Imaginative Generalization as Epogoge
by Gregory Reichberg
Gregory Reichberg studied in France at the Centre Independent de Recherche Philosophique and received a Master’s degree from the University de Toulouse. He is now a doctoral candidate at Emory University, Atlanta, GA 30305. The following article appeared in Process Studies, pp. 152-162, Vol. 17, Number 3, Fall 1988. Process Studies is published quarterly by the Center for Process Studies, 1325 N. College Ave., Claremont, CA 91711. Used by permission. This material was prepared for Religion Online by Ted and Winnie Brock.
(I am grateful to Professors Thomas Flynn, George Lucas, Jr., and Richard Patterson for helpful comments on earlier versions of this paper.)
Since the publication of Karl Popper’s The Logic of Scientific Discovery, it has become commonplace in Anglo-American philosophy to cast a disparaging eye on induction. Much of the contemporary interpretations of science based on paradigm shifts and the incommensurability of rival theories are founded on the presumed invalidity of the inductive movement. Induction has been accused of many shortcomings, but the common denominator of the various criticisms leveled against it, from Popper to Kuhn to Feyerabend, is that belief in induction is responsible for a naive empiricism which views science as based on uninterpreted observation and direct verification of theories by the "facts."
Whitehead was not unaware of the difficulties involved in such a simplistic approach to induction. In Science in the Modern World, he notes that "It is in respect to the process of verification for the particular case that all the trouble [with induction] arises" (SMW 35). Whitehead then adds somewhat enigmatically that "The theory of Induction is the despair of philosophy -- and yet all our activities are based on it." However paradoxical this statement may seem at first glance, it nevertheless indicates the fundamental direction taken by Whitehead in elaborating his own approach to the problem of induction. On the one hand, Whitehead is fully cognizant of the difficulties inherent to the so-called Baconian method of induction. In particular, he repudiates both a naive verificationism and the corresponding belief in pure or uninterpreted observation of independent facts. On the other hand, although he shares with contemporary epistemologists the view that all observation is "theory-laden," he does not thereby conclude that induction should simply be discarded to the junk heap of worn out ideas. Whitehead’s philosophical project can, in part, be construed as an attempt to rehabilitate induction as an essential feature of experience.
Unlike most contemporary philosophers, who restrict their examination of induction to the modern sense of the term, in which it is construed as a method of inference which permits some prediction of future events on the basis of past events, Whitehead also recognizes the importance of the ancient meaning of induction. For the Greeks, particularly Socrates and Aristotle, induction (epogoge) is the process of seeing a general principle exemplified in particular cases known by experience. This type of induction might be called abstractive induction, since it involves the drawing out of the universal from the particular instance. Whitehead explicitly recognizes the importance of abstractive induction in his description of the method of speculative philosophy. In this paper I will attempt to give a sketch of Whitehead’s reappropriation of the ancient Greek procedure of epogoge. Whitehead is relatively well known for his rethinking of induction in the modem sense of the term, which is a foreknowledge of future events in the light of past experience. It is at this juncture that he enters the contemporary debate concerning the so-called "problem of induction," which is primarily an ongoing discussion on the validity or invalidity of Hume’s critique of causal connection. This paper will not directly address this latter sense of induction, on which several excellent studies have been written.
In a surprising move for a mathematician turned philosopher, Whitehead explicitly eschews the deductive method as the key procedure to be followed in elaborating metaphysical truth. To follow the deductive method properly one must begin with axiomatic principles and then proceed in a rigorous manner in unfolding the consequences and applications of those principles. In metaphysics, however, the central issue is not to posit principles axiomatically and then proceed more geometrico, but rather to pursue those first principles themselves. Postulation of the first principles is thus the goal of philosophy and not its starting point. "Metaphysical categories are not dogmatic statements of the obvious," writes Whitehead; "they are tentative formulations of the ultimate generalities" (PR 8/12). The central preoccupation of the philosopher should therefore be the discovery and accurate description of those ultimate generalities which explain all actual entities Whereas the special sciences seek to uncover the explanatory principles which govern one particular genus of entities, metaphysical inquiry seeks to uncover truly universal principles which apply to all actual entities insofar as they are actual entities. And since "apart from things that are actual, there is nothing -- nothing either in fact or in efficacy" (PR 40/64), then the subject matter of metaphysics is necessarily universal in scope. "The metaphysical first principles can never fail of exemplification. We never catch the actual world taking a holiday from their sway" (PR 4/7).
To the above characterization of metaphysics, Aristotle would most certainly nod in approval. If metaphysics is indeed the elaboration of the first principles upon which all experience depends, then it is essential to get clear on both what those principles are and how one might proceed in securing a knowledge of their basic structure. Whitehead and Aristotle are generally in agreement as to the method by which the first principles come to be known, although the articulation of the principles themselves will be substantially different in the two cases.
For Aristotle, induction is generative of both the first principles of demonstration and the middle term of the syllogism. It can be characterized as a movement whereby the mind passes from a consideration of individuals to the intuitive grasp (nous) of a universal property. In the famous concluding chapter (Book II, chap. 19) of the Posterior Analytics, where Aristotle describes how the mind ascends to the first principles on which all science is grounded, he points out that the immediate point of departure of the inductive movement is not mere sense perception, but "experience": "So from perception there comes memory, as we call it, and from memory (when it occurs often in connection with the same thing), experience; for memories that are many in number form a single experience. And from experience, or from the whole universal that has come to rest in the soul . . . there comes a principle of skill or of understanding . . ." (100 a 3-9). This passage makes it clear that experience is constituted by a combination of sense perception and memory, and that it has for its object the discernment of similarities held in common by a series of individuals. Moreover, if one recalls that memory, for Aristotle, is that faculty whereby past events are retained in images, then it should not be surprising that the action of the imagination should be required for the elaboration of universals through induction. Universals and first principles can come "to rest in the soul," only after the data of sense experience has been properly ordered by the imagination and memory into a unified whole which is manifested to the intellect in a mental image.
The Aristotelian universal should not be thought of as an abstract essence which has only a contingent relationship to the particulars which are subsumed under it. On the contrary, "the reference to the individuals which form a certain class and present, in this respect, a certain identical structure, is not contingent . . . but is constitutive of the universal qua universal" (KUP 307). In other words, the universal can only be truly known when the mind actively refers back to those individual substances in which the universal is realized in concrete existence. It is for this reason that some commentators of Aristotle posit a descent from universal to particular as an integral part of the overall inductive process. On this view, the universal principles, which are arrived at by means of abstraction from particulars, retain an intrinsic link with the particulars subsumed under it. The universal principle is explanatory of particulars which alone can be said to exist in the full sense of the term, for according to Aristotle "no universal exists apart from the individuals" (Meta. 1040 b27). To syllogize on the level of the abstract intelligible with no further reference to concrete individuals would constitute a variety of "misplaced concreteness," hardly consonant with Aristotle’s firm realism.
Aristotle himself gives some indication that induction involves both ascent from particular to universal as well as descent from universal to particular, when he notes in Post. An. 81 b6 that one cannot have episteme of particulars -- "for neither can one get to them from universals (sc. universal propositions) without epogoge, nor can one get them through epogoge without sense perception." He also notes in Pr. An. 67 a 22 (against the Platonic theory of recollection) that "it never happens that we know the particular previously, but we get the knowledge of the instances along with epogoge, recognizing them as it were."2 An explicit reference to induction as a movement of both ascent and descent can be found in the Aristotelian logic of John of St. Thomas (1589-1644). The passage in question is worth quoting, because it presents a good framework from which to approach imaginative generalization, which constitutes Whitehead’s own version of "abstractive induction."
Induction, then, is defined as ‘advance from sufficiently enumerated singulars to the universal.’ . . . And since opposites have the same intelligible content, from this definition of induction, which is ascent, we understand its opposite, which is descent, i.e. advance from universal to singulars. And induction, inasmuch as ascent, is directed to discovering and proving universal truths, under the aspect of being universal, i.e. inasmuch as they are evident from the singulars comprehended under them. For you cannot prove that something is universally so, except because its singulars are so. Descent however from the universal to singulars is principally directed to demonstrating the falsity of the universal, under the aspect of being universal. For you best show the falsity of the universal by descending from it and by showing that the singular is not so. Nevertheless, where the truth of the universal was established and discovered by means of ascent, even descent serves to show the correspondence of the universal to the particulars comprehended under it. (AL 60/104-5)
At the outset of Process and Reality, Whitehead gives a description of the process which leads to the discovery of first principles which is analogous to the Aristotelian treatment of the matter. Significantly, he calls this procedure "imaginative generalization."’ The expression "inductive generalization" is avoided ,4 probably in order to avoid any possible confusion of this approach to metaphysics with Bacon’s inductive approach, which Whitehead explicitly rejects.5 At any rate, although the term "induction" is not used, it is clearly induction as epogoge that Whitehead has in mind when speaking of "philosophic generalization" "The true method of discovery is like the flight of an aeroplane. It starts from the ground of particular observation; it takes a flight in the thin air of imaginative generalization; and again lands for renewed observation rendered acute by rational interpretation" (PR 5/7).
Induction is here defined as a movement of ascent and descent, from particulars to a universal principle and back again, which is accomplished by means of a structured use of the imagination. In a manner analogous to Aristotle’s grounding of induction in "experience," Whitehead is quite emphatic in stating that direct observation is incapable of serving as the springboard for arriving at the larger generalities. A belief in sheer observation, unaided by imagination, is precisely the core of the Baconian method of induction, which, as Whitehead notes ironically, "if consistently pursued, would have left science where it found it" (PR 5/7). In contrast to this "rigid method of empiricism," imagination will exercise an essential role in the search for the ultimate first principles.
Whitehead recognizes that the "appeal to the facts is a difficult operation" (PR 11/16) and cannot be accomplished by a simple appeal to direct observation. What is often called "direct observation" is in point of fact a highly sophisticated mental function in which the causal impact of objects on the observer is interpreted selectively by observers according to their purposes. The aim of imaginative generalization is not to purify observation of interpretation, for if such were the case we would be left with little more than the bland experience of the stone: "If we desire a record of uninterpreted experience, we must ask a stone to record its autobiography" (PR 15/22). The aim, therefore is not to excise subjective intensity from the experience of perception, but rather to strip our experience of the world of that abstract selectiveness which is the natural accompaniment of perceptual immediacy. The illusion that there are uninterpreted "self-sustained facts, floating in nonentity" (PR 11/17) is the direct outcome of Bacon’s attempt to describe detailed matters of fact in separation from a metaphysical interpretation of the experienced world as a unified whole.
The role of imaginative generalization consists therefore in relating the particular occasions immediately experienced with the larger totality from which the particular occasion originates and which it embodies. The practical concerns of ordinary life require that observation be selective, so that the unity experienced in the mode of causal efficacy is obscured by the need to separate experience into clearly delimited areas of concentrated activity. Philosophy arises as an attempt to recover, on the plane of conceptual analysis, "the totality obscured by the selection" (PR 15/22). In the opening pages of Process and Reality Whitehead describes the way in which the imagination functions as a means to an inductive generalization. In the first place, he notes that imagination is essential in order to free experience from the habit of focusing on the same selected observations, which have become solidified and thus transformed into "matters of fact." The problem here is to overcome the "benumbing repression of common sense" (PR 9/13) so that events which have become commonplace can come to be experienced with new meaning, when viewed in the light of an imagined contrast. "Such thought," notes Whitehead, "supplies the differences which the direct observation lacks. It can even play with inconsistency; and can thus throw light on the consistent, and persistent, elements in experience by comparison with what in imagination is inconsistent with them" (PR 5/7). Imagination operates in this regard as a "propositional feeling" which uncovers new elements in the field of observation through a comparison of some possibility with what is actually given.
The above function of imagination, which enables the observer to discern features of actual entities by means of contrast, should most likely be seen as a necessary condition of the imaginative generalization, rather than the generalization itself. Its role is analogous to Aristotelian "experience," which is the necessary jumping off point of epogoge, but is not itself an instance of epogoge. Moreover, a supplementary condition is required for the success of an imaginative generalization, insofar as the generalization should always take its point of departure from within some particular branch of human learning. This is important, since the intention is not simply to imagine any arbitrary combination or contrast of observed features, but rather to start with some limited generalization arrived at by careful reflection in one of the branches of intellectual research. Whitehead construes the various possible areas of research very broadly, listing physics, physiology, psychology, aesthetics, ethical beliefs, sociology, or in "languages conceived as storehouses of human experience" (PR 5/7).
Once the above two conditions have been fulfilled, the actual act of imaginative generalization is ready to be accomplished. The generalization begins by an act of extrapolation, in which an insight obtained in one of the above fields of interest is extended, through an imaginative leap, beyond the "restricted locus from which it originated" (PR 5/8). Whitehead describes just such a leap in Science in the Modern World (219-223). in conjunction with his description of how he arrived at the philosophical realization that all actual entities exist as an interlocked community (principle of relativity). In that case, the generalization began with the accepted scientific view regarding the electromagnetic field of activity pervading space and time, and rose beyond the limits of that physical theory to posit the ontological framework which the theory itself presupposes. Whitehead points out that the science of physics presupposes the principle of universal relativity, but that such a principle cannot itself be arrived at within physics, since it is a postulation about intrinsic reality and from the limited perspective of physics "there is no intrinsic reality" (SMW 223).
Thus, the imaginative generalization begins with some salient feature of reality viewed within the perspective of some particular intellectual discipline and then posits a principle which is exemplified within that discipline, but whose scope is not limited to the discipline in question. Whitehead notes in this regard that "the field of a special science is confined to one genus of facts, in the sense that no statements are made respecting facts which lie outside that genus" (PR 9/14). The aim of the imaginative generalization consists in seeing how each genus of facts is, in reality, a limited expression of some universal principle which is equally exemplified in some very different genus of facts. Imaginative generalization tends therefore to unify, from the metaphysical standpoint, the various genera of facts which, if viewed from the standpoint of each particular science, seem utterly irrelevant and disconnected. Whitehead describes this act of "philosophic generalization" in terms reminiscent of Aristotle’s own account of "first philosophy," when he notes that such a generalization is "the utilization of specific notions, applying to a restricted group of facts, for the divination of the generic notions which apply to all facts" (PR 5/8).
I mentioned above that imaginative generalization "begins with an act of extrapolation." In effect, in order to arrive at some general principle which applies to all sectors of reality, more is needed than just an extrapolation beyond the limits of some particular science to a metaphysical principle which that particular science presupposes and which metaphysics alone can adequately explain. In order to justifiably assert the universality of the principle in question, it must be seen to apply to a nexus of occasions apart from its original point of origination. This involves a descent from the general principle to renewed observation of facts within an entirely different science. From those particular facts one again rises to the general principle of which those facts represent just one particular order of exemplification among many possible orders of exemplification.
Science in the Modern World can be read as an exercise of the process of imaginative generalization, as it has just been described. The principle of universal interconnectedness (relativity) is arrived at from within modem field theory and is then seen to be operative in various other fields of human experience: psychology, physiology, poetry, etc. It is essential here to comprehend that the principle of relativity (which states that all actual entities are internally related) is not simply applied to physiology or psychology, etc., but rather, in each instance the principle is arrived at in an original way from within the particular facts of the particular field of learning in question. In other words, positing the principle of relativity as a universal principle covering all experience, is the result of a series of distinct, limited generalizations, in which the principle is extracted each time from a particular group of facts. Whitehead applies the term "imaginative generalization" both to the limited generalizations that I have just described, as well as to the entire process in which repeated generalizations lead to the universal generalization that the scope of the principle is indeed universal.
In elaborating a notion of imaginative generalization founded on repeated generalizations from distinct starting points in the various sciences or arts, Whitehead is conscious of the danger of misplaced concreteness which can arise from an unjustified extrapolation from one disciple to another. Mechanism, for instance, began as a limited theory about the structure of matter, and was subsequently extrapolated throughout the range of human experience. Since the fundamental principle of the mechanistic philosophy -- all bodies are externally related within instantaneous configurations of matter -- is not universal in scope, its cultural dominance throughout several centuries created two types of intellectual difficulties. On the one hand, certain zones of experience are viewed as impermeable to mechanistic explanation (poetry or religious inspiration, for example) and are thus simply excluded from relevance. On the other hand, areas of research such as biology and psychology are subjected to a mechanistic interpretation which tends to deprive them of their specificity as sciences.
A key consequence of thus mistaking a partial abstraction for an ultimate explanation is that various dualisms are thereby created: subject-object, primary-secondary qualities, extended substance-mental substance, etc. When a partial abstraction is assumed to be an adequate explanation of concrete reality, a divided, disjointed view of reality seems to be the inevitable outcome. On the other hand, a sign that a truly ultimate principle of explanation has been reached would consist in showing how this principle is capable of unifying the diverse aspects of experience. Whitehead presents organic mechanism as a constructive theory in which an ultimate principle of explanation can unify the various orders of nature, precisely because the principle operates throughout the whole of nature, from the smallest constituent parts (electrons, etc.) to the highest organisms.
Imaginative generalization operates as the fundamental method of the organic philosophy. The process of repeated ascent and descent is required in order to arrive at a truly organic conception of nature, in which the principle of universal connectedness is seen to arise from within each of the particular orders of experience, rather than be imposed from above by philosophical fiat. The movement of descent, from the universal principle down to concrete reality, is of special importance in avoiding the pitfall of speculative "inadequacy," in which "failure to include some obvious elements of experience in the scope of the system is met by boldly denying the facts" (PR 6/9). The inductive descent exercises a role not unlike Popper’s falsification. A principle arrived at by abstraction from one order of facts, is confronted with facts from another order of experience, as a test of speculative applicability: "The success of the imaginative experiment is always to be tested by the applicability of its results beyond the restricted locus from which it originated" (PR 5/8). However, unlike Popper’s falsification, which is most interesting when the theory in question is refuted by confrontation with the facts, Whitehead’s version of testability is most interesting when the attempted application actually works.
The point that I wish to emphasize is that what I have described as the inductive descent plays a much more important role in Whitehead’s philosophy than the mere search for confirmation or falsification of some theory by the facts. The aim of the descent is primarily to establish a positive correspondence of the universal principle with the particulars covered by the principle, a correspondence which should nevertheless not be equated with the search for confirming instances. Popper is unable to see any positive sense in which a theory can be said to correspond to the facts, because he tends to view such a correspondence in terms of a search for certitude or confirmation. In order to avoid what he perceives as a misguided emphasis on certitude, Popper exalts the virtue of successive conjectures and refutations.’ Whitehead, on the contrary, seeks a constantly renewed confrontation of general principles with observation of concrete reality, not primarily to confirm, but in order to illuminate experience:7 "The partially successful philosophic generalization will, if derived from physics, find applications in fields of experience beyond physics. It will enlighten observation in those remote fields, so that general principles can be discerned as in process of illustration, which in the absence of the imaginative generalization are obscured by their persistent exemplification" (PR 5/8).
The primary role of the inductive descent, "the renewed observation rendered acute by rational interpretation" (PR 5/7), is not to confirm, but rather to propel the process of speculative discovery forward to novel and unforeseen dimensions of experience. With each new application of universal principles to novel facts, it is not just the facts, but the principles themselves which are illuminated and reinterpreted, consonant with the greater breadth of experience which has thus been obtained. It is for this reason that Whitehead is careful to insist on the tentative nature of the ultimate generalities, which are always susceptible of reinterpretation in the light of the evolving facts of experience.
In conclusion, I would like to make it clear that the aspect of universality, which is characteristic of the ultimate generalities of speculative metaphysics, is not regarded by Whitehead as a fixed point known with definite certitude, at some stage in the process of discovery. The movement of imaginative generalization, which I have described above as the discovery of a general metaphysical principle and its repeated application and rediscovery within the diverse branches of human learning, is not intended to fulfill a condition of "complete enumeration of particulars" which would ground the affirmation that the principle is indeed of universal scope. In other words, the repeated descent from a principle to its exemplifications in experience, is not meant to be a method to determine if the acquisition of the universal principle by inductive means is valid.
On this score, Whitehead departs from the traditional Aristotelian discussion of induction, with its emphasis on the problem of complete enumeration of particulars as a justification of the inference from particular to universal. Imaginative generalization is a method of discovery which seeks to recapture the unity of experience by successive insights into the overall interconnectedness of actual entities. If some synoptic or universal vision is thereby attained, it will necessarily be a provisional grasp of unity, based on the structure of experience interpreted within some particular epoch in the ongoing adventures of actual entities. The question of how an inference of a fixed universal proposition from enumerated particulars can be justified no longer needs to be raised, since the relation of particular to universal is no longer construed in quite the same way. Particulars are capable of generating propositions of universal import, precisely because the particulars are themselves universal, in the sense that each actual entity is constituted by a synthesis of all the other actual entities in the universe. The principle of universal relativity turns out, in the last analysis, to be the ontological foundation for the process of imaginative generalization.
This last point would, in my opinion, merit careful examination, because it represents a possible solution to an inherent difficulty in the Aristotelian approach to universals and particulars. Commentators of Aristotle have often noted an unresolved tension at the center of his philosophical system, inasmuch as the Aristotelian ontology is centered on the primacy of individual substances, while his epistemology is centered on the intelligibility of the universal. The impression of a fundamental dualism is thereby created. The theory of abstraction is elaborated precisely in order to bridge the gap between an ontological world of subsisting individuals and the epistemological world of universals. Induction is proposed as the means by which the universal is drawn out from concrete particulars.
From the standpoint of Whitehead’s philosophy of organism, where the particular, actual entity is universal, the epistemological problem of how to bridge the gap between the two orders (the order of existence and the order of knowledge) is thereby resolved. Whitehead’s approach is, in my opinion, unique among modem philosophical systems because he attempts to resolve a long-standing epistemological difficulty by an appeal to ontology. His solution to the problem of universal and particular is thus inverse to the nominalist approach of most moderns.
A critical appraisal of Whitehead’s ontological "reduction" of the universal/particular dichotomy would need to address the following questions:
(1) Since the principle of internal relatedness has been posited as the ontological foundation of the intellectual process of imaginative generalization, and it has also been affirmed that this principle is itself arrived at via imaginative generalization, do we thus find ourselves trapped in a sort of vicious circle? In other words, does Whitehead’s novel solution lead to a new version of the "riddle of induction"? To my mind, this difficulty might best be approached in the light of Whitehead’s analysis of causality. Is his analysis sufficiently rich to allow for different levels and specific types of causality, such that causes of a different kind can be understood to cause one another reciprocally, causae ad invincem sunt causae (to use a Scholastic dictum drawn from Aristotle), thus avoiding true circularity?
(2) As was mentioned above,8 Whitehead views the universal/particular distinction as inherently misleading, because "the ‘particular’ is thus conceived as being just its individual self with no necessary relevance to any other particular." Whitehead traces this metaphysical error back to Aristotle, to whom he attributes a metaphysic of "solitary substances," inherently opposed to the "democracy of fellow creatures" affirmed by the philosophy of organism. However, in defense of Aristotle, it might be asked whether Whitehead has in fact conflated two distinct senses of "universal" which for the sake of clarity ought to be kept apart?
On the other hand, "universal" can be used as a synonym for "common property," and is intended to signify some form or structure shared in common by a multiplicity of entities. Here, "universal" is indeed opposed to "particular," for although entities possess certain properties in common, each thing also includes certain incommunicable, individuating properties, which sets it apart from all other beings and makes it a unique particular. On the other hand, we can speak of something being "universal" because it is in some way related to a very large number or even the totality of other beings. Hence we speak of someone being "universally known," "the sun’s universal influence upon all bodies on earth," or even of the intellect, which Aristotle says "has the virtue of becoming all things" (De Anima, 430 a15). In this second sense, being "universal" is not opposed to being a concrete, particular thing, since it is the particular itself which is related to others in manner sufficiently great to be qualified as universal. In this way, nothing precludes an Aristotelian primary substance from possessing certain incommunicable, exclusive properties which render it fully individual, while being at the same time in vibrant communication and interrelation (through the exercise of causality, knowledge, affection) with other substances.9 An adequate explanation of any substance would necessarily have to include reference to the other entities to which it is thus related.
(3) Finally, if the metaphysical principle of universal relativity is adopted as a kind of first principle of knowledge, which illuminates and guides our investigation of actual entities, the objection might be raised that such a principle actually accomplishes the contrary of what is intended, and would in fact exclude any proper knowledge of existing things. For if each singular entity mirrors the entire universe within itself and is thus constituted as a synthesis of all the manifold beings that compose the universe, should we not therefore conclude that the ontological structure of any given actual entity is hopelessly beyond our ken? For who can pretend to describe (even inadequately) any specific actual entity if all the other actual entities in the entire universe (past, present and future) must necessarily enter into its description? This objection is in no way a novel one. Nicholas of Cusa, Pascal, and Locke all advance the doctrine of internal relations as evidence for the skeptical claim that human knowledge is severely limited and radically incapable of penetrating the fabric of nature.10
AL -- John of St. Thomas. Ars Logica. Vol. 1 of Cursus Philosophicus Thomisticus. Ed. B. Reiser. Turin: 1930. [A section of AL has been translated as Outlines in Formal Logic, trans. Francis C. Wade (Milwaukee: 1955). When this translation is used in a citation its page number will be given after the page number of the Reiser edition.]
CWA -- The Complete Works of Aristotle. Ed. Jonathan Barnes. 2 vols. Princeton: 1984.
KUP -- Walter Leszl. "Knowledge of the Universal and Knowledge of the Particular in Aristotle." Review of Metaphysics 26 (December 1972): 278-313.
1When speaking of "abstractive induction" I mean to include the passage from sensible singulars to the grasp of either single universals or axioms. Aristotle himself uses the term "epogoge" to cover these two possibilities. It should also be noted that I do not intend to directly address the much debated question concerning the respective roles of epogoge and nous in the knowledge of first principles. In this paper I take induction to signify the passage from individuals to the universal, and nous the terminus of the inductive movement wherein the universal is finally grasped.
2Translated by D. W. Hamlyn, "Aristotelian Epogoge," Phronesis 21 (1976): 169-70. Hamlyn notes that "epogoge is involved in the application of general principles to cases, not just in the argument for the general principles themselves" (170). He adds that "the application of principles to cases is an essential part of the Socratic arguments that Aristotle calls ‘inductive’" (170, note 5).
3Whitehead also uses the related terms: "imaginative rationalization," "imaginative construction," "descriptive generalization," and "philosophic generalization."
4Whitehead also tends to avoid such terms as "abtractive induction" or "inductive generalization" because of his unhappiness with the particular-universal distinction itself: "These terms, ‘universals’ and ‘particulars,’ both in the suggestiveness of the two words and in their current philosophical use, are somewhat misleading. The ontological principle, and the wider doctrine of universal relativity, on which the present metaphysical discussion is founded, blur the sharp distinction between what is universal and what is particular. The notion of a universal is of that which can enter into the description of many particulars; whereas the notion of a particular is that it is described by universals, and does not itself enter into the description of any other particular. According to the doctrine of relativity . . . both these notions involve a misconception. An actual entity cannot be described, even inadequately’ by universals; because other actual entities do enter into the description of one actual entity. Thus every so-called ‘universal’ is particular in the sense of being just what it is, diverse from everything else; and every so-called ‘particular is universal in the sense of entering into the constitutions of other actual entities" (PR 48/76). Whitehead adds several pages later that the metaphysical misconception of the particular-universal distinction is historically rooted ,n the Aristotelian ontology of substance, in which the ‘particular’ is "conceived as being just its individual self with no necessary relevance to any other particular" (PR 50/79).
5A reading of Bacon’s New Organon reveals a more nuanced and less empiricist approach to induction than Whitehead (and other twentieth-century philosophers) usually give him credit, One text in particular refers to the ascent and descent characteristic of imaginative generalizations: ". . . from the new light of axioms, which have been educed from those particulars by a certain method and rule, shall in their turn point out the way again to new particulars, greater things shall be looked for. For our road does not lie on a level, but ascends and descends; first ascending to axioms, then descending to works" (Book I. aphorism 103).
6Popper writes, for instance, that "the rejection of our theories by reality -- is, in my view, the only information we can obtain from reality: all else is our own making" (Karl R. Popper, Quantum Theory and the Schism in Physics [Totawa, New Jersey: 1982] 3). For an analysis of Popper’s approach to induction, confirmation, and truth, see my "Popper en question -- Quelques critiques sur la croissance du savoir," Revue Thomiste 83 (1985): 38-68; 431-56.
7In a similar way, Aristotle notes in the Posterior Analytics (91b 34) that "someone who gives an induction [does not] demonstrate, but he nevertheless makes something clear" (i.e., some truth is made manifest to the knower). In the same vein, John of St. Thomas writes that induction does not aim to furnish a proof or to impose assent upon the mind, but rather to introduce the intellect to universal things: "[non est] ordinata ad probandum seu convincendum intellectum, sed ad introducendum in universalia" (AL 200).
8See the passage from PR 50/79 quoted above in note 4.
9On this score, Whitehead’s transformation of the universal/particular distinction could he profitably confronted with Thomas Aquinas’ reformulation of the Aristotelian philosophy. St. Thomas makes a more explicit attempt than the Stagarite to develop the view that substance is self-communicative through action. It is because Thomas takes the act of being as the deepest metaphysical principle, an act which he holds to be diffusive of its very nature (De Potentia, q. 2, art. I), that he is able to articulate and harmonize the dual exigencies of individuality and presence (through real relation) to other subjects. It would he especially interesting to contrast Thomas’ doctrine of "intentional being" (esse intentionale) with Whitehead’s theory of "objective immortality," since both aim to explain, through an ontological analysis, how one entity can be really present in another entity.
10On this point see Pascal, Pensées, § 355 (ed. Brunschvicg) and Nicholas of Cusa, De Docta Ignorantia, Book 2, chap. 2-5. The case of Locke is particularly intriguing, inasmuch as Whitehead writes in the Preface to PR that "the writer who most filly anticipated the main positions of the philosophy of organism is John Locke in his Essay, especially in its later books" (PR xi/v), If one refers to the section of the Essay (Bk. IV, ch. VI, § II) cited by Whitehead in his footnote, one does indeed come across a passage that closely echoes Whitehead’s metaphysical insight that all entities are internally related. The sticking point occurs, however, when one considers the use that Locke makes of the insight that all entities are thus interrelated, Locke’s intent in this chapter is to point out the essential limitations imposed on our knowledge of corporeal substances. His point is that we only know the real essence of some substance when we know the operations of that substance and the diverse causes that concur in the accomplishment of such operations. He concludes that it is impossible for us to attain a knowledge of those causes, since in order to do so we would have to penetrate the entire nexus of causes operative in the universe. The result is that we know hopelessly little about the things of nature and that we are better off applying our limited minds to those areas of knowledge (mathematics, religion. jurisprudence. ethics) in which our intellect stands as the measure of what is, instead of letting our thou g his stray "into the vast Ocean of Being." Such is Locke’s conclusion, a conclusion which one might conceivably interpret as an objection to the very possibility of a philosophy of organism along the lines laid out by Whitehead.