although the effort has repeatedly been made. 1 Consequently, we have to face squarely a fundamental question about all theories of evolution: How can more complex 1 Even positivistic philosophers of science have not been able to eliminate the principle of causality as a necessary assumption of science, although they have striven to give it a Humean form by arguing that it is not an inductive generalization, but a rule of thinking which is necessarily required by any theoretical science as long as science retains the goals which it has historically accepted. See the discussion in Ernest Nagel, The Structure of Science (Harcourt, Brace and World, Inc.: N.Y. 1961), pp. 316-324. "But it is difficult to understand how it would be possible for modem theoretical science to surrender the general ideal expressed by the principle (of causality) without becoming thereby transformed into something incomparably different from what that enterprise actually is." p. 324. See also Mario Bunge, Causality, The Place of the Causal Principle in Modern Science (Harvard University Press: Cambridge, Mass., 1959). 199 200 BENEDICT M. ASHLEY and highly integrated entities arise out of simpler and less organized entities? How can the " greater come from the less"? How can a new entity" emerge"? What is the proportionate cause of this emergence? Some have tried to escape the difficulty by arguing that "evolution" (as the etymology of the word indicates) is only an " unfolding," an explicitation of what is somehow already there, like the development of an embryo. Others have argued that it is only subjective to consider an elephant " greater " than an amoeba. But neither argument is more than an evasion of a genuine problem. We now have a rather detailed knowledge of various evolutionary processes, and none of these resemble embryological development except by the loosest of analogies. Again there is a precise, objective, and empirical sense in which an atom is a more complex and integrated system than an electron, a molecule than an atom, an organism than a molecule, a mammal than a protozoan, the human brain than a bird brain. 2 I£, therefore, we are to have a coherent, philosophical understanding of the evolutionary view of the world and man which modern science has shown to be the only plausible account, we must identify in that world-picture a proportionate cause, a sufficient agent of evolutionary emergence. Four principle levels of this emergence are commonly distinguished today: 8 (I) Nuclear evolution which proceeds by nuclear synthesis and gives rise to atoms. Chemical evolution which proceeds by chemical reactions and gives rise to molecules of greater and greater complexity. • Ludwig von Bertalanffy, General System Theory (George Braziller: New York, 1968), pp. £7-£9, referring especially to the work of Kenneth Boulding. • Melvin Calvin," Chemical Evolution and the Origin of Life," American Scientist, 44 (July, 1956), £48-£63 proposes this four-fold evolution and gives the following time table. Nuclear evolution-10 billion years; chemical evolution-£lh billion years; biological evolution-! billion years; psychosocial evolution lh million years. See also his Chemical Evolution: Molecular Evolution towards the Origin of Living Systems on Earth and Elsewhere (Oxford, 1969). CAUSALITY AND EVOLUTION flO I (3) Biological evolution which proceeds first by abiogenesis, and then by genetic mutation and natural selection to give rise to the species of living organisms of increasing complexity and greater flexibility in adapting to environmental changes. (4) Psychosocial evolution by which the human species produces a vast array of cultures which are not genetically determined but invented, and in which there has been a progress toward control of the environment by scientific technology, and the emergence of self-directed human personalities. These four kinds of evolution take place through radically different processes and are only analogously called by the same term " evolution," yet they form a sequence in which the more complex process presupposes the simpler. The higher the level of evolution, the more strikingly novel, diverse, and unique are the products. At the nuclear level only about a hundred atomic species emerge (a few hundred if we count isotopes). Hundreds of thousands of kinds of chemical molecules occur in nature, but the species of living organisms are counted in the millions. Finally, although there is only one human species biologically considered, psychosocially considered there are billions of unique human personalities playing their roles in a vast variety of human cultures. The more advanced the culture, it would seem, the more the individual personality becomes conscious of its own uniqueness in history, and the more this uniqueness is valued and cultivated. Evolution and Anti-Evolution It would be a gross error to think that all natural, cosmic processes are evolutionary, that is, processes of emergence. On the contrary the more universal cosmic processes are anti-evolutionary, while evolutionary processes appear to be only local and temporary. Anti-evolutionary processes, tendencies by which every system in the universe is disorganized, disrupted, and dissolved into a universal random flux of particles in an equilibrium of undifferentiated and minimal occurrences, are everywhere monotonously evident. In most of the vast regions of space, and most of the immense epochs of time, nothing 202 BENEDICT M. ASHLEY new, or at least not much ever happens. 4 Complex systems whether they be societies, organisms, molecules, or atoms, seem doomed to perdure only in a few places and for a short while. The law of increasing entropy (or second law of thermodynamics) states that in a closed system all processes ultimately tend to a state of maximum entropy or disorder, because every process in which order is increased in a sub-system involves an increase of disorder in the total closed system. 5 This law is vividly illustrated for us by our present "pollution crisis." Every process by which human technology makes man's immediate environment more orderly, necessarily results in greater disorder of the total environment. In our universe regions of order are oases in an encroaching desert. " Entropic doom " is inevitable and must ultimately prevail over every evolutionary process. It is wrong, therefore, to think that the second law of thermodynamics is contradicted by the fact of evolution. The law predicts that ultimately a closed system must tend to maximum entropy, but it does not determine the rate of this increase of entropy. It is an eschatological prophecy without a date for Doomsday. Entropy is a matter of probabilities, and in every run of probable events there are fl.uctuatigns to either side of a trend. Evolutionary processes appear as such fluctuations in sub-systems within a total system that is as a whole becoming more and more disorderly. These evolving subsystems emerge here and there like gleaming counter-eddies in the dark universal river of decline and then smooth out again. On the other hand, it is also an error to suppose that the • Evidence is accumulating, however, that some important chemical evolution does take place in inter-stellar space, producing organic molecules of relative complexity. See Science, 170 (4 Dec., 1970), pp. 1116-1117, Donn Bertram, "Interstellar Molecules and Chemistry " "At present five diatomic and five polyatomic species are known (in interstellar space). The most complex molecule thus far is cyanoacetylene, CN- C = C- H." • On the problem of entropy and evolution see Harold F. Blum, Time's Arrow and Evolution (Princeton University Press, 1951) and Albert L. Lehninger, Bioenergetics: The Molecular Basis of Biological Energy Transformation (W. A. Benjamin, Inc.: N.Y., 1965). CAUSALITY AND EVOLUTION 208 second law of thermodynamics as such explains these evolutionary counter-currents. Every evolutionary process involves an increase of order (negative entropy or negentropy) and this increase requires an appropriate causal explanation, unless we are to abandon the principle of causality which we have assumed. If the term " order " seems too vague, we can think of other equivalent terms such as " pattern," " arrangements," " gestalt," or " system." Perhaps the most useful term today would be the one borrowed from communications-theory: information.6 The decrease of noise (random, disordered, unpatterned) sound in a radio signal means an increase in patterned sound, and it is this pattern which carries " information." When any process becomes more orderly, when its degree of information increas,es, we must look for a cause of this increase in orderliness. We cannot simply attribute it to chance, because chance is precisely an occurrence which is random, unpatterned, lacking any determinate probability. 7 "Information," although not easy to define with complete generality, can be defined precisely and operationally in specific cases. For example, in chemical evolution we can define the degree of information for various molecules by the number and strength of the chemical bonds required to form each molecule. 8 In the case of organisms • See Jagit Singh, Great Ideas in Information Theory, Language and Cybemetica (Dover, 1966) . Chapter VII "Information and Entropy," pp. 78-88 and W. Ross Ashby, Introduction to Cybemet·ics (John Wiley and Sons: N.Y., 1968), pp. 174-191. For some objections to the use of the concept by an anti-reductionist see C. H. Waddington, Towards a Theoretical Biology, Vol. 1 (Aldine Publishing Co.: N.Y., 1968), Prolegomena. 7 When, in throwing dice, we say that the " chance," i. e., the probability of a given combination is such-and-such, we really mean that the sequence of combinations is chance (without any pattern or order) but that the frequency in which a given combination occurs in the sequence is determinate (has a definite probability). This probability has a cause, namely, the shape of the dice, the arrangement of the markings, and the force of the throw; the exact sequence is chance, has no cause, and is random. For a helpful discussion see David Hawkins, The Language of Nature (Doubleday Anchor Book: Garden City, New York, 1967), c. 6 "Chance and Probability," p. 165-196. 8 Or in terms of the " energy of configuration." " Complex organic molecules have a large potential energy of configuration: when they are burned they are degraded BENEDICT M. ASHLEY we will probably soon be able to define the degree of information for a fly or a rhinoceros in terms of the complexity of the genetic codex of each. Another way to look at this concept of " information " is to take it in a very literal sense as the amount of information we would need to reproduce artificially any product of a natural evolutionary process. Thus, a chemist who wishes to synthesize the chlorophyll molecule needs to understand the details of its structural formula and the processes by which this can be replicated. In principle, at least, it would seem that if man had sufficient information about any natural entity, atom, molecule, or organism, he could reproduce it by repeating the evolutionary processes required, perhaps in more efficient, abbreviated form than the natural ones. A temporary evolutionary trend within a sub-system of the universe, therefore, means an input of information-bearing energy into that sub-system. Nuclear and Chemical Evolution Whether the first stages of nuclear evolution took place in a "big-bang" or primordial explosion or not, 9 it seems certain that such evolution continues within the interior of stars, forging heavier atoms out of hydrogen and helium atoms by nuclear fission and fusion. 10 These processes are possible only to simple stable products ... which have a much lower energy content." Lehninger, op. cit., p. 15. • George Gamow, The Creation of the Universe (Viking Press: New York, 1961). This "big-bang " hypothesis of cosmic origins still seems to have the edge over the Hoyle-Bondi "steady-state" hypothesis. See William H. McCrea, "Cosmology Today," American Scientist, 58 (Sept.-Oct. 1970), pp. 521-527 and the work of Maarten Schmidt of California Institute of Technology reported in Scientific American, 224; 11 (Jan. 1971), p. 46. 10 " Before the Sun was formed, almost every possible stellar temperature, density and life history had been experienced somewhere in our Galaxy. The residues are the many kinds of atoms in the universe. Some of the processes that synthesize one element will destroy others; the enormously complicated composition of our bodies, for example, requires that many different stars contributed atoms to the raw material out of which our Sun, the planets, and ourselves were born." J. L. Greenstein, "Stellar Evolution and the Origin of the Chemical Elements," American Scientist, 49 (Dec. 1961), pp. 449-473. CAUSALITY AND 9l05 at very high temperatures and pressures. Here the supply of free energy is great, but matter is unorganized, with particles moving in the wildest explosive disorder. Such conditions are rare and in our solar system exist only in the sun, or in a nuclear reactor. Chemical evolution, by which molecules are built from atoms and more complex molecules from simpler molecules, is much more widespread in the universe, but it does not progress to the higher levels of organization except in very select situations, where temperatures are moderate and there is a delicate balance between a multitude of factors. 11 The more complex the molecule the more complex and balanced the situation required, so that extensive chemical evolution seems more favored on the surface of our earth than at any other site yet known in the solar system. For brevity's sake I will omit an analysis of nuclear evolution and consider only chemical evolution in order to compare it with biological evolution. If we examine the situation in which a molecule emerges by the chemical combination of atoms, we can distinguish three phases: 12 First, not only must there be the required materials (the atoms) but a complex set of conditions must exist if a particular chemical combination is to take place. Commonly the atoms must be in a liquid or gas solution of an appropriate temperature and pressure so that they will come in close contact with each other. They must also be properly orientated, since each atom has its own special configuration and must be "fitted " to the atom with which it is to combine. Second, there must be supplied an energy of activation. Before the moment of combination the atoms are stable, independent units which resist disruption of their own internal order. This stability of the isolated atom is a barrier to reaction. When the energy of activation is supplied in the form of 11 However, see note 4 above for evidence that these conditions may be met in unsuspected situations. 12 See Arthur J. Campbell, Why Do Chemical Reactions Occur? (Prentice-Hall: Englewood Cliffs, N.J.), 1965. 206 BENEDICT M. ASHLEY heat, mechanical, or radiant energy, this barrier is overcome. Each atom loses its individual stability and is modified and integrated into the new molecule. Third, there is a spontaneous " chemical reaction " in which in most cases superfluous energy is released in the form of heat. This means an increase in the entropy of the surrounding environment, since heat is the random, unpatterned movement of particles. The higher order within the new molecule has been purchased at the expense of increased disorder in its surroundings. It is to be noted that this usually means that in a solution there is an equilibrium situation in which some molecules are formed as others are broken down. It is in the second of these three phases that the old units lose their individual existence and the new molecule emerges. The third phase may be understood as a kind of" settling down " process in which the new molecule, already formed, becomes stable. By losing superfluous energy to the environment the molecule retains just that internal energy required for its specific type of organization. It is apparent, therefore, that atoms do not " spontaneously " combine purely through forces inherent in the atoms. The spontaneous attractions and repulsions due to the electromagnetic forces in the atoms come into play in the third phase, after the moment when the new organization is initiated by the energy of activation. We can conclude that it is this energy, not the fundamental electromagnetic forces inherent in the combining atoms, which is the proper cause of the new unit, and which is, so to speak, " built into it." This conclusion, however, raises a grave difficulty. The new molecule is a complex unity, more complex and more integrated than either of the atoms from which it was formed. 13 How can the energy of activation which is supplied in the form of heat, 18 Thus the nature and properties of a molecule depend not only on its component parts (composition), and on the spatial arrangement of these parts (structure), but also on the chemical bonds which unite the parts (constitution). These bodies are " fields," a concept that cannot be reduced merely to the arrangement of particles in space but which is essentially dynamic. See H. Remy, J. S. Anderson, J. Kleinberg, Treatise on Organic Chemistry (Elsevier Pub. Co.: Amsterdam, 1956), vol. 1, p. 298. CAUSALITY AND EVOLUTION 207 mechanical or radiant energy be the source of the information required to build this new system? How can a generalized force produce so specific an effect, as if a strong wind could produce a house out of scattered planks? One answer would be to posit a virtuality in fundamental cosmic forces of gravitation, electromagnetism, etc., like the rationes seminales of ancient Stoic philosophy/ 4 by which they are able to produce all the variety of chemical species. This would mean that somehow in these general forces there is a hidden code, an embryonic supply of information analogous to the genetic code in the fertilized zygote. Such a hypothesis seems too fantastic, a return to the " occult forces " of the alchemists. Another answer given by reductionists is to interpret chemical combination as a simple, mechanical addition of parts. In such a combination no greater comes from the less, since a "sum is equal to its parts." This interpretation, however, is not adequate to our present understanding of the molecule which has wave-mechanical unity in which the constituting atoms perdure only in a modified and integrated form. Thus the orbital electrons of the constituting atoms may no longer belong to a single nucleus within the molecule but to several. A new network of relations between the elementary particles within the molecule forms a unitary system, not a mere juxtaposition of previous systems. 15 14 See E. Vernon Arnold, Roman Stoicism (Routledge, Kegan Paul: London, 1958 (reissue)), Sec. 178, "The Word of 'seed-power' (logos spermatikos) of the universe is one: it is the primal fire in its work of creation. . . . But there are also in individual objects, animate and inanimate, indestructible seed-powers, countless in number, displaced alike in growth, procreation, and purpose; these seedpowers are, as it were, spirits of deities, spread throughout the universe, everywhere shaping, peopling, designing, multiplying; they are activities of fiery spirit working through tension (t6nos, intentio) in its highest development. But the seed-power of the universe comprehends in itself the individual seed-powers; they are begotten of it and shall in the end return to it," p. 161 f.; Also see: Max Pohlenz, Die Stoa (Vandenhoek-Ruprecht: Gottingen, 1948), 2 Vol. Vol. I, p. 78, and Johnny Christensen, An Essay on the Unity of Stoic Philosophy (Scandinavian University Books: Minksgaard, 1962), p. 86. 15 See F. Brescia, J. Arents, H. Meislich, A. Turk, Fundamentals of Chemistry, 208 BENEDICT M. ASHLEY It is much more plausible to say that the information built into the new molecule is contained neither virtually in the fundamental forces, nor in the combining atoms, but rather in the concurrence of all the factors required for the chemical reaction. The energy of activation considered as free energy, or as reducible to the fundamental cosmic forces, does not itself contain the necessary information, but as specified by the total situation it can produce a determined pattern in the new molecule. This " total situation " is not merely static but is a sequence of events in which the various factors come into play in an orderly fashion. The formation of .a complex molecule does not take place in a single step but sequentially in an evolutionary, constructive process in which at each step there must be a concurrence of a complex of factors. Although there may be alternative pathways in this evolution, there are more dead-ends (points at which the chemical process may be aborted because of some missing or obtrusive factor) than there are successful paths to the goal. The chemist who attempts an artificial synthesis of such a compound must reproduce such a successful sequence of situations and events. 16 This seems to be a sufficient answer to the question of how a new molecule can emerge out of materials less well organized without violating the principle of causality by asserting that a " greater has come from the less." The materials themselves are not the originating cause of the new system. The originating and proportionate cause is the energy of activation. This energy is nothing other than the recognized fundamental cosmic forces (gravitation, electromagnetism, and derivatives such as heat, pressure, etc.). No new fundamental force is required. However, these forces do not exist in a generic condition, but as specified by the situation in which they act and by the sequence of such actions. A new molecule can emerge only out of a highly ff. A Modern Introduction (Academic Press: N.Y., 1966), c. 11 and 12, pp. for a description of the molecule as it is now understood. 16 See the description of R. B. Woodward's synthesis of chlorophyll in Walter Lwowski, "The Synthesis of Chlorophyll" in L. P. Vernon and G. R. Seely, The Chlorophylls (Academic Press: N.Y., 1966), pp. CAUSALITY AND EVOLUTION 209 ordered situation undergoing a highly ordered sequential process against the general entropic trend. The information or patterning or negentropy contained in this ordered sequence is proportionate to the information built into the new molecule. The ordered sequence of ordered situations is equal to, not greater than, the emergent system we call a molecule. BIOLOGICAL EvoLuTION The passage from non-living molecules to living organisms (abiogenesis) is still a field of conjecture, but a key to the mystery is the discovery that the development of an organism and its power of reproduction is rooted in the nucleo-protein molecule DNA which by its variations provides a "genetic code" that determines the individual organism's structure and makes it possible to pass this inheritance on to its descendants. It is recognized, however, that the DNA molecule is not itself an organism, nor can it function except as part of an organism, usually within the chromosomes contained in a cell nucleus. Consequently, the origin of life was not merely the emergence of DNA macromolecules but of simple organisms containing such molecules as a principal feature of a complete living system. 17 Theories of abiogenesis do not rely on some special " vital force " to explain the emergence of living organisms. Instead they try to reconstruct imaginatively a sequence of situations 17 See Harold F. Blum, "On the Origin and Evolution of Living Machines," American Scientist, 49 (Dec. 1961), 474-501. Also Richard M. Lemmon, "Chemical Evolution," Chemical Reviews 70, 95 (1970), pp. 95-109, who says "The principal ideas of how this (origin of life) took place are the 'coacervate' theory of Oparin and the ' microsphere ' concept of Fox. Both of these ideas ... are based on the notion that the emergence of life is the inevitable outcome of the associational and organizational forces inherent in the macromolecule's chemistry." (p. 108) This " inevitable outcome," however, only means that no new forces are required, provided that these forces are specified by the necessary sequences of situations and events which Oparin and Fox posit. Blum (ibid.) argues that the limiting conditions of life are stricter than many scientists realize, and the rare events required are numerous. Consequently, we should not be so sanguine about life elsewhere in the universe. He calls it perhaps a "tenuous possibility." 210 BENEDICT M. ASHLEY and events in which the necessary free energy, and the suitable mixture, orientation, conditions of temperature, etc., would be present to build up step by step the structures of a simple organism containing DNA. In particular it is necessary to imagine the formation of some kind of membranes by which the interior of the organism could be separated from the environment while permitting the controlled in-put and out-put in relation to the environment required to maintain the dynamic equilibrium characteristic of living things. 18 The organism is not a closed system but a steady-state system in which the tendency to maximum entropy is constantly compensated by a controlled influx of energy. Since at any point in the sequence of steps that produced the first living organisms the process might have been aborted, it is necessary to reconstruct a plausible history of the origin of life. At the present time "spontaneous generation" does not take place, so that the hypothetical situation for abiogenesis is not now observable. However, without any gross violation of probability, such a situation in the early history of our planet can be posited. Furthermore, it is already possible to reproduce some phases of this process in the laboratory, so that there is hope that some day we will be able to synthesize living organisms out of nonliving materials. The amount of information required to do this, however, will be enormous. 19 Once the first living organisms had emerged, biological evolution, " the origin of species," began; and for this we now 18 " The DNA is not an autonomous part of the cell; it is not the "secret of life," but, as Barry Commoner persuasively argues, rather "life is the secret of DNA." It is the whole cell which is alive. And it is only the whole cell which is the minimal structure so far clearly recoguized as being capable of carrying on living activities." From an unpublished paper of my colleague A. S. Moraczewski, "Is Viral Republication a form of Biological Reproduction?" (1969) quoting B. Commoner, American Scientist, 52:365 (1964). 19 Melvin Calvin, "Chemical Evolution and the Origin of Life," American Scientist, 44 (July, 1956), 248-263, says "Although every one of the processes that I have described is probable--there is no great improbable event that is requiredthe selection amongst the random probable events of a particular sequence is a highly improbable thing and has required the billion years or so that it took to do it." CAUSALITY AND EVOLUTION 211 have a highly developed and very plausible theory, backed up by extensive paleontological, genetic, and other evidence. 20 It is commonly admitted today, as Mayr has shown 21 that a biological species is not merely a taxonomic convenience but a natural system which at any given time is sharply discontinuous with other species. This discontinuity is not only morphological (as in the case of the chemical species) but also functional. A species is an inter-breeding population absolutely or relatively isolated from other populations in the process of reproduction. In the course of time a species may (1) become extinct; (2) merge with another species from which it is only relatively isolated in reproduction, forming a hybrid species; (3) break up into two or more new species by the accumulation of genetic mutations reinforced by a period of geographic isolation or some other mechanism by which the divergence is permitted to proceed to the point that the two or more populations can no longer interbreed even when in contact. Current theories of biological evolution do not propose a single evolutionary force or law nor suppose any inherent tendency in a species to evolve. In fact, many species are remarkably enduring. As Deeley, following Waddington, has analyzed neo-Darwinism, this theory views evolution as due to the interaction of several types of inter-related factors. It is not the individual that evolves but the species, and the species evolves not from some inner teleology but through interaction with the environment (natural selection). This environment is an ecosystem composed not only of geography and climate but also of other living things in mutual competition and symbiosis. •• For a careful analysis of the different kinds of convergent evidence for biological evolution see Raymond J. Nogar, The Wisdom of Evolution (Doubleday: N.Y.), 1963. 21 E. Mayr, Animal Species and Evolution (Harvard University Press: Cambridge, Mass.), 1963. •• John N. Deeley, The Philosophical Dimensions of the Origin of Species, Institute for Philosophical Research (Chicago, 1969), pp. 96-111, referring to C. H. Waddington, " Evolutionary Adaptation " in The Evolution of Life, Sol Tax ed. (University of Chicago Press: Chicago, 1960), vol. I, pp. 381-4W and The Ethical Animal (Atheneum: N.Y., 1961), pp. 84-100. 212 BENEDICT M. ASHLEY The ecosystem itself is under pressure from the nuclear and chemical evolution of the earth and the whole solar system. Thus the energy which produces biological evolution has its source in chemical and nuclear evolution and can be traced in large part to events within the sun. 23 Nevertheless, evolution cannot be understood merely as an increase or decrease of total available energy but only in terms of the way this energy is applied in a sequence of extremely complex situations and events on the earth's surface. Deeley, ingeniously using the classical four "causes" of Aristotle to show the intimate interrelation of these factors (causae sunt invicem causae) , summarizes them as follows: 24 (I) epigenetic factors: the tendency of interbreeding population to reproduce itself in a stable manner and increase in numbers ("formal causality," i.e., the maintenance of type). genetic factor: the tendency to variation resulting from constant small random mutations in the genetic code (" material causality," i. e., a variety of differing individuals within a species capable of transmitting their differences). (3) selective factor: natural selection by the environment which eliminates those variants which are less effective in reproducing their kind (" efficient causality," i.e., the agent determining in which direction species-change will take place). ( 4) exploitative factor: the flexibility of living things by which they are able to occupy new niches in the changing environment ("final causality," i. e., a feed-back mechanism which guides the selective process toward a new type which can exploit new environmental possibilities). It is the directive bias of the selective and exploitative factors which biologists now believe is responsible for the progressive, apparently teleological, character of evolution. In spite of the many dead ends, the interaction of all these factors results not only in the increasing adaptation of each species to its environ•• For a detailed account of the exchanges of energy involved in biological evolution see Albert L. Lehninger, Bioenergetics: The molecular bases of biological energy transformation (W. A. Benjamin: N.Y., 1965) . .. Op. cit., p. 105 sq. CAUSALITY AND EVOLUTION ment but also in the direction of organisms which are more and more complex, highly integrated, and relatively independent of their environment. Higher organisms have an" internalized environment." For example, mammals are able to maintain a constant internal temperature which makes it possible for them to remain active in heat or cold that compel reptiles to lie dormant. The culmination of this tendency to internalize the environment is found in man. By his intelligence man is able to survey his environment and to control it to a remarkable degree. Our man-made air-conditioning systems are an example of this humanization of the environment. It is most clearly seen in the wonderful development of the human brain as an organ which receives a maximum of information from outside, processes it extensively, and uses it to control and manipulate the body and the total environment. Another way to put this is that the " best adaptation to the environment is for an organism to become adaptable to changes in the environment," and the capacity to learn and to invent new ways of behavior is the highest form of adaptability. 25 Certainly in this sense the evolution of man seems to be a " greater coming from the less," i. e., a highly adaptable animal originating from less adaptable organisms. However, it should be noted at once that this progressive tendency of evolution culminating in man is not uni-directional. It does not result in a perfect hierarchy of forms in which the higher contains all that is in the lower forms. Thus, the autotrophic species (green plants) and the heterotrophic species (animals) are mutually dependent on each other. Animals could not live unless plants produced food by photosynthesis of which the animals are incapable, nor could most plants live without the supply of carbon-dioxide produced by animals. The plant kingdom and the animal kingdom are superior to each •• For a striking discussion of " adaptability as an adaptation " see George G. Simpson, C. S. Pittenrigh, and L. H. Tiffany, Life: An Introduction to Biology (Harcourt Brace: N.Y., 1957), c. 18 "The Evolution of Adaptation," pp. 488-458. 214 BENEDICT M. ASHLEY other in different respects, so that it is impossible to classify them in an absolute hierarchy of forms. Similarly, insects are a culmination of a line of evolutionary progress different from the parallel line which culminates in man. Thus, although there is a general progress in a vertical hierarchy of forms, it is overlaid and complicated by a horizontal or coordinate tendency by which each new level of organization spreads out and occupies all available environmental niches. The air is a niche which has been successively occupied by flying organisms belonging to very different generic levels of organization. There are flying fishes, reptiles, birds, and mammals, and also non-flying species at each of these same levels. Aristotle, the " father of biology," was already aware that living things cannot be fitted into any simple hierarchy of dichotomous forms. 26 The sense in which evolution produces the greater from the less is with regard to generic not specific levels of organization. 27 When the evolutionary trees provided by paleontology are drawn, the fact of horizontal branching does not eliminate the fact that there is also a vertical dimension of increasingly elabor•• " It is impossible then to reach any of the ultimate animal forms by dichotomous division." Parts of Animals, I, c. 3, 644a 9. See cc. and S, 5 following for his reasons. 27 This seems to be the basic difficulty with the well-known argument of Mortimer Adler (recently utilized by John N. Deeley, op. cit., C. VIII, pp. that an Aristotelian-Thomistic metaphysics requires that there be only five species of material beings, i.e., man, animal, plant, compound, element. Adler began with the Aristotelian dictum that " essences are like the integers." The integers form a perfect hierarchy in which a number totally contains all lesser numbers. Consequently, if we know the definition of man (i.e., a rational, sentient, living, compound, material substance), we know all the species less than man. But, at least in a Thomistic interpretation, Aristotle's dictum must be understood to apply to the hierarchy of existing beings only analogously, both because of the potentiality of matter and the potentiality of essence, from which mathematics and the mathematical concept of number abstract. Hence, Aquinas holds that only God, as the infinite Ens a Se, contains all the perfections of lesser beings, even to their specific differentiae. Among creatures the hierarchy is imperfect, so that the higher only contain the generic perfections of their inferiors. The potentiality of creatures make them finite, and finite being cannot contain " opposed perfections." Only in God is there a total coincidentia oppositorum. See Summa Theologiae I, q. 55, a. 1 ad 3. CAUSALITY AND EVOLUTION 215 ate and integrated organization. Nor is there any reasonable doubt that man, with his remarkable brain, marks a level of organization higher than any other, since no other organism is so perfectly the master of its environment. Now if we ask how this "greater" comes from the "less," modern evolutionary theory gives a clear answer. The proportionate cause of the emergence of new types or organisms of increasingly complex organization and independence of the environment is not any single law or force but a concurrence of many causes in an evolutionary event, or better, a history. A population of interbreeding organisms interacts with the ecosystem of which it is a part so as to evolve and differentiate into new reproductively isolated species, each of which develops an integrated type adapted to a special environmental niche, clearly distinguished from other populations for many generations. Thus nuclear, chemical, and biological evolution, although involving very different kinds of events, have this in common: atom, molecule, and organism are products of historical events no less complex and sequentially ordered than the entities which they produce. The new species is not a " greater emerging from the less," because the amount of information it contains in integrated form is no greater than the amount of information present in the historical evolutionary process. What is spread out in history is condensed, as it were, in the emerging new species. Sartre's saying that " man is his history " was not intended to express the truth of evolution, but it does. I am reminded of Mozart's famous remark that he could hear one of his compositions " all at once." PsYcHo-SociAL EvoLUTION The human organism exists in an interbreeding population, the human species, but this species is social in a special sense not found in other animals, at least in a developed form. This species lives by communication through a true language, i. e., one in which signs stand for universal, reflexive concepts. Fur- 216 BENEDICT M. ASHLEY thermore, it is social in the sense that it develops a culture which transcends determined or instinctual patterns of behavior and includes inventions which are transmitted for many generations not genetically but by acculturation and education. This power of communication and invention which rests on an internal and external language, and hence is a power of dealing with the environment, with other human beings, and with one's own behavior through symbols, we call human intelligence. It is the mode of operation of the human organism as a whole, but it is centered in the principle organ, the human brain. 28 Science is now attempting to understand the human brain on the analogy of an electronic computor, i. e., as a device for storing and retrieving information, ordering this information in new combinations, and regulating or correcting its own programmed behavior. 29 The computor, however, is not a living organism, and if man is to produce a " machine that thinks," it would seem that he must first produce a living machine and then develop it to the point that it can think. It is entirely possible, as far as we can see, that someday man will synthesize human, thinking beings out of non-living chemicals,S0 but to 28 For an extensive analysis of the present state of this question see Mortimer J. Adler, The Difference of Man and the Difference it Makes (Holt, Rhinehart, Winston: N.Y.), 1967, esp. c. 8, "The Pivotal Fact: Human Speech," p. ff. Also see Charles F. Hockett and Robert Ascher, " The Human Revolution," Current Anthropology, 5:3 (June, 1964), pp. 135-168. This does not preclude the possibility of the foreshadowing of language among non-human primates on which much study is now being done, see R. A. Gardner and B. T. Gardner, and D. Premock, "Language in Primates," Science, 165: 664 (1969). 29 See W. Ross Ashby, Design for a Brain (Chapman and Hall: London, John Wiley and Sons: N.Y., 1960; ed.). 30 See Neil P. Hurley, "The Coming of the Humanoids," Commonweal, 91:10 (Dec. 5, 1969), pp. who quotes the anthology ed. by William F. Nolan, The Pseudo-People, as saying "The birth of the first android, therefore is a lot closer to us than we might imagine. Artificial hearts, lungs and arteries are already being developed in science; the artificial brain is the next major step toward the creation of humanized robots." More seriously C. F. von Weizacker, the Relevance of Science: Creation and Cosmogony (Harper and Row: N.Y., 1964): "It is an ancient dream to make a human being. I do not see that our present knowledge proves that this is impossible. Probably, if we could build a man, it would be a horrible thing really to do it. It might be the final sacrilege, and its consequences CAUSALITY AND EVOLUTION 217 do this we must have all the information contained in the organization of the brain and that presupposes thorough understanding of the lower life processes as well. If it is possible for man to know himself so perfectly that he even understands the working of the brain by which he thinks and the process of thought itself, then this implies that human intelligence is a capacity for total reflexivity. To make ourselves, we must know to the very core just how we are constituted. All the information which is built into us by evolution in physical form must also be present in us in psychic or symbolic form, so that we can then use these symbols to reconstruct a physical man. It is this transformation of information from the physical to the intentional mode which is the body-mind polarity. 81 The evolution of human culture can be viewed as a process by which the human community is tending to this total, reflexive, and constructive self-knowledge. Cultural anthropology and world history have shown how man has step by step developed the symbolic systems and technological skills by which he has learned more and more to control his environment. Each step in discovering the nature of our environment has also meant a step in increased self-understanding, since the human species has evolved through the struggle with its environment. This is Teilhard de Chardin's "hominization" process. Man has moved from a self-understanding through metaphorical language (myths), through an understanding in terms of universal concepts (classical philosophy), to our efforts to understand ourselves in a scientific manner by reconstructing the course of evolution. Further, it seems likely that we are moving into a fourth period in which the reductionistic and rationalistic might be disastrous. Perhaps we are rightly afraid of it, and our fear takes the form of the belief that it is impossible. I think many of our beliefs are disguised fears. But the reason might just be that what you need to make a man is history; perhaps it cannot be done in less than four thousand million years," p. 140. 31 The notion of intentionality is common to many philosophies of mind. See Henry B. Veach, "Minds: What and Where in the World are They?" in Jordan M. Scher, ed., Theories of the Mind (The Free Press: N.Y., 1962), pp. 814-829. 218 BENEDICT M. ASHLEY restrictions of knowledge which have predominated during the scientific epoch will yield to a more integrated view of the world in which the complementarity of different modes of knowledge is accepted. Among other indications of this new stage of human thinking is the recognition by philosophers of science that science itself is a creative, humanistic mode of thought, not pure objectivity. Perhaps the term "creative" best describes this fourth phase of human self-understanding. 82 Human intelligence, therefore, includes and transcends chemical and biological evolution in that man comes to understand and control evolution in a creative way by processes that are not only physical but first of all symbolic. Man's behavior is penetrated by intentionality. It is here that his creativity resides, since once he understands nature he is not only able to reproduce it but to re-create it, to introduce genuine, freely chosen novelty into the world. The possibility of this intelligent, organic life originated among arboreal primate mammals who had a highly developed, internalized environment, an excellent nervous system with good vision and hearing, and who had an erect posture that freed the upper limbs, making for great mobility and capacity easily to survey and manipulate the environment and to communicate through gestures and vocal signs. Most important of all, such primates lived socially in a cultural rather than an instinctive insect-like society. 33 It is thought that in Africa arboreal apes were forced to the ground by environmental changes and began to communicate •• Comte's three-fold scheme of the development of human thought: the theological, the philosophical, and the scientific seems to have survived as one of the best ways of summarizing the development of human-thought modes, but we now tend to see it as cumulative not as an evolution in which later modes render the earlier obsolete. This understanding is itself an indication that we are moving in a fourth epoch. The developments in the philosophy of science referred to are stated brilliantly in a popular article by Paul Feyerabend, " Experts in a Free Society," The Critic (Nov.-Dec., 1970), pp. 59-69. •• See Hockett and Ascher, op. cit. and V. Reynolds, The Apes (E. P. Dutton and Co.: N.Y., 1967), pp. 106 ff. Reynolds thinks an important element in social behavior was " festival gatherings " which have been observed among apes. CAUSALITY AND EVOLUTION 219 by true speech. It is probable that this true speech and the symbolic, social mode of behavior which it implied proved of such survival value even when these capacities were still very rudimentary that natural-selection pressure worked in favor of the rapid evolution of the large brain which makes it possible for homo sapiens to turn his environment into a culture. 34 Thus, if we attempt to reconstruct the situation in which man emerged it is not sufficient merely to posit biological evolution operating in the sort of situations which explain the origin of sub-human species. It is necessary also to posit in the ecosystem factors which account for symbolic behavior. Unless proto-man began to act symbolically by some type of true language, it was not possible for natural-selection to begin to shape him in the direction of homo sapiens. It seems established that a human infant cannot develop speech or humanly intelligent behavior except in an environment which includes symbolic behavior. Does it not then seem difficult to imagine how the first men began to speak in a situation where symbols, intentionality, were not a part of the ecosystem in which he lived? 85 It is necessary to suppose, therefore, that the first men originated in a situation which was more than a biological "environment" because it already had the character of a rudi•• Hockett and Ascher, op. cit. argue that rudimentary but true speech may have been possible when the brain was still close to the level of present non-human primates, and this seems supported by Gardner, Gardner, and Premock, op. cit. There are a great variety of current theories on the development of tool-making and speech, e. g., Grover Krantz, "Brain Size and Hunting Ability in Earliest Man," Current Anthropology, Vol. 9, 5 (Dec. 1968), pp. 450-51 argues that man's hairlessness and large brain is the result of persistent hunting because to pursue an animal for a long time man must be able to keep cool while running and to remember what he is chasing. See also the variety of opinions expressed in the discussion of Donald L. Wolberg, "The Hypothesized Osteodontokratic Culture of the Australopithicinae," ibid., 11: 1 (Feb. 1970), pp. 23-27, and the discussion by John Lewis and Bernard Towns, Naked Ape or Homo Sapiens: A reply to Desmond Morris (Garnstone Press: London, 1969). 35 On the steps from primate to human use of signals see John E. Pfeiffer, The Emergence of Man (Harper and Row: N.Y., 1969), C. 19, "The Evolution of Language," pp. 392-414. 220 BENEDICT M. ASHLEY mentary " culture." This means that it included features which in relation to proto-man were capable of functioning as signs, symbols, physical bearers of intentionality. It is here that modem child psychology is of help as it begins to unravel the ways in which the child develops as a person in a world of meanings which require symbolic expression, although the child is at first aware only of physical sensations. Somehow these sensations perceived in a social context act as symbols through which the child communicates with others and develops a selfunderstanding and personal identity as he gradually learns to speak. The original sensations are only at the biological level, but they gradually acquire intentionality and become symbols. 36 Man must have emerged in a social setting in which speech and thought were somehow already pre-contained. Today a child originates in a culture in which the necessary information for his thought is pre-contained in the artifacts of the culture, with its verbal and non-verbal symbolism. This culture is gradually internalized by the child by a process of acculturation or " education." Therefore, the event out of which man arose must have been already a "meaning-full" event, so that the environment appeared to man as a "world" (in the sense of that term used by phenomenology) ,07 as something filled with 86 On current views as to how children learn to speak see Hermina Sinclair-deZwart, "Developmental Psycholinguistic" in David Elkund and John H. Flavell, eds., Studies in Cognitive Development: Essays in Honor of Jean Piaget (Oxford University Press: N.Y., 1969), pp. 315-336. Piaget and his followers insist that a child first learns to think and then to talk. He learns to think by exploring and interacting with the environment, first learning to recognize the continuity and permanence of objects and then to " know that he knows " these objects. Only then is he ready to name and talk about them. Also Heinz Werner and Bernard Kaplan, Symbol Formations An Organismic Developmental Approach to Language and the Expression of Thought (Clark University: John Wiley and Sons, N.Y., 1963), which emphasizes that language does not originate in merely pragmatic activities of the child but in cognitive ones (see esp. the analysis of Helen Keller's experience on p. 110 ff.) and requires the social experience of "sharing" a common interest in objects, pp. 71 ff. 87 On meaning of term " world " in phenomenology see William A. Luijpen, 0. S. A., Existential Phenomenology (Duquesne University Press; E. Nauwelaerts: Louvain, 1960), pp. 15-33. CAUSALITY AND EVOLUTION wonder and meaning, not as an assemblage of brute facts or mere " stimuli." This world communicated something to man, as it continues to do, although this meaning remains ever perilously balanced on the knife-edge of ambiguity. The existentialists who today declare the universe to be absurd are saying in effect that the waves of entropic doom are eating away at the foundations of the livable world in which man can feel "at home." Man's effort to find meaning in the world and to express it in words seems ever about to be engulfed by the rising tide of random noise. " Life is a tale told by an idiot, full of sound and fury, signifying nothing .... " THE UNIVERSAL AND THE INDIVIDUAL At this point it is necessary to raise a very old question, that of realism and nominalism. When we discuss novelty and emergence, are we speaking of a species or of an individual? Darwin's great book was called The Origin of Species, but obviously what originates and is genuinely new and unique in the world is always an individual. When novelty has spread to many instances it is already losing its freshness. It is true that for the biologist the problem of evolution is the origin of a new inter-breeding population reproductively isolated from others. For the cultural anthropologist what emerges is new functionally integrated cultures. Even at the molecular and atomic level there is a real sense in which there are "species," since not only is there a quantitative identity of composition and structure between all H20 molecules, or all silver atoms, but there is also a tendency of like atoms or molecules to form homogeneous crystals or liquids. Yet even in these collective realities in which all the members are very much alike, there is also a genuine uniqueness and novelty in the individual. Some have imagined that every electron was the same as every other electron except for its spatio-temporal location. However, the fact that the behavior of sub-atomic entities can be predicted only by statistical laws seems to indicate that these BENEDICT M. ASHLEY entities cannot be perfectly described by a general definition. 88 The existence of isotopes among the elements and the complexity of molecular structures also indicate that the periodic table of the elements and the chemical formulae of compounds is only a rough classification of the vast variety of chemical entities, so that no two atoms or two molecules need be thought of as absolutely identical in structure. Once the organic level is reached, no two individuals within the same species are found to have identical genetic composition. Even" identical twins" perhaps differ in the cystoplasmic genes which are at least a secondary factor in the development of the individual. 39 At the psycho-social level we see that not only are cultures in a constant state of development and interchange, but that a culture has power to survive and progress to the degree that it helps each individual member achieve a unique personal identity and a power of creative invention. 40 The direction of evolution, therefore, is toward the emergence of unique persons. If men achieve self-understanding, so that each individual feels that he must " make himself," then each human person will become a work of fine art, and like such works, will be unique. What then becomes of the classical distinction which underlies all Western philosophy between essence and accident? 88 See the discussion of the statistical nature of quantum-mechanics in Ernest Nagel, The Structure of Science (Harcourt Brace and World, Inc.: N.Y., 1961), pp. 805 ff. For macroscopic events there are universal deterministic laws, but these reflect the cancelling out of irregularities in sub-atomic events which are governed only by statistical laws. Nagel shows that these statistical laws do not reflect a breach of the principle of causality at the sub-atomic level but simply the fact that we can only observe and predict the behavior of aggregates, not of individual particles. •• See Amram Scheinfeld, Twins and Supertwins (J. P. Lippincott: Philadelphia, 1967) and Helen L. Koch, Twins and Twin Relations (University of Chicago, 1966), which show that although identical twins as they mature grow more alike physically, they are capable of fully distinct personality. •o See Charles A. Moore and Aldyth U. Morris, eds., The Status of the Individual in East and West (University of Hawaii Press: Honolulu, 1960), a symposium in which noted philosophers of all the great world traditions struggle with the question of the dignity of the individual person and seem to agree that all these traditions converge in an attempt to establish the free, conscious, responsible individual. CAUSALITY AND EVOLUTION 228 Must we finally accept nominalism? Nominalism took from Aristotle the conviction that nothing is real but the individual. It also took from him the axiom that " science is of the universal." It then drew the conclusion that science, (i.e., essential knowledge of reality) is impossible, hence science is an affair of names designating a collection of accidents and not of essential natures. In the evolutionary perspective a different possibility emerges. " Science " for Aristotle was a matter of universal knowledge, because our knowledge of the essence of things is possible only by abstraction or generalization. He did not deny, however, that individuals do in fact have unique essences but only that an intellectual knowledge of this uniqueness is possible for us. 41 Now we begin to see that the theory of evolution provides us with a way to understand the uniqueness of the individual in an essential manner. Aquinas, basing himself on Aristotelian principles, held that God, because he made each unique thing, has an essential understanding of the individuaJ.4 2 Evolutionary theory aims at achieving such a practical knowledge of the individual that we can say what information was required to produce this unique organism, beast or man. This explains also why modern science does not insist, as Aristotle did, that scientific knowledge should be "certain and necessary." Our reconstruction of the history of an individual can never be perfect, and hence modern science, which seeks to know the individual through evolutionary process, is always conjectural, probable. Yet this does not mean that everything we know about an individual is only probable. 43 There is no Posterior Analytics, I, 31, 87b 27 sq. •• Summa Theologiae, I, q. 14 a. 11. Aquinas argues that "it pertains to our (human) perfection to know the singular," hence God must also; but while man knows the singular by a knowledge which is partly of intellect, partly of sense, God knows the singular by a purely intellectual knowledge. Aquinas further argues th,at, since God produces the creature in its totality, including the matter by which it is individuated, he must know it is individual. •• Nothing is more generally accepted by modern science than that all scientific knowledge is only probable, which usually ends by saying that all knowledge is only probable. Thus " the historical development of physics led to the result that 41 224 BENEDICT M. ASHLEY real doubt that this organism named Mr. Jones, my neighbor, is a human being and not a chimpanzee. Or that this liquid is water and not sulphuric acid. The hypothetico-deductive mode of thinking came to dominate science precisely when it became apparent that to understand the solar-system in which we live it is necessary to look beyond pure universal laws to the contingent situation, i. e., that the solar system is made up of these particular planets with these particular orbits and velocities, none of which is predictable from any general law but only from the history of the solar system. It then became apparent that the universal law of gravitation can be verified only by assuming particular, historic situations. 44 There is never any problem in discovering universal laws of nature, i.e., which might be true in some hypothetical universe. The problem is always to know what laws are operative in our universe and that universe is the production of an evolutionary history. We can, however, formulate a universal law of gravitation, and we the probability concept is fundamental to all statements about reality. Strictly speaking, we cannot make a single statement about reality the validity of which can be asserted with more than probability." Hans Reichenbach, The Theory of Probability (University of California Press: Berkeley, 1949). This view rests on the notion that certitude is a property of analytic propositions, while synthetic propositions (the only ones that concern "reality") are verified by induction (or prediction) which can never yield universal and necessary truth. To this it can be replied: (1) there are alternatives to the positivistic epistemology of science; (2) it is a reductio ad absurdum to say that no statement about reality is certain, because then no statement could be probable either, since determinate probability implies some certitudes as Bertrand Russell showed in Human Knowledge (Allen and Unwin: London, 1948), p. 416; see the discussion of Reichenbach, C. L. Lewis, and Nelson Goodman in The Philosophical Review, 61, 2 (April, 1952), pp. 147-175. Nelson gives the best argument again Russell, stating "That we have probable knowledge then, implies no certainty but only initial credibility." (p. 163) However, this merely pushes the difficulty back to the basis of credibility. How is a thing credible unless it at least has some determinate probability? Michael Polyani, Personal Knowledge (Harper Torch books, Harper and Row: N.Y., 1962), C. 9, pp. 269-298, "The Critique of Doubt " shows that the fear of certitude is not even a good heuristic principle for the sciences. «Thus Newtonian science seemed to give a wonderfully adequate account of the solar system, but it was soon realized that in fact this explanation presupposed a history. Hence, Kant and others began to attempt to reconstruct this history in the form of the "nebular hypothesis." CAUSALITY AND EVOLUTION 225 can even be certain that this law is somehow operative in our actual universe, but there is always a range of uncertainty when we come to say just how this law is operative in our world, because our knowledge of the world situation in its historic development remains always imperfect. The world itself is essentially imperfect just because it is in historical process. Does this mean that the essence-accident distinction, or the notion of a species, a universal essence, is finally eliminated? No, because there still remains an important sense in which all human beings have a common" human nature," but we must understand this abstraction as having its foundation in the real inter-relation and inter-action between unique individuals. Their uniqueness is not " accidental " to this community but essential. 45 Among human beings community in nature is found not so much in mere similarity of structure and faculty as in the mutual inter-communication which makes it possible for them to share a common culture. Similarly, on lower levels, species is to be found more in common process than in identity of structure or potentiality. Animals form a single species because they inter-breed. Perhaps we could say that molecules and atoms are the same species because they can form crystals. In each case the individual brings to this interaction its uniqueness, and it is this unique contribution which is of the utmost significance. In human society it is the individual personality which makes for flexibility and progressive change. In biological evolution it is the mutation and the novel combination of genetic factors in the individual that makes progress possible. Even in chemical evolution chemical process begins with some unique encounter of particles in which a crystal begins to form or a reaction begins to take place in a determinate direction. Furthermore, in the unique individual there remains a real difference between what is essential and what is accidental. The •• Aquinas touched on this when he insisted that God could never have made any two things in the universe exactly alike, since mere repetition adds nothing to the perfection of the universe. On this see Charles De Koninck, " In Defense of St. Thomas," Laval Theologique et Philosophique, 1: !'l (1945), pp. I. 103, pp. 25 fl'. BENEDICT M. ASHLEY essence is that structure and fundamental set of activities which provide the individual with a stable identity and continuity. This identity is, of course, not eternal, but it persists through many states, conditions, situations which modify it in its relation to other things without destroying it. Finally, without a doubt, we can distinguish in the thing between its essence and its " properties," since there is an empirical difference in a thing between its primary structures and functions and those that are secondary. 46 Thus, in an animal the brain and heart are essential organs and metabolism an essential function for its survival in a way that its limbs or its power to digest are not, yet all are necessary to its integrity, full function, and survival. NATURE AND HISTORY I have emphasized this shift from a science of the universal to an evolutionary science of individuals, because it entails a shift from a science of " nature " to a science of " history," the significance of which, it seems to me, scientists themselves have not fully realized. For the classical tradition science deals with nature, which is to be understood in terms of universal natural laws, while history deals with the accidental and is incapable of real scientific understanding. 47 In an evolutionary scheme, however, the " nature " of reality is profoundly historical. Nature is the history of the emergence and disappearance of unique individuals. They originate in unique events, participate in unique events, and then are destroyed in the entropic flood which finally overwhelms all that is unique and distinctive. There are as many unique " natures " as there are unique individuals. Nevertheless, these individuals •• The point is often missed that when Aristotle spoke of essence, properties, and accidents, he had in mind a method of definition based on the empirical study of primary and secondary functions in an organism. See De Partibus Animalium, which is the best exemplification of what the logical doctrine of the Posterior Analytics meant in actual application. 07 For a discussion of the way in which the concept of "nature " tends to give way to the concept of "history" in modern thought see, R. G. Collingwood, The Idea of Nature (Oxford, 1945), pp. 174-177. CAUSALITY AND EVOLUTION 227 are grouped into interacting collectivities of similar things (an inter-breeding population, for example) and have originated in similar events. Knowledge of the individual is possible by the reconstruction of the historic happenings from which they have emerged in terms of the concurrence of " general laws " which are expressive of the fundamental cosmic forces of gravitation, electromagnetism, etc. Each of these historic events is seen also as embodying past history which has prepared the new event in an evolutionary manner by which the past is partially built into the present. The " information " required to produce each unique individual and which gets built into its essential structure is contained, spread out as it were, in all the lines of history that converge in the creative event out of which that individual emerges to play a role in further historic happenings. THE GREATER FROM THE LEss: 11m NEW FROM THE OLD The foregoing analysis has attempted to establish two points: (1) Evolution in all its phases requires no other forces in the nature than the fundamental cosmic forces of gravitation, electromagnetism, and the nuclear forces. (2) The specification of these general forces necessary to explain how they can produce new and ever more complex systems can be accounted for not in terms of special natural laws but in terms of history, of the concurrence of forces in special situations and in appropriate sequence. Consequently, evolution does not contradict the principle of causality, since when new things emerge, the matter, the energy, and most important, the information necessary to build them are all accounted for in a satisfactory way by current scientific theories. Even the emergence of men as spiritual beings, that is, capable of intuition, speech, choice, invention all rooted in symbolic behavior, can be explained in these terms, if we can historically account for a situation in which man began to be aware of meaning in the world, as a child begins to understand language. 48 •• The papal magisterium (notably Pius XII in Humani Generis and E. Dhanis, S. J., and Jan Visser, C. SS. R., The Supplement to a New Catechism [Herder 228 BENEDICT M. ASHLEY However, this way of understanding evolution raises a deeper question: how do we explain history? We cannot have recourse only to universal natural laws, since what above all requires to be explained is precisely the element of novelty and uniqueness by which history transcends the regular, stable pattern of events which natural law summarizes. History presupposes and includes natural and universal laws and does not violate them, but it is not deducible from them. Yet, the existence of evolutionary processes is empirical evidence that history is not without intelligibility. The truth is that historical explanation is inevitably mythical in character. 49 By this I mean that, when we attempt to "exand Herder: N. Y., 1969], p. 518, reporting the results of the papal commission which examined the " Dutch Catechism ") insists on " the special creation of the human soul." As Dhanis and Visser point out, however, this by no means excludes the role of the parents (and hence of the whole evolutionary process) in the generation of the total human person as such. In any theistic view of evolution the creativity of the created agents is always a participation in the creative action of God. At each new state of evolution this participation takes on a new mode. In the generation of the human person the parents truly share but in a very different manner than do merely animal parents. At the same time the mode in which God creates the human person more direct and, as it were, personal than the manner in which he produces non-persons. The continuity of the evolutionary process is not broken by the origin of man, since evolution is from the beginning rooted in God, but it enters onto a strikingly new and special phase at this point. In the origin of man, a person, God appears on the scene, as it were, in person and directly. The Yahwist document in Genesis with marvelous insight, conveys this sense of God's special presence in the creation of man and woman. For a discussion (not altogether satisfactory in my opinion) of the magisterial documents, see Robert North, S. J., Teilhard and the Creation of the Send (Bruce: Milwaukee, 1966), esp. cc. 7-8, pp. 204-289. •• I use "myth" here much as it is defined by Melville, J., and Frances S. Herskovits, in Dahomean Narrative (Evanston, lli., 1958), "A myth is a narrative which gives symbolic expression to a system of relationships between man and the universe in which he finds himself." (p. 81) History is a narrative obviously, and when this narrative is understood as humanly meaningful it expresses man's relationship to the world. This expression, although factual and rooted in empirical evidence, critically tested, is nevertheless " symbolic " since experienced external events are an epiphany of the inner reality of man's existence. That history is mythical does not mean that it is a regression to primitive modes of thinking but rather that it synthesizes the mythical stage of thought with philosophical and scientific modes of thinking, thereby overcoming their limitations. CAUSALITY AND EVOLUTION plain " historical events, we can do so only by attributing to them some meaning. Purely " empirical " historical explanations simply come down to descriptions of the various lines of natural causality that concurred in the event, but the concurrence must either be called merely a coincidence, mere chance (and then there is no explanation) , or we must see in it some kind of importance, some kind of meaning. For example, the assassination of a president can be empirically explained in terms of sociology, psychology, ballistics, and physiology, but these explain only why some president might be assassinated, for not a few are. It does not explain the assassination of John Kennedy rather than Lyndon B. Johnson, and it is precisely this unique event that is to be explained. Consequently, we feel compelled to make some sense out of it mythically, that is, by seeing in John Kennedy and his strange story something of special human meaning. Similarly, accounts of cosmic or biological evolution always are presented with the implied myth that all of this is remarkable because it has finally produced us, human beings capable of understanding what has happened. Confronted with this obvious element of myth in evolutionary theory, empirical scientists are methodologically compelled to deny its importance and to insist that science stops short with tracing the various strands of causality that enter into the events of evolutionary history, without attempting to make evolution as such intelligible. In such a picture it appears simply as the back-eddy of the entropic decline of the universe. The myth appropriate to evolutionary theory, however, need not be that of creationism in the sense of the occasional intervention of a God conceived as another force added to the cosmic forces to reverse entropy, nor as an inherent vital force in the manner of panpsychists like Julian Huxley, 50 nor merely •• Religion without Revelation, rev. ed. (Harper: N.Y., 1957), "If as is the case, mind and matter coexist in the higher animals and man; and if, as is now certain, the higher animals and men are descended from lower animals, and these in turn from lifeless matter, then there seems to be no escape from the belief that all reality has both a material and a mental side, however rudimentary and below the level of anything like our consciousness that mental side may be." (p. 41) 280 BENEDICT M. ASHLEY as an Omega point drawing the universe as for Teilhard de Chardin, 51 nor as a Creator who has no power to share his creativity with others, as for Thomas Aquinas, 5 2 but as a recognition that the universe is a place in which creative events constantly occur as a basic feature of all natural processes, in which man's own creativity is a summation of this cosmic creativity. Undoubtedly, this myth implies a Creator, but one who shares his creativity with the world and with man in history. BENEDICT M. AsHLEY, 0. P. The Institute of Religion Texas Medical Center Houston, Texas 61 See Robert North, S. J., op. cit., c. 4, "Creation as Alpha Point," pp. 83-118. "The Alpha Point (apparently Teilhard does not actually use the term) must have exhibited a millionfold more intensely that ' Complexity latent in simplicity ' which every ovum exhibits. Moreover, this Alpha Point must, like Omega, possess some special identifiability with Christ or God." (p. 116) This, in my opinion, is the weak point of Teilhard's magnificent myth; it tends to reduce the historicity of the universe, with its creativity, freedom, and play, to a natural process, the inevitable unfolding of seed (which is the Stoic idea, if the Alpha Point is the primordial chaotic matter) based on the inevitable emanation of the universe from the Logos (which is Neo-Platonism, if the Alpha Point is Christ). But modern evolutionary theory does not support this lawful interpretation of the phenomena of evolution. •• It is of course true that Aquinas denies that God can share creatio ex nihilo with creatures, because a created agent cannot produce without acting on preexisting matter (cf. Summa Theol., I, q. 45, a 5). But if "creation" and "creativity" are used (as common usage has it today) not in view of the material but the final cause, i.e., the novelty and uniqueness of what is produced, then even in Thomistic metaphysics God can and does share his creativity with his creatures. The shift of point of view, however, is significant. Aquinas as a philosopher saw the universe in Aristotelian terms in which history and novelty are only secondary features of the world; although as a Christian theologian he realized this was not the whole story. In the foregoing I have used the terms " creation " and " creativity " in the broad sense in which creation ex nihilo is the mode of creativity proper to God, while creatures participate in this only in their own mode as secondary causes acting to perfect the existing universe. ARISTOTLE AND AQUINAS ON THE FREEDOM OF THE MATHEMATICIAN I T IS NOT unusual to find contemporary mathematicians who claim to have an unlimited degree of freedom in their discipline. Some even maintain that they can study (at least symbolically) anything and everything. The mathematician, they say, simply posits any definitions he pleases concerning any group of symbols and relations among them, defines the operations thereupon, and then proceeds logically. Needless to say, these mathematicians do not consider themselves bound in any way to treat entities which resemble real physical things. (Indeed, they not infrequently give the impression that they have little or no concern as to whether their mathematical considerations have any application to physical reality.) Nor do they consider mathematics to be a science of abstracted quantity in the traditional sense, fearing that to assert this would needlessly restrict the range of their science. The purpose of this essay is not to pass judgment on the claims of today's mathematicians regarding freedom in their science. I intend rather to investigate the philosophies of mathematics of two much earlier men, Aristotle and Thomas Aquinas, both of whom considered mathematics to be a science of quantity, in order to determine the degree of freedom each allowed the mathematician in his science. Specifically, I will show that the medieval theologian's doctrines contain significant advances in this area over those of his Greek predecessor. Moreover, it will be suggested that to designate mathematics as a science of quantity, as these two thinkers do, still allows for a tremendous degree of freedom on the part of the mathematicianthough it is not claimed that either man envisioned, or would agree with, the degree of freedom claimed by some mathematicians today. 231 THOMAS I. C. ANDERSON THE QUESTION Let us begin by returning to a point just mentioned, that for both Aristotle and Aquinas mathematics is considered to be a science of quantity. Let us hasten to add, however, that the quantity studied in mathematics is, according to both thinkers, a quantity not found as such in real things but a quantity abstracted from such things. As is well known, this abstraction involves mentally setting aside all the nonquantitative atributes of things and retaining only their quantitative ones. In his famous text of the M etaphyf!ics, a text which Thomas repeats with approval in his Commentary, the Stagirite speaks of the mathematician "stripping away" all features of things but their quantitative attributes, ... the mathematician investigates abstractions (for before beginning his investigation he strips off all the sensible qualities, e. g., weight and lightness, hardness and its contrary, and also heat and cold and other sensible contrarieties, and leaves only the quantitative and continuous, sometimes in one, sometimes in two, sometimes in three dimensions, and the attributes of these qua quantitative and continuous, and does not consider them in any other respect, ... 1 Of course, it is precisely because of this mental abstraction, or subtraction, that the quantities studied in mathematics are said by both men to acquire their specific features as immobile, nonsensible, free from time and place and from sensible matter, and often possess less than three dimensions. And yet, though the features of abstract mathematical quantities and quantified things are radically different, this does not mean that these quantities are totally dissimilar; indeed, both philosophers stress that it is in fact the quantities of physical things that the mathematician studies. However, they add-it is not as quantities of phyl!ical things that they are studied. One text of Aristotle's which makes this clear is the following: 1 Metaphysics, XI, 3, 106la !'l9-36. Thomas's commentary is In XI Metaphysics, L. 3, !'l!'lO!'l. FREEDOM OF THE MATHEMATICIAN 233 Obviously physical bodies contain surfaces and volumes, lines and points, and these are the subject-matter of mathematics .... Now the mathematician, though he too treats of these things, nevertheless does not treat of them as the limits of a physical body, nor does he consider the attributes indicated as the attributes of such bodies. That is why he separates them; for in thought they are separable .... 2 Thomas Aquinas makes exactly the same point in his commentary on this passage. He affirms that the mathematician and the natural philosopher both treat the same things, but not in the same way. The mathematician and the natural philosopher treat the same things, i. e., points, and lines, and surfaces, and things of this sort, but not in the same way. For the mathematician does not treat these things insofar as each of them is a boundary of a natural body, nor does he consider those things which belong to them insofar as they are the boundaries of a natural body. But this is the way in which natural science treats them .... Because the mathematician does not consider lines and points, and surfaces, and things of this sort, quantities and their accidents, insofar as they are the boundaries of a natural body, he is said to abstract from sensible and natural matter. 3 Clearly then for both men the mathematician does treat real quantities but not as real. And this brings us to the heart of the question of this study. If mathematical quantities are nothing more than abstracted real quantities; if they are gained simply by "stripping away " all nonquantitative attributes of things, does this mean that for Aquinas and Aristotle the mathematician is limited in his science to treating objects which in their quantitative features resemble the quantitative attributes of physical things? It is true that both men give as examples of geometrical objects rather elementary figures, circles, triangles, angles, etc., which could easily be gained by abstraction from similarly figured sensible things. 4 But does this mean that they believe that • Physics, IT, 193b • In II Physics, L. 3, 160-61. • Heath points out both in A History of Greek Mathematics (Oxford: Clarendon 234 THOMAS C. ANDERSON mathematics is limited to just such quantities, quantities which bear almost a one-to-one relation to real quantities? If this is the case, then clearly the freedom of the mathematician is severely restricted. In order to answer this crucial question we will turn to a more detailed consideration of what psychologically is actually involved in mathematical abstraction according to both men. This will aid us in determining just how free each considers the mathematician to be in his act of abstraction. First, Aristotle. II. THE FREEDOM oF THE MATHEMATICIAN AccoRDING TO ARISTOTLE In the famous text of his Posterior Analytics where he describes the general procedure of obtaining the universal from sense experience 5 Aristotle refers to the presence of what he there calls "memory." Animals which have memory, he says, are able to retain sense impressions and so provide for themselves some stability in the changeable data of sense experience. Actually what Aristotle there calls memory he will later more precisely designate imagination. 6 Thus the role of imagination in all abstraction (using this term now in a wider application meaning the mental act of obtaining the universal from the sensible particular) is evident. This would mean, of course, that imagination is present in mathematical abstraction, too, for it also begins with perception of changing sensible particulars. However, and this is a point which should be emphasized, Aristotle never refers to imagination as having a particular or special part in mathematics or mathematical abstraction. 7 Press, 1960), I, 341 and Mathematics in Aristotle (Oxford: Clarendon Press, 1949), p. 1, that Aristotle refers only to the most elementary geometrical figures. As for Aquinas, I can only state that in my reading of him I have found nothing that would invalidate this same conclusion. • Posterior Analytics, II, 19, 99b 86-100b 1. • De Anima, III, 8. • Some authors, particularly those inclined to read Aristotle through the eyes of St. Thomas, ignore this fact. See for example, Mere St. Edouard, " La division FREEDOM OF THE MATHEMATICIAN It may be that he simply did not develop this point, or, of course, it may be that he did not think imagination had any special role in mathematical abstraction. An elaboration of this second possibility is in order. According to the Stagirite, imagination" has the objects of sense for its object." 8 Imagination is said to be the act of a sense faculty (though just what sense faculty is not clear) 9 and is clearly distinguished from the acts of the mind, affirmation and negation, and the knowledge of incomposites. 10 But the objects of mathematics according to the Stagirite are not sensible for, as we noted, the mathematician leaves out the proper sensibles. Though his abstraction is based upon perception of the common sensibles, it is not these qua sensible which he studies. Since mathematical quantities are not sensible, it would apparently follow that they are not imaginable either, for, as was said, imagination is the act of a sense power, it has "the objects of sense for its objects." Mathematicals, then, would be knowable only by the mind. We might note in support of this last statement that Aristotle calls the matter of mathematicals "intelligible"; he never refers to it as " imaginable." 11 And yet, from another point of view it would seem that this very notion of intelligible matter indicates that mathematical aristotelicienne des sciences, selon le professeur A. Mansion," Laval Theologique et Philosophique, XV (1959), 228 and M-V. Leroy, "Le savoir speculatif," Revue Thomiste, XL VIII (1948), 808 ff. Frere Augustin-Gabriel, "Matiere intelligible et mathematique," Laval Theologique et Philosophique, XVII (1961), 187, admits Aristotle does not have the doctrine and says one must " read between the lines " to find it. 8 De Anima, III, 8, 428b 18. • In his On Memory and Reminiscence, Aristotle states that imagination is an " affection of the sensus communis." (1, 450a 12) In the De Somnis, on the other hand, he distinguishes between that power which is the controlling or judging sense faculty (apparently the sensus communis) and that which presents images (2, 460b 16-18; see also 8, 461 18-81). Furthermore, he explicitly identifies the imaginative faculty with the sensitive faculty qua imaginative, though he does not say what this sensitive faculty is. (1, 459a 15-16) 10 De Anima, III, 8, 482a 9-14. 11 For a discussion of Aristotle's notion of intelligible matter, consult my article "Intelligible Matter and the Objects of Mathematics in Aristotle," The New Scholasticism, XLTII (1969), 1-28. THOMAS C. ANDERSON quantities must be imaginable, for intelligible matter for Aris, totle is viewed by him precisely as the principle of individuation of mathematical forms. 12 Since individuals are attained directly only by sense and not by mind which is directly of the universal/3 individual mathematicals could be grasped directly only by a sense faculty. But since the quantities studied in mathematics are not possessed of any proper sensible features, they cannot be grasped by the exterior senses. Would it, then, be imagination which grasps them? To be sure, Aristotle does speak in the Metaphysics of individual mathematicals as known by " intuition." But when we come to the composite thing, e. g., this circle, i. e., one of the singular circles, whether sensible or intelligible (I mean by intelligible circles the mathematical, and by sensible circles those of bronze, or of wood) -of these there is no definition, but they are known with the aid of intuition or of sensation; and when they pass out of this actual cognition it is not clear whether they are or not; but they are always expressed and known by the universal formula. 14 But is this intuition imagination? Some have so interpreted it; 15 Aristotle himself does not say. This much is clear from his text; it is not an act of direct sensation, nor is it an act of mind, that which grasps the definition, the universal formula. In the absence of statements to the contrary, it is logical to presume that it is imagination which is meant. 16 Though exactly how such entities could be imaginable, in view of the fact that they lack sensible qualities, is still a question. But if Aristotle never mentions it, why this stress on my part on imagination? The reason is, and admittedly we are Metaphysics, VII, 11, 1036b 35-1037a 4. De Anima, III, 4, distinguishes sense knowledge from intellectual. See explicitly 429b 10-33. Also see Metaphysics, VII, 10, 1036a 1-12 and Posterior Analytics, 12 18 I, 31, 87b 36-40; II, 19, 100a 15-100b 1. u Metaphysics, VII, 10, 1036a 1-8. '"St. Thomas Aquinas interprets this intuition as imagination in In Vll Metaphysics, L. 9, 1494-95. 16 Diego Pro, "Filosofla de la matematica en Arist6teles," Sapientia, XI (1956), 99, discusses Aristotle's obscurity on this point. FREEDOM OF THE MATHEMATICIAN 237 looking ahead to Thomas Aquinas, if individual mathematical objects have their locus in imagination, it would follow that there is a certain degree of freedom on the part of the mathematician in regard to his objects. The Stagirite himself refers in various places to the freedom men have in imagining. 17 If the locus of individual mathematicals were the imagination it would seem to follow that the mathematician would be free to deal with objects which do not closely correspond to anything found in the physical world. There would be no reason to limit him to simply studying abstracted quantities which resemble the quantities of things, but he could treat quantities which he himself had devised in imagination which have no one-to-one correspondence to any physical quantities. Indeed, an epistemological basis could be provided for the tremendous development in modern times of nonrepresentational mathematical systems such as the nonEuclidean geometries. Now it is true, as we mentioned earlier, that the Stagirite always cites as examples of geometrical objects :figures which could easily be gained by abstraction from similarly figured sensible things. But our question is, does Aristotle in his philosophy of mathematics hold that the mathematician must limit himself to such easily abstractable entities? In attempting to answer this question it might be helpful to realize that it is only the most general and basic elements of the genus quantity, e. g., lines, planes, etc., that he explicitly mentions as obtained by abstraction. 18 Apparently all other mathematical objects are to be constructed out of these basic abstracted entities. No science, Aristotle says, demonstrates the very existence of the subject with which it deals. 19 The mathematician, then, apparently at first posits the existence of these most basic eleDe Anima, III, 8, 427b 18-20; 11, 484a 9. Thomas Greenwood, "Aristotle on Mathematical Constructibility," Thomist, XVII (1954), 89 and 98. The fact that these elements are so general and hence so easily abstracted may well be the reason why Aristotle says that little experience is needed in order to become a mathematician (Nicomachean Ethics, VI, 8, 1142a 16-19). 19 Posterior Analytics, I, 10, 76b 8-28. 17 18 238 THOMAS C. ANDERSON ments of the genus quantity gained by abstraction 20 and then through construction using these elements goes on to " demonstrate the existence" and investigate the properties of all the other objects he dectls with. (Aristotle does say that before the properties of a mathematical object can be investigated it must be demonstrated that that object exists. 21 The actual practice used at his time to " demonstrate " the existence of a particular mathematical quantity was to construct it.) 22 Our question is then is the mathematician free to use these basic elements to construct (and hence demonstrate the existence of) any figure he desires-any figure that is, whose very existence is not self-contradictory (like square circles)? Certainly the most basic abstracted elements, those whose existence is simply posited, are so general as to be able to form any figure or number. And yet the Stagirite never states that the mathematician has the freedom to construct these elements into any non-self-contradictory objects he pleases. In fact, it is just the opposite as we have said, the only objects of geometry he cites are those which closely resemble physical magnitudes. Could this indicate that he never thought of allowing the mathematician freedom to construct and treat objects not resembling quantified physical things? 23 On the other hand, it might be suggested that Aristotle would never have intended such a limitation of mathematics since numbers by their very nature as more abstract than magnitudes are clearly not able to be closely bound to physical quantities. 10 Ibid., 76b 8-7. "'Ibid., 76b 8-10. •• This is pointed out by Heath, ... Greek Mathematics, I, 887 and 877; Greenwood, " ... Mathematical Constructibility," 89-98; H. G. Apostle, Aristotle's Philosophy of Mathematics (Chicago: University of Chicago Press, p. Euclid, for example, always constructed a particular mathematical entity before making use of it in a demonstration; for example, only after he had constructed a square did he go on to study it; only after he had constructed a perpendicular to a straight line did he use lines at right angles to one another. Though Aristotle does not explicitly say what he means by the demonstration of the existence of a mathematical, it seems most reasonable to conclude that the Stagirite has in mind the common Greek practice of construction. •• Greenwood, " ... Mathematical Constructibility," 98-94 and "The Characters of the Aristotelian Logic," Thomillt, IV seems to hold this position. FREEDOM OF THE MATHEMATICIAN In reply to this last point we must bring out some interesting features concerning the way the Greek mathematicians of Aristotle's time tended to look upon their science. In the first place, it should be pointed out that among the Greeks arithmetic was closely tied to geometry and to actual physical magnitudes. In general number theory was treated by them in the framework of geometry. 24 From the time of the Pythagoreans on, numbers were often represented geometrically. 25 Euclid, for example, (about a generation after Aristotle) represents numbers by straight lines, planes, squares, cubes, etc. 26 This is especially true of irrational numbers, e. g., the square root of two which could not be assigned a definite numerical value but could be represented by magnitudes. 27 Furthermore, the Greeks had no notion of imaginary numbers or of negative numbers, numbers which could hardly be said to correspond to numerical aspects of physical things. Instead, the only numbers they used were the ordinary whole numbers and ratios, 1, 8, i, t, etc. Interestingly enough, it is not until Diophantes (late third century A. D.) that we find any mathematical equations used which involve numbers raised to any power above three, the cube. 28 Apparently, because there is no physical •• Heath says, " With rare exceptions ... the theory of numbers was only treated in connexion with geometry, and for that reason only the geometrical form of proof was used, whether the figures took the form of dots marking out squares, triangles, gnomons, etc. (as with the early Pythagoreans), or of straight lines (as in Euclid VII-IX) .... " ( ... Greek Mathematics, I, 16) Heath also points out that even problems which we would call algebraic were only solved geometrically by the Greeks. (Mathematics in Aristotle, p. 223, also ... Greek Mathematics, I, 379 ff. See also his explanation of "geometrical algebra," pp. 150-154.) See also M. R. Cohen and I. E. Drabkin, A Source Book in Greek Science (Cambridge, 1958), p. 1 and p. 14, n. 1. •• Heath, ... Greek Mathematics, I, 76 ff. •• Heath, ibid., I, 16, 98 and 379 ff.; Mathematics in Aristotle, p. 222. •• The square root of two would be represented simply by drawing a square of sides one and one whose diagonal would then be the square root of two. Many authorities feel that it was the discovery of the irrational that turned the Greeks in the direction of geometry and accounted for the " geometrizing" of number. See, for example, Marshall Clagett, Greek Science in Antiquity (New York: Abelard-Schuman, Inc., 1955), p. 57 and Cohen and Drabkin, op. cit. •• Cohen and Drabkin, A Source Book ... , p. 25. 240 THOMAS C. ANDERSON magnitude which has more than three dimensions, the Greeks felt any higher power would be meaningless. The very terms they used in arithmetic, some of which are still in use today, probably show more than anything else the geometrical framework in which this study was carried on. Our terms like square (a number is squared when it is multiplied by itself once) and cube (a number is cubed when it is multiplied by itself once and this in turn multiplied by the given number) clearly indicate their geometrical origin. (Plato even refers to square and cube numbers as planes and solids respectively.) 29 Indeed, numbers were referred to by the Greek mathematicians as cubes, squares, as oblong, triangular, polygonal, diagonal, as sides, as rectilinear, scalene, spherical, circular-all fundamentally geometrical terms. 80 A certain kind of proportion between numbers was called a geometrical proportion. 81 Various quadratic equations were solved geometrically using the construction of figures. 32 Clearly, as we said, Greek arithmetic was closely tied to geometry and then to physical magnitudes. Since Aristotle, too, uses some of these geometrical terms in reference to numbers,S 3 this could indicate that he shares the views of his countrymen that arithmetic is closely related to geometry and thus that numbers somehow relate to physical magnitudes. Thus, the arithmetician also may be considered by the Stagirite to be restricted to constructing and hence treating objects in some way corresponding to physical things. 34 •• The reference to Plato is in Heath, ... Greek Mathematics, I, 89. 30 All these expressions can be found between pages 76 and 117 in Heath, ... Greek Mathematics, I. Heath, ibid., I, 85. •• Heath, Mathematics in Aristotle, p. 223; ... Greek Mathematics, I, 379 fi. B. L. van der Waerden, Science Awakening (New York: Science Editions, 1964), pp. 118-126. 33 Physics, III, 4, 203a 13-15; Posterior Analytics, I, 12, 78a 4; Nicomachean Ethics, V, 3, 1131b 12-15. A particularly significant text is in the Metaphysics, V, 14, 1020b 3-6, where he refers to number in one or more dimensions, " ... numbers which are composite and not of one dimension only, viz. those of which the plane and the solid are copies," [italics mine] and of other similar features of numbers which he calls their " qualities." •• I do not mean to imply by this that Aristotle denies the specific distinction 31 FREEDOM OF THE MATHEMATICIAN True, he in no place explicitly states that there is this restriction, on either geometry or arithmetic. Yet neither does he give an indication that he feels that the mathematician, either geometer or arithmetician, is free to construct or consider objects which do not in some way correspond to physical quantities. And most important, though there is nothing in his philosophy of mathematics which positively precludes this freedom, compared to St. Thomas, there is precious little that could form the epistemological basis for such freedom. It seems reasonable to conclude, then, in the absence of statements to the contrary, that Aristotle in this respect is a man of his time, i.e., he considers the objects of mathematics to be idealized representations of actual physical quantities and the mathematician to be restricted to such objects. In concluding this section we should note the one text that some claim gives some indication (though I believe it to be extremely slight) that the Stagirite has some recognition of the freedom of the mathematician. 35 Aristotle refers to the necessity present in mathematical science as of a hypothetical type. He states specifically that " It is impossible, for instance, on a certain hypothesis that the triangle should have its angles equal to two right angles .... " 36 On a different hypothesis, if a straight line, for example, is defined in a different way, the value of the interior angles will be two right angles. Does this imply that either hypothesis is permissible? To generalize, does this mean that the mathematician is free to construct and define his figure any way he pleases? Note clearly that Aristotle never between arithmetic and geometry, between number and magnitude. Just the opposite. For instance, he criticizes the Pythagoreans for turning units into magnitudes. Nevertheless, even though he does assert the specific difference between the objects of arithmetic and of geometry, there is no indication that this leads him to disagree with his contemporaries who consider number in a geometrical context as representative of magnitudes. Numbers certainly are not magnitudes; they cannot be reduced to magnitudes; but still they can represent (Aristotle calls them copies in text of previous footnote) magnitudes. •• Two who make this claim are Greenwood, " ... Mathematical Constructibility," 91-93, and Heath, Mathematics in Aristotle, p. 101. •• De Caelo, I, U, 28lb 5-6. 242 THOMAS C. ANDERSON says this. Indeed, it seems impossible to say he is even implying that either hypothesis is permissible. He is saying simply that if a different hypothesis were chosen different conclusions would follow. He never says that either one can be chosen. At best the passage shows that he does recognize that different conclusions follow from different premises, but nowhere does he really say that the premises are a matter of free choice. Indeed, in the light of all we have already seen, viz., that the only geometrical objects he mentions are those resembling real quantities, and that numbers, too, at his time corresponded to physical things and their quantitative features, the indication that he broke with the prevalent view of his time that mathematical objects are limited to representation of physical quantities seems very slight. Let us now consider the philosophy of mathematics of Thomas Aquinas with a view toward seeing if he has any more explicit recognition of or epistemological basis for the freedom of the mathematician. III. THE FREEDOM OF THE MATHEMATICIAN AccoRDING TO AQUINAS We should remind ourselves at the very beginning of the areas of agreement of Thomas and Aristotle. For Thomas, like his predecessor, mathematics is a science of quantity abstracted from physical things, i. e., of real quantity not considered qua real. Does this mean that he limits mathematics to quantities closely resembling real things? We must reply that it is only such quantities that he, like Aristotle, explicitly mentions. And yet there are doctrines of his, doctrines not explicitly expressed by the Stagirite, that seem to provide the basis for a greater freedom on the part of the mathematician. One such doctrine has to do with mathematical abstraction itself and the objects which are its result. In one text, Thomas describes these objects in a manner that indicates that he is much more aware than Aristotle of their great independence from (even though they are based upon) physical things. FREEDOM OF THE MATHEMATICIAN 248 Aristotle, of course, clearly affirmed that mathematical quantities exist as such (i. e., with their peculiar mathematical characteristics) only in the mind of the mathematician. Aquinas not only agrees with this but goes on to describe the objects of mathematics in terms which he uses to describe beings of reason. 37 He explains that, like the logical notions of genus, species, etc., a mathematical is not simply a likeness of realities existing outside the mind but instead is a consequence of man's way of knowing some things outside the mind. Things of this type, he says, are intentions which our intellect devises (adinvenit) because of its knowledge of extramental things. And he adds, significantly, the proximate foundation for such intentions is not " in things, but in the intellect, however the remote foundation is the thing itself." 38 The expressions used here by Aquinas to describe mathematical entities are the same as those he uses in other places to describe beings of reason. 89 This is not to say that mathematical quantities are simply created by man's intellect, for the intellect's act is of course rooted in physical things. But this is to say that that which immediately gives mathematicals their reality, that which is their proximate foundation, is the activity of the mind itself. (This is not, of course, the case with the beings studied in either physics or metaphysics. They exist in their own right apart from any act of a human intellect.) I would like to suggest a contrast, or at least a difference in emphasis, between Aquinas and Aristotle on this point. The difference as I see it is that, compared to St. Thomas, Aristotle tends to view the mathematician as more passive in his act •• In I Sententiarum, d. q. 1, a. S c (Parma edition, VI, p. (Incidentally, this passage was written by Aquinas late in his life and inserted in his Commentary. It should, therefore, give his mature position on the subject. On this point, see A. Maurer, "A Neglected Thomistic Text on the Foundation of Mathematics," Medieval Studies, XXI (1959), 187.) •• In I Sent., loc. cit. •• In In IV Metaphysics, L. 4, 574, for example, St. Thomas states that in contrast to a natural being an ens rationis is strictly speaking an intention which reason devises from the objects it considers, an intention which is not found in the nature of things but is a consequence of the consideration of reason. THOMAS C. ANDERSON of abstraction. To be sure, he " strips away " all the nonquantitative features of physical things-and this " stripping " itself is an activity on his part. Yet when it comes to the actual grasping of physical quantity the connotation is that the mathematician simply grasps what remains after all nonquantitative features are removed. He simply " liberates," so to speak, the real quantities of things from their sensible, mobile, material existence, and proceeds to study them-real quantities but not qua real. Now it is certainly true that Aquinas in many places, especially his Commentaries, speaks of the mathematician's abstraction in the same terms that his Greek predecessor uses. (See, for example, texts cited in my first Section.) Nevertheless, in the passage discussed in the previous paragraph he shows, I believe, more recognition of the activity of the intellect in the actual production of mathematicals. The mathematician does not just grasp real quantity stripped clean, he does not simply study a likeness of real quantities, rather his object is directly a product of his intellect's own activity-granted that the activity has its remote foundation in the experience of physical quantities. Now in putting stress on the intellect as the proximate foundation of mathematicals, in stressing therefore that these entities are not mere likenesses of physical things, in describing mathematicals as similar to beings o£ reason, it seems to me that St. Thomas indicates much more clearly than did the Stagirite that he recognizes that the mathematician's activity of abstraction, and hence the object of his science, is not simply a replication of real physical quantities. And there are other doctrines o£ Aquinas which also have as their result the freeing of the mathematician from strict dependence on physical quantities, doctrines which also bring more precision into Thomas's statement that "the intellect" is the proximate foundation of mathematicals. 0£ great significance is his teaching on the role o£ imagination in mathematics. We will first discuss that role in general and then its specific relevance to the question of freedom in mathematics. As is well known, the imagination for Aquinas plays a vital FREEDOM OF THE MATHEMATICIAN 245 role in all knowledge, for he believes there can be no intellectual knowledge without the phantasms it supplies. 40 Of particular import to our topic, however, is the special role it has in the science of mathematics. Unlike Aristotle, Thomas leaves no doubt that he holds that mathematicals, some at least, are imaginable. His texts which assert this are numerous; I will cite only one. When sensible characteristics are removed there remains something which is apprehended by the imagination .... Now mathematicals are of this sort.U Of course, in speaking of mathematicals being grasped by the imagination, Thomas is referring to individual mathematicals, not to mathematical essences which are grasped only by the intellect. We noted in the previous section that in one place Aristotle spoke of individual mathematicals as grasped by "intuition," and distinguished this from mathematical essences which are grasped by the mind. We noted also that he defined this intuition no further. St. Thomas clearly refers this intuition to imagination. 42 Individual mathematicals as such are not attained by external senses, nor as individual are they present in the intellect which is directly of the universal. Yet as individual they must be grasped by a sense power-the imagination.43 And yet, to say that individual mathematicals are imaginable presents problems of its own. We noted in the previous section that Aristotle never asserts that mathematicals are imaginable, •• Summa Theologiae, I, q. 85, a. 1 c; In III De Anima, lect. 12, 781. u De Trinitate, q. 6, a. 2 c. Other texts which affirm that mathematicals are imaginable are: De Trinitate, q. 6, a. 1 c and a. 2 c; De Veritate, q. 15, a. 2 c; In VII Metaphysics, lect. 10, 1495; In III De Anima, lect. 8, 715-6; Summa Theol., I, q. 7, a. 3 c; In III Physics, lect. 7, 341; and In VI Nic. Eth., lect. 7, 1210, 1214. •• In VII Metaphysics, lect. 10, 1494-5. •• In the following passage Thomas clearly distinguishes the individual mathematicals which the imagination grasps from the essence of these mathematicals which is grasped by the intellect. "In the case of mathematics it can be shown that that which knows the essence, i.e., the intellect, is distinct from what apprehends mathematical objects themselves, i.e., the imagination." (In III De Anima, lect. 8, 715) 246 THOMAS C. ANDERSON and we suggested why. The imagination is a sense power, but in his abstraction the mathematician leaves aside sensible qualities. How then can nonsensible mathematicals be grasped by the imagination? Because of this difficulty, some commentators have suggested that the mathematicals which Thomas designates as imaginable are not really the individual, quality-less, non-three-dimensional objects of mathematics but only individual sensible objects which come very close to being like them, e. g., a colored line made up of very small dimensions but not actually colorless or unidimensional. 44 But this interpretation is contrary to too many explicit statements by Aquinas. In no uncertain terms he asserts that mathematical objects (in other words, the qualityless, uni- and bidimensional entities) are in the imagination. For example, in the De Trinitate he asserts: Mathematicals themselves come under the senses and are objects of imagination, such as figures, lines, numbers and the like.45 And there are countless places where he makes the same assertion.46 In fact, mathematics is the most certain science, he says, precisely because its objects are free from sensible matter and yet imaginable. 47 The problem, therefore, remains-how can objects lacking sensible qualities be apprehended by a sense power? The solution must lie in showing that Aquinas believes mathematicals to be sensible; in other words, in showing that mathematical abstraction does not leave aside all the sensible attributes of quantified physical things. Bear in mind that quantity is a common sensible and that the common sensibles, u Some who hold this view are Bernard Lonergan, "Note on geometrical possibility," Modern Schoolman, XXVII (1950), 127; E. Winance, "Note sur !'abstraction mathematique selon saint Thomas," Revue Philosophique de Louvain, LIII (1955), 509; F. Collingwood, "Intelligible Matter in Contemporary Science," Proceedings of the American Catholic Philosophical Association, XXXVIII (1964), 110. '"De Trinit., q. 6, aa. 1, 2 c. •• See the texts cited in footnote 41. 07 De Trinitate, q. 6, aa. 1, 2 c. FREEDOM OF THE MATHEMATICIAN 247 like the proper sensibles, are directly, not incidentally, sensed/' 8 Would it not be possible then for the imagination, which is able to combine and divide imaginary forms and so end up with images " even of things not perceived by the senses," 49 to present an image of an originally apprehended physical thing which image would be of only part of that thing, viz., of some or all of its dimensions minus all of its proper sensible qualities? This ability of the imagination would explain how Thomas can say in reference to mathematicals that " even when sensible characteristics are removed there remains something which is apprehended by the imagination." 50 At least some mathematicals are sensible, and hence imaginable, because they are the abstracted dimensional quantitative features of physical things. 51 However, these imagined dimensions are mathematical and not physical because by the power of imagination they have been separated from the other sensible characteristics of physical things and may have even been reduced in dimension from the physical three dimensions. What I am suggesting in effect is that the imagination itself performs an abstraction on the common sensibles; after all, it is not only the intellect which abstracts according to Aquinas. 52 •• Summa Theol., I, q. 78, a. 3, ad •• Ibid., a. 4 c. 80 De Trinitate, q. 6, a. c. 81 I say " at least some " (not all) mathematicals are sensible and hence imaginable. In In Ill De Anima, lect. 7, 758, Thomas, following Aristotle, apparently says that points, which are dimensionless units having position, and units, which are both dimensionless and positionless, precisely because they lack all dimension cannot be grasped by any sense power but are only known mentally by negation. It would follow that a number, which is a plurality of units, would not be imaginable, though some symbol representing it could be. "' To abstract, St. Thomas says, is to consider one entity without another when they are actually together in reality. (De Trinitate, q. 5, a. 3 c) Since each sense power considers only what is proper to it and omits all other features of the material thing, it can truly be said to abstract. Cf. Summa Theol., I, q. 85, a. 3, One should not identify this abstraction of the imagination with the second degree of abstraction, else he will end up with the difficulty Winance has, "Note sur !'abstraction mathematique ... ,'' 507 fl'. He clearly sees that merely eliminating sensible qualities by the imagination does not result in an object of a different 248 THOMAS C. ANDERSON Incidentally, the fact that St. Thomas continually refers to mathematicals as "nonsensible " does not contradict this conclusion. For in making such statements it seems clear that the sensible features from which he considers the mathematician to abstract are the accidents which follow after the accident of quantity. "Accidents," he says, befall substance in a definite order. Quantity comes first, then quality, then passions and action. So quantity can be considered in substance before the sensible qualities, in virtue of which matter is called sensible, are understood in it. 53 Clearly, the sense qualities he is talking about, those which follow quantity, are only the proper sensibles. Since the mathematician does not abstract from the accidents of quantity neither does he abstract from all sensible features, for quantity is a common sensible. The dimensional figures studied by mathematicians are not sensible inasmuch as they lack all proper sensible qualities. Since it is " the sensible qualities [which follow after quantity] in virtue of which matter is called sensible," the mathematicals can be called nonsensible. They are sensible, and hence imaginable, however, inasmuch as they are abstracted dimensions, for dimensions are sensible. 54 degree of intelligibility, or indeed in any intelligibility at all. Therefore, because he has identified this abstraction of the imagination with the second degree of abstraction, he denies it any validity as a means of distinguishing the inteiligible objects of the sciences, 5IO. The degrees of abstraction for St. Thomas refer to abstraction by the intellect from matter and motion, De Trinitate, q. 5, a. I c. 53 De Trinitate, q. 5, a. 3 c. See also Summa Theol., I, q. 85, a. I, ad 54 In the previous section in order to emphasize the fact that Aristotle never refers to mathematicals as imaginable, we pointed to his use of the term inteiiigible, rather than imaginable, to designate the special kind of matter found in mathematicals. Some have in fact suggested that since some mathematicals are imaginable according to Aquinas he should have designated their matter as imaginable, rather than retaining the Aristotelian designation of it as intelligible. (Winance, "Note sur !'abstraction mathematique ... ," 508-510) However, such a change of terminology is unnecessary, since in its most fundamental sense inteiligible matter designates for Aquinas substance as the substrate of only the accident of quantity. But he notes, " the sense powers do not reach a comprehension of substance,'' (De Trinitate, q. 5, a. 3 c) only the intellect does. Therefore, substance as the substrate of quantity is properly termed "intelligible" matter. On this point, see my article, FREEDOM OF THE MATHEMATICIAN 249 It follows from all of this that the imagination has an especially important role in mathematics for Aquinas-a role which, as we have said, is never mentioned by the Stagirite. For, in addition to providing a stable image from which the universal can be abstracted (this it does in all abstraction) ,55 in mathematics it furnishes to the intellect perfectly appropriate individual mathematicals, which simply cannot be found in nature, individuals from which the mathematical essence can then be abstracted. The direct senses are able to supply an appropriate object for the abstraction of physical essences; for the intellect's abstraction the imagination simply provides a stability in the changing objects grasped by sense. But the direct senses themselves cannot provide a perfectly appropriate object for abstraction of mathematical essences, for mathematical objects as such are not attainable by these senses. Rather the imagination, through its abstraction discussed above, provides the proper object, the suitable individual mathematical quantity, from which the mathematical essence can be abstracted. By locating individual mathematicals in imagination, Thomas has served to further liberate the objects the mathematician studies from a close dependence on physical quantities. This freedom is even more clearly brought to the fore by his assertion that the judgments of mathematics need only terminate in the imagination. In a passage of the De Trinitate Aquinas distinguishes between the origin and the termination of man's knowledge. 5 6 "Now the beginning of all our knowledge," he writes, "is in the senses "; however, the termination of knowledge is different in each of the three general kinds of science, "Intelligible Matter and the Objects of Mathematics in Aquinas," The New Scholasticism, LXIII (1969), 555-576, in which I distinguish the various meanings of intelligible matter in Aquinas. 55 De Trinitate, q. 6, a. 2. On this point one might profitably consult the articles by C. De Koninck, "Abstraction from Matter: Notes on St. Thomas's Prologue to the Physics," Laval Theologique et Philosophique, XIII (1957), 140-1 and W. Gerhard, "Natural Science and the Imagination," Thomist, XVI (1953), 190-216. 58 De Trinitate, q. 6, a. 2 c. 250 THOMAS C. ANDERSON metaphysics, mathematics, and physics. " Judgment in mathematics," he asserts, " must terminate in the imagination." I take this to mean that these judgments are true of, refer to, imaginable entities. Thomas explains that, if a judgment is true of realities which are only intelligible, it must stop, " terminate," in the intellect, as do metaphysical judgments; it could not refer to imaginable or sensible realities and still be true of purely intelligible entities qua intelligible. Thus, if a judgment is true of imaginable entities which are not sensible, it must stop, " terminate " in the imagination: ... because, when sensible characteristics are removed there remains something which is apprehensible by the imagination, we must judge about such things according to what the imagination reveals. 5 1 Finally, a judgment true of sensible realities, as in physics, must stop in the senses. To repeat, since mathematicals according to St. Thomas are neither sensible things of nature, nor purely intelligible realities, but (some at least) are imaginable, a judgment about these objects cannot terminate in the senses, nor simply in the intellect, but rather must do so in the imagination. In order to be true, judgments dealing with imaginable objects must refer to what the imagination presents. There is another way of looking at this notion that judgments about mathematicals terminate in the imagination. According to Aquinas, in the mental act of judging we grasp the existence of an object, we grasp an entity as it is. This is distinguished from the act of apprehension which only grasps the nature of a thing and not its act of existence. 58 Now since some individual mathematicals exist as such by and in the imagination, it stands to reason that the act of judgment must refer to, terminate in, that which the imagination presents. In this connection, we mentioned in the previous section that Aristotle maintains that before a mathematical entity can be examined it must be " demonstrated " that it exists. Though he never said exactly how demonstrations of existence take place, judging from the common practice of his time he is referring to 17 Ibid. •• Ibid., q. 5, a. S c. FREEDOM OF THE MATHEMATICIAN 251 the construction of these objects. Thomas also speaks of demonstrations of existence in mathematics, and he designates them as "operational" since they are by construction. 5 9 Now since this construction can only be of individual mathematicals (it makes no sense to speak of " constructing " a mathematical essence), it must take place in a sense power. But the only sense power which grasps individual mathematicals as such is the imagination. Hence, the locus of the construction of individual mathematicals must be this power. In other words, it is in the imagination that mathematicals are shown to exist, and this, of course, squares with the previously mentioned point that judgments of their existence must terminate in and only in the imagination. Of course, as we have pointed out, if the mathematician's judgments need only refer to imagined entities, this makes the mathematician very free in his choice of objects and the operations he performs on them. While in physics and metaphysics the intellect must conform itself to sensible being and intelligible being respectively as they are in reality, in mathematics the intellect need only conform to beings which exist in the mathematician's imagination. Both this position and the earlier one which stressed the intellect's activity as the proximate foundation of the objects of mathematics clearly show that Aquinas considers the mathematician to be free from treating only objects which resemble physical things. Yet how free? Is the mathematician free to construct any mathematical he can and then go on to investigate its properties? Perhaps it would be of some help to look more closely at the passage in which Aquinas speaks of mathematical demonstrations of existence-for this passage also sets forth clearly his analysis of the general procedure of the mathematician in his science. (One will note that it is the same general procedure Aristotle recognized.) •• In I Posterior Anolytics, lect. 2, 5. Thomas also refers to construction in mathematics as the means of demonstrating the existence of mathematicals in In II Posterior Analytics, lect. 6, 4. .25.2 THOMAS C. ANDERSON There is supposed in these [mathematical] sciences those things which are first in the genus of quantity such as unity and line and surface and other such. These being presupposed, certain other things are sought by demonstration, such as the quadrilateral triangle, the square in geometry, and other such things. These demonstrations are said to be, so to speak, operational, as is: On a given straight line to construct an equilateral triangle. This having been proved, certain further passions are proved, as that its angles are equal or some other such thing .... 60 The mathematician supposes that those entities " which are first in the genus quantity" exist (in imagination) and using these entities goes on to construct, to demonstrate " operationally " certain figures or numbers composed of them. These constructions show that these composite objects do exist, and he then proceeds to prove the properties of these figures or numbers. As for the freedom of the mathematician in his demonstrations of existence, it would seem that he is at liberty to construct in imagination any mathematicals he can, and this would apparently mean any quantities whose existence is not self-contradictory. As far as the most basic quantities are concerned, these seem to present no limitation either. Certainly, as St. Thomas says, these elements-units, points, lines, and surfaces-are ultimate in the genus quantity. Nothing more basic could be abstracted and " supposed " by the mathematician-and indeed, since they are the most basic quantities, how could the mathematician do anything else but "suppose " them? 61 These certainly contain no built-in limitation as to what the mathematician can study, for they are able to make up any mathematical object in the imagination. They present no limitation other than that the mathematician must deal with quantity. 60 In I Posterior Analytics, lect. 5. We might point out here that it is not up to the mathematician as such to investigate the real foundation of those elements whose existence he assumes. He simply takes them and goes to work from there. It would seem to be the province of the philosopher of nature to show the basis in reality of these quantitative elements and hence to show that they are not mere mental fictions. 61 FREEDOM OF THE MATHEMATICIAN IV. CoNCLUSION We have stressed the fact that, because individual mathematicals are located by Aquinas in the imagination and hence mathematical constructions of existence and scientific judgments need refer to only such entities, the mathematician is radically free in his choice of objects, and more specifically he need not consider himself limited to dealing with mathematical quantities which closely correspond to and/or resemble physical quantities. We have also suggested that this freedom is indicated by Thomas's teaching that it is the intellect's activity, not things, which is the proximate foundation of mathematical objects and, following from this, his description of mathematicals as similar to beings of reason (though one might quarrel with Aquinas and propose that it would be more accurate to say rather that the imagination's activity under the direction of the intellect is the proximate foundation of individual mathematicals) . Though these doctrines provide an epistemological foundation for the freedom of the mathematician from physical things as far as his object is concerned, it remains the case that, like Aristotle, Thomas also refers only to mathematical quantities which in fact resemble physical quantities. The only geometrical figures and solids he mentions are those of Euclidean geometry. He too refers only to real numbers (not negative or imaginary) , and he refers to them in terms which may indicate that they are still being viewed as related to physical magnitudes. For example, he refers to numbers as surfaces, as solids, as two and three-dimensional, as squares, cubes, etc. (though he clearly recognizes that such words are used metaphorically) ,62 and he never refers to a number raised to any power higher than three, the cube. It is true, of course, that by the thirteenth century mathematical objects were not considered to be simply idealized representations of actual physical quantities, at least not to ""In V Metaphysics, lect. 14, 974; lect. 16, 989-991. 254 THOMAS C. ANDERSON the degree that they were in Aristotle's day. For one thing, the algebra had been introduced by the Arabs and put into Latin by some of the earliest translators. 68 According to historians of mathematics, the most prominent mathematics book in Latin during Aquinas's time was probably the Liber Abaci by Leonardo Fibonacci (Leonardo of Pisa) , published in 1202, and it was devoted to arithmetic and elementary algebra. Though it contained no recognition of negative or imaginary numbers, 64 it did have, in addition to the algebra, the use of the zero and of fractions and operations upon them. 65 Furthermore, during Aquinas's day symbols were more and more being used to represent quantities; in fact, one who pioneered this was a friar, Jordanus de Nemore, who in 1222 became general of the Dominican Order. Certainly, the use of symbols, instead of figures or numbers related to figures, to stand for quantities, implies a view of mathematics which sees its objects removed from direct correspondence to physical quantities. In fact, the use of the zero alone indicates this, for it has no physical counterpart, and, indeed, for this reason it was,looked upon by many as suspect. It is difficult to believe that Thomas Aquinas, who in other areas was so keenly cognizant of the newly introduced knowledge of his time, would not at least have been aware of these developments in the mathematics of his day. Indeed, one author speculates that St. Thomas as a student used in his •• Maurer, "A Neglected Thomistic Text ..• ," 185. •• First used by Rafl'ael Bombelli, 1550. (D. Struik, A Concise History of Mathematics [New York, 1948], p. 114) •• For information on this book, its author, and the general state of mathematics in the thirteenth century, consult F. Cajori, A History of Mathematics (New York: The Macmillan Company, 1951), pp. 117-125; H. Eves, An Introduction to the History of Mathematics (New York, 1961), pp. 209 fl'. See also T. Greenwood, Etudes sur La Connaissance Mathematique (Ottawa: Ottawa University Press, 1942)' pp. 66 fl'. •• Greenwood, Etudes sur ... , p. 65. However, Vernon Bourke, in his more recent work, Aquinas' Search for Wisdom (Milwaukee, 1965), says that the quadrivium was no longer followed in the thirteenth century because masters proficient in the mathematical sciences were scarce, p. 22. And he gives nothing to support the view that Thomas was taught the "new mathematics." FREEDOM OF THE MATHEMATICIAN 255 studies the Liber Abaci, for it was a commonly used text in the quadrivium. 66 Be that as it may, I know of no place in Aquinas's writings where he explicitly refers either to the algebra or to the zero or to the use of symbolism in mathematics. He, like Aristotle, refers only to figures and numbers which correspond to physical quantities. Nevertheless, in spite of this, it seems clear to me that the aforementioned epistemological doctrines of Aquinas go much further than Aristotle's toward allowing great freedom to the mathematician. It may well be that Thomas himself was barely aware of the consequence of his own position. But it still remains that his teachings which emphasize that it is man's intellectual activity not physical things which is the proximate foundation of mathematical objects, and in particular his stress on the role of the imagination as that in which individual mathematicals are demonstrated to exist and in which mathematical judgments terminate, are at best only implied in Aristotle. And it is these doctrines which serve to liberate mathematics from any requirement of dealing with quantities which match real quantities. THOMAS Marquette University Milwaukee, Wi8consin c. ANDERSON IS "SELF-VALIDATING" RELIGIOUS EXPERIENCE LOGICALLY POSSIBLE? M OST PHILOSOPHERS nurtured on the canons of empiricist methodology have looked with more than a little collective distrust upon the claim that "selfvalidating" encounter-experiences with God constitute the unimpeachable foundation for theological commitment, i. e., that there is a uniquely religious mode of knowing. 1 To begin with, and as pointed out by Frederick Ferre, the logic of encounter seems to be guilty of some serious question-begging 2 insofar as the very category of encounter entails an objective referent that is encountered. Nonetheless, proponents have continued to insist that" encounter" is the only term equal to the intensity and authority of such experience. Ferre argues further that the person to person "I- Thou" encounters which function as the analogical base for putative encounter with the divine are fraught with difficulties. For example, since illusion is often present in "encounter," how can we ever know that a putative encounter-experience is ever veridical as opposed to subjectivist? How disillusioning, after a prolonged period of silent " encounter " with a friend, to have the spell broken by hearing a sudden snore issuing from the other "Thou" who, it turns out, has been asleep the whole time! How shattering to discover that someone who has been throughly known, it seems, through " encounter " is really quite a different person from the one formerly imagined! 3 1 Cf. C. B. Martin, "A Religious Way of Knowing," in New Essays in Philosophical Theology, edited by Anthony Flew and Alasdair Macintyre (New York: The Macmillan Co., 1955), pp. 76-95, for a very poignant critique of the "unique" logic of religious encounter. • Frederick Ferre, Language, Logic and God (New York: Harper and Row, 1961)' p. 94. • Ibid., p. 103. 256 " SELF-VALIDATING " RELIGIOUS EXPERIENCE fl57 One response to Ferre here might be that, since the experience with a snoring friend could not legitimately be considered an encounter-experience, it thereby presents no significant threat to the logic of encounter. Simply because there are fake practicioners of medicine, this does not at all entail that the practice of medicine as such is bogus. Consequently, insofar as there can be encounter-experiences (whether with persons or God) , would they not thereby be veridical? Surely the notion of a necessarily veridical or self-validating experience (if logically intelligible) would serve to clarify what is meant by "encounter-experience " as opposed to the " ordinary " kind of experience so often prone to error and illusion. However, the issue of religious encounter as such can surely be addressed quite independently of the exceedingly problematic notion of self-validating experience. While many have argued vigorously in support of the plausibility of direct experience of God, they have argued just as forcefully against the notion that the mode of verification and corroboration of such experience is disparate from that of experience of other sorts. George Mavrodes, for example, has contended that With respect to corroborating experience of other sorts, by other people, the status of religious experience is fundamentally similar to, not different from, that of other types of experience. 4 Hence, insofar as the status of religious experience is not one which is epistemically unique, then while social corroboration might not be forthcoming in a given case of putative religious experience, it would always be (logically) relevant to the consideration of its veridicality. However, such corroboration or lack of it could have no logical relevance whatsoever in that regard for those who have maintained that religious experience is self-validating, i.e., that the experience as such carries with it its own guarantee of infallibility. Hence, according to the logic of self-validation, nothing beyond the experience-as-such could conceivably (in principle) call its veridicality into ques• George I. Mavrodes, Belief in God (New York: Random House, 1970), p. 77. 258 ROBERT A. OAKES tion. However, for Mavrodes and thinkers like him, this does not mean that I am obligated to abandon my putative religious experience as subjectivist (or nonveridicfl.l) simply because I cannot get others to share it. On the contrary, testing procedures cannot always be employed even with regard to experience other than the putatively religious, but this does not at all mean that we are duty-bound, in such cases, to regard the alleged experience as erroneous rather than veridical. I may claim to see a wolf in the brush/ which, due to the speed and initiative of the wolf, my friends are unable to see upon rushing to the appropriate spot. Suppose there is no way, regardless of how hard I try, to enable them to see the wolf. Must I treat my claim to have seen a wolf as subjectivist rather than veridical? Surely not. Checking procedures both succeed and fail for all types of experience, and, consequently, the failure to achieve social corroboration with regard to any given case of putative encounter-experience with God is no more a reason for construing that experience as subjectivist than it would be for so construing the cited case of the wolf in the brush. Rather, as pointed out by Mavrodes, not every veridical experience is capable of corroboration; hence, to demand it is " simply to exhibit a foolish disregard for the relevant facts." 6 However, even though there can be veridical experiences which we cannot corroborate, this does not at all entail that social testing procedures can be dismissed as irrelevant in principle to the veridicality of any putative experience, including the putatively religious. Hence, the significant implication of Mavrodes' position in this regard is that there is not a unique logic of religious knowing; rather putative religious experience can be verdical without being necessarily verdical or self-validating. Consequently, it would be a most serious mistake to identify those who have argued the plausibility of direct experience of God with those who have argued the epistemological uniqueness or self-validating character of such experience. The two issues • Ibid., p. 79. • Idem. " SELF-VALIDATING " RELIGIOUS EXPERIENCE 259 are clearly separate even though many thinkers have failed to treat them as such. Nevertheless, to claim that social corroboration is not logically superfluous to the veridicality of religious encounter-claims, i. e., to reject the claim that religious experience is epistemically unique, is to invite the rather standard but still cogent observation that such corroboration has not, in fact, been very frequent. Consequently, this might help to explain the emphasis placed by many proponents of religious encounter on the epistemically unique or self-validating character of such experiences. There seems much to be gained by the encounter-theorist if it could indeed be established that the notion of a selfvalidating experience is a logically intelligible one. Let us then turn to a consideration of whether or not there can be experiences which are self-validating, i.e., is it logically possible for there to be a certain kind of experience which carries with it its own guarantee of veridicality? While such a notion has been criticized severely, many theists have been just as vigorous in their support of the intelligibility (and indeed the actuality) of such experience. As pointed out by Ferre in his explication of R. B. Martin's critique of the existential significance of a putative self-validating experience with God, when the theist is confronted with the challenge that introspective procedures-as opposed to deductive and inductive reasoningcan never establish existence, the theist argues that This one kind of experience is capable of providing a foundation for ontological claims despite the lack of predictive power or testing procedures that are usually required for vindicating an existential claim.7 Surely, then, strictly from a phenomenological point of view (i. e., to suspend for the moment the question of their logical intelligibility), such experiences are most significant. Steven M. Cahn, for example, has argued that a self-validating experience is the only relevant foundation for belief in God since the philosophic " proofs " are simply unable to compel such belief: Y Ferre, op. cit., p. 106. ROBERT A. OAKES A supernaturalist believes in God because of a personal selfvalidating experience ... A philosophic proof of the existence of God is thus of no use to the supernaturalist. If the proof is shown to be valid, it merely confirms what he already knows on the much stronger evidence of personal experience. If the proof is shown to be invalid, it casts no doubt on a self-validating experience. 8 Hence, if Cahn is correct here with regard to the total irrelevancy of proofs as opposed to self-validating experiences, 9 then the question of the logical status of such experiences becomes a most important one to resolve. One apparently serious criticism of the notion of self-validating experience has been that experiences as such are not subject to any kind of verification or validation whatsoever, 10 let alone self-validation. Rather, only propositions are subject to validation, and then, of course, only by means of public testing procedures. Also, it is argued that the claim of incommunicability would seem to protect the theist from the falsifying testimony of those who may have had the theist's experience without drawing his conclusions. Can these rather widelysupported criticisms be countered? First of all, it appears that the argument that only propositions, as opposed to experiences, are subject to validation is extraordinarily weak. Any appeal to ordinary thought and language reveals that we do talk about "veridical" versus" erroneous" experience and know what we are talking about when we draw such a distinction. Insofar as all experience involves mediation and thereby interpretive judgment (hence, the rejection by encounter-theorists such 8 Steven M. Cahn, " The Irrelevance to Religion of Philosophic Proofs for the Existence of God," American Philosophical Quarterly (Vol. 6, No. Q), April, 1969, p. 17Q. • While I believe that Cahn makes a very good point here, it might be important to note that, while such experience constitutes a sufficient condition for belief in God, it could not legitimately be held as a necessary condition for theological belief. Hence, even if a self-validating experience is the only justification for belief in God, we must recognize that there are a significant number of people who believe in God without justification. I have discussed this point in somewhat more detail in an essay, "Pragmatism, God, and Professor Matson: Some Confusions," forthcoming in Philosophy and Phenomenological Research. 1 ° Ferre, op. cit., pp. 106-107. " SELF-VALIDATING " RELIGIOUS EXPERIENCE as John Smith 11 of mystical immediacy as the kind of" experience " by which we could come to know the reality of God; on the contrary, proponents of mystical immediacy are really the "naive" epistemological monists of religious encounter), experiences qua the judgments involved in them are subject to verification and falsification. Consequently, structured or intelligible experience, as opposed to " raw feels," necessarily involves the conceptual or the intentional. As such, it entails propositional attitudes, though not necessarily propositions. 12 Hence, while we do not and need not express through verbal performance or propositions all of the judgments involved in our experience of the world, this in no way entails that experience can take place without interpretive judgment. Consequently, it is perfectly meaningful to speak of experiences as subject to verification and falsification. Concerning the second point of criticism, it would seem to be quite unprofitable to argue that the claim of " incommunicability " protects the theist from the opposing testimony of those who may have had his experience without drawing his conclusions, since the theist could simply respond here that, since the experience of God is self-validating, it would be tautologically impossible for someone to have it and not believe that he had experienced God. Rather, if someone believed that the experience in question was not an experience of God, this necessarily entails that the experience was not selfvalidating and thereby not an experience of God. Hence,. according to the theist, it follows that there could be no other conclusions drawn if the experience involved were (qualitatively) identical to his. However, since the plausibility of the theist's response here depends totally upon whether or not the concept of self-validating experience is logically intelligible, then this dispute cannot be resolved independently of, and hence brings us full-circle back to, the original and central question regarding such intelligibility. 11 Cf. John Smith, Experience and God (New York: Oxford University Press, 1968)' p. 52. 12 Cf. Richard Bernstein, " Sellars Vision of Man-in-the Universe, (Part ll) ," Review of Metaphysics (Vol. XX, No. 2), December, 1966, pp. 807-811. ROBERT A. OAKES However, granted that experiences as such (and not just propositions) are subject to verification and falsification, and granted that if self-validating experiences are logically possible then it would follow tautologically that they could not be misinterpreted, we still seem to be no closer to a solution of whether or not such experiences are logically possible. Can there be a kind of experience which, taken by itself, is sufficient to guarantee its own veridicality? As a preliminary to a defense of the thesis that there can be such experiences, I would suggest that the difficulty involved in resolving this question satisfactorily has resulted largely from the prevalent positivistic prejudice that methodological/epistemological questions are philosophically (logically) prior to substantive or existential ones. In this regard, it would seem that the question before us provides us with an excellent paradigm of the difficulties resulting from such a perspective. Specifically, and insofar as the issue of self-validating experience has been most pronounced within the context of the fundamental question of the reality of God, it would seem clear that the epistemological question regarding such experience cannot be answered prior to, i. e., independently of, the metaphysical question of God's existence; and that the distortion inherent in the positivist perspective becomes especially apparent insofar as we do attempt to answer it independently of the metaphysical question. For example, if we address the question of theological proof, it seems clear that we cannot decide the epistemological question of whether there can be a proof of God's existence 18 without a prior or at least concurrent decision on the ontological question, i. e., a proof of God's existence is possible only if God exists; there cannot be such a proof if God does not exist. Consequently, the epistemological question of the possibility of theological proof is seen to be logically posterior to the metaphysical question of God's existence. The general proof-question cannot decide the " legitimacy " or " cognitive meaningfulness " of the God-question; rather, it is the God-question which must ultimately decide the 18 Cf. Mavrodes, op. cit., pp. 47-48. "SELF-VALIDATING" RELIGIOUS EXPERIENCE 268 proof-question. Only if God exists can "God exists" be the conclusion of a sound argument for his existence. However, if God does not exist, then no sound argument for his existence is possible. Hence, insofar as the theological question provides us with a very clear paradigm of the essential confusion in the notion that epistemological questions of " proof " and " confirmation " are philosophically fundamental,. it is clearly time for an unequivocal rejection of this widely-held positivistic perspective that epistemological questions logically precede, and adjudicate the cognitive significance of, questions of existence. However, what does all of this have to do with the question of self-validating experiences? Simply this: If it is indeed correct that the metaphysical question of God's existence is logically prior to epistemological considerations in this regard, i. e., if the question of the logical possibility of arriving at knowledge of the reality of God cannot be decided independently of a decision (whether correct or not) on the metaphysical question of God's existence, then the answer to the epistemological question of self-validating experience becomes contextual. Specifically, if and only if God exists are self-validating experiences logically and factually possible (though perhaps never actual). However, the nonexistence of God would clearly seem to entail the impossibility of such experience. That is, if theism be correct, then there is a transcendent God who, by virtue of the infinite power and authority indigenous to his nature/ 4 could see to it (since an experience of God could not occur without a revelation from God) that an experience of (or encounter with) him would be sufficient to guarantee its own veridicality. Surely there seems to be no logical problem in the notion that the Being with the infinite power and authority to create the universe ex nihilo could insure that, insofar as he chose to reveal himself to man, our experience of him would be self-validating, in which case there could not conceivably (in principle) be subsequent experiences of any kind which would constitute a justification for rescinding our com14 We are, of course, confining ourselves here to theism as classically understood. 264 ROBERT A. OAKES mitment to the veridicality of the original experience. If there could conceivably be subsequent justification for rejecting the original experience as nonveridical, then, of course, such experience could not legitimately be construed as self-validating. Hence, within the context of God's existence (i.e., if and only if the answer to the logically prior metaphysical question is Yes), the concept of a self-validating experience is logically intelligible insofar as there could be uncorroborated experiences about which we could not possibly err. While there is always, assuming the corrigibility of any human experience not controlled by God, the logical possibility of error with regard to our experience of other sorts, it is consistent to maintain that the Being who is God, precisely because he is God, could guarantee that experiences of him are no less than self-validating. Hence, if and only if God exists can there be a kind of experience which is necessarily veridical. Consequently, if what has been argued thus far is sound, then, contrary to what is often taken to be philosophically axiomatic, existential fact can decide questions of logical possibility at least in the unique case wherein the existential fact is God's existence, and the logical possibility concerns that of self-validating experience. This is not at all to make the clearly nonsensical claim that God's omnipotence includes the ability to achieve what is clearly logically impossible, i. e., arrange for a circle to be a square, or a bachelor to be married, since, as has been widely pointed out, there is nothing to accomplish in this regard except an unintelligible arrangement of language. Further, while the categories of" square" and" bachelor" have a precision of meaning which is logically independent of the question of God's existence, this is surely not the case with regard to the category of " possible kinds of experiences," since, in the case of God's existence, the latter category takes on a range and a dimension which is surely unthinkable if God does not exist. In this regard, it might be important to clarify that, while the existence of God is the necessary and sufficient condition " SELF-VALIDATING " RELIGIOUS EXPERIENCE for the possibility of self-validating experiences, i.e., that selfvalidating experiences can occur if and only if God exists, this does not at all entail that, given God's existence, such experiences have in fact occurred or will occur. Rather, it is quite possible that God has chosen not to reveal himself by selfvalidating experiences. Hence, while it seems clear that God's existence guarantees the intelligibility (or possibility) of selfvalidating experience, it seems equally clear that his existence does not at all guarantee their actuality. Hence, the actuality of such experience remains a very difficult question indeed. I suppose it might be argued that, granted God's existence and hence the logical possibility of self-validating experience, it would be more likely than not that God would choose to actualize this possibility. However, such reasoning might be far from persuasive. What exactly, then, are the implications of all of this for the vigorous dispute concerning the epistemic uniqueness of religious knowing, i.e., the issue of self-validating experience? First of all, if, as we have argued, it is the case that the epistemological question regarding the possibility of such experience cannot be answered independently of the metaphysical question of God's existence, then, while interesting and important, the former question is nonetheless seen to be a derivative or subordinate concern insofar as an answer to it must necessarily presuppose an answer to the metaphysical question. This is not, of course, in any way incompatible with the notion that we might well come to know the reality of God through direct experience. Hence, it is not the plausibility of encounter-experience with God which is at issue here; there is no logical problem whatsoever in the notion that we can experience the reality of God just as we can experience the reality of anything else. However, insofar as there is not a unique logic of religious knowing, then the veridicality of any putative religious experience cannot be said to be guaranteed simply on the basis of the experience as such. Rather, social corroboration would always be logically (if not psychologically) relevant to the question ROBERT A. OAKES of the veridicality of such experience (though, as we have seen, the failure to achieve corroboration does not at all entail that the experience in question is nonveridical). Consequently, and quite apart from what we have taken to be the plausibility of the claim with regard to religious encounter-experience as such, we have addressed the bolder and seemingly much more problematic claim that such experience constitutes a unique mode of knowing (i.e., is self-validating), and have concluded that such experience is possible, but only in the context of God's existence; consequently, we cannot know such experience is possible unless we know that God exists. Such is the problem: To have solved the question of self-validating experience is already to have solved the logically prior metaphysical question of God's existence. Consequently, the epistemological question with regard to self-validating experience cannot be decided or resolved in a metaphysical vacuum; the answer to the metaphysical question must be known or at least decided first. Hence, while progress in epistemology /methodology is an unquestionable philosophical desideratum, we must cast off those vestiges of positivism whereby we seek to achieve such progress without addressing ourselves to what clearly have shown themselves to be the prior metaphysical or substantive questions involved. Surely, the issue of self-validating experience affords us an excellent opportunity to regain this balanced philosophical perspective. RoBERT Univermty of Missouri Rolla, Missouri A. OAKES JESUS THE MAN AND JESUS THE CHRIST: DID BULTMANN CHANGE? R UDOLF BUL TMANN'S POSITION on the question of the relationship between the Jesus of history and the Christ of the kerygma is-from one point of viewa much easier topic to discuss today than it would have been prior to 1959. In that year, Bultmann delivered an address to the Heidelberg Academy of Sciences in which he answered the critics of his position and in so doing clarified what his position really was. 1 Prior to 1959, this position was difficult to state with precision not only because his ideas were discussed in a number of books and essays spanning a number of years but because at times his views seemed contradictory. We read, for example, in his highly controversial 1941 essay entitled "New Testament and Mythology " that the agent of God's presence and activity, the mediator of his reconciliation of the world unto himself, is a real figure of history. Similarly the word of God is not some mysterious oracle, but a sober, factual account of a human life, of Jesus of Nazareth, possessing saving efficacy for man. 2 All of this seems to indicate that Jesus of Nazareth is-in his own personal history-the means of our salvation. And yet in another passage we read what appears to be the opposite: " The Jesus of history is not kerygma, any more than my book was. 3 1 Rudolf Bultmann, " The Primitive Christian Kerygma and the Historical Jesus " (hereafter PKHJ), in The Historical Jesus and the Kerygmatic Christ, ed. and tr. Carl E. Braaten and Roy A. Harrisville, (New York: Abingdon Press, 1964), pp. 15-42. • Rudolf Bultmann, "Kerygma and Myth" (hereafter K&M), tr. R. Fuller, (New York: Harper [Torchbooks], 1961), p. 44. • Ibid., p. 117. The "book " to which Bultmann refers here is his Jesus and the Word. See complete citation below. 267 268 JEFFREY G. SOBOSAN For in the kerygma Jesus encounters us as the Christ-that is, as the eschatological phenomenon par excellence. Neither St. Paul nor St. John mediate an historic encounter with the historic Jesus." 4 And again: "I am deliberately renouncing any form of encounter with a phenomenon of past history, including an encounter with the Christ after the flesh, in order to encounter Christ proclaimed in the kerygma." 5 Contradictory statements and ideas such as these are inevitable whenever a thinker is trying to develop an orginal idea. But his students and followers appreciate clarification. This is precisely what the 1959 Heidelberg Address accomplished: it clarified and refined what before had been at most an ambiguous position. But I submit that the Address did not alter his position. This I feel has always remained the same. The task of this essay will be to demonstrate why and how this assertion can be made. THE VocABULARY oF THE EssAY Before I can develop Bultmann's position, it is important to arrive at some initial and perhaps unsophisticated understanding of the terms involved, and then, secondarily, the nature of the problem. But the terms and the problem are not separable; in fact, because of Bultmann's use of the terms, the terms are the problem. This is because for Bultmann the terms signify two distinct realities: the Christ of the kerygma is an event, an understanding, a revelation apart from the Jesus of history whose life has ended and who cannot be present to our existence. Traditional Christology, while at times retaining the two terms, will apply them to one reality: the kerygmatic Christ is the Jesus of history who was put to death and raised to life for our justification (Rom. 4: 25) and who lives as present to our personal histories as a transcendent but living person. The reasons for the split between the historical Jesus and the kerygmatic Christ are based on two conclusions Bultmann • Ibid. "Ibid. DID BUl/l'MANN CHANGE? draws from his study of the New Testament which are fundamental for any understanding of his position. Bultmann observes that Jesus did not proclaim himself as the savior; that is, he did not demand faith in himself precisely in the role of Savior of the World. Jesus's accomplishment was rather the announcement-in the Israelite prophetic tradition-of the imminent coming of the Reign of God, and the teaching-in the pedagogic style of the Palestinian rabbis-of an ethics of the will of God. Secondly, the Jesus of history had no consciousness of his redemptive mission; thus, for example, he could not possibly have understood his own death as a redemptive sacrifice. Why, then, and how did this Jesus give rise to the proclamation in the early Church of the kerygmatic Christ? Briefly, it was due to the meaning that Jesus gave to the religious lives of his followers. He came to be called or understood by them as Redeemer or Savior, and this is how-in mythological language -he is described in the non-dominical units of the New Testament. All of this will be seen in greater detail later. It is introduced here to set the stage for Bultmann's schematic description of what he feels is the essence of the distinction between the Jesus of history and the Christ of the kerygma: 1. In the kerygma the mythical form of the Son of God has appeared in place of the historical person of Jesus (as the Synoptic Gospels present it to the critical eye) . 2. While the preaching of Jesus is the eschatological message of the coming-more, of the breaking-in of the kingdom of Godin the kerygma Jesus Christ is proclaimed as the one who died vicariously on the cross for the sins of men and was miraculously raised by God for our salvation. In Pauline and Johannine theology the decisive eschatological event has thereby already occurred. 3. For Jesus the eschatological proclamation goes hand in hand with the proclamation of the will of God, with the call to radical obedience to God's demands culminating in the commandment of love. To be sure, ethical preaching is not abandoned in the Christ-kerygma, but when Paul and John connect ethical demands and above all the commandment of love, with the 270 JEFFREY G. SOBOSAN they do not do so by resuming Jesus's exposition of the will of God as it appears in the Synoptic Gospels.6 CRITIQUE oF THE PosT-BULTMANNIANs The clarifying Heidelberg Address came in response to several members of a school of German theologians who have been given the collective designation of "the Post-Bultmannians" or "the Marburgers." 7 Their collective grouping derives not only from their shared name and theological position but also from the fact that they were all, at one time or another, former students of Bultmann. The most prominent members of the group are Ernst Kasemann (Gottingen), Gunther Bornkamm (Heidelberg), Ernst Fuchs (Berlin), Hans Conzelmann (Zurich), and one American, James M. Robinson (Claremont School of Theology, California) .8 Although each maintains and develops slightly different approaches, they are united in the common belief that their former mentor places too much " distance " between the historical Jesus and the kerygmatic Christ, especially in the area of Jesus's messianic awareness. Their task is to close the gap by attempting to demonstrate that if the kerygma presents Jesus as Lord, as God's means of bringing redemption to men, as being in his person the inauguration of the eschatological era, 9 then the kerygma must reveal something of Jesus's own PKHJ, p. 16. • Bultmann calls Marburg his " academic home." He studied there under such luminaries as Adolf Jiilicher and Johannes Weiss (Scripture) and Wilhelm Herrmann (Systematic Theology). He received his doctorate there in 1910 writing his thesis on Der Stil der Paulinischen Predigt und die kynischstoiche Diatribe. After a few years teaching at Breslau and Giessen, he returned to Marburg in the autumn of 19!