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Three Dogmas of Western Science
THOMAS B. FOWLER
[From Faith & Reason, Vol. VII, No. 3 (Fall, 1981), p. 188-220]
One of the most baffling problems faced by modern Christians is the relationship between religion and science. On the one hand, scientists, buoyed by centuries of success in the material order, have tended to use science as a reason to exclude both the inexplicable and the supernatural from meaningful human discourse; on the other hand, apologists for the Faith, certain of their relationship with a Being both inexplicable and supernatural, have tended to seek refuge in a stubborn insistence that the conclusions of science in specific areas are necessarily, though unprovably, wrong. In the seminal piece which follows, Thomas Fowler continues a line of thought begun in F&R VI, 1 (Spring 1980) and thoroughly analyzes the metaphysical presuppositions upon which modern science is most frequently based. His goal? To properly redefine the relationship of science to human knowledge in a way that enables the sciences to enhance rather than restrict man's perception of reality itself. (For a complete understanding of the details and examples of Mr. Fowler's argument, readers will need considerable scientific and mathematical knowledge; however, the broader outlines and essential points are accessible to those of little scientific background, and these points are a sufficiently rich reward for a careful reading of the entire text.)
The influence of experimental science in Western Civilization has grown steadily during the past 400 years, and has now reached the point where it is, in many quarters, regarded as the supreme form of knowledge before which all else must bow. In the words of Xavier Zubiri, reigning Spanish Catholic philosopher of science:
During the modern era, since about 1700, man has lived so persuaded that reality is discovered to him by science that nothing seems able to male him even notice the existence of this basic persuasion. For him, there is no room for the least doubt about it Perhaps science happens to be somewhat fragmentary and changeable; but modern man sees in these two characteristics something more than a sad human condition: he has elevated them to the category of formal structure of science, and has thus made science a constitutive approximation to reality.(1)
Such an enthronment of science has implications which are quite profound, for it entails that "...everything there is in reality which is accessible to man, has to be so in a way eminently scientific." (2)
Is this state of affairs justified? To be sure, the scope and accomplishments of science are undeniable. In many respects it is the supreme achievement of Western Civilization, fully comparable to Roman Law, Greek metaphysics, and Hebrew monotheistic religion. Moreover, it has in no small way conditioned the development of Western Civilization, and hence the entire world, especially during the last 200 years.
But perhaps science has overstepped its boundaries; or rather, perhaps its authority and prestige have been used to establish notions and beliefs which are not justifiable on the basis of science itself. In particular, it appears that science has been mixed liberally with metaphysics during the past four centuries, and the combination of the two enshrined as pure "science". This extremely potent combination has contributed significantly to the dislocations currently on the verge of destroying Western Civilization, and so must be carefully analyzed to determine if it is in any way necessary for the conduct and purposes of science. Three notions, which may justifiably be referred to as "dogmas", appear to be at the root of the problem.
I. NATURE IS LA W
Physical science and mathematics have grown up almost in parallel since the Renaissance, at least in the sense that scientists have often made immediate use of the latest mathematical advances, and indeed frequently sparked new mathematical research themselves. Sometimes the mathematician and the scientist have been the same person, as in the case of Newton, for whom his mathematical work was carried out to facilitate his scientific research. This has had a rather unfortunate consequence with respect to the epistemological foundations of science. The problem centers about the implications of applying mathematical formulae to phenomena. Recall that since the time of Galileo, physics has expressed itself through algebraic equations and analytic geometry, and by the end of the 17th century it employed differential equations as well. For instance, Newton's laws are expressed in the form
F = ma = m d2x/dt2
Now, any such equation has a solution which can be made arbitrarily precise in the numerical sense. That is, if the independent variables are specified to some arbitrary accuracy, then the dependent variables are likewise available with that accuracy after some calculation.(3) For instance, if the motion of a springmassdashpot system is described by the following differential equation (derivable from Newton's Second Law),
m d2x/dt2 + b dx/dt + kx = 0 (a)
a solution may be found as,
and for any t, the value of x may be determined to whatever accuracy is desired simply by evaluating the expression shown. One may, indeed, graph the equation, and since graphs may be drawn to any arbitrary degree of accuracy (because of the continuity of the real numbers), learn whatever detailed information may be required from the graph.
Two notions tended to come out of this, reading backward, as it were, from the equations to nature. First, observing that they were dealing with natural phenomena, and hence nature, and that nature could be described and predicted with these formulae, the scientists made an implicit identification of nature with the law. That is, the law, expressed in the formula, became more real, so to speak, than the phenomena which were instances of it. Everyone knew that any physically constructed springmassdashpot system would not exactly satisfy eq. (a) because of various imperfections in the spring and dashpot, as well as air resistance, etc. Nonetheless, one could approach the equation as closely as desired with a physically constructed device because nature really is such that
F = m d2x/dt2
That is, the scientist had, as it were, read through the vagaries of experience and ferreted out the law, the truth about how nature really is, in its ultimate detail. The absolute reality of nature became the law, and science, the method of reaching it.
Second, there was an even more subtle but persistent tendency to take the equations literally and conclude that nature must be completely deterministic. That is, if we obtain a solution such as is shown in (b), and if the equation of which it is a solution represents what nature is, then it immediately follows that to any arbitrary degree, nature is determined by the law, i.e. nature is fully deterministic. Thus, the mathematical fact that differential equations have numerical solutions capable of being carried out to any arbitrary number of decimal places led to the physical conclusion that the measurable quantities these solutions represented were likewise determined with arbitrary accuracy.
There was, at the same time, an extremely powerful force at work which tended to reinforce both of these conclusions, to the degree that it is difficult to see how anyone could have come to any other conclusion. This had to do with the intellectual hegemony of Aristotelian thought about nature and natural science, in particular, Aristotle's theory of science as expounded in the Posterior Analytics:
We suppose ourselves to possess unqualified scientific knowledge of a thing, as opposed to knowing it in the accidental way in which the sophist knows, when we think that we know the cause on which the fact depends, as the cause of that fact and of no other, and further, that the fact could not be other than it is. Now that scientific knowing is something of this sort is evident-witness both those who falsely claim it and those who actually possess it, since the former merely imagine themselves to be, while the latter are also actually, in the condition described. Consequently the proper object of unqualified scientific knowledge is something which cannot be other than it is.(4)
Aristotle, of course, had been very impressed by the recently developed science of Euclidean geometry, and in particular by the elegant and formal proofs which appeared therein and which have become familiar to all subsequent students of the subject. And he established a paradigm which nearly every philosopher after him would follow. Indeed, not only every philosopher, but every scientist as well: explanations must give a knowledge which is necessary, logically deducible from first principles, and incapable of being otherwise. This notion, rather than being an explicitly formulated theory about which the scientists debated, was an implicit assumption they held in common, and one which seemed selfevident beyond doubt. The passage from philosophical to scientific knowledge was very natural, and virtually no one stopped to think that what was appropriate for metaphysics might not be so for the new sciences. But then apparently no one gave much thought to the proposition that the new sciences might be radically different from metaphysics; recall the title of Newton's work, Principia Mathematica Philosophiae Naturalis. This particular subject will be taken up in greater detail below, as it forms the second of the three dogmas. For now, suffice it to say that the implications of expressing physical laws in the form of algebraic and differential equations were in full agreement with the 2000 year old Aristotelian paradigm of scientific knowledge.
Hence, even if the theory of probability had existed in anything other than the most rudimentary form during the 17th and 18th centuries, it would have certainly been considered as an inferior way to describe nature or as a poor framework for Physical science because it appears to violate the canons of knowledge as laid down by Aristotle. That is, because statisticallybased arguments and theories can only give probabilities of events, not certainties, they would have appeared to scientists as an inferior, or at best a provisional, form of knowledge, especially since the arbitrarily accurate methods of algebra and differential calculus were readily available and apparently quite adequate.
The idea that nature could be captured in a mathematically expressed physical law so enthralled the European mind that it and the problems it created became a persistent subject of philosophy for the next three centuries. In particular, the problem of reconciling the apparently inexorable determinism of nature with a belief in free will called forth a response on the part of every major philosopher Though the subject is outside the scope of our concerns here, the reader may be directed to the ingenuity expended on this problem by, among others, Malebranche, Leibniz, and Berkeley.(5)
Nature as law perhaps reached its apogee in the late 18th and early 19th centuries, and found its most thoroughgoing expression in the philosophy of Kant. As is well known, Kant believed that the mind, due to its makeup, synthesizes experience in such a way as to agree with Euclidean geometry and Newtonian physics. For this reason, they both have the character of necessary truths. Thus the significance of Kant's "Copernican Revolution" is that the laws of nature are removed from nature in an exterior sense, and placed in nature as projected by man onto his experience. But nonetheless nature still is law in an absolutely irreducible sense, and the only way to knowledge about nature, the only way to knowledge of causes, is through science. The other way to resolve the dilemma posed by Hume's critique of causality and the undeniable existence of casual relations in the world apparently never occurred to Kant: discard the notion of Nature as law, and of science as dealing with reality directly, and recognize that science is a different kind of knowledge about the world than is philosophy. But more about that later.
Cracks in the edifice of science built up around this metaphysical principle began to appear in the 19th century from three sources: first, further development of mechanics by Hamilton; second, the development of electromagnetic theory by Ampere, Faraday, and others, culminating in Maxwell; and third, the development of the new science of thermodynamics.
It was certainly well and good for Nature to be Law, and for man to be able to learn how to describe nature through differential equations; without doubt,
F = m d2x/dt2
had great intuitive appeal; after all, the notions of position, velocity, and acceleration are part of everyday experience. And the idea of nature composed of billions of tiny billiardball like particles, all behaving according to the laws of Newtonian mechanics, seemed to be the complete description of nature that had eluded philosophers for so long. Indeed, the confidence in this combined metaphysicalscientific picture was so great that it led Laplace to describe his famous demon; in the words of the French physicist Leon Brillouin:
More than a century ago, Laplace invented a demon who was supposed to know exactly the positions and velocities of all atoms in the universe, and to compute exactly the future evolution of the whole world (exact determinism).(6)
Had Laplace's scheme been realizable, the task of the physicist would simply have been to determine the positions and momenta of all the atoms at some instant and, since Newton's laws were already in hand, merely solve the appropriate equations to learn about any happening, past or present, in the universe. Thus at one stroke the problems of epistemology and metaphysics would have been forever resolved-or so it was believed.
Now Hamilton noticed that the formulation of mechanics could be considerably simplified by introduction of a function, known as the Lagrangian, which is the difference between the kinetic and potential energies of a system, expressed in generalized coordinates which do not necessarily correspond to the physical coordinates of position and velocity:
L = T-V
He determined that any conservative system will evolve in such a fashion that
That is, the time integral of the Lagrangian is stationary. At this point the situation with respect to Nature as Law becomes a bit less comfortable. After all, if a formulation of Newtonian mechanics so different from the original one is possible, can we be so justified in asserting a onetoone correspondence between our equations and the way reality is put together? Worse yet, the variables of the new formulation are not necessarily the same as the old, so that the comforting association of x's with the position of particles is gone. Indeed, one might ask, not altogether facetiously, how an object knows to move in such a way as to render a particular integral an extremum. With Hamilton's reformulation of mechanics, the idea of science in an extremely radical descriptive sense was becoming more forceful, but not yet forceful enough to displace the old metaphysical picture.
2. Electromagnetic Theory
There was another problem. The science of electromagnetic theory had been developing rapidly during the first half of the 19th century; and during the second half, Maxwell was able to codify it into his famous four equations:
There was precious little contact between these equations and the laws of Newtonian physics. How could the notion of absolute reality as tiny billiardball like particles bouncing around be reconciled with that of the forces described by Maxwell's equations? The point of contact was Hamilton's principle(7), because it only required expression of potential and kinetic energy, independent of source (mechanical, electrical, etc.). But perhaps one could just believe that Nature was still law, this time including Maxwell's equations, even if the naive intuitive picture of the billiardball particles was fading. Maybe God really did say
and there was light.(8) Though distressing, this was still not decisive. But there was more.
With the advent of the new science of thermodynamics, problems began to arise which ultimately would bring the entire edifice of classical physics crashing down. All the physicists had implicitly assumed the usual metaphysical principle of matter being composed of the billiardball like atoms; and so naturally when Gibbs went to calculate the entropy of an ideal gas, he based himself squarely on this picture, and determined that it was given by
A second quantity of gas, at the same temperature and volume, would have its entropy given by the same formula, of course. Now since entropy is an extensive property, if the two are mixed, we would expect the total to be
This however, is not the correct answer. To get the correct answer to this problem, known as the Gibbs paradox, Gibbs had to introduce the ad hoc assumption that the particles in a gas are absolutely indistinguishable, in the sense that if any two are interchanged, there is absolutely no difference in the gas. This assumption goes directly contrary to the intuitive notion of billiardballs (and the metaphysical notions of science built upon them), for which, if any two are interchanged, we know that they have been interchanged and the resulting state is different; ordinary billiardballs, that is, have an identity as it were (recall the trancendentals ens, res, unum, aliquid, and bonum); and so it had been assumed for the billiard balllike particles constituting the gas. The concept of identity was certainly implicit in Newtonian mechanics, and even if a metaphysical one, seemed to be eminently justifiable. Obviously a serious clash had developed between the metaphysical picture which the scientists assumed as the basis of their physics and the experimental facts they had to explain. But no one demurred.(9)
Probability first enters science through thermodynamics, too, specifically in the theory of gases, where we find ourselves dealing with enormous quantities of particles, on the order of Avogadro's number (6.023 x 1023) or more.
On the basis of Newtonian mechanics-or so it was believed-one could write down the equations of motion for all these particles, solve them simultaneously, and thus determine the behavior of the gas univocally. But the obvious practical difficulties of dealing with 1023 equations led to other methods, based on statistics, for calculating quantities of interest. This new discipline, known as statistical mechanics, permitted determination of the quantities of interest (energy, temperature, pressure, etc.) with mathematics that was tractable. But no one doubted that the statistical treatment of the gases was any more than a convenient abbreviation for the more complete, deterministic treatment available if desired through Newton's mechanics.
There were other serious problems arising from thermodynamics. For instance, there was the paradox that from strictly reversible mechanical laws (specifically, Newton's laws governing particle behavior), we have irreversible thermodynamics.(10) Then there was the famous ultraviolet catastrophe, which arose from the failure of classical mechanics to correctly predict the energy radiated by a black body as it was heated. (11) This particular problem was the proximate cause of classical physics' demise, and it led Planck to introduce the notion of the quantum.
And indeed it was with the development of quantum mechanics in the first three decades of this century that the decisive break with deterministic notions was finally thrust upon an often unwilling scientific community. For the first time, the notions of probability enter into physics in an essential way through Schrodinger's equation:
Here is not an ordinary variable such as position or momentum; rather, the square of its absolute value gives the probability of finding the particle at a particular point x. Thus probability appears in a way which is not an abbreviation for a "real", deterministic knowledge that is available if desired; there simply is none. Consequently, the epistemological and metaphysical situation is radically altered: if one wishes to read backward from equations to reality, it seems that reality is only determined in the sense. of probability rather than in the sense of strict determinism. Indeed, Schrodinger's equation implies what has become known as Heisenberg's Uncertainty Principle:
That is, the uncertainty in our knowledge (i.e. measurement) of a particle's position () times the uncertainty of our knowledge of its momentum () is always greater than or equal to a fixed number, h, which has the value 1.055 x 10-34 Jsec. The implications were profound: since position and momentum could, theoretically, at best be measured to only a certain degree of accuracy, science itself was limited to telling us about things only to that level; the old notions of absolute position, momentum, etc. could no longer be given physical meaning; they were finally seen in their true light as metaphysical presuppositions. And science had to abandon the cherished goal of explaining all happenings-all change-in the universe. But many were unwilling to accept such a radical conclusion, in particular the implication that science does not look for causes in the metaphysical sense. Zubiri sums it up:
...not only is it untrue that the idea of cause gave rise to modern science, but in fact modern science had its origin in the exquisite care with which it restricted this idea. That renunciation was for the representatives of the old physics the great scandal of the epoch. How is it possible for physics to renounce explanation of the origin of all movement? This heroic renunciation, nonetheless, engendered modern physics.(12)
This is the key to the entire problem: how indeed could physics renounce explanation of all movement? As deterministic metaphysics it could not-which is why the representatives of the old physics, that was really physics plus disguised metaphysics, were scandalized. For physics as pure physics there is no problem because as we shall see the physicist's task is in fact much more modest: to fit experimental data to mathematical structures. The metaphysical goal of explaining all change in terms of causes is not part of that task. If physics was compelled to renounce explanation of all movement in order to explain observed facts(13), there was no cause for scandal, but rather for rejoicing; this, in Zubiri's words, gave to physics its ultimate stroke of purity.
A new concept of nature emerges from the wreckage of classical physicsmetaphysics: Nature has no longer the sense of law, but rather the sense of phenomena as the primary reality. Physical laws are not ultimate, but only mathematical structures which describe the succession of phenomena in the sense of telling us information about what will be observed under certain conditions. There is no requirement for anything beyond a description of what can be observed. Nor is there any justification for asserting that reality is coextensive with or in any way identifiable with the phenomena which physics observes; the phenomena are one thing, and reality another(14). The greatest care must be taken to avoid reading more into science than in fact it gives; in particular one must avoid mixing metaphysics with science and then serving the result as pure science and scientifically justified truth about reality.
II. REALITY IS EXHAUSTED WHEN KNOWN SCIENTIFICALLY
There has been a persistent tendency in the West to believe that when science explains some phenomenon, the objects dealt with therein have been in a sense "demystified" and their reality completely exhausted. That is, once something is known scientifically through the concepts of science (i.e. in a complete phenomenological sense), or rather in proportion as it is so known, its reality is exhausted. For example, if a scientist can predict in detail the behavior of a projectile in motion, say, then (such is the inference) there is no need for any sort of metaphysical explanation in terms of causes which are outside the scope of science. So, once one knows the time sequence of observable phenomena, e.g. in Newtonian mechanics
F = m d2x/dt2
then the reality of the situation in question has been completely dealt with. And so there is nothing more philosophers, theologians, poets or anyone else can intelligently say about it. This belief, or dogma, is the conclusion of an argument which runs as follows: All of our knowledge is through concepts, i.e. concepts are our access to reality; only science can provide us with reliable concepts; therefore reality, or at least as much of it as is accessible to us, is exhausted when known scientifically.
There are several questionable points here, but let us concentrate for now on one, namely that all knowledge is through concepts. This may appear to be the most innocuous, but in fact it is the most far reaching, especially with respect to science.
Aristotle is in some respects the source of this notion, though he spoke in terms of the definition of a thing, rather than its concept:
...definition is of the essential nature or being of something, and all demonstrations evidently posit and assume the essential nature- mathematical demonstrations, for example, the nature of unity and the odd, and all the other sciences likewise.(15)
That is, we know about a real thing only when we know the essence of it, and the essence is expressed in the definition. The definition, in the sense of being the rigorous scientific concept of a thing, thus becomes the cornerstone of knowledge. But there is a significant epistemological problem here, as Zubiri has keenly observed:
If the essence is taken as a real correlate of the definition, one must say at the very least that we are dealing with an extremely indirect way of arriving at things. Because...instead of going directly to reality and inquiring then what might be its essence, we take the roundabout route via the definition. This would be admissible if it were no more than a roundabout route. But it is more; it is a roundabout route based on an exceedingly problematic supposition, viz. that the essential part of each thing is necessarily definable.... (16)
Regardless of whether one agrees with Zubiri on this point, he has put his finger on the key question: what is the relationship between rational knowledge and reality? The suppressed premise here is that one can, through concepts expressed in language, explain the ultimate reality of each thing. This notion became deeply ingrained in Western thought during the centuries after Aristotle, and when modern physics arose, it became part of the physicists' credo as well in the sense that knowledge of reality was through the concepts of physics. Such concepts are, for example, those of velocity, energy, momentum, and force, for which there are operational definitions to be sure, but which definitions supposedly had a real correlate, viz. the real velocity, the real energy, the real momentum, etc. Consider as an example the defining equations for velocity and momentum:
v = dx/dt
p = mv
Outside of these concepts, and whatever reality they implied, there was only crude intuition, not rigorous knowledge.
The notion persisted as well in the development of philosophy, both in the English empirical tradition and for the continental rationalists. Recall Locke's simple and complex ideas, Berkeley's esse est percipi, and especially Hume's relations of ideas. Indeed, this tradition tended more and more toward scepticism as the philosophers realized that there was a chasm between the ideas and the reality they were supposed to depict. But recall as well Descartes' clear and distinct ideas; indeed, for Descartes, the idea tended to become the reality itself: L'idee est la chose meme concue. One of Leibniz' goals was to devise a universal combinatory system that would permit, by studying various combinations of concepts, the investigation of reality as if it were a mathematical problem. And of course Spinoza cast his philosophy in the form of a geometrical system in winch concepts of reality were manipulated as if they were mathematical concepts such as point, line, etc.
Now, this is not to say that there is no knowledge through concepts-manifestly there is, and probably most of our knowledge comes this way. The problems arise from the much stronger assertion that all knowledge is so obtained.
The belief that knowledge is only through concepts, though having a distinguished pedigree, as indicated, perhaps reached its apogee in the philosophy of Kant, for whom, as is well known, knowledge is always the result of synthesis of experience through the categories, i.e. our ideas are the result of the mind's active synthesizing of experience. This inevitably led to the famous analyticsynthetic distinction, and the division of all propositions into a priori and a posteriori, according to the wellknown scheme;
a priori a posteriori analytic X synthetic X X
In this scheme, all knowledge can be divided into analytic truths,
...in which the connection of the predicate with the subject is thought through identity...as adding nothing through the predicate to the concept of the subject, but merely breaking it up into those constituent concepts that have all along been thought through in it, although confusedly...(17)
and synthetic truths,
...in which this connection is thought without identity...[and which]...add to the concept of the subject a predicate which has not been in any wise thought in it, and which no analysis could possibly extract from it....(18)
The implicit dependence on the assumption that knowledge of reality must be through concepts is obvious. Recall that for Kant, the propositions of mathematics, physics, and metaphysics were all synthetic a priori judgements(19), of which, he believed, those of metaphysics could not be justified. Equally obvious, however, is the fact that if this assumption is incorrect, then the entire antimetaphysical argument based upon the analyticsynthetic distinction and the question of the synthetic a priori will collapse because metaphysical knowledge cannot be identified with judgements in any such sense. We shall not enter further into a discussion of this subject, except to say that not only are certain classes of mystical phenomena obvious instances of a direct (i.e. not mediated by ideas) knowledge of reality, but indeed it may be that our normal perception of reality is likewise not mediated but has the character of a direct experience as well.(20)
Moreover, it does not appear to be the case that the mind's first operation, when placed in contact with the world, is to formulate concepts, or "judgements", as Kant thought. Consider Zubiri's remarks:
If the formal function of the understanding were to form concepts, to conceive or to "ideate", then everything with respect to the intellect would repose upon its respect to the concepts, and the radical truth about things would be their ontological truth. But...the formal function of the understanding is not to conceive but to apprehend real things as real. Forming concepts is an ulterior function which reposes upon the other primary function and which derives from it. And this is true whether one refers to human or divine understanding. God does not primarily know real things qua real in objective concepts qua concepts, but rather in a "vision" of the qua real or realizable.(21)
Regrettably, however, the notion that all knowledge is through concepts has persisted for science which, since it is compelled to acquire this knowledge through concepts, has tended to conclude that anything which is not knowable through scientific concepts must be regarded as nonexistent, or at least its existence it notrationally knowable. That is, there has been an implicit identification of the real and the scientifically knowable, to the extent that things such as colors, beauty, etc. are relegated to the periphery of "Reality". In a sense, Quine's "To be is to be the value of a variable" epitomizes this notion. The absurdities to which it can lead, when applied to experience as a whole, can perhaps best be illustrated by the following quotation from J. B. Watson, founder of behaviorism:
The behaviorist has nothing to say of "consciousness". How can he? Behaviorism is a natural science. He has neither seen, smelled, nor tasted consciousness nor found it taking part in any human reactions. How can he talk about it until he finds it in his path.... Behaviorism's challenge to introspective psychology was: "You say there is such a thing as consciousness, that consciousness goes on in you-then prove it. You say that you have sensations, perceptions, and images-then demonstrate them as other sciences demonstrate their facts."(22)
In a similar vein, the publisher of prestigious Scientific American, when confronted with recent evidence of the authenticity of the Shroud of Turin, remarked that as far as his journal is concerned, the Shroud does not exist.(23)
Now, since the belief that all knowledge is through concepts is clearly of philosophical provenance, and also can have rather profound implications, we may proceed to inquire how critical it is for the conduct of science, and whether it can be established or otherwise justified on the basis of science itself. To begin note that science has an experiential basis which is scarcely compatible with any sort of belief that reality is coextensive with what the concepts of science cover. As the German Thomist philosopher of science Wolfgang Strobl has pointed out,
Scientific investigation always starts from, and must necessarily start from, observable experiences in the qualitative world which we perceive through the senses. If physical realism subsequently discards the qualitative world as a mere subjective projection, it deprives itself of the basis of its own raison d'etre, because in order to explain something nonexistent as an objective reality-the reality qualitatively perceived-one must not recur to another reality, essentially different toto caelo from the first. More concisely: if the qualitatively perceived world in which we live, the world of 'light and sound'-I shall call it henceforth the 'anthropocosmos'-is a subjective perception of man, then the anthropological and psychological sciences would suffice to explain the 'dream of the world', and there would be no need of physical science, astronomy, etc.(24)
And Strobl's argument can be strengthened considerably. For it is not simply that science is ultimately founded upon qualitative perception, i.e. takes its origin in the perceptions of the senses, such as observations of colors or sounds. But moreover every day and in each step of its progress and application, science must make use of qualitative perception, be it in reading meters, or looking at bubble chamber photographs, computer printouts, and oscilloscopes. Thus qualitative perception is an essential part of ongoing science; and if its veracity were ever questioned, science as a rational enterprise would collapse immediately. Or in other words, the very things often relegated to the periphery of science-or rejected altogether-such as colors, smells, etc., are epistemologically prior, and absolutely indispensable for science to exist.
Science does require concepts in order to function; but however much it may be dependent upon concepts for the knowledge it produces, the inference that all knowledge is of this form and that reality (or at least that part of it which is accessible to us) is given in the concepts of science does not follow, and indeed would destroy science if carried to its logical conclusion. Science only requires the much weaker belief that there are constraints in the behavior of things whose manifestations in the realm of phenomena can be given mathematical expression. Man cannot fly, nor can he run as fast as he likes. Does this mean that the equations of mechanics and aeronautics explain man? No-only that they give expression to certain constraints that phenomena exhibit, and man is part of the phenomenological world. Again, one must be careful when trying to read backwards from equations to reality.
The situation is rather that science does not exhaust reality through its concepts, but rather presents more of it to us so that we can understand it better and ultimately make appropriate use of it visavis our spiritual existence. The knowledge we receive through scientific concepts thus represents a beginning, rather than an end. As Zubiri has observed with respect to scientific explanation:
For science, a force acts on account of its own proper nature uniformly. A scientific study of force is only complete when the conditions under which it appears and the way in which it acts are univocally determined. That is, one must determine a conjunction of manifestations which follow other earlier ones. Only when the former are found necessarily linked to the latter can we properly speak of scientific knowledge. In other words, precise formulation of the uniformity in nature's actions is the goal science pursues, this is the lex, law. But in terms of causes, this uniformity, this law, is not an object but the very problem: How must things be so that they act uniformly?(25)
Science, in short, instead of answering all of our questions about reality, compels us to ask more questions about it.
III. KNOWLEDGE IS UNIVOCAL
It is rather commonly believed that science has finally provided us with a method for reaching the goal of full and strict knowledge about reality set by Aristotle. Indeed, we saw in connection with the first dogma how instrumental Aristotle's paradigm became. However, Aristotle's own theories about reality have been largely abandoned. What does this mean? In what sense has science changed? Or has it? Are there more "sciences" than one, perhaps? No, not in the common belief, according to Zubiri:
...if one inquires about what should be understood by "science", regardless of the specific reply given, emphasis is always on the science, in the singular, as a univocal effort to intellectually conquer the reality of things.(26)
When, in fact, the Nuova Scienza arose about the year 1500, and modern thought began its offensive against Aristotelian knowledge, the methodology of the new sciences was presented as a critique of Aristotle's syllogistic and science, and indeed as a new substitute for it. But the novelty affected only method and content, not the intellectual intent itself.(27) That is, Aristotle's goal remained unchanged; only his methods (i.e. philosophy) were deemed unfit and inadequate for the task, to be supplanted by the modern tools of experimental science. So we see that as science developed, the scientists and philosophers implicitly assumed that they were simply carrying on-albeit employing more efficacious methods-the work originally begun by Aristotle, viz. that of determining what the physical world is, and explaining it in a satisfactory manner.
Exactly what constitutes a "satisfactory manner" is the crux of the problem. For Aristotle it was through the four causes; for modern science it is through mathematical formulae. These two different ways of explaining the world have generally been regarded as mutually exclusive. In particular, the scientific view has been regarded as superseding the old philosophical view:
Everything seems, then, to lead us to the idea that what the Greeks called episteme signifies the same thing which we call "science", and that the great work of modern science has consisted in showing the falsity or at least the poverty of Aristotelian "science", while at the same time giving man a new method for reaching the same goal. Although variously realized, and with different results in different moments of its history, science is thus always a univocal force directed toward intellectual conquering of the reality of things.(28)
The implicit assumption here, of course, is that knowledge of the world is univocal in the sense that either we acquire it through the four causes, or through the mathematical descriptions uncovered by scientific research, but not both. In particular, once we have scientific knowledge of anything, there is no longer any need to seek for any other "knowledge" about it; such presumed knowledge would inevitably turn out to be superfluous and totally useless.
Closely related to this assumption is the belief that once something has been explained scientifically, its reality is thereby exhausted-the dogma which was discussed in the last section. Indeed, it is the combination of these two dogmas that tends to make controversies over such subjects as the theory of evolution so heated: the scientists naturally take for granted that man's existence and capabilities are univocally and satisfactorily "explained" and essentially exhausted by the gradual development from lower forms of life according to the scenario proposed by Darwin and modified on the basis of molecular genetics.(29) The opponents of evolution tale this for granted as well (30), and believe that the only way to salvage man's unique spiritual existence is to deny the theory of evolution essentially in toto. Thus the battle lines are drawn.
But must this battle be joined? If knowledge is not univocal, then phenomenological knowledge of life forms is not the soughtafter complete picture. An if it is not true that phenomenological knowledge of the temporal succession of life forms is the only knowledge about the origin of man, then the theological view of man as a spiritual creature is not necessarily in jeopardy. Recall that for St. Thomas, the soul "informs" the body such that the two form a radical unity:
Whence we must conclude that there is no other substantial form in man besides the intellectual soul; and that just as the soul contains virtually the sensitive and nutritive souls, so does it contain virtually all inferior forms, and does alone whatever the imperfect forms do in other things ...on the withdrawal of the soul, no part of the body retains its proper work, although that which retains its species or form retains the action of the species. But act is in that of which it is the act, and therefore the soul must be in the whole body, and in each part thereof.(31)
And basing himself upon the scientific research done since the time of St. Thomas, Zubiri argues along similar lines:
...the biochemical structure of the germinal cell is not a mere dispositional cause but something deeper: it is an exigent cause of the human psyche. The psyche is not only a psyche of this body but is a psyche which, because it is demanded by this body, must have as its essential intrinsic factor the type of sentient psychic constitution that this body determines. In its turn, the intellective psyche of itself demands a body, and not just any body but precisely this body with this type of structure.... A species having the transformed somatic structures that the hominized hominid has, and not possessing an intellective psyche, could not have subsisted biologically....(32)
This intellective psyche is not just the ability to react to stimuli as in the phenomenological scheme, but transcending that it is the ability to perceive real things as real and the capacity to deal with them as such. It is this and what it entails which is not accessible to science: free will, consciousness of being, truth, and beauty, for example. Thus man could be a product of evolution in the biochemical sense described by evolutionists, but these biochemical structures studied by science are not the only form of knowledge about man because they give only constraints, not the complete picture of man as a conscious animal:
...mere sensation cannot produce of itself an intelligence: there exists between the two an essential, not a gradual difference. No matter how complicated the mere stimuli and their form of apprehension are, they can never arrive at constituting stimulating realities and intellective apprehension. At this point the appearance of an intellective psyche is not only a matter of degree but is essentially something new....the human psyche is determined by the transformation...of the mere hominid into man but is not brought about by the transformation. Because of this it can only be an effect of the first cause, just as at its time the appearance of matter was: it is the effect of a creation ex nihilo.(33)
The biologists, as much as the physicists, are compelled to remain within the realm of the phenomenological; consequently there are aspects of man which are not within their purview-not in the sense that man as an organism violates any scientific laws, but in the sense that those laws do not account for all aspects of man's development and behavior; they only constrain it. To be sure, God could have created a different world, one which was fully deterministic in the metaphysical and phenomenological senses, and in which phenomenological laws would be adequate to explain all change. But we are in the world that was in fact created, and in which phenomenological laws, for the most part statistical, give only constraints, not unique determination. The consequence with respect to man and evolution is straightforward:
...evolution must integrate with itself the advent of an intellective psyche which is essentially irreducible to pure sensation. If evolution is within the competence of science, the characteristic of intelligence is within the competence of philosophy. In recurring to the creative cause, philosophy does so by integrating the creation of the psyche with the evolutional mechanism.(34)
The general question of the univocal nature of our knowledge has been discussed elsewhere(35), but the arguments there developed may be summarized as follows: scientific knowledge deals with the temporal succession of phenomena; we understand something scientifically when we can give the mathematical equations governing the appearance of its associated phenomena. For example, with respect to motion, we understand motion scientifically when we have an equation which tells us what we will observe at time t1 and what we will observe at time t2, given certain initial conditions, even though the mathematical expression may be statistical. On the other hand, we know something in the sense of a thing, as something which forms a part of reality, defined as "all and only that which acts on other things or on itself in virtue, formally, of the characteristics which it possesses,"(36) when we know its place in the cosmos and why it acts as it does, i.e. when we know its essence(37). Moreover, "the phenomena of nature are not the things of the world."(38) The phenomena upon which science acts are just that: phenomena; reality is what forms the object of philosophy and, indeed, the object of everyday knowledge. The reality of many things is known through their phenomenological manifestations; but this does not imply that phenomena are identifiable with reality. The phenomena we experience are only a means to the end of perceiving reality, an end which is prior both epistmologically and metaphysically.
So we may conclude that while science is a form of knowledge, the crucial inference that knowledge is univocal and that science therefore displaces all other knowledge of reality is both unnecessary for the conduct of science and false as well. And as we shall see, the assumption that science deals directly with reality is not required for the conduct of science either; it is possible to give a complete and consistent phenomenological interpretation of science which, at the same time, resolves many longstanding epistemological problems associated with scientific explanation.
We may capsulize the discussion thus far as follows. The three dogmas of Western science are:
Nature is Law.
Reality is exhausted when known scientifically.
Knowledge is univocal.
Together they imply:
Science is identifiable with knowledge.
The real is the scientifically knowable.
Which in turn imply:
There is no philosophical or theological knowledge properly so called.
There is no spiritual reality.
Man need not be assumed to be more than a purely natural being, subject only to the laws of nature as disclosed by science.
Not a single one of the three dogmas is required for the conduct of science. They are the foundation of a complex of scientific and philosophical ideas that has comprised part of the intellectual baggage of the West for several hundred years, and which has been accepted in a rather uncritical manner because of the success of positive science. God alone knows how many souls have been lost because they too believed that science was built upon these three dogmas, and then drew the indicated conclusions. But we can now affirm that however widespread the belief in these dogmas may be, their plausibility is gone and they can only remain as an obstacle to scientific progress and the correct understanding of science as a human enterprise.(39)
A NEW VIEW OF SCIENCE AND THEORY
It is appropriate at this point to sketch out a new and hopefully more satisfactory view of the nature of scientific knowledge and its relation to reality as a whole, one which will avoid the pitfalls of identifying science with some particular metaphysical scheme such as that represented by the three dogmas discussed above.
This new view arises in part from a correct resolution of a very critical problem: the relationship between mathematics and science. If this relationship is misunderstood, as it was for the most part until the later part of the 19th century, there is little hope of coming to a correct understanding of science as a human enterprise. Now, if mathematics is not our way of synthesizing experience, as Kant thought, and therefore not a type of necessary truth about the world, what is it? Without plunging into the disputes over the foundations of mathematics(40), we may say that mathematics, rather than dealing primarily with numbers, deals with possible structures (e.g. fields, groups, rings, vector spaces, etc.). Whence the nature of physics as a scientific enterprise becomes clear: it is not identified with any particular branch of mathematics (e.g. Euclidean geometry, as Kant thought); rather, it must fit a mathematical structure to observed phenomena. That structure might be nonEuclidean geometry, for example, as in the case of me General Theory of Relativity. Or it might be recursive function theory as applied to linguistics, or me notion of Banach spaces applied to nonlinear systems. There are no a priori restrictions on which structures may be employed, just as there are no a priori restrictions on what phenomena may appear. In the words of Strobl:
That mathematics and physics are not interchangeable, that the task of physics is, rather-based upon an experience perfected through experiment-to fix which from among the infinite mathematical structures ideally possible are the real structures that determine the mode of being of natural physical laws: this is something perfectly known by philosophy, the theory of the sciences, and the particular sciences.(41)
That is, with respect to phenomena-what can be observed and measured-science seeks to determine a mathematical structure which will permit it to predict further observations on the basis of past observations. It does not require the hypothesis that mathematics is the way nature is put together, nor that the application of mathematics to nature will necessarily unlock all the secrets of reality. To repeat in other words: the metaphysical hypothesis that nature is put together mathematically is not required for the conduct of science. Only the much weaker condition that mathematics can be employed to describe observed phenomena required. Regrettably, however, it was the first view which dominated up to the twentieth century, as we discussed above. As Dampier puts it,
...men were inclined toward the most rational side of Platonism which also defends the opinion that one can reach eternal truth via an innate truth or internal illumination, but continues interpreting mathematical or geometrical harmony as the essence of things. This style of thinking led, through the ideas of Galileo and Kepler, to the mathematical system of Newton. It took the internal force or illumination as the foundation of reason, and theory was then converted into a form of intellectualism, which seeks the truth of the essence of the divine as much in the physical order of the universe as in the moral law.(42)
Modern physics clearly demonstrated that this entire scheme had to be abandoned, as we have seen. The key point that has been retained is the fact that we can perceive more of reality through the structures which science delivers to us. To quote Strobl once again,
The directrix function of mathematicalstructural thought, with its symbolic form of representation...[shows]...that the whole orientation of...[experimental science]...does not tend to give a mere series of measurement ciphers, but relations, links, mutual correlations among observable data.... The symbols which serve to designate the structural elements in these systems of relations do not allude only to quantitative extensions, but also to qualitative intensities (e.g. force, energy, electric charge).(43)
It is this ability to use the products of science (e.g. our understanding of charge as part of the material constitution of physical bodies) to extend our everyday perception of reality that is the unique perogative we have as spiritual creatures.
Note that the fact that science does not deal directly with reality does not mean that it does not deal with or is not ultimately based upon reality; it obviously is. Virtually every scientist feels that he is investigating "reality", and he is right. The problem is that the passage to reality involves an intermediate step, the ability of a human person to perceive reality through phenomenological experience (and the laws describing it). The scientists, not recognizing this, have for the most part assumed that it was science itself that was opening reality to them, rather than simply amplifying their normal perception of it.
There is, in addition, something very positive that can be said about the knowledge which is delivered to us in scientific laws; indeed, something which permits a rather old and recalcitrant problem to be solved.
Anyone having the slightest acquaintance with science knows that any scientific theory contains hypotheses which are empirical, and therefore subject to refutation. He is probably also aware that in the course of its history, many hypotheses have been refuted. Such, for example, was the case with Newton's laws of motion, the caloric theory of heat, the geocentric theory of the universe, the theory of continuous energy emission, and so forth. So what does it mean to say that today we have knowledge in the form of scientific theories about the universe, about atoms, molecules, etc. if they are all subject to refutation upon discovery of some new empirical fact? In what sense is science bringing us closer to nature if overnight the entire picture could change?
This last question is, it should be noted, only a problem for those who maintain the univocal view of science as accomplishing the goal, long ago set by philosophers, of giving us knowledge of nature simpliciter. As long as science is restricted to the phenomenological level, i.e. as dealing with systems of phenomenological relations, there is no problem provided that information is included in the conceptual picture. For what we see is that any scientific theory is limited to dealing with a certain range of phenomenological relations, and within that range, gives information in the phenomenological sense about other succeeding relations. Thus Newton's laws, for instance, are not 'false' in the sense of being completely wrong; rather, they give correct results-correct information-provided that the initial conditions represent phenomena within a certain range: objects not too small or large, velocities not too large, fields not too great in strength, etc. And every one of these conditions is itself expressable in terms of numbers, specifically inequalities such as
10-20 <m< 1025 Kg
50 < T< 1000 °K
which represent typical values (44), so there is no ambiguity. Thus in a sense, the successive scientific theories simply represent an increasing range of conditions under which the initial phenomena observed may be used to accurately predict later ones, i.e. give information about them. (Of course, this only applies to theories which in fact give correct results under at least some circumstances). If any theory or purported theory does not permit the inference of information in the phenomenological sense, it is useless for the purposes of science.
Now, information is not some vague metaphor referring to knowledge about the world. Rather, it has a very precise meaning due to the work of Shannon(45), Brillouin(46), and others. In particular, one may determine the amount of information which, say, an observation gives by the following formula:
I = log2 P0 /P1
where P0 is the number of possibilities before the observation, and P1 the number after it. For example, if it is known that there are from 50 to 100 people in a room before counting them, and exactly 76 after counting them, the number of possibilities has been reduced from 51 to 1, so
I = log2 51/1 = 5.67 bits
Any meaningful scientific theory or action will have some reference to the acquisition or manipulation of information; and any theory which does not, e.g. the theory that the universe is characterized by some uniform rectilinear motion, must be discarded.
In general, the process of extracting information about future observations will require a recasting of the raw theory, say Newton's laws, into a form suitable for "input" of observations, and arrangement for computation of the desired results. Take the case of the distance a particle travelling at speed v can cover in time tl, its mean lifetime,
d = vtl
If we have a mechanism capable of observing such a particle in motion, and determining the velocity at which it travels, and if we know tl, the mean lifetime, we can arrange to feed this information to a computer, which will output the distance d travelled by the particle. Specifically, the above formula will give a number n bits of information approximately equal to the number of bits of accuracy to which the mean lifetime t1 is known, or the velocity v, whichever is less, until the velocity v begins to approach the speed of light, c. Then the number n begins to decrease until at about 0.5c it is down to 3 bits, and at 0.9c it becomes less than 1. Of course, if the theory of relativity is employed instead, then the number of bits of information will not decrease under this circumstance. This is the sense in which successive theories represent improvement in our dealing with the phenomenolgical world. There is, as explained above, no need to assume that such theories deal directly with reality in the metaphysical sense; that is beyond the scope of science.
SUMMARY AND CONCLUSION
We may conveniently summarize the discussion with an enumeration of those beliefs which are and those which are not required for the conduct of science. First, the latter:
The belief that nature is identifiable with scientific laws is not required for the conduct of science.
The belief that reality is exhausted when "explained" by science is not required for the conduct of science.
The belief that knowledge is univocal is not required for the conduct of science.
Several other beliefs, which are derivatives of the above, also call for enumeration:
The belief that nature is strictly determinate is not required for the conduct of science.
The belief that science seeks to find causal relations (in the metaphysical sense) is not required for the conduct of science.
The belief that science deals with ultimate reality is not required for the conduct of science.
The belief that science has to tell how all change occurs, in its ultimate detail, is not required for the conduct of science.
Turning now to the other side of the question:
The belief that mathematical structures can be used to describe phenomena is required for the conduct of science.
The belief that science gives us information (in the quantitative sense) about phenomena is required for the conduct of science.
The belief that no a priori restraints can be placed on phenomena is required for the conduct of science.
The belief that phenomenological laws represent constraints on how things may behave is required for the conduct of science.
The relation between science and reality would seem to be the following:
We have the capability of perceiving reality through phenomenological experience, more of which science is capable of delivering to us. The actual perception of reality is not directly through science as is usually assumed; rather, it requires the intermediate step of human intelligence.
Hopefully the foregoing will serve to purge science of its unnecessary and detrimental metaphysical baggage, and set forth the minimal conditions which are necessary for its viability as a human enterprise within the context of man's total existence. Science, one of Western Civilization's most splendid creations, must not be perverted by illconceived metaphysics and turned into the instrument that destroys the Western, Christian Civilization which alone was capable of giving it birth.
1 Xavier Zubiri, Nature, History, God, translated by T. B. Fowler Washington, D.C.: University Press of America, 1981, p. 59.
3 This is true regardless of whether a closed form solution can be obtained.
4 Aristotle, Posterior Analytics 71b 815, quoted from The Basic Worlds of Aristotle, ed. by Richard McKeon, N.Y.: Random House, 1941, p. 111.
5 Spinoza, however, chose to bite the bullet and accept determinism making it an integral part of his philosophy: "In nature there is nothing contingent, but all things are determined from the necessity of the divine nature to exist and act in a certain manner." (Ethics, part 1, proposition 29, quoted from The European Philosophers from Descartes to Nietzsche, ed. by M.C. Beardsley, N.Y.: Modern Library, 1960, p. 158.)
6 Leon Brillouin, Science and Information Theory, 2nd edition, N.Y.: Academic Press, 1962, p. 308.
7 Zubiri, op. cit., p. 261.
8 For further discussion of this point see T.B. Fowler, "Xavier Zubiri: Science, Nature, Reality", Faith & Reason, Vol. 6, No. 1 (Spring 1980),
9 For more details on the Gibbs paradox see F. Reif, Fundamentals of Statistical and Thermal Physics, N.Y.: McGraw Hill, 1965, p. 243246.
10 For further discussion, see Brillouin, op. cit., p. 316318.
11 Arthur Beiser, Perspectives of Modern Physics, New York: McGrawHill, 1969, p. 375379.
12 Zubiri, op. cit., p. 253254.
13 There are those who have never accepted this conclusion, and who continue to insist on what have become known as "hidden parameters". However, they have never been able to adduce much evidence to support their position, which is based more on a refusal to accept limitations to physical knowledge than on experimental evidence. For a discussion of the status of these "hidden parameter theories" see Bernard d'Espagnat, "The Quantum Theory and Reality", Scientific American, Vol. 241, No. 5 (1979), p. 158ff.
14 Fowler, op. cit., p. 1012.
15 Posterior Analytics 90b 3033, quoted in McKeon, op. cit., p. 161.
16 Xavier Zubiri, Sobre La Essencia, Madrid: Sociedad de Estudios Y Publicaciones, 1963 p. 89 (author's translation).
17 Critique of Pure Reason, translated by Norman Kemp Smith, N.Y.: St. Martin's Press, 1965, p. 48.
19 Ibid, p. 5255.
20 The similarity between ordinary perception and mystical experience, with respect to the character of immediate veracity both produce, has often been observed Professor Robert Wolff, of Columbia University, author of the wellknown work Kant's Theory of the Mental Life, admitted in a class which the present author had with him, that Kant would be committed to denying the possibility of this type of nonsynthetic experience, i.e. mystical experience. Or conversely, its existence would be a refutation of Kant's theory.
21 Zubiri, Sobre La Essencia, op. cit., p. 65.
22 J.B. Watson, The Ways of Behaviorism, N.Y.: W.W. Norton & Company Inc. 1928, pp. 3, 7.
23 Reported in National Review, May 30, 1980, p. 643644. The publisher of Scientific American is Gerard Piel.
24 Wolfgang Strobl, La Realidad Cientifica Y Su Critica Filosofica, Pamplona: universidad de Navarra, 1966, p. 324 (author's translation).
25 Zubiri, Nature, History, God, op. cit., p. 7071.
26 Ibid, p. 5960.
28 Ibid, p. 60.
29 This does not imply that the present author believes the theory of evolution is a plausible or satisfactory one from the purely scientific standpoint. Rather, it seems that the question of its adequacy cannot be resolved at the present time simply because a sufficiently general theory of system behavior does not exist. The major problem has to do with system optimization: a highly optimized system consisting of a large number of interacting subsystems can only be significantly improved by major modifications to many or all of the subsystems simultaneously, possibly with the addition of new subsystems as well. How or even whether this could occur under the assumptions of random genetic mutation (which is assumed to be the fundamental mechanism of evolutionary charge) is not clear. See T.B. Fowler, "Computation as a Thermodynamic Process Applied to Biological Systems", Int. J. BioMedical Computing, Vol. 10 (1979), p. 477489.
Moreover, the theory of evolution in general is considerably more problematic than most biologists are willing to admit. They should spend a little more time studying the history of science. Newtonian physics, which had been verified to a rather high degree of accuracy and better than the theory of evolution by several orders of magnitude, and which had been accepted as the absolute truth about the universe by scientists for 200 years, met its demise when it sought to explain the null result of an obscure experiment on the speed of light. How many such experiments lurk for the biologists, especially considering the state of development of biology visavis physics? Moreover, the proponents of Newtonian physics, unlike the evolutionists, did not need to rely upon longrange extrapolation to obtain results, either.
30 Paula P. Haigh, "Evolutionism, Creationism and Christianity" in F&R I, 2 (Fall 1975).
31 Translation from The Basic Writings of Saint Thomas Aquinas, ed. by A. C. Pegis, N.Y.: Random House, 1945, p. 70809, 716.
32 Xavier Zubiri, "The Origin of Man" reprinted in Contemporary Spanish Philosophy, edited and translated by A.R. Caponegri, Notre Dame: University of Notre Dame Press, 1967, p. 6769.
33 Ibid, p. 6566. Italics mine.
34 Ibid., p. 74. The present argument assumes that there are occurences which are not explainable by science in the sense of being predictable but which are not forbidden by it either. This is clearly possible if phenomenological laws are statistical and yield only probability distributions of events. When such laws are combined with respect to events occurring in temporal succession, it can quickly become impossible to predict anything other than that certain future happenings are forbidden by the laws, but what will actually occur is quite undetermined by them. It is in this sense that they yield the constraints described in the main body of the article. If phenomenological laws were all completely deterministic, and formed a totally closed system, it would be considerably more difficult to integrate the phenomenological world with the cosmos of everyday experience, and correlatively, man's spiritual characteristics with his physical body. In no case does the truth of Christianity rest upon the truth (or falsity) of particular scientific laws because as we have seen, such laws do not deal with reality directly. But in an environment dominated by deterministic scientific thinking (e.g. 16th19th century Europe), there is a tendency for an everwidening chasm to open between the "material" and the "spiritual" a la Descartes, with the attendant acute mindbody interaction problem.
35 Fowler, "Xavier Zubiri...", op. cit., p. 1222.
36 Zubiri, Sobre La Essencia, op. cit., p. 104 (author's translation).
37 The problem of determining essences, however, is an exceedingly difficult one, and so this does not imply that knowledge of reality is quickly or easily achievable.
38 Zubiri, Nature, History, God, op. cit., p. 259.
39 Of course, the fact that the initial three dogmas are false does not guarantee that the conclusions shown are false; that would be the fallacy of denying the antecedent. Rather, it only shows that the truth of these conclusions (or absence of it) cannot be established on the basis of the mixture of science and metaphysics which has been "science" in the minds of most intellectuals for the past 200 years.
40 The interested reader is referred to Haskell B. Curry, Foundations of Mathematical Logic, N.Y.: Dover Publications, Inc., 1976, pp. 816. Curry makes some rather disconcerting remarks on p. 16, however, which indicate he might like to see mathematics assimilated to the experimental sciences.
41 Strobl, op. cit., p. 103 (author's translation).
42 Quoted in Strobl, p. 67.
43 Ibid, p. 100.
44 Exact values will depend upon the application.
45 C.E. Shannon, "The Mathematical Theory of Communication", Bell System Tech. J., Vol. 27 (1948), pp. 379423, 623656.
46 Brillouin, op. cit.