Transdisciplinarity and the Philosophy of Science

1) The Seamless Garment of Knowledge

Transdiciplinarity, rigorously speaking, is a term which conveys that knowledge in the ultimate sense transcends the restricted and compartmentalized scope of our many individualized disciplines and highly specialized sciences. We aim to scale such a summit of knowledge only partially when we allow ourselves to realize the interdisciplinary potential of this vast variety of disciplines. In such cooperative ventures we often learn the holistic lesson that a whole can be more, much more, than the sum of its parts, while still realizing the benefits which accrue when we augment the resources of a discipline which is ill equipped by itself to deal with all the difficulties of a particular theoretical problem by allowing other disciplines to come to its aid. Interdisciplinarity is but a steppingstone to any bona fide transdisciplinary perspective. From an interdisciplinary perspective the emphasis is upon the complementarity of tasks, as when for example, the allied sciences of astronomy, astrophysics, and cosmology all contribute to solving problems pertaining to our understanding of the origins and large scale structure of the universe. Or also, when Galileo invoked the Pythagorean insight in Il Saggiatore (1623) that the book of the world is written in the language of mathematics, as part of the overall reclamation project that was the renaissance, he and many like-minded contemporaries began the process which led to the full mathematization of science. Thus ended the divorce between mathematics and science that had been theoretically instituted by Aristotle, and began an era of unlimited progress which continues unabated to this very day. If I may be permitted to twist a well known biblical phrase slightly out of its normal context: what God has joined together let no Greek put asunder, not even Aristotle.

And from the domain of the life sciences we might consider the extent to which the gainful employment of the revolution in molecular biology inaugurated by Watson and Crick in 1953 still cannot do without the explanatory services of related sciences such as cytology, embryology, and physiology.1 Such examples can be multiplied ad infinitum. One must of course tread a fine line in claiming a complementarity between disciplines in that the exclusivity of respective disciplinary spheres of competence might perhaps serve as a hedge against the reducibility thesis, which holds that many specialized disciplines are reducible in principle to an underlying master discipline that is more general in scope. In the interdisciplinary case of the relationship between science and religion, echoing the words of Kant’s unification of continental rationalism and British empiricism, Einstein professed that “science without religion is lame, religion without science is blind.” The same sentiment holds true on the grander scale. No discipline is an island insulated from all the others. C.P. Snow in a very public way cried out for the tearing down of the wall of separation between our literary and scientific cultures. More recently Edward O. Wilson has brandished the sword of unification in an attempt to bridge the gap between seemingly disparate fields of intellectual inquiry. According to his principle of consilience all disciplines need to be understood as umbilically connected to the master and overarching subject matter of science. Etymologically, the Latin word scientia once was used to signify all of knowledge and not just science alone.

2) Interdisciplinarity and the Philosophy of Science

Hints of transdisciplinarity can be discerned within the various interdisciplinary symmetries which stretch beyond the boundaries of any individual discipline. The philosophy of science offers us an excellent means for tackling this task. Let us then consider three examples drawn from traditional topics within the philosophy of science, having to do with different types of metaphysical orientation, the fact/theory distinction, and the use of analogy respectively.

2.1) Ontology and its Discontents

A main topic in the philosophy of science is that of the proper metaphysical commitment, or lack thereof, due to entities referred to by our scientific theories. One school of thought argues in favor of a realist interpretation of theoretical reference. Theories are construed as real when their theoretical terms are thought to refer to actual entities, such as atoms or the now defunct electromagnetic ether of yesteryear. For those who do not espouse a realist interpretation of theories there exist two major alternatives: 1) Social Constructivism; and 2) Conventionalism. The former is the view that scientific theories are socially constructed in that their factual or observational bases are themselves laden with the baggage of a background theory. What we learn by means of an electron microscope, for example, is dependent upon, if not tainted by, our current theoretical model of the electron. Both Copernicus and Aristotle might observe the same sunset although they will vary in their respective heliocentric and geocentric explanations of the phenomenon. When Carl Anderson first uncovered the proof for Paul Dirac’s prediction of antimatter while studying the effects of cosmic rays upon photographic plates, his experimental success was facilitated because his observations were framed within a theoretical framework that had been unavailable to predecessors in possession of similar evidence. While empiricists, like the apostle Thomas, contend that seeing is believing, the social constructivist would add that one first has to believe something in order to see it. For the social constructivist, like Thomas Kuhn, there are no theoretically uncontaminated facts.

A third way of evaluating the ontological merits of scientific theories is with the perspective known as conventionalism. Conventionalists maintain that scientific theories merely preserve the phenomena they embody in a model which may or may not square with any underlying interpretation or ontology, as in the tradition of the Platonic noble lie. For conventionalists, like Pierre Duhem or Bas van Fraassen, scientific theories are freely chosen conventions that are backed by a rational consensus of those professional practitioners of science who value the predictive efficacy and utility of a theory more than its veridical character. Both social constructivism and conventionalism can each easily be thought of as either negative or neutral in relation to the issue of ontology.

Both the problem of universals within the philosophy of language, which so preoccupied the philosophical thought of the Middle Ages, and the debates which raged over the metaphysical foundations of mathematics about a century ago exhibit a similar, although admittedly not exact, pattern in regard to the issue of metaphysical orientation. From the chronological point of view the problem of universals is actually the senior statesman among the three topics whose metaphysical orientations and strategies are being compared. But we can disregard this historical fact for our purposes. Each of the three main ways just outlined of explaining scientific theories is to an extent mirrored within both the problem of universals and the foundations of mathematics. Analogous to scientific realism are the realist dispositions in regard to universals and mathematical entities. Analogous to social constructivism, although this is debatable, are conceptualism in connection with universals and L.E.J. Brouwer’s intuitionism in relation to issues within the foundations of mathematics. Analogous to conventionalism are nominalism in the case of universals and David Hilbert’s formalism in the case of mathematics.

Students of philosophy will quickly realize that the analysis of many concepts can be sifted through the same prism of explanatory possibilities. Take the concept of time for instance. Either time is real or it is not. If real then it originates either within the mind or without. If without, then its explanation will either be rooted in our sensory experience – which is to take a naturalistic or scientific approach; or beyond our sensory experience – which is to take a supernatural or religious approach. If within, then it is related to consciousness in some way, which would make it part and parcel of our human psychology. If we exclude the possibility, just for the sake of argument, that the explanation of time in any way belongs to the sphere of the supernatural, then we are left with roughly the same three approaches that we encounter in the cases of the philosophy of science, the problem of universals, and the foundations of mathematics. Either the meaning of a concept is the result of some consensus or agreement, is in some way manufactured by the mind, or is part of the sensible and/or intelligible fabric of what constitutes our external or extra-mental reality.

That the logical framework for the evaluation of meaning might be similar for various disciplines and concepts should come as no surprise. After all, scientific and mathematical concepts comprise but specialized cases of language in general. And the cause of linguistic meaning is either mental, extra-mental, or a matter of consensus – which of course still begs the question of origination. On the other hand it is certainly not the case that there exists any exact or isomorphic correspondence between the metaphysical orientations of the three problem areas under consideration. Mathematical realism, for instance, involves an affirmative attitude in regard to the existence of intelligible entities, as does linguistic realism in regard to universals; whereas the scientific realist is committed to some physical reality underlying theoretical concepts. Thus realism is not employed univocally in every case. But such a distinction does not seriously jeopardize the claim that the entities of science, mathematics, and language can be understood through the lens of the same logical framework of general metaphysical possibilities.

Let us however consider one serious obstacle to the symmetry of metaphysical orientations I am proposing. One might legitimately argue that social constructivism is not, strictly speaking, a proper counterpart to either conceptualism or intuitionism. Yet it is nonetheless true that social constructivism, like conceptualism and intuitionism, maintains that experience is not something which is simply given to the observer. Just as Berkeley once argued that primary qualities are never experienced in the absence of secondary qualities; and Kant later tried to broker a synthesis between the powers of mind and the phenomena of experience; likewise social constructivists assert that observation is annexed to background theoretical commitments that forge a conception of scientific reality that is, at least partially, of our own making. Social constructivists, nominalists, and intuitionists alike all share the commitment that not all meanings are fully presented to passive spectator minds which just sit back and enjoy the show of sensory and/or intelligible extra-mental experience While the problem of attempting to fully consolidate the logistics of metaphysical assessment in the areas of science, linguistics, and mathematics is far from solved, I think that even the barest outline of a typology that can tie these disciplines together is a worthy philosophical endeavor. At least I view the parallels I have drawn as a basis for possible enhancement, or even as a whipping post for criticism that might demonstrate an unbridgeable gap that cannot be overcome with wishful thinking.

2.2) Theory-Laden Facts and the Depositum Fidei

The social constructivist concern in relation to the contamination of facts by theoretical considerations, which is a staple problem and topic within the study of the philosophy of science, can be brought to bear upon the problem of the development and permanence of doctrinal meaning within the discipline of Catholic theology.2 That is to say that Catholic doctrine consists of a certain content which is nonetheless cast within a plethora of different contexts or forms. Just as purported scientific facts are conditioned by differing theoretical contexts or frameworks, a set of religious precepts is not set in stone, but within a vast network of linguistic and cultural factors that must be taken into account. Such a content/form dichotomy within Catholic theology for instance has implications for the possible success of ecumenism as well as for the role played by culture in the formation of unique Christian ethnic identities. The late Pope John Paul II was himself a champion of the view that sensitivity to cultural individuality was necessary to the continued success of global evangelization.

John Henry Newman developed an analysis of the development of Catholic doctrine over a century ago which asserted that Catholic doctrinal belief progresses in a deductive rather than in an inductive manner. By this he meant that the core of Catholic teaching in regard to fundamental issues of belief can never be innovative, but must constitute a fleshing out of what is already implicitly believed and understood as true by the faithful throughout the entire post-apostolic history of the Church. Since the Reformation Christendom has been split into many factions, all of which differ on doctrine to varying degrees. Ecumenical efforts to restore Christian unity encounter the problem of latitude in that it remains to be determined whether articles of belief can be expressed in some compromised linguistic form without suffering any loss of original meaning. The goal of ecumenism is to heal the breach within what should be one Church, while not forsaking the idem sensus that is thought to characterize doctrinal meaning in the process. Related to the problem of ecumenism is that of the impact of the encrustation of a culture and various ideological perspectives upon doctrinal commitments.

Is it possible for a set of unchanging theological beliefs to cater to a plurality of different cultural identities without being in some way revised in the process? One relatively recent example of a tampering with Catholic doctrine by means of ideological accretion, at least from the perspective of the magisterium, is that of liberation theology in which the teachings of the Gospel are mixed in with the teachings of Karl Marx. It is no easy task to disentangle so-called theological facts from the accoutrements of human culture and language. One important question is: do the contingencies of history and culture allow for a flexibility of formulation in the articulation of beliefs such that doctrine itself might be allowed to change under the weight of modernizing pressures? But must the interpretation of doctrinal meaning bend under the weight of new scientific understanding? The simple and orthodox Catholic response to such questions is negative. Yet it is undoubtedly the case that several conciliar and post-conciliar documents reveal a willingness on the part of the magisterium of the Church to recognize the role of theological pluralism in the advancement of agendas such as ecumenism and evangelization. Those who adopt a proleptic or future-oriented interpretation concerning the development of Christian doctrine, such as that to be found in process theology or in the post-modern perspective forged by Ted Peters, assert a positive response to the historicity of doctrinal development.

In the conciliar document known as the Decree on Humanism (Unitatis Redintegratio), for example, the Church as a corporate body acknowledges its commitment to Christian reconciliation as well as to the variety which exists in the formulation and expression of Christian belief.

The ‘ecumenical movement’ means those activities and enterprises which, according to various needs of the Church and opportune occasions, are started and organized for the fostering of unity among Christians. These are: first, every effort to eliminate words, judgments, and actions which do not respond to the condition of separated brethren with truth and fairness and so make mutual relations between them more difficult….While preserving unity in essentials, let all members of the Church, according to the office entrusted to each, preserve a proper freedom in the various forms of spiritual life and discipline, in the variety of liturgical rites, and even in the theological elaborations of revealed truth….Therefore, if the influence of events or of the times has led to deficiencies of conduct, in Church discipline, or even in the formulation of doctrine (which must be carefully distinguished from the deposit of faith), these should be properly rectified at the proper moment….The manner and order in which Catholic belief is expressed should in no way become an obstacle to dialogue with our brethren. It is, of course, essential that doctrine be clearly presented in its entirety. Nothing is so foreign to the spirit of ecumenism as a false conciliatory approach which harms the purity of Catholic doctrine and obscures its assured genuine meaning. At the same time, Catholic belief needs to be explained more profoundly and precisely, in ways and in terminology which our separated brethren too can really understand….What has already been said about legitimate variety we are pleased to apply to differences in theological expressions of doctrine. In the investigation of revealed truth, East and West have used different methods and approaches in understanding and proclaiming divine things. It is hardly surprising, then, if sometimes one tradition has come nearer than the other to an apt appreciation of certain aspects of a revealed mystery, or has expressed them in a clearer manner. As a result, these various theological formulations are often to be considered as complementary rather than conflicting.3

In the Pastoral Constitution on the Church in the Modern World (Gaudium et Spes) the Church professes its desire to foster harmony between the ways of the world and Christian understanding.

Furthermore, while adhering to the methods and requirements proper to theology, theologians are invited to seek continually for more suitable ways of communicating doctrine to the men of their times. For the deposit of faith or revealed truths are one thing; the manner in which they are formulated without violence to their meaning and significance is another. In pastoral care, appropriate use must be made not only of theological principles, but also of the findings of the secular sciences, especially of psychology and sociology. Thus the faithful can be brought to live the faith in a more thorough and mature way. Literature and the arts are also, in their own way, of great importance to the life of the Church. For they strive to probe the unique nature of man, his problems, and his experiences as he struggles to know and perfect both himself and the world. They are preoccupied with revealing man’s place in history and in the world, with illustrating his miseries and joys, his needs and strengths, and with foreshadowing a better life for him. Thus they are able to elevate human life as it is expressed in manifold forms, depending on time and place….May the faithful, therefore, live in very close union with the men of their time. Let them strive to understand perfectly their way of thinking and feeling, as expressed in their culture. Let them blend modern science and its theories and the understanding of the most recent discoveries with Christian morality and doctrine. Thus their religious practice and morality can keep pace with their scientific knowledge and with an ever-advancing technology. Thus too they will be able to test and interpret all things in a truly Christian spirit.4

Whereas the philosophy of science seems to have fairly unanimously rejected the positivistic stance of the myth of the framework, which denies any anthropological dimension to knowing, the epistemology of theological pluralism is not as easily understood as its rhetoric may be effective. Convincing everyone that the Church needs to be open to ecumenical dialogue, and that there is an infiltration of culture into the way that religious beliefs are formulated, is far easier than the epistemological problem of neatly disentangling an underlying content of belief from its outward form. The commitment of the Church to theological pluralism is a sincere means of both preserving and strengthening the faith in the face of changing times. It can attract new converts and invites unity between divided brethren. But it is difficult to pinpoint exactly how one can extend the horizon of doctrinal meaning without undermining it. The success of the Thomistic synthesis in the Middle Ages remains a model of how the Church can absorb the secular into the sacred without loss of meaning. But the elasticity of doctrine can only allow for so much stretching. In the attempt to unite what is divided within it and to fit more easily into the flux of a rapidly changing world the Church has to remain cautious that it doesn’t do irreparable damage to the deposit of faith which has guided it for the past two millennia. When Pope John XXIII addressed the Second Vatican Council in its first session he charged those in attendance not to forget that “The deposit of faith is one thing; the way it is presented is another. For the truths preserved in our sacred doctrine can retain the same substance and meaning under different forms of expression.”5 While such words ring with the echo of transubstantiation, in which the substance of Christ is not challenged by outward appearances, the pope assumes a heavy philosophical burden in declaring that the deposit of faith can remain undamaged despite varying modes of presentation. The theme of belief awaiting understanding is being struck once again.

Antipositivist criticism in the philosophy of science was able to show that scientific facts are conditioned by anthropological factors which nevertheless do not undermine the objectivity of science. Likewise, attention to the analogous tension which exists in the consolidation of a set of doctrinal beliefs over time can cast light upon how opposing or differing religious views can continue to profess confidence in religious meaning without the specter of theological relativism haunting all efforts to grasp theological truth. That is to say that a proper understanding of theological pluralism need not imply theological relativism or a willingness to concede what is true in a spirit of conciliation and compromise. There can exist an objectively true and unchanging corpus of theological beliefs. Furthermore, not even the relativistic and skeptical tools of postmodernity need prevail against it, for they can just as easily be employed for the purpose of plumbing the dynamically conditioned yet still stable essence of a theological truth which is constantly assailed by the onslaught of time and the advancement of learning. In the fourth essay of Pragmatism William James pronounced the ancient problem of the One and the Many to be the perennial problem of philosophy. It would seem that he was right in even more ways than he knew. For Christian meaning retains an undivided sameness or oneness that is ever ancient yet ever new.

In the case of aesthetics relativism as to the beauty and worth of an art object is widespread. Kant had to do a lot of fancy footwork in order to cogently argue that autobiographical differences in preference can be linked by a set of intersubjective criteria. The Thomistic description of beauty as id quod visum placet (That which being seen, pleases), coupled with the aesthetic criteria of integritas, proportion, and claritas fares no better in the effort to pinpoint objective criteria for beauty that stand incontestably aloof from interpretive differences. And yet both Kant and Aquinas held that beauty is objectively knowable. If Keats was right to equate truth with beauty, then perhaps the former requires just as much flexibility as the latter. In the sphere of morality for instance the Thomistic tradition maintains that there can be only one absolutely ultimate end for human life, but acknowledges that there exist multiple embodiments by which such an end can be realized according to the varying contexts and circumstances of particular human lives. While Catholic moral theology espouses the view that circumstances do not dictate the intrinsic moral worth of an act, they nevertheless do serve as mitigating or enhancing factors in the overall determination of an act’s precise magnitude within the spectrum of good and evil. From the vantage point of transdisciplinarity it would seen that the unity of the transcendentals calls out for a parity between truth, beauty, and goodness that extends to the realization of just how slippery and evasive the objective character of even religious truth can be. Our current paradigm in physics states that there are four fundamental forces: gravity, electromagnetism, the strong force, and the weak force. Yet it is also believed these forces were once one. They are all manifestations of a single underlying force which was fractured by a series of phase changes that took place in an earlier period of cosmological evolution. Our understanding of religious truth, as fixed yet subject to historical pressures which reveal themselves as culturally idiosyncratic differences, might be profitably understood in a similar manner. To reiterate, I am not defending the claim that Catholicism, for example, should renege upon any of its beliefs. I am just attempting to make sense of the conciliar commitment to theological pluralism in light of a set of doctrinal beliefs which do not allow for the possibility of modification.

Karl Rahner kept a close eye upon the problem of theological pluralism as a parallel to the types of debates that permeated the philosophy of science between the decline of logical positivism and the rise of the spirit of aggiornamento symbolized by the second Vatican Council. The post-conciliar declaration entitled Mysterium Ecclesiae clearly articulates that doctrinal meaning cannot undergo revision despite changes in formulation. Rahner’s critique of this document is a clarion call to the epistemological difficulties which lay hidden beneath the surface of such a sincere but facile statement.6 Rahner argues that the magisterium does not do justice to the technical difficulties involved in distinguishing between what Guarino calls the “unchangeable meaning” of doctrinal belief, or that which belongs to the depositum fidei and which is thus dogmatically binding, and its “changeable form,” or that which is the result of socio-cultural conditioning.7

The challenges of ecumenism due to doctrinal frictions between Christian factions, progress in the ongoing work of evangelization, and the maintenance of a unified Catholic identity in a world where cultural differences cannot be ignored are intimately related from the perspective of a theological pluralism that is sensitive to the form/content distinction. Evangelization involves the quest of extending the invitation to follow a particular pathway of Christ to a larger number of people. In order to foster the intellectual conversion which leads to both moral and religious conversion the magisterium has to contend with the problem of how to frame the truth without diluting it so as to make it maximally appealing to cultures with strangely different customs, many of which are at different stages of development. The forging of distinct cultural identities within the worldwide community of Catholics addresses essentially the same problem, the main difference being that of the extension versus the consolidation of a base of believers and what they believe. The breach between Catholic, Orthodox, and Protestant Christianity might seem not to involve the same type of socio-cultural factors as are involved in the preservation of doctrine in the cases of Catholic evangelization and the Catholic adaptation of doctrinal content to differences of culture. For differences in doctrine between Protestants and Catholics emerged for the most part, one might argue, as the result of major doctrinal differences that could not be primarily attributed to the slippery slope of minor formulaic variations which over time widened into a serious schism. The similarity of ecumenism with evangelization and acculturation lies in what is involved in the attempt to reverse the damage of centuries of bickering. According to Rahner, an examination of its own doctrinal development reveals that the Church has not always been able to isolate its essential doctrine from the historicized conceptual models devised to showcase and interpret it. In maintaining that the essence of Christianity is forged from a marriage between scripture and tradition, Catholic theology enabled both a deepening of its own understanding of what it professes to be true as well as allowed for the possibility of contextualist contamination. Regarding the latter, Rahner writes that “what is involved is precisely the question…of whether something is part of what is really meant or merely an historically conditioned interpretation…belonging to a particular period and able to be eliminated at a later period.”8 As a result of the difficulties involved in straining what is culturally contingent from what is theologically true Rahner calls for an increase of both patience and understanding on the part of the magisterium. Perhaps paradoxically, by magnifying the difficulty of pinpointing what is eternally true beyond the idiosyncrasies of language and culture, the possibility of fraternal harmony in coming to a common understanding without compromising what is true might be facilitated. On this note I recall what G.K. Chesterton once said in regard to the perpetual disagreements that characterized his lifelong relationship with his brother Cecil. While they quarreled incessantly, they never argued. Such is the spirit of fraternity to which a proper understanding of theological pluralism should give rise.

2.3 The Power and Poverty of Analogy

Analogies have the power both to unify and to mislead. No one discipline can claim a monopoly on their use, for analogies cut across all disciplinary boundaries. Analogies are tools of discovery and of pedagogy alike. They can facilitate understanding, but sometimes also introduce irrelevancy into the mix of what we are trying to comprehend. Analogy comprises a species of inductive reasoning, but derives from the Greek analogia, which was originally intended to convey a mathematical sense of proportionality. It occurs in science – and is in fact a recurring topic within the philosophy of science, in colloquial language, in religion, in literature – in the forms of simile and metaphor, and even in jurisprudence – in the guise of legal precedent, and in innumerable other areas of intellectual endeavor. When Machiavelli tells his readers in The Prince that the successful ruler must possess the virtues of the lion and the fox in order to perpetuate his power, he is of course invoking the power of analogy to carry his message. When Aquinas and Suarez contemplate the relation between divine and other forms of being they conclude that there exists a relation of analogy between creature and creator. And when Richard Feynman employed his funny little diagrams in order to simplify the complex computations involved in particle interactions he too was employing a conceptual model or analogy as a substitute and shorthand for what is really going on in the physical world. Feynman diagrams are a computational labor saving device which have both heuristic and expository value. Analogy is both a fundamental and unifying technique in the art and science of thinking.

If understanding proceeds by means of comparison, as Descartes claims in the Regulae, then it is legitimate to suggest that analogy is more than a mere artificial tool for linking ideas. As a conceptual form of interdisciplinary glue that binds various conceptual frameworks together in thought its function might even be described as transdisciplinary. When Wittgenstein abandoned the picture theory of the Tractatus for the more game-like approach to linguistic meaning propagated in the Philosophical Investigations, he nevertheless continued to acknowledge the power of pictorial correspondence as a simple case of his full-blown theory of language. Even that Holy Grail of speculative physics known as superstring theory is no stranger to the lure of analogical thinking. In an interview Edward Witten, one of the high priests of superstring theory, told Paul Davies that “what we expect exists in string theory, and it’s what we would like to discover more than anything else, is an analogous, conceptual, logical framework in which string theory is as natural as General Relativity is in its terms.”9

If a scientific theory can be put into a one-to-one or isomorphic correspondence with a semantical interpretation of some sort, then the latter is said to be a model or analog of the former. To be a little more precise it is fair to say that the scientific model is most often construed in the scientific literature as a structure or construct which bears a greater degree of similarity to what it depicts than does an analogy. Going back to Rudolf Carnap in the 1930’s, we find that models can be described as structural analogs which follow deductively from the calculus of a theory by means of a set of correspondence rules. The equation of a circle and the circle itself share an equivalence that is certainly more exact than the Machiavellian metaphor of the successful prince who must possess both the virtues of the lion and the fox, or the simile of Lord Byron who likened the sheen of Assyrian spears to stars on the sea in his poem about the destruction of Senacherib. For the most part however I will use the term analogy to embrace varying degrees of similarity. Logic after all allows for analogies which are either strong or weak, the latter being the culprit which can most offset what the analogy is designed to accomplish.

Analogies can function in either a positive or negative manner. I suggest the following working typology as a basis for discerning their role within science. It is not uncommon for a specific scientific analogy to exhibit more than one of these analogical types. In the case of Feynman diagrams one can easily make a case that all five of the analogical types listed below come into play.

Uses of Analogy in Science

1) Justificatory - Where the lack of an analogy is thought to be damaging to the potential truth of a theory. In this sense it functions in the capacity
of a necessary condition.

2) Heuristic - Analogies are employed as an aid to or means of discovery. They can act as catalysts of discovery.

3) Expository Analogies can facilitate understanding and are often used in the capacity of an explanatory or pedagogical device.

4) Economic - Analogies can simplify calculations. An example would be the Feynman diagram. Compare the labor involved in solving the equations of QED using Feynman’s pictorial method as opposed to the solutions of Schwinger and Tomonaga.

5) Misleading - Analogies can mislead us into falsehood. This problem can be thought of in two ways. While analogies can be seriously misleading and thus retard the advance of scientific progress in an overt way, one always has to keep in mind that analogical relationships by definition never rise to the level of identity. Thus there is always a trade off in the case of any analogy.

In a letter dated September 12, 1638 Descartes tells a correspondent named Morin that the lack of a suitable analogy would be sufficient to falsify a scientific hypothesis.10 This is a prima facie example of the justificatory use of analogy. Descartes thus would have approved of Einstein’s mathematical spinning of General Relativity out of the physical intuition represented by the principle of equivalence between acceleration and gravity, but would have been highly suspicious of superstring theory on justificatory grounds. For similar reasons Descartes would have rejected Newton’s purely mathematical and physically uninterpreted presentation of the Law of Universal Gravitation, although it is true that Newton engages in some highly ingenious speculation about the nature of gravity in the Queries section of the Opticks. Descartes’ near contemporary and fellow purveyor of method Francis Bacon held an opposing position to that espoused by the French philosopher. In various works Bacon pressed the view that analogies were theatrical idols which misled the imagination away from scientific truth. He insisted that they be stripped of any cognitive credentials granted to them by the superstitions of the religious and magical traditions of the past. In the 19th century Lord Kelvin liberally resorted to the use of models and analogies yet nevertheless castigated them as rude and crude. Rudolf Carnap thought that scientific models possessed both heuristic and expository value for physical theory, but rejected their justificatory importance.

N.R. Campbell is perhaps Descartes’ closest kin in recent times concerning the justificatory connection between analogy and physical theory. In his book entitled Physics, the Elements (1920) he also argued for what in essence amounts to a necessary connection between scientific theories and models or analogies. He writes that “analogies are not ‘aids’ to the establishment of theories, they are an utterly essential part of theories, without which theories would be completely valueless and unworthy of the name.”11 Ernest Nagel echoes the justificatory sentiments of both Descartes and Campbell. “Were a theory stated as a set of uninterpreted postulates, exhibiting not even a formal analogy to some already familiar system of abstract relations, the formulation would provide no clues as to how the theory could be applied to concrete physical problems.”12 An utterly remarkable exemplification of the justificatory function of analogies in modern theory occurs in the case of Feynman diagrams. Freeman Dyson has proven that the infinities which arise in QED are always of the kind that can be eliminated by renormalization. If a prospective hypothesis in particle physics is not renormalizable it will often be rejected. To determine whether such a shortcoming applies an attempt is made to construct the Feynman diagram which mirrors the relevant processes and interactions. Failure to construct the requisite analog in the form of the diagram casts suspicion upon the merits of the hypothesis.

Early modern scientific analogies which likened the molecular activity of gases to collisions between billiard balls were accompanied by the unintended baggage of size and color. These needed to be abstracted from any consideration having to do with gas particles. Many other theoretical conceptions, such as the original 1913 Bohr model of the atom, or the attribution of fluidity to thermodynamic processes, actually engendered a misimpression about the nature of reality. While it might be amiss to claim that the analogical misconceptions of the past should serve as a basis for banishing analogies from future scientific speculation, still the potential for being misled by them is seriously real in terms of the possibility of slowing down scientific progress. In quantum physics however it is quite commonplace to think that no legitimate analogies are even possible. Percy Bridgman once identified the resistance of physicists to the new quantum theory as due to a sense of loss stemming from a view of the world which could no longer be grasped in terms of any model. But analogous thinking is by no means dead or dormant in quantum theory. The wave equation of Schrödinger, which was modeled upon the Hamiltonian form of the equations of motion in classical mechanics, puts the lie to the lament of Bridgman. Another interesting analogy is that of the field operator Φ (x) from quantum field theory, which regulates the emergence and disappearance of the vacuum in an analogous manner to that of the predictive power of the equilibrium state in statistical mechanics. In the study of non-linear or chaotic systems the analogous divergent behaviors of many phenomena suggest that they be understood in a similar manner.

Galileo was perhaps the master of the expository or explanatory analogy in early modern science. During the second day of the Dialogue, for example, Salviati illustrates the concept of relative motion in analogical fashion.

“For consider: Motion, in so far as it is and acts as motion, to that extent exists relatively to things that lack it; and among things which all share equally in any motion, it does not act, and is as if it did not exist. Thus the goods with which a ship is laden leaving Venice, pass by Corfu, by Crete, by Cyprus and go to Aleppo. Venice, Corfu, Crete, etc. stand still and do not move with the ship; but as to the sacks, boxes, and bundles with which the boat is laden and with respect to the ship itself, the motion from Venice to Syria is as nothing, and in no way alters their relation among themselves. This is so because it is common to all of them and all share equally in it. If, from the cargo in the ship, a sack were shifted from a chest one single inch, this alone would be more of a movement for it than the two-thousand-mile journey made by all of them together.13

Descartes also supported the heuristic employment of analogies as tools of discovery. In Rule 8 of the Regulae he recommends resorting to analogy in order to solve the Keplerian problem of the anaclastic – that is, of determining the shape of lens that will cause parallel incident rays of light to converge upon one single point.14 Speaking of Kepler, his own predictions regarding planetary motions in general were based upon analogous inferences stemming from his painstaking analysis of the various motions of Mars. In considering whether an analogy will be pragmatically useful we must weigh it against its potential to mislead us. An important criterion in evaluating the utility of an analogy is its specificity. Navier, Cauchy, and Poisson all did work on the equations of motion for an elastic medium. Poisson demonstrated that both longitudinal and transverse waves were required for travel through such a medium. The ether, one of the major foci for model building in 19th century science, would eventually be discarded from the mainstream of electromagnetic theory because it was no longer needed, but also because it could not accommodate a whole host of engineering problems that were behind the design capabilities of the time. Kelvin showed the mathematical equivalence between lines of force in electrostatics and lines of heat flow in analogous thermal problems in an infinite solid. But he could never manage to solve the problem of heat dissipation in terms of a mechanical ether.

In his famous paper entitled “On Faraday’s Line of Force” James Clerk Maxwell refers to “physical analogy” as a guide to both ongoing research in general and theory construction in particular.15 For example, he notes the partial but useful analogy which holds between the refraction of light when it passes from one medium into another and the passage of a particle through a narrow aperture which then undergoes a change of direction due to various forces. In this case the analogy is directional only, and does not hold for changes in velocity. He also refers to the analogy of an inverse square law which holds between phenomena as diverse as heat conduction and the gravitational force. Maxwell claims that such analogies were pivotal in enabling him to mathematically model electricity upon the motions of incompressible fluids. From a justificatory perspective Kelvin rejected Maxwell’s electromagnetic theory due to its lack of a satisfactory model. This problem of deficiency has a counterpart of excess in the Poincaré theorem which stipulates that if a mechanical model for a phenomenon can be constructed then so can an infinite number of alternative models.

3) E Pluribus Unum

The philosophy of science is but one of many portals that can offer us a glimpse into the inner sanctum that is the unity of all knowledge. For practically two centuries, until being superseded by the familiar but constitutionally challenged motto “In God We Trust,” our national pulse beat to the drum of a more Latinate recognition of the unitary principle that binds us all together as one nation under God. E pluribus unum, which literally means “From many, one,” is an adage with a colorful past. Prior to its selection by the Great Seal committee of 1776, who chose it as emblematic of the knitting together of thirteen independent colonies into one unified republic, the phrase had been employed in a poem by the German mystic Jakob Böhme in 1612 with reference to the integration of the disparate ingredients that are tossed together to become a salad. On a more serious note St. Augustine invokes the phrase in Book IV of his Confessions in connection with the harmonization of souls that occurs in an act of friendship. But E pluribus unum also provides us with a perfect signature phrase to capture the essence of what is meant by transdisciplinarity. The simplicity of truth which underlies all of our manifold and multidisciplinary efforts to penetrate beyond the veil of ignorance that keeps us at a distance from the source of reality is a one constituted of many parts. Despite our hubris and all that we think we know it seems that we have not yet outdone the earliest Greek cosmologists who first sought for the solitary element or explanatory principle that could explain the diversity and the plurality of our experience. Thus it is not unfair to proclaim that the PreSocratics are always with us.

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Notes

 

1 Philip Kitcher, “1953 and All That: A Tale of Two Sciences,” The Philosophical Review 93 (1984), pp. 335-373.

2 Thomas Guarino, “Rahner, Popper and Kuhn: A Note on Some Critical Parallels in Science and Theology,” Philosophy and Theology, Volume 8, Number 1 (Autumn, 1993), pp. 83-89. I apologize to the reader for skewing the issues I discuss in this subsection of the paper from a primarily Catholic perspective. Many would profit, for example, by reading what Ted Peters has to say about the issues of ecumenism and evangelization in relation to the explication of various types of symbolism and conceptual models that pervade religious concepts and beliefs. See Ted Peters, God – The World’s Future: Systematic Theology for a New Era, second edition (Minneapolis: Fortress Press, 2000).

3 Walter M. Abbott, S.J., General Editor, The Documents of Vatican II (Association Press, 1966), see Unitatis Redintegratio, pp. 341-366. The passages I cite are taken from articles 4,6,11,17.

4 The Documents of Vatican II, Gaudium et Spes, pp. 268-270.

5 Acta Apostolicae Sedis 54 (1962), p. 792.

6 Karl Rahner, “Mysterium Ecclesiae,” in Theological Investigations, volume XVIII, translated by Edward Quinn (New York: Crossroad, 1983), p. 151. My own point of departure in relation to the conciliar and post-conciliar statements which link theological pluralism to the fact/theory dichotomy within the philosophy of science stems from the Guarino article listed above. It was from this article that I first learned of Rahner’s views concerning this issue.

7 Guarino, p. 86.

8 Karl Rahner, “Yesterday’s History of Dogma and Theology for Tomorrow,” in Theological Investigations, volume XVIII, translated by Edward Quinn (New York: Crossroad, 1988), p. 13.

9 Paul Davies and Julian Brown, editors, Superstrings: A Theory of Everything (Cambridge: Cambridge University Press, 1988), p. 98.

10 René Descartes, The Philosophical Writings of Descartes, 3 volumes, translated by John Cottingham, Robert Stoothoff, Dugald Murdoch (Cambridge: Cambridge University Press, 1984 – 1991), vol. 3, pp. 120-123.

11 N.R. Campbell, Foundations of Science: The Philosophy of Theory and Experimentation (New York: Dover, 1957), see pp. 129 ff. This is a reprint of the 1920 edition.

12 Ernest Nagel, The Structure of Science (Indianapolis: Hackett, 1979), p. 113.

13 Galileo Galilei, Dialogue Concerning the Two Chief World Systems, in The Tests of Time: Readings in the Development of Physical Theory, edited by Lisa Dolling, Arthur Gianelli, and Glenn Statile (Princeton: Princeton University Press, 2003), p. 111.

14 Descartes, volume 1, pp. 28-29.

15 James Clerk Maxwell, “On Faraday’s Lines of Force,” in The Scientific Papers of James Clerk Maxwell, volume I. My immediate source however is Ernest Nagel’s The Structure of Science, pp. 109-110.

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