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An empirical critique of empiricism.

I. Introduction

Empiricism has never been a uniform doctrine. Taken as a general attitude, there is something about empiricism that rings with a robust sense of reality that philosophers and scientists share as human beings who spend most of their waking hours outside of the classroom or laboratory. Most of us have probably come across the Thomas Paines of society who embody an almost self-assured realism that verges on the naive, the kind that professes a healthy dose of skepticism and common sense as antidotes against beliefs that lack "empirical" rigor: embodied, in short, by the kind of person who thinks he is qualified to make statements about science and religion but is an expert in neither. In addition, there are accomplished scientists who interpret reality according to the scope of a particular field of positivistic science and its theoretical models of phenomena (most of which are mathematical) without examining the philosophical presuppositions that go unnoticed in the process. Given these caricatures, and given the nuances involved, a thorough definition of empiricism is no simple task.

In this article, we will instead attempt an overarching exposition of two overlapping but divergent paradigms of empiricism: (a) strict empiricism, representing most of the British empiricists and ancient skeptics and (b) mitigated, or metaphysical, (1) empiricism represented by Aristotle and St. Thomas Aquinas. Sense experience is the unifying departure point for both, but while (b) says that human knowledge begins with sense experience, (a) tends to ultimately reduce knowledge to sense experience. Concerning structure, our article is divided into two parts. The first consists of two sections: (1) a philosophical critique of strict empiricism from the viewpoint of mitigated empiricism and (2) an account of how both versions of empiricism view causality. The second part consists of a critique of strict empiricism from the point of view of mathematics and modern physics. Since the very scope of these topics has generated a vast literature, the sole aim of our thesis can be only to raise questions about certain empiricist presuppositions that enjoy wide appeal, especially in the English-speaking world. Beyond the philosophical benefits of critiquing the strengths and weaknesses of an influential tradition such as British empiricism against a philosophical tradition that is often neglected or misunderstood, some of the advances in mathematics and the physical sciences over the last 250 years suggest that the complexity involved in the study of the natural world raises serious questions about any version of strict empiricism, specifically, the development of nonlinear dynamical systems, special and general relativity, and quantum mechanics, all of which challenge the presuppositions of a strict empiricism.

II. Strict Empiricism and Metaphysical Empiricism

A. A Critique of Strict Empiricism It may seem irrelevant at this juncture to mention the name Parmenides, but in reality this ancient Greek philosopher represents the state of the question. To Parmenides, the universe offers a convincing impression of motion, multiplicity, and change, all of which are registered by our senses. But human reason "sees" something the senses do not: that what all things have in common is that they exist. For Parmenides, existence does not come in degrees because:

(1) The already existent cannot be the source of more existence (existing is existing, period);

(2) The existent cannot emerge from that which does not exist (to say that existing and not existing is the same thing is a contradiction that reality does not permit).

If the difference between thing x and thing y is nothing (since they both exist), sense experience and change must be at best an illusion. Unable to arrive at the concept of the potentially existent (not to be confused with possibility, which is a logical category), Parmenides affirms the principle of noncontradiction at the price of severing any causal connections between a conclusion of reason and the input of the senses. Parmenides comes close to making an explicit discovery of a distinction that would elude the British empiricists: the distinction between sense knowledge and intellectual knowledge.

Leaping across centuries, we find that Descartes himself is unable to escape relative nonexistence. I may doubt the testimony of my senses; I may even doubt everything, but someone has to doubt. To even begin with consciousness requires me to begin with reality. What Descartes discovers reveals a possible similarity with the two Parmenidean principles mentioned above:

(1a) The most immediate empirical datum is the absolute certainty I have of my existence. To think that my thoughts are only appearances or nonexistent is absurd.

(1b) Conclusion: Cogito ergo sum: I think, therefore I am.

(2) Given the identity between my thinking and my existing (2a), I am a thing that thinks, and since I can't help having some ideas that are clear and distinct and others that are not, I can embrace no other reality except the self or (2 b) remain immune to error by not giving assent, that is, by an act of will, to ideas that are not clear and distinct.

The Cartesian cogito (i a) is really a recapitulation of Parmenides's error on the level of consciousness. If human beings are saved from error in a static universe in which the existent is always the actually existent, Descartes thinks he will have avoided error by elevating the intellect to the status of an absolute. But because Descartes imposes hyperbolic doubt on the real difference between the real and the unreal, he commits a far graver error than Parmenides and is led into equating the absolute statement "I exist" (i a) with the idea that consciousness is absolute or always in act (2a). Hence emerges the need to attribute cognitive features to the will to account for error, as in (2b). When I perceive a tree or some object, I have the existential perception of knowing that I am knowing; but this does not make consciousness absolute. A tacit indication of why it is insufficient to remain within the "I" or self to avoid having to judge if anything is real is Descartes's subsequent (and inevitable) desire to prove the existence of the external world. To remain in a state of suspended judgment is naturally repulsive to our subjectivity; and this explains why the [TEXT NOT REPRODUCIBLE IN ASCII] [impassiveness] of the ancient skeptics is the least prevalent of all convictions and cannot pass for an empirical outlook. Even error is more natural to us than solipsism. (2)

And even if one were to try suspending one's judgment to avoid ever having to be wrong about anything, the very experience of correcting oneself when one realizes something is not real is when consciousness discovers itself as consciousness of the real. The experience of mistaking the real for the apparent is yet another indication that all idealisms and skepticisms are partial, or that reality measures consciousness. Realism, which may be defined as "knowledge of trans-subjective entities," (3) is what in Kantian language allows us to even speak about the condition of the possibility of error. (4)

Although Descartes also believed that the senses could not be trusted, he was consumed by a passion for the clarity (and certainty?) reflected in the mathematical sciences (which is curious, considering that mathematics is a formal science that provides no clear indication of how its objects relate--at least directly--to reality). Descartes took the empirical nature of our subjectivity into account but was perhaps misled by a naturally inevitable metaphysical reflection turned inward. Nevertheless, Descartes will assert that the conceptual domain of quantity is least susceptible to doubt; for even in dreams there can be correct mathematical thinking, aside from the obvious appeal mathematical objects elicit because of their clarity and individuality. But correct mathematical thinking is not necessarily correct metaphysical thinking. In relation to modern science, Cartesian dualism marks the solidification of the contemporary attitude that sense experience combined with quantitative description is the most valid paradigm of knowledge and the most objective reflection of reality. (5) What Descartes does next will influence the empiricism of Locke, Berkeley, and Hume. He goes on to inject a hyperbolic doubt into Parmenides's discovery of the object of metaphysics--the existent as such--along with a metaphysical twist that is not wholly original: How do I know that the very objects of my thoughts, even uncomplicated geometrical forms, exist?

As is well known, Descartes finds his bridge from the certainty of the self to the existence of an external world in a third principle: the idea of God, whose essence involves existence. For Descartes, this is the only idea that carries the distinct assurance that the objects of clear and distinct ideas correspond to reality, especially space, extension, motion, numbers, and so on. It is important to remember that to Descartes, anything that is not pure thought (e.g., emotion, passion, feeling, volition, sensation, etc.) does not count as a clear and distinct idea and is at best opaque. A human being is simply a machine that thinks: that which is not pure thought is only mechanical (i.e., matter extended in space). Thought alone retains a purity that distinguishes it from the material or physical. While embracing Descartes's radical separation between mind and matter, even Locke does not hesitate to make thought subject to a mechanistic or corpuscularian conception that flirts with the kind of materialism that finds favor with most Anglophone philosophers today. (6) Locke's "dark room" metaphor is an interesting caricature of a materialist reduction of mind to a passive receptacle of material "globules" that it must rearrange to produce knowledge:
   I pretend not to teach, but to inquire; and therefore cannot but
   confess here again that external and internal sensation are the
   only passages I can find of knowledge to understanding. These
   alone, as far as I can discover, are the windows by which light is
   let into this dark room. For, methinks, the understanding is not
   much unlike a closet wholly shut from light, with only some
   openings left, to let in external visible resemblances, or ideas of
   things without: would the pictures coming into such a dark room but
   stay there, and lie so orderly as to be found upon occasion, it
   would very much resemble the understanding of a man, in reference
   to all objects of sight, and the ideas of them. (7)


The thesis that "all knowledge derives from sense experience" is close to meaningless if the only thing to which we have access is a passive television screen of inner perceptions. Locke may not have been exactly sure what the nature of mental states are, or what exactly a mind is, but even he finds great difficulty in accepting the idea of a complete dependence of the mental on the physical despite his inability to explicate their respective natures. (8) Continuing now with our previous point about thought, both Descartes and Locke nevertheless take "idea" to mean any object of inner perception: volition, sensations, and whatever the mind perceives in itself or is the immediate object of inner or immediate perception, thought, or understanding. (9) Locke's "psychologism" is a study of how perceptions and sensations give rise to some of our ideas. The only thing that Locke does is to try to break down Descartes's clear and distinct ideas into their most basic elements. (10) Simple ideas, such as extension, can be explained vis-a-vis a combination of different sense impressions or from a single sense faculty. (11) A combination of simple ideas forms complex ideas such as that of substance. "Substance" is a complex idea implying a substratum in which qualities reside, a composite of sensations or the "we know not what" (12) that lies beneath them. But the only reason, perhaps, that Locke assumes that these ideas correspond to external realities is because he does not question Descartes's metaphysics. In a very Cartesian fashion, Locke proceeds to privilege certain qualities, such as extension, shape, or motion, which he calls primary qualities, probably because he thinks, like Descartes, that these are the simplest of ideas and very hard to doubt. While primary qualities are real, secondary qualities (e.g., color, taste, smell, etc.) are not.

For some reason, Locke will nevertheless relegate some ideas (e.g., substance) to internal experience, the basis of which is Cartesian self-consciousness, while the others are assigned to sense impressions that come from external things said to exist outside of the mind by a Cartesian leap of faith. When a more metaphysical thinker like Berkeley looks upon Locke's philosophy, he faces a similar dilemma. Why give

privilege to extension? Why make that a primary quality and not color? Locke insisted that primary qualities are real properties found in external things. But if tastes and colors are also impressions or ideas, why not numbers, motion, and extension? (13) The only possible direction to take is immaterialism: "to be" is "to be perceived." If in Locke an external thing consisted in ideas composed of impressions of external things, in Berkeley reality is purely and simply perception that knows nothing of external things. Nevertheless, my thoughts are in fact my thoughts, and there is still an "I." Following Descartes, the Bishop Berkeley can only appeal to a Cartesian God who is as immaterial as perception itself.

Only now can the gauntlet of strict empiricism be cast down with full severity in the figure of Hume. While insisting that any idea that does not correspond to a sense impression (i.e., whose origin is not a clear impression registered by one of my senses) is suspect, Hume ironically exhausts the dark room metaphor: "the mind has nothing but perceptions and cannot possibly reach any experience of their connection with objects." (14) Sartre seems to be the only philosopher who was able to turn Locke's metaphor into an art, except that in British empiricism's version of No Exit, hell is not other people but a stream of perceptions. Descartes's attempt at a static dissection of sensation and thought succeeded in exalting man to a quasi-angelic being whose life consists in pure thought and whose materiality is pure mechanism; but by the time Hume is done deflating this theoretical castle in the sky, man is one step away from becoming the pitiable insect of Kafka's Metamorphosis, a Humean life form that cannot even be confined to a dark room because there is no such room, let alone a person or self that houses it. For such an insect, life is an amorphous apologue of perceptions without connection, except those that pragmatically drive it from place to place. Rather than stopping at the unity of phenomena or association as in Locke's semiempiricism, Hume even questions the unity of a self that may contemplate such things.

Hume is a typical example of how a strict empiricist proclaims skepticism and denies that we can go beyond experience but behaves as an ambiguous realist. Like those before him, he accepts the Newtonian understanding of motion as a line composed of mathematical points that have no causal relation, and he proceeds to translate this into his view of consciousness. Sense impressions are nothing but atoms of consciousness, a view that dogmatically assumes the Parmenidean metaphysic of pure actuality that Descartes attributes to thought and a Newtonian model of physics (and the presence of any scientifically solidified model that attempts to elaborate upon experience already assumes more than the limits Hume imposes on experience). Prior to any talk of theories or models, observation and experimentation become impossibilities if there is nothing stable about reality and our knowledge of it. A genuine empiricism acknowledges that science requires the formulation of concepts and theories that go far beyond things merely observable in ordinary experience; and even when the inevitable time comes to decide which circumstances remain fixed and which variables to manipulate in an experiment, a scientist must have an adequate concept not only of a thing and its properties, but of the procedures and instruments needed to measure them, to say nothing of the interpretive hypotheses involved in more complex theories in which observation and experimental control are severely limited. (15) If impressions are therefore only actual and momentary, then my past impressions are at best uncertain. If I feel cold now and hot five minutes later, it is questionable whether I am the same person! Hume atomizes the unity of the human person because he does not question the Cartesian and Newtonian residue that creeps into his philosophy. Hume is simply assembling "mindstages out of perceptions and minds out of mind-stages," (16) as if the nature of consciousness could be explained by a Newtonian pattern of physics where chronological succession supersedes ontological dependence.

If such epistemic anarchy is all there is to human experience, one might as well deny, like Berkeley, that there are concrete corporeal sense organs; or that they are materially affected by sense-perceptible things external to a unified knowing subject. Yet, by reiterating the thesis that the apparent presupposes the real, and consciousness reality, the senses no longer have to be channels severed from an unlit Cartesian theater that has no access to them. A realist account may just prove to be more faithful to our ordinary experience of error in at least two ways: (1) when I realize, for example, that the stick I saw in the water only looked bent, I realize (contra Berkeley) the materiality of this experience, at least of my corporeal organs; and if I posit that knowledge is nothing more than a bundle of sensations or completely material, than the sensible presence (i.e., appearance) of a stick that looked bent should continue to seduce me even after I realize I judged falsely; but (2) the fact that the sensible presence that was judged to be real remains as an object before my consciousness in its facticity even after I realize the stick only looked bent shows that this judgment is not a mere material process and that error is more complex than sensation. (17) The fact that I may initially suspend judgment about the stick further reveals that any sense datum remains neutral towards the real and the not real, something that it could not do if errors and judgments are merely mechanistic. (18)

What these observations ultimately suggest, among many other things, is a crucial doctrine that the Aristotelian-Thomistic tradition has maintained since its birth: unlike psychical acts, such as judging, the senses as such are not reflexive, and the testimony they offer to us will always be in accord with the specificities of their proper objects. They may be occasions for errors in an accidental way, as deficient instrumental causes, the way a painter might use a brush poorly, especially if the brush is damaged or defective. (19) The senses grasp real things, but they do not know that what they are grasping is real. "What they inform us of is no different from what they sense ... but the senses have no 'sense' of reality." (20) A corollary to this doctrine is that the senses are never wrong with respect to their proper objects, unless the corporeal organ in question is damaged or diseased. Aristotle and Aquinas would insist on an existential "solidarity" that marks sensation and thought while respecting their distinct roles. (21) Human beings think with and through the senses, and even if we know through theoretical reflection that they are somehow distinct, to try to isolate one from the other completely is the wrong way of elucidating the relationship between them. In this sense, the existential complexity of sensation and thought does not allow us to know what it is like to think without any sensation whatsoever or to sense without the involvement of our intellect. Subsequent to its faulty constructionism, strict empiricism ultimately leads to a static deconstructionism that attempts to dissect sense and thought in a way that is destructive of their unity.

Now, the capacity to grasp or know that things are real and not simply things that are real is the overarching critique of the Aristotelian-Thomistic tradition. In the language of Aristotle and Aquinas, there is an essential distinction between sense knowledge and intellectual knowledge. (22) Strict empiricism falls short in viewing this difference as a blurry and opaque difference in degree rather than kind. With some reflection, most of us would know what was being de scribed to us if someone told us there is a difference between being color-blind and saying that the act of seeing is colorless. No matter how refracted sense experience may seem, my knowledge of a color is not itself a color. If I strike a match to light the stove, the flame that becomes an object of my cognition does not burn my mind the way it might burn my hand. What it is to be fire, as opposed to fire, is not something I can touch, taste, hear, smell or see. (23) Every word on this page is as concrete and material as I am, but to know that many individual human beings have individuality in common cannot possibly be a matter for the senses to detect, even if they register individual and material things. Every sense faculty has a corresponding individual object (e.g., color for sight, which is always of this or that thing, etc.); but to attribute individuality to many individual things, or to know that what many individuals have in common is that they are individual, is metasensorial.

What Locke does to secondary qualities, or "proper sensibles" in Thomistic language, is partially symptomatic of a lack of this distinction. If secondary qualities lack "transsubjective" value, for example, if sight has no immediate transsubjective grasp of its proper object (i.e., color), then there is simply no point in looking into microscopes or telescopes, for these material extensions of our sense faculties would simply be empty extensions of their utter subjectivity. (24) It actually makes more sense to convert from Locke's "semi-empiricism" to Berkeley's "immaterialism" and retreat into inner perception alone. As with the inconsistency between Hume's philosophical views and his adoption of Newtonian science, this is indeed counter to the sensibilities of today's average empirical outlook that places so much stock on the possibility and reliability of "concrete" scientific conclusions about "concrete" realities. These inconsistences arise only because people like Hume fail to contemplate that human thinking is primordially and spontaneously ontological. If, however, we cease in insisting that the senses should perform the prodigious cognitive leap of giving us more than what can be given in them, then the same material extensions that play a similar instrumental role in science (e.g., microscopes, telescopes, and most scientific instruments) will not be expected to pass philosophical judgments on what is real and what is not. The material configuration of the eye of a dog, for example, may make it more sensitive to some portions of the electro-magnetic spectrum; but a dog could never appreciate a Dali.

In contrast to the psychological sensism of strict empiricism that is a partial sketch of human knowledge, what it is to be x (as opposed to something that is x) is what metaphysical empiricism posits as the proper object of human cognition, the immaterial "what" (quidditas) of material realities. (25) Human knowledge has the capacity to form universal concepts of real natures that the sciences attempt to refine. But there is also a foundational class of universal principle presupposed by all science and all reasoning, principles that are unprovable because their evidence is immediate and direct (e.g., propositions such as "there is no middle term between existing and not existing," or "something cannot be and not be at the same time and in the same respect" or "the whole is greater than the part"). These principles are dependent on the real natures in the world and the relations that hold among them, not on the psychology or belief-structure of any given epistemic subject. (26) Although these principles function as the principles of indirect evidence or deductive reasoning that are presupposed by the sciences, they, and any basic knowledge we have of universal natures prior to the contribution of the sciences, always begin with sense experience. (27) But here, at the very suggestion of anything "immaterial" or "universal," is where the rational sobriety of strict empiricism coincides with some of its greatest oversights.

Aristotle and Aquinas never thought of a universal nature (28) (such as "man") as a sum-total of individuals, even though reality is about concrete and individual things: "there are no things except the things there are." British empiricism displays an understanding of universals that is consistent with the lack of distinction between sense knowledge and intellectual knowledge. Consider the following passage by Berkeley:
   Universality, so far as I can comprehend, [does not consist] in the
   absolute, positive nature or conception of anything, but in the
   relation it bears to the particulars signified or represented by
   it: by virtue whereof it is that things, names, or notions, being
   in their own nature particular, are rendered universal. Thus when I
   demonstrate any proposition concerning triangles, it is to be
   supposed that I have in view the universal idea of a triangle;
   which ought not to be understood as if I could frame an idea of a
   triangle which was neither equilateral nor scalene nor isosceles.
   But only that the particular triangle I consider, whether of this
   or that sort it matters not, does equally stand for and represent
   all rectilinear triangles whatsoever, and is in that sense
   universal; all which seems very plain and not to include any
   difficulty in it. But here it will be demanded, how we can know any
   proposition to be true of all particular triangles, except we have
   first seen it demonstrated of the abstract idea of a triangle which
   equally agrees to all? For because a property may be demonstrated
   to agree to some one particular triangle, it will not thence follow
   that it equally belongs to any other triangle, which in all
   respects is not the same with it. (29)


An adapted response from Aquinas or Aristotle would involve two considerations. First, knowledge of a specific nature--which is always universal--is not acquired by an endless empirical comparison of individuals. Second, both would insist that knowledge does not involve any crude copy or sensory-laden representationism that falls between the mind and the thing being known. Knowledge is more like an intentional possession of reality: there is an identity of intentionality between the thing known and the act of knowing it. (30) What characterizes the nature of knowledge is a relationship of essential identity and existential difference:31 the known reality in our intellect (as something known), and the real object existing in objective reality, are identical in their essence or "what"; the only difference is the manner of existing of this "what." (32) Gyula Klima, a contemporary Thomist, provides a simple but potent analogy that illustrates how our "intellectual images" or concepts of things are formal signs (33) (as opposed to conventional or instrumental signs, such as words) whose objective reality consists only in remitting to the reality that is known through (quo) it:
   When you look into the mirror to fix your tie, you see your tie
   only through seeing its reflection. Still, of course, you do not
   fiddle with the reflection to fix your tie. Instead, you reach for
   your tie, because what you see by looking into the mirror is your
   tie, the ultimate object of your act of sight, which you see
   through its immediate object, the reflection. Indeed, for the
   reflection to be this immediate object is for it to function only
   as something that directs your act of sight to its ultimate object.
   That is to say, to be this immediate object is to be recognized
   only as something through which [quo] you see the object you want
   to see, and, at the same time, not to be recognized as that which
   [quod] you want to see, as the ultimate object, to which your
   intention, attention and action are directed through or by the
   former. (34)


Unlike the epistemology of the Pre-Socratics and modern materialists (there is little difference in their materialistic realism except technological advances that extend the range of observation), to know a stone does not imply that I somehow must have stone in my brain. This is perhaps the most colorful sketch of the ultimate conclusion that knowledge is the result of a simple rearrangement of cerebral matter, a position that renders any talk of an objective reality existing outside of consciousness contradictory. (35)

There is a similar tendency in a strict and materialistic empiricism to reify (literally, "to make into a thing") ideas, images, and even concepts. Empiricists of the British kind never seem to consider that someone's thought or understanding of a triangle need not be accompanied by a sense-image. If this were the case, every mathematician would need to embark on the impossible empirical adventure

of comparing every single triangle in the world to verify a definition of a particular kind of triangle. One can speak of "triangularity," but triangularity is neither a triangle stripped of all of its specific differences nor a triangle that somehow includes or subsumes into itself every single kind of triangle. (36) Sense-images were never meant to be the primary content of knowledge, but given that the senses are not reflexive, our intellect must somehow anchor a concept by a "turning-back" to the sense-images (conversio ad phantasmata) that accompanied a particular thing:
   Thought is essentially universal. The thought to which seeing Ludo
   first gives rise is a thought of a cat, not of Ludo ... What makes
   a thought of Ludo a thought of Ludo and not just a thought of a cat
   is its being a thought of, say, the one-and-only cat I saw with
   such-and-such coloration in such-andsuch a place at such-and-such a
   time. This gives us a perfectly good thought of Ludo, though it is
   one specified in general terms. It is also clearly produced by an
   intellectual activity: no image need be arising in us when we have
   this thought. Nevertheless, the information from which we produce
   this thought comes from our sense-image of Ludo at some time when
   we saw him. (37)


The true classical view of Aquinas and Aristotle, though misunderstood by many philosophers, is a breath of simplicity that is more faithful to human experience. In their view, human beings simply do not see mental processes, impressions, or bundles of qualities, but things that are already a unity outside of the mind. Our contention, however, lies not in the necessary reliance we have on our senses, but with the general failure of certain empiricists to see that immateriality is the root of knowledge. (38) To know a stone or a triangle, for example, ultimately means knowing it in an intelligible or immaterial way; (39) and even though knowledge does presuppose physiological modifications in the organic faculties of a knowing subject, these changes alone are not yet knowledge as such. (40) The account provided by Aristotle and Aquinas of how external things act on the senses and how sense data is then elevated to the level of thought cannot be given an adequate treatment here. (41) Suffice it to say that the transition from sense knowledge to intellectual knowledge is not something we are conscious of: we discover it a posteriori through philosophical reflection. (42) Of course, when the ancients questioned the how of things, they assumed that there was some sense to this "how" or "why," both of which are synonyms for the experience of "causality."

B. CAUSALITY

Few subjects are as philosophically riveting as causality. What was once a rich, metaphysical analysis of causality ultimately became a victim of Hume's reductionist epistemology:
   When any natural object or event is presented, it is impossible for
   us, by any sagacity or penetration, to discover, or even
   conjecture, without experience, what event will result from it, or
   to carry our foresight beyond the object, which is immediately
   present to the memory and senses. Even after one instance or
   experiment, where we have observed a particular event to follow
   upon another, we are not entitled to form a general rule, or
   foretell what will happen in like case.... But when one particular
   species of event has always, in all instances, been conjoined with
   another, we make no longer nay scruple of foretelling one upon the
   appearance of the other, and of employing that reasoning, which can
   alone assure us of any matter of fact or existence. We then call
   the one object Cause; the other, Effect. We suppose that there is
   some connection between them; some power in the one, by which it
   infallibly produces the other, and operate with the greatest
   certainty and strongest necessity. (43)


Hume goes on to say:
   The only immediate utility of all sciences is to teach us how to
   control and regulate future events by their cause.... Yet so
   imperfect are the ideas which we form concerning it, that it is
   impossible to give any just definition of cause, except what is
   drawn from something extraneous and foreign to it. Similar objects
   are always conjoined with similar. Of this we have experience.
   Suitably to this experience, therefore, we may define a cause to be
   an object, followed by another, and where all the objects, similar
   to the first, arefollowed by objects similar to the second. Or in
   other words, where, if the first object had not been, the second
   never had existed. The appearance of a cause always conveys the
   mind, by a customary transition, to the idea of the effect. (44)


These conclusions flow from overly empirical assumptions that fail to take into account the following correctives. First, the general idea "cause" is not a sensorial datum of experience, and our analogical use of the word is an indirect indication of this. Linguistically, "cause" comes from the Greek (OITIOO, a term that has a wide range of meanings that are not restricted to a sequence where B follows from A, or from any empirical observation. "Cause" is determined from a specific context and is an analogical concept whose meaning is as wide as the existent (ens), the most universal and concrete concept into which all other concepts are resolved. (45)

Second, this notion of causality is subject to the same defect that permeates the general epistemic framework of the British empiricists: the failure to distinguish sense knowledge from intellectual knowledge. The origin of the notion of causality can be intellectually grasped through abstraction from internal experience in at least three ways:46

(1) Some of my interior acts depend on other acts that are also my own;

(2) Things outside of me exert an influence on me and affect me;

(3) I also affect and exert an influence on things outside of me.

Apart from these three things, what we never experience directly are the ways that one external thing influences another external thing. Hume's redeeming quality is his insistence on this fact, even if an exaggerated insistence. At the very least, the experience of (2) is an inadvertent restatement of a critique suggested earlier against the Cartesian cogito: it is impossible (for a finite consciousness at least) to think about myself without thinking of other things. A causality trapped within solipsism denies, without reason, that we are aware of being affected by realities that are distinct from ourselves.

Incidentally, Hume himself errs not so much in his subjectivism but in his logic: "The argument that custom or habit is responsible for our naturally expecting B to follow from A, like our natural desire to find the unity of phenomena and why we associate some with others, is viciously circular. If we naturally expect a causal sequence to unfold, and if this is driven by the force of habit, must we not admit that habit is its cause?" (47) This chain of reasoning is a tacit confirmation of the causality involved in (1). Are internal acts (such as thinking and willing) mental fictions or are they as real as the external things they affect? Returning to Locke, we once again come across the assumption that external things indeed affect our corporeal organs: In the notice that our senses take of things, we cannot but observe that several particulars, both qualities and substances, begin to exist; and that they receive their existence from the due application and operation of some other being. From this observation, we get our ideas of cause and effect. (48) Locke, like Hume, pins the false realism of association on a corollary to this assumption, namely that a cause must precede an effect chronologically. For Aristotle and Aquinas, a cause is not truly a cause until an effect is produced. The casual action is identically the producing of the effect, or the immanence of the cause is at work in the effect so long as the effect is being actually produced. (49) Causality is therefore defined by an ontological relationship of dependence, not a temporal sequence of events between phenomena. Understood thus, cause and effect are simultaneous.

If you take Locke's dark room metaphor seriously, the only thing the mind can do is associate globules of ideas that represent objects that it can never access. In yet another Cartesian leap of faith, the conformity between these representations is said to be "caused" by the things they represent; but if a raw "representationalism" most adequately accounts for human knowledge, a more consistent objection to this deus ex machina insertion of causality is that the causality that produces ideas is not at all represented in those ideas. (50) Since the mind is a dark and passive space that associates perceptions, no amount of association will explain the unity of phenomena. Association is not causation. The association between night and day is a stronger type of association than Hume's famous example of the billiard balls; but while there is a stronger process of contiguity in the former, would any sane person say that day is the cause of night?

The strict empiricism of Hume remains a splendid example of what happens when psychology (mixed with an implicit adoption of a Newtonian conception of physics) overtakes ontology and logic. By the time British empiricism culminated with Hume, logical laws become consumed by a psychologism that can speak only of approximate regularities in successions of matters of fact, an assumption that permeates Hume's theory of causality. (51) Apart from Husserl's contention that an anthropological relativism of logical laws is "counter to the self-evident conditions for the possibility of a theory in general," (52) Hume seems to think that his account of causality can stand on an appeal to the logical category of necessity even though Hume's philosophy of knowledge would lead one to think that if the necessity of logical laws do not have corresponding sense impressions, then they therefore depend on us. (53) Philosophy and science after Hume would eventually deal a serious blow to the idea that causality implies necessity. (54) In place of this "derivativeness of the effect," causality is often mistaken in modern science for predictability according to laws (i.e., that given A, one can predict B). (55) But unless causality is understood to be an ontological relationship of dependence, science itself becomes a senseless enterprise that retreats into the intersubjectivity of minds that define external reality against scientific models that are adopted today and replaced tomorrow. When indeterminism took the place of determinism in modern physics (especially through the philosophical pronouncements of Bohr and Heisenberg), an equally destructive inattention was given to the distinction between ontological questions and scientific questions. Given that physics is but a formal or quantitative description of relations among perceptions, there is no scientific way of measuring, on the atomic or on the ordinary level, the process known as cause and effect, the validity of which is not only a thoroughly ontological or metaphysical inference, (56) but one of many realities (distinct from the thoughts of the physicist) in the natural order of things that is presupposed by the methods of experimental science. (57)

These cogent observations should pose a worthy dilemma for anyone who is convinced that knowledge is derived from the "pure" data of experience or from models that aspire to be their perfect mirrors. As we shall see, even science is not exempt from reflecting on some of its own attempts to refine the intelligibility of the real.

III. Perspectives from within Mathematics and Physics

In our discussion of causality, a faint hint of one implicit catalyst in the development of strict empiricism was given in passing. This catalyst was the great success of classical mechanics.The foundational presupposition held by many empiricists--that reality can adequately be described by systems of (deterministic) differential equations-is based on this fact. This situation was exacerbated by the strong support from the nineteenth-century French mathematical physicist, Pierre-Simon Marquis de Laplace. (58) Stephen Hawking has concisely described Laplace's belief: "[If one ] knew the positions and velocities of all the particles in the universe at one time, the laws of physics would allow us to predict what the state of the universe would be at any other time in the past or in the future" (59) Laplace posited an "intelligence," which we would now call a computer, to make these calculations. This view may be considered a different manifestation of the error Hume made in pinning necessity to causality. Aquinas, for example, would say that the natural effectiveness of the material world is contingent and that necessity applies only to logical laws. (60) He would also say that nothing material, let alone a program implemented by a computer, bears the characteristic of logical necessity. (61) Laplace's "physical determinism" is a prolongation of strict empiricism in the line of Hume.

But there are many other empirical problems with such assertions. Newton's and Laplace's notions of time and space suffer from several defects. One of the realities that these early modern physicists did not foresee in general is the effect of nonlinearities on solutions to systems of differential equations, in particular, the existence of chaotic systems. About seventy years after Laplace's death, Jules Henri Poincare was the first mathematician to discover deterministic chaotic systems. (62) He showed how a small perturbation to the initial state of a system could lead it to evolve to a radically different state. Nonlinear systems (63) do not satisfy the superposition principle. Their output is not proportional to their input (i.e., a small change in input can yield a large change in output). Most natural systems are in fact nonlinear, but some can be well approximated by being linearized and subsequently studied locally with linear analytic methods.

Students of mathematics and physics are often introduced to this topic with the example of an unforced, rigid pendulum. Consider a pendulum with a mass M on the end of a rigid, massless rod of length L. It is connected to a point P on a ceiling and under the force of gravity with acceleration g. Motion is initiated by displacing the mass M some distance 9 away from the rest position and regular, periodic motion is observed. This system is described by the differential equation:

[??] + [g/L] sin[theta] = 0

Realizing that ([theta]) [approximately equal to] [theta] for small [theta], one can make an approximation and simplify the differential equation:

[??] + [g/L] [theta] = 0

and therefore approximate the motion of the pendulum as linear. Next, it is easy to obtain the periodic solution:

[theta](t) = [[theta].sub.0] cos (wt + [psi])

where

w = [square root of (g/L)]

If one cannot make the small angle approximation (e.g., one is considering a pendulum that is perturbed from the equilibrium with a large [theta]), one must take another approach to study this nonlinear system. No closed-form solution of this nonlinear differential equation is known, so one approach to understand the system is to linearize it locally around the equilibria. This is easily done by rewriting the equation as a system of two first-order differential equations, writing the Jacobian matrix, and solving it at the equilibria.

The situation becomes much more complex if another force is introduced into this system. Consider an electromagnet (64) that is placed beneath the pendulum and activated at a regular rate, that is, every second. The effect of the magnet turns out to be nontrivial. One might presume that given the periodic motion of the pendulum and the constant rate of magnet activation, one would observe new periodic behavior (e.g., the mass swinging to a greater or lesser angle). In reality, the mass begins to swing in a highly erratic manner and an observer cannot begin to guess where it will swing from one moment to the next--chaos has emerged.

A. DYNAMICAL SYSTEMS THEORY

Contrary to popular belief, chaotic systems can be (mathematically) deterministic; their behavior does not arise from stochastic factors. A system S is chaotic if S contains a Bernoulli shift. (65) The simplest chaotic dynamical system is the Bernoulli shift described by Julian Palmore (66):

[x.sub.n+1] = [Dx.sub.n]mod 1

where D is an integer larger than i. In base D arithmetic, x is written as:

x = [a.sub.1][a.sub.2]

where a(i) takes values [0, 1,..., D-1]. (67) At each application, the D-point is shifted to the right by one digit and the bypassed digit is removed. So 0.[a.sub.1][a.sub.2][a.sub.3][a.sub.4] ... [right arrow] 0. [a.sub.2][a.sub.3][a.sub.4] ... and small differences, 8, in starting values, grow exponentially as [D.sup.N][delta] after N applications. Probably the most popular example used to illustrate chaos is the so-called Butterfly Effect: "the notion that a butterfly stirring the air today in Peking can transform storm systems next month in New York." (68) Or put more rigorously, a small perturbation in the atmosphere could yield qualitatively different conditions in another portion of the globe. In fact, this might actually occur if damping were not present in real world systems.

However, the complexity of chaotic systems may be better illustrated with the problem that motivated their discovery. Consider the seemingly straightforward system of the motion of three celestial bodies. This is a classic problem in astronomy that is usually generalized to the N-body problem. If one models the celestial bodies as point masses and considers their motion with regard to their mutual gravitational attraction, an interesting problem develops. If N = 2, the system is integrable and elliptic, parabolic, and hyperbolic solutions emerge. However, if N = 3, there is a Hamiltonian system with nine degrees of freedom that may be reduced to four degrees using all ten classical integrals of motion, but the general problem is still intractable. (69) The only way to gain insight into this problem is to apply simplifications that drastically reduce the generality of the solution or to develop a numerical simulation. This complexity is a major obstacle to achieving Laplace's scientific determinism.

Another problem has to do with computability. Laplace lived in a time when computability concerns (70) were not recognized, even theoretically. Therefore, he could not have appreciated the need to maintain computations within the field of computable numbers. Computable numbers (71) are the real numbers that can be computed to and within any desired precision by a finite, terminating algorithm. The theoretical obstacle to any long-term calculation in unstable systems is an inherent problem with arithmetic in the real number system.

As a very simple experiment (72) to illustrate the fundamental problem with numerical calculations, consider an N-bit binary computer where N = 2. The binary numbers represented are .00, .01, .10, and .II. Now perform binary arithmetic operations:

.01 X .11 = [.0011]

.0011 is not on the binary grid so one must round to a point on the grid, perhaps selecting .01. Field properties are not maintained and one has to establish addition and multiplication tables for all pairs of numbers represented, which is not feasible for large N. This problem arises with any fixed precision (noninfinite) computer. In chaotic systems, therefore, long-term prediction is impossible without the existence of attractors of the computations, thereby making Laplace's goal unattainable.

Synthesizing the principles that have been elaborated above with regard to the emergence of chaos and the challenge of computation, McCauley and Palmore (73) succinctly explain that: "Deterministic chaotic systems can magnify small errors exponentially so that a change in a single digit on an initial condition leads to a completely different orbit. In fixed-precision computation, truncation and round-off can introduce such digit changes at every iteration of a map so that the resulting computed orbit (pseudo-orbit) is not an orbit of the dynamical system. Rather, it is an artifact of the chosen computational process." Seth Lloyd also points out a serious practical problem for building a computation machine for "computing the universe": "Even if the underlying laws of physics were fully deterministic, the computational ability of simple systems such as colliding spheres implies that to perform the type of simulation Laplace envisioned, the calculating demon would have to have at least as much computational power as the universe as a whole. Since, as we shall see, computational power requires physical resources, Laplace's demon would have to use at least as much space, time, and energy as the universe itself." (74) Other objections to the feasibility of Laplace's "computer" can be offered based on entropy and irreversibility in thermody namics, Godel's incompleteness theorems (any computer designed to reason about the universe is itself part of the universe), and the Heisenberg uncertainty principle, which will be discussed below.

B. SPECIAL AND GENERAL RELATIVITY THEORY

Albert Einstein's special (75) and general (76) theories of relativity also challenge the classical Laplacian/Newtonian mindset that underlies the empiricist position. Newton assumed that "time and space were a background in which events took place but which weren't affected by them." (77) But according to special relativity, the laws of physics are only guaranteed to be the same for all observers in inertial frames of reference in uniform motion relative to each other. Additionally, it is assumed in special relativity that the speed of light in a vacuum is constant regardless of the relative motion of the light and the observers. Both of these postulates directly contradict the foundations of Newtonian mechanics. The consequences of special relativity are extraordinary: time dilation, length contraction, and the famous mass-energy equivalence relation E = [mc.sup.2].

Einstein's theory of general relativity further erodes the notion of space and time as immutable. It states that light rays bend in the presence of a gravitational field; (78) time slows down for a clock (79) moving into a lower gravitational potential, that is, closer to a massive body; and rotating bodies "drag" space-time around them, that is, frame dragging. (80) The effect of acceleration on a clock is a particularly interesting. In 1908, Hermann Minkowski (81) posited the notion of proper time to explain it: "Proper time is time measured by a single clock between events that occur at the same place as the clock. It depends not only on the events but also on the motion of the clock between the events. An accelerated clock will measure a proper time between two events that is shorter than the coordinate time measured by a non-accelerated (inertial) clock between the same events." (82)

To understand this phenomenon more clearly, it is helpful to consider the definitions applied to the oscillations of a simple, nonlinear pendulum used as a clock in an accelerating frame of reference. (83) The inertial observer will measure a longer time between oscillations and conclude that the clock has slowed. As the acceleration is increased, the effect will increase and the inertial observer will measure an increased slowness in the clock. By the equivalence principle of gravity and acceleration, a pendulum on the surface of the earth will be seen by an inertial observer to run slower, for example.

Now consider the example of a clock falling into a black hole. With increased g, the pendulum's proper time between oscillations will be slowed (as period T for small oscillations is proportional to g'1/2). So there are two effects here: the behavior of the proper time of the clock as gravity increases and the measurement by an inertial observer of coordinate time as the clock accelerates. Note that any external measurements of a clock falling into a black hole before reaching the event horizon will be of coordinate time. Clearly, the epistemic foundations of the scientific determinism that underlies empiricism are seriously challenged by relativity.

C. QUANTUM THEORY

Finally, one must consider the consequences of quantum mechanics on the Laplacian/Newtonian foundations of the empiricist mentality. Many strange phenomena are observed at the quantum level. One such phenomenon is quantum tunneling. According to classical physics, if a particle does not have sufficient energy to surmount a potential barrier, it will have zero probability of being found across the barrier. However, it has been observed experimentally, for example, in a tunnel diode, that particles are present on the opposite side of a potential barrier for which they do not have sufficient energy to surmount. Analysis of the quantum mechanical wave function, which describes either a single particle or an ensemble of systems depending on the interpretation, indicates that there are no solutions with a probability of exactly zero, so there is always a possibility of finding a particle across a (classically) insurmountable barrier. Other well-known effects include quantum superposition and the related phenomenon of quantum entanglement.

Quantum theory is unique for at least two reasons according to the "Copenhagen interpretation" of Niels Bohr. First, it appears to be inherently probabilistic in a radical way. Second, the role of the "observer" is distinct from a merely material system. In fact, logical problems arise when the observer is incorporated into the mathematical model of events. (84) There are a variety of interpretations of quantum mechanics, not only that of the Copenhagen school. (85) Unfortunately, interpretations often get confused with the equations themselves. The Copenhagen interpretation suggests that the uncertainty that arises is not due to limited knowledge on the part of the physicist. Rather, it would assert that quantum theory produces probabilistic results because the universe is probabilistic. (86)

Interestingly, Albert Einstein and Louis De Broglie did not accept this view. The British nuclear physicist, Peter Hodgson, succinctly summarizes their position: "(According to Einstein) the wave function describes the average properties of a large number (or ensemble) of similar systems. This leaves open the possibility that in the future there will be a more detailed theory that will enable quantum paradoxes to be resolved. On this view, quantum mechanics is rather like thermodynamics, which describes the properties of a gas in terms of macroscopic quantities like pressure and temperature. We know, however, that these may be expressed as averages over the motion of a large number of particles." (87) To this day, the Einsteinian interpretation is still a possible approach in understanding quantum phenomena.

The simplest way to understand quantum theory is to consider a single, free, subatomic particle. Because of the principle of waveparticle duality, one may develop a model in which its properties, that is, quantum state, are described by a wave. A wave function maps the possible states of the particle (or ensemble) into the complex numbers. Erwin Schrodinger's equation (88) describes how the quantum state changes with time. Ultimately, it would be very useful to know both the position and the momentum of the particle, although Heisenberg's theory suggests that this is not possible. (89) In a classical Newtonian situation (e.g., when the "particle" is a ballistic projectile), such information could be used to accurately predict where the projectile would land. However, in quantum phenomena, the position of the particle is most likely to be found where the wave is concentrated and the momentum is obtained from the wavelength. Therefore, a strictly localized wave has an indeterminate wavelength, while its associated particle has a well-defined position and an ill-defined momentum. A wave having a well-defined wavelength, on the other hand, is very spread out and the associated particle, while having a well-defined momentum, has an ill-defined position. In fact, the particle's momentum will be uncertain by an amount inversely proportional to the accuracy of the position measurement. (90)

It is interesting to note that Leslie Ballentine, a promoter of the ensemble interpretation of quantum mechanics, developed an experiment in which he fired a single electron at a screen and was able to determine its momentum in the direction perpendicular to the incident beam to a much greater accuracy than the uncertainty principle would permit. (91) A possible conclusion of this experiment would be that the wave function does not apply to a single particle. Rather, the wave function is an abstract mathematical entity that describes an ensemble of similar systems. The experiment indicates that "Heisenberg's uncertainty principle thus gives the relation between the spreads in position and momenta of a large number of particles. It does not mean that we cannot measure the position and momentum of a single particle with higher accuracy. Nonetheless, we cannot predict which way an electron will go although it is conceivable that a more developed theory will allow such a prediction in the future." (92) Whichever interpretation wins out in the end, to entertain the thought that "what cannot be measured exactly does not take place exactly," (93) is a fallacy more problematic than sloppy science. And even if the "ensemble" (i.e., nonstochastic) interpretation receives further empirical support in the future and becomes the definitive interpretation, the classical Laplacian/Newtonian (empiricist) worldview is untenable.

IV. Conclusion

It is truly a monumental task in our day to convince any child of Descartes or British empiricism that even an open attitude toward various philosophical outlooks is measured by the realism that they are unable to jettison. Even for a scientist like Stephen Hawking, there appears to be only one solution: "From the viewpoint of positivistic philosophy, however, one cannot determine what is real. All one can do is find which mathematical model describes the universe we live in." (94) Such comments are symptomatic of a prejudice that begins with William of Ockham that looks upon the value of the real and the unreal with indifference. This indifference was taken to its logical extremes by the British empiricists and the Circle of Vienna, to the point that epistemological anarchy would eventually fill the void left by the collapsed edifice of logical positivism. For Aristotle and Aquinas, nature is not inert but manifests a dynamic ontological order in which the existent [ens] is the prerequisite condition of its intelligibility. Science studies the existent as quantified (mathematics), or as subject to motion (physics), or as living (biology); but the existent is the concrete universal nature all entities have in common since even the differences between entities are real and therefore not restricted to a determined manner of existing (e.g., as a property or modification of a subject, as quantified, as living, etc.). (95)

In fact, given the nature of scientific activity as a planned or deliberate scrutiny of nature beyond its stable ontological "structure," the theoretical contents of which must ultimately relate (in a coherent manner) to controllable data obtained through experimentation, (96) Aristotle and Aquinas would probably prefer to use the phrase "experimental science" to talk about today's "empirical science." (97) But while contemporary empiricism tends to inject formulas and scientific models into its sensualist epistemology to achieve the semblance of order, it was very clear to Aristotle and Aquinas that a failure to employ ontological reflections in science can lead to an even graver philosophical leap that attaches an inordinate amount of existential consistency to models that are fluctuating expressions of quantitative description:
   The importance of creativity and interpretation in experimental
   science should be emphasized. Although the use of models in
   experimental science is habitual, how can we then delimit with
   greater precision the nature and function of models in experimental
   science? As is the case with concepts, there are also two basic
   roots to all models: reference and signification. Models refer to
   aspects of reality. For instance, the supposition behind the study
   of the particles of kinetic theory is that they represent real
   components of gases (though in a simplified way). There is also the
   supposition that corpuscular and undulatory descriptions correspond
   to real aspects of subatomic particles; and something similar
   applies to any model whatsoever. Nevertheless, this reference is
   conditioned by the way the characteristics of a model are defined:
   what a theory really studies is the ideal model whose roots are
   defined through theoretical concepts. Models therefore have a
   signification that is determined theoretically and a reference to
   reality whose value must be judged by comparing results acquired
   from the model with experimental results. In a way, a model has a
   life of its own. A model can be constructed and elaborated again
   and again with freedom, and its signification would be fixed
   according to theoretical considerations. But when a model is
   applied to reality, it is at that moment that we must fall back
   upon empirical data. The variety of models used will of course
   depend on the type of phenomenon being studied and the conceptual
   and experimental possibilities at our disposal. There is no reason
   to demand that only one kind of model be used. Given the sheer
   variety of possible models, their reference to reality admits of
   different variations in every case. (98)


A metaphysical empiricism would see a lot of truth in physical and mathematical models while understanding that quantitative unity presupposes ontological or substantial unity. Apart from the limitations of models, the harmony between ontological descriptions and scientific descriptions of reality depends on two other specificities: the nature of the object being studied and how susceptible it is to observation. In this dialectic between our capacity to know real natures and experimentation, experimental control varies between two extremes: (1) the certainty obtained through the rigorous description of observable phenomenon, as in the morphology of cells, and (2) experimental support, as in the Big Bang Model. (99) There are, of course, a variety of intermediate cases, such as the physical law concerning the equivalence between energy and mass, which is unobservable. If indeed many of the abstract theoretical constructions used in science do not reflect real structures and processes exactly, a hasty or philosophically skewed rejection of our ability to retain basic concepts of real natures, which a metaphysical empiricism affirms, leads to the problematic conclusion that our basic concepts differ every time a new experimental definition or model is offered by a particular science. (100)

The necessity and dignity of science consists precisely in unlocking the properties of things that exceed the scope of common sense, which is sometimes vague and in need of correction. Such was the case in Galileo's time with the unquestioned fundamental force in the physical world known as "the void" or "nature's abhorrence of the void" (horror vacui) that was refuted by Torricelli's vacuum experiment. In other cases the reverse occurs: classificatory concepts in science that are taken from common experience become enriched and further removed from ordinary experience with the introduction of quantitative concepts, (101) such as the use of differential equations to study physical processes. Although Aristotle and Aquinas recognized that change and properties in nature are real, they realized that what nature manifests to us is limited in scope and therefore requires a common language. Aquinas in particular contributed to this necessity in at least three ways: (1) in his vigorous assertion of the necessity of sense experience in the natural sciences and the provisional and conditional character of the physical based on the observation of phenomena; (2) in positing quantity as the first accident of bodies, thereby recognizing the priority of extension over qualities and providing the basis for the necessity of a mathematical treatment of physical phenomena; and (3) for expressly recognizing the application of mathematics to physics. (102)

For both thinkers, however, a remote but nonetheless relevant consequence of scientific reductionism is either a theory of double truth in response to propositions of faith (e.g., "my faith tells me that x is true but reason and science tell me otherwise") or an emotive rejection of anything associated with God. Since faith and reason have God as their source they can never contradict each other. But God can never be the proper object of any science that is not metaphysics because science is primarily concerned with the quantifiable and observable aspects of corporeal entities (subject to experimental control). (103) In this vein, Thomistic empiricism never confuses global skepticism (which it rejects) with the legitimate difficulty of reaching global truth or what the philosophers of old described as "wisdom," a view of things from their ultimate cause.

To dismiss the valid and penetrating responses of Aristotle or Aquinas just because their science contains a considerable amount of unfounded conjecture is to assume that improved science has bettered the rigor of their philosophical insight. The dogmatic Aristotelians of the Renaissance of Galileo's time (not Aristotle) may have misunderstood the role of proper scientific inquiry; but it does not follow that the metaphysical and epistemological reflections of their master are also faulty. The method of experimental science is not the method of the science that is metaphysics, and there is no reason to assume that the progress of both should occur in any one historical period pari passu.There is great potential for a metaphysically rich philosophy of nature to be an intellectual platform for the empirical sciences, if only the modern mind would approach Aristotle and Aquinas with the attitude that their vision is more like a vast universe than a geocentric monotony of rotating fictions.

Notes

(1.) Although the term does not fit into one simple definition, it would perhaps be benefical to point out that the "metaphysics" of the New Age movement is not quite the "metaphysics" of Aristotle or Aquinas. The latter seeks a true and rigorous etiology of things that are faithful to human experience and reflection on sensible facts, the aim of which is a "philosophical legitimization of experience and an explanation of how the diverse can be so and how the variety is unified." (John Haldane, Faithful Reason: Essays Catholic and Philosophical [London, NewYork: Routledge, 2004], 135.) Although much more could be said about the unfortunate use of the term "metaphysics" in New Age spirituality, this is far beyond the scope of our study.

(2.) Antonio Millan-Puelles, La estructura de la subjetividad (Madrid: Ediciones Rialp, 1967), 22.

(3.) Ibid., 34.

(4.) Antonio Millan-Puelles, Lexicojilosofico (Madrid: Rialp, 1984), 354.

(5.) Cornelio Fabro, God in Exile: Modern Atheism; A Study of the Internal Dynamic of Modern Atheism from its Roots in the Cartesian Cogito to the Present Day (Westminster: Newman Press, 1968), 1122.

(6.) Johnathan Bennett, "Locke's Philosophy of Mind" in The Cambridge Companion to Locke, ed. V. C. Chappell (Cambridge: Cambridge University Press, 1994), 114.

(7.) John Locke and Kenneth Winkler, An Essay Concerning Human Understanding: Abridged and Edited, with an Introduction and Notes (Indianapolis, IN: Hackett Publishing, 1996), Bk. II, Chap. xi, 17. Emphasis added.

(8.) Bennett, "Locke's Philosophy of Mind," 100-01.

(9.) Alejandro Llano, El Enigma de la Representacion (Madrid: Editorial Sintesis, 1999), 220.

(10.) Manuel Garcia Morente, Lecciones Preliminares de Filosofia (Buenos Aires: Editorial Losada, 1943), 136.

(11.) Locke, An Essay Concerning Human Understanding, Chap. xii, i.

(12.) Professor Christopher Martin offers a relevant account of how this view is far from being the "classical" notion of substance:
   [Aquinas begins from realities]. But it is important to notice that
   Aquinas makes just as much use of what he calls the "logical way,"
   introducing the metaphysical notion of substance by way of the
   logical notion of a subject. Aquinas says, for example, that what
   needs to have a subject included in its definition is not a subject
   in a principal sense, and so cannot be a substance. One way Aquinas
   uses to reach the true notion of substance is to ask what counts as
   a proper answer to the question "What is it?" [In its most basic
   sense the answer is] a substance, a substantial individual like
   Socrates, or the cat, or the tree outside the window, or this lump
   of gold.... If Socrates's nose has changed then Socrates has
   changed as regards his nose. If we ask "what is it that has
   changed?" then the answer "Socrates's nose" already includes
   another subject, Socrates.


Martin then goes on to contrast this view from that of Locke:
   It will be noticed that while we began with a discussion based on
   change, we continued it with the consideration of what is the
   ultimate subject: a consideration that belongs to "the way of
   logic." People often talk as if accidents were that which can
   change, and the substance that which does not change: this is very
   alien to the manner of speaking of Aristotle and Aquinas. For them,
   it is precisely the substance that changes, that is the subject of
   change: the accidents do not change at all.... This erroneous way
   of talking leads people in the end to suppose that the substance is
   a "bare particular," that has no accidents, that has no colour or
   shape, that is a "something I know not what" that is completely
   unknowable. This degenerate scholastic doctrine--associated chiefly
   with the name of Locke because he was the first one brave enough to
   put it into English--has, sad to say, been attributed to Aquinas
   and Aristotle: but it is definitely not their doctrine.


Thomas and C. F. J. Martin, The Philosophy of Thomas Aquinas: Introductory Readings (New York: Routledge, 1988), 63.

(13.) Manuel Garcia Morente, Lecciones Preliminares de Filosofia (Buenos Aires: Editorial Losada, 1943), 137-40.

(14.) David Hume, An Enquiry Concerning Human Understanding (Indianapolis and Cambridge: Hackett Publishing, 1993), section 12, part I.

(15.) Cf. Mariano Artigas, Knowing Thingsfor Sure: Science and Truth (Lanham, MD: University Press of America, 2006), 15-19.

(16.) Bennett, "Locke's Philosophy of Mind," 105.

(17.) Millan-Puelles, La estructura de la subjetividad, 46.

(18.) Ibid., 57.

If the Cartesian explanation of error is marked by excessive voluntarism in its attribution of cognitive features to the will, than the Kantian explanation of error is excessively naturalistic. Kant admits a certain intervention of the senses in the experience of error. For Kant, error is produced when the mind is misled by the senses. But there are two problems with Kant's position. The first consists in a question: Why is it that the mind is sometimes misled by the senses and other times not? The sense datum of a rectified error still remains present in the knower and is not sufficient for an erroneous judgment. Kant attributes a dynamic and cognitive function to the sense and eliminates the influence of the will. The second problem is this: The "objective foundation" of a judgment (whether true or not) is the rationale that explains, even if partially, what is being judged, and not a mere physical cause.

Kant bases his explanation on a model of classical physics: neither the senses nor the mind err alone, but error is produced by a concurrence of sensation and thought, like "a diagonal between two forces." But a judgment is not a mere physical act, and a merely physical cause does not determine a judgment. A judgment is something "representative," signifying something distinct from the judgment itself. I am aware of what is given in the senses: the objective basis of the judgment that bent stick is that I see a stick that looks bent. This is not just an uncon scious physical force, but something known to me, something that is on object of thought. Therefore, to give such errors an objective basis, one must appeal to something that doesn't go unnoticed in the moment of error, because there is something upon which the erroneous judgment rests that serves as its rationale. Millan-Puelles, La Estructura de la Subjetividad, 46.

(19.) Cf. Summa centra gentiles III, 107, and Aquinas's commentary on Aristotle's De Anima III, 6, 664-65.

(20.) Millan-Puelles, La estructura de la subjetividad, 65.

(21.) Ibid., 52.This expression does not belong to Aristotle or Aquinas, but it is at least one way of expressing the same point made by both philosophers.

(22.) A more literal expression would be "intellection." In modern idiom, we could also say "thought," but intellection conveys through its etymology (from the Latin intuslegere) what it is that sets it apart from sensation: only thought can penetratingly read (legere) into (intus) the nature of a thing.

(23.) Cf. Aristotle De Anima, III, 4, 429b 10.

(24.) For further elaboration on this point, as well as a more profound discussion of the classical understanding of "quality" (and how it compares to the views of Locke and other modern philosophers), see Millan-Puelles, Lexico Filosofico, 201-02.

(25.) Cf. Summa Theologica, I. q. 85. a. 6.

(26.) Scott MacDonald, "Theory of Knowledge," in The Cambridge Companion to Aquinas, ed. Eleonore Stump and Norman Kretzmann (Cambridge and New York: Cambridge University Press, 1993), 182-84, 187.

(27.) "Universal principles are had by induction ... reflecting on and comparing particular cases causes the universal contained in the particular to be grasped. Hence knowledge of universals is not automatic or simple. It requires (i) induction and (2) repeated encounters with sensible particulars and accumulated experience." Ibid., 183.

(28.) Attributing the nature of "man," for example, to all human beings would be impossible and meaningless if every human being did not bring this nature into realization in themselves. Because of this nature I can say that Peter is a man; but I cannot say that Peter is a corresponding term or a respective formal concept. In a word, universal natures are realized in a plurality of things and therefore have something in common with them. Only then can a universal be considered as such in nature [and not by mere signification]. [...] What is universal is common, though not everything that is common is universal. The room that I happen to find myself in is something common to me and the objects inside of it; we are all in the same room, but the room is not in us. With the common nature of "man", on the contrary, what is universal in nature is something that is found in every man, but not every man in the universal. The difference, at the root, lies in this: the merely common is not realized in the individuals that participate in it, while what is a universal in essence is realized in those individuals as something that they really are.

Millan-Puelles, Fundamentos De La Filosofia (Madrid: Ed. Rialp, 1955), 101.

(29.) Berkeley, A Treatise Concerning the Principles of Human Knowledge, sections 15-16.

(30.) Cf. ST, I, q. 85. a. 2.

(31.) Josef Pieper, Living the Truth (San Francisco: Ignatius Press, 1989), Kindle Edition, loc. 1455.

(32.) Ibid.,1402-03.

The identity between the intellect and the object, a true and actual self-sameness, is brought about by the immaterial, spiritual image of reality which impresses itself upon the intellect, as the seal impresses itself upon wax.... It is the proper task of the spontaneous power of our mind (called intellectus agens [agent intellect] by Saint Thomas) ... to free this super-material core of "what-ness" in the real object from its material limitations.... The intelligible image, then, is on the one hand a representation of reality; indeed, in the "what" it is identical with the objective reality.... "The intelligible image is in a certain sense the essence and nature of the reality itself, not according to natural being, but according to intelligible being." [Quol. 8, 4]

But "natural being" and "intelligible being" are two ways of being, so to speak, of the same reality.

(33.) Millan-Puelles, Fundamentos De La Filosofia, 99.

(34.) Gyula Kilma, "Nulla virtus cognoscitiva circa proprium obiectum decipitur," retrived from http://faculty.fordham.edu/klima/

(35.) Fabro Cornelio, God in Exile: Modern Atheism; a Study of the Internal Dynamic of Modern Atheismfrom Its Roots in the Cartesian Cogito to the Present Day (Westminster, MD: Newman Press, 1968), 1132.

(36.) Llano, El Enigma de la Representacion, 223. Emphasis added.

(37.) C. F. J. Martin, The Philosophy of Thomas Aquinas: Introductory Readings (London and NewYork: Routledge, 1988), 121.

(38.) Reginald Garrigou-Lagrange, Reality:A Synthesis, a. i.

(39.) Ferrariensis Sylvestris, Commentary on the Summa Contra Gentiles I, 44.

(40.) Alejandro Llano, Gnoseology (Manila: Sinag-Tala Publishing, 2001), 74.

(41.) There are many excellent texts available today that compare and contrast the relationship between knowledge and sense experience while constantly referring back to the language of the British empiricists (which we have been equating with a "strict" conception of empiricism). The reader is encouraged to consult the following works: Aquinas; The Cambridge Companion to Aquinas; Mind, Metaphysics andValue (in particular chapters 2, 7 and 8); and especially El Enigma de la Representacion (which, unfortunately, has not yet been translated into English).

(42.) Eleonore Stump, Aquinas (London; New York: Routledge, 2003), 249-50. On the subject of the interaction between mind and body see: Richard Cross, "Aquinas and the Mind-Body Problem" in Mind, Metaphysics andValue.

(43.) Hume, An Enquiry Concerning Human Understanding, Section VII, Part II.

(44.) Ibid.

(45.) W. Norris Clarke, The One and the Many: A Contemporary Thomistic Metaphysics (Notre Dame: University of Notre Dame Press, 2001), 192.

(46.) Tomas Alvira, Luis Clavell, and Tomas Melendo, Metaphysics (Manila: Sinag-Tala Publishing, 1991), 176.

(47.) Millan-Puelles, Lexico Filosofico, 81-82.

(48.) Locke, Ch. 26, i.

(49.) Clarke, The One and the Many, 190

(50.) Llano, El Enigma de la Representacion, 213.

(51.) Victor Velarde-Mayol, On Husserl (Belmont, CA: Wadsworth, 2000), 19-20.

(52.) Edmund Husserl, Logical Investigations, vol. I, section 30.

(53.) I have frequently considered what could possibly be the reason why all mankind, though they have ever without hesitation, acknowledged the doctrine of necessity in their whole practice and reasoning, have yet discovered such a reluctance to acknowledge it with words.... But being once convinced, that we know nothing farther of causation of any kind, than merely the constant conjunction of objects, and the consequent inference of the mind from one to the other, and finding, that these two circumstances are universally allowed to have place in voluntary actions; we may be more easily led to own the same necessity common to all causes. And though this contradicts the systems of many philosophers, in ascribing necessity to the determinations of the will, we shall find, upon reflection, that they dissent from it in words, not in their real sentiment. Necessity, according to the sense in which it is here taken, has never yet been rejected, nor can ever, I think, be rejected by any philosopher.

Hume, An Enquiry Concerning Human Understanding, Section VII, Part I.

(54.) Knowledge of causes is possible without any satisfactory grasp of what is involved in causation. Compare the possibility of wanting clarification of "valency" or "long-run frequency," which yet have been handled by chemists and statisticians without such clarification; and valencies and long-run frequencies, whatever the right way of explaining them, have been known. Thus one of the familiar philosophic analyses of causality, or a new one in the same line, may be correct, though knowledge of it is not necessary for knowledge of causes. There is something to observe here that lies under our noses. It is little attended to, and yet still so obvious as to seem trite. It is this: causality consists in the derivativeness of an effect from causes. This is the core, the common feature, of causality. For example, everyone will grant that physical parenthood is a causal relation. Here the derivation is material, by fission. Now analysis in terms of necessity or universality does not tell us of this derivativeness of the effect; rather it forgets about that. For the necessity will be that of laws of nature; through it we shall be able to derive knowledge of the effect from knowledge of the cause, or vice versa, but that does not show us the cause as source of the effect. Causation, then, is not to be identified with necessitation.

G. E. M. Anscombe, The Collected Philosophical Papers of G.E.M. Anscombe (Minneapolis: University of Minnesota Press, 1981), 136.

(55.) W. Norris Clarke, The One and the Many: A Contemporary Thomistic Metaphysics (Notre Dame: University of Notre Dame Press, 2001), 192.

(56.) Ibid., 122.

(57.) Artigas, Knowing Thingsfor Sure: Science and Truth, 18.

(58.) Nous devons donc envisager l'etat present de l'univers, comme l'effet de son etat anterieur, et comme la cause de celui qui va suivre. Une intelligence qui, pour un instant donne, connaitrait toutes les forces dont la nature est animee, et la situation respective des etres qui la composent, si d'ailleurs elle etait assez vaste pour soumettre ces donnees a l'analyse, embrasserait dans la meme formule les mouvemens des plus grands corps de l'univers et ceux du plus leger atome: rien ne serait incertain pour elle, et l'avenir comme le passe, serait present a ses yeux. L'esprit humain offre, dans la perfection qu'il a su donner a l'Astronomie, une faible esquisse de cette intelligence. Ses decouvertes en Mecanique et en Geometrie, jointes a celle de la pesanteur universelle, l'ont mis a portee de comprendre dans les memes expressions analytiques, les etats passes et futurs du systeme du monde.

Pierre Simon, Marquis de Laplace, Essai philosophique sur les probabilities (1840).

(English Translation: We ought then to regard the present state of the universe as the effect of its anterior state and the cause of the one which is to follow. Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it--an intelligence sufficiently vast to submit this data to analysis--it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present in its eyes. The human mind offers, in the perfection which it has been able to give to astronomy, a feeble idea of this intelligence. Its discoveries in mechanics and geometry, added to that of universal gravity, have enabled it to comprehend in the same analytic expressions the past and future states of the system of the world.)

Pierre Simon, Marquis de Laplace, A Philosophical Essay on Probabilities, trans. Frederick Truscott and Frederick Emory (NewYork: John Wiley, 1902), 4.

(59.) Stephen Hawking, The Universe in a Nutshell (NewYork: Bantam, 2001), 104. Emphasis added.

(60.) Alvira, Clavell, and Melendo, Metaphysics, 207.

(61.) This general argument was proposed by Franz Brentano, an important German philosopher with a strong affinity for Aristotle. The authors are indebted to Victor Velarde for suggesting this argument concerning computers and artificial intelligence.

(62.) Jules Henri Poincare, "Sur le probleme des trois corps et les equations de la dynamique. Divergence des series de M. Lindstedt," Acta Mathematica, 13 (1890): 1-270.

(63.) Linear systems must obey the superposition principle:f(x + y) = f(x) + f(y) and exhibit homogeneity:f(ax) = af(x).

(64.) Paul Trow, "Chaos and the Solar System," accessed December 14, 2011, http:// ptrow.com/articles/Chaosand SolarSystem5.htm.

(65.) For continuous systems, one applies this definition to surfaces of section. The definition has the three attributes of transitivity, dense set of periodic orbits, and sensitive dependence on initial conditions.

(66.) A rigorous definition is provided here: Julian Palmore, "Chaos, Entropy and Integrals for Discrete Dynamical Systems on Lattices," Chaos, Solitons & Fractals, 5:8 (1995), 1401.

(67.) Charles Herring and Julian Palmore, "Random Number Generators are Chaotic," ACM SIGPLAN Notices, 24:11 (1989): 78.

(68.) James Gleick, Chaos: Making a New Science (NewYork: Penguin, 1988), 8.

(69.) David Arrowsmith and C. M. Place, Dynamical Systems: Differential Equations, Maps, and Chaotic Behaviour (NewYork: Chapman & Hall, 1992), 259.

(70.) For more on computability, see the seminal work: Alan M. Turing, "On Computable Numbers, with an Application to the Entscheidungs Problem," Proceedings of the London Mathematical Society, Series 2, 42 (1937), 230-65.

(71.) Although all real numbers can be defined as limits of infinite sequences of rationals, almost all of these numbers are noncomputable in the sense that they cannot be computed via any possible algorithm. It follows from this that chaos theory, in so far as one is concerned with prediction or computation, should be built upon computable numbers, and computable functions. The computable numbers then provide the framework for understanding the sense in which deterministic orbits can be regarded as chaotic.

Joseph L. McCauley Jr. and Julian I. Palmore, "Computable Chaotic Orbits," Physics Letters A 115:9 (1986): 434.

(72.) Email conversation with Julian Palmore, February 15, 2011.

(73.) McCauley Jr. and Palmore, "Computable Chaotic Orbits," 433.

(74.) Seth Lloyd, Programming the Universe: A Quantum Computer Scientist Takes On the Cosmos (NewYork: Knopf, 2006), 98.

(75.) Albert Einstein, "Zur Elektrodynamik bewegter Korper," Annalen der Physik 17 (1905) 891-921.

(76.) Albert Einstein, "Die Feldgleichungen der Gravitation," Sitzungsberichte der Preussischen Akademie derWissenschaften zu Berlin (1915): 844-47.

(77.) Hawking, Universe, 32.

(78.) The bending of light can also be explained partially with special relativity and the relation between mass and energy. Photons can be assigned mass as an energy equivalent and the bending can be computed using the gravitational potential.

(79.) This has been observed experimentally in atomic clocks in which the frequency standard decreases.

(80.) NASA's Gravity Probe B experimentally confirmed this phenomenon.

(81.) Hermann Minkowski, "Die Grundgleichungen fur die elektromagnetischenVorgange in bewegten Korpern," Nachrichten von der Koniglichen Gesellschaft derWissenschaften und der Georg-August-Universitat zu Gottingen (Gottingen: 1908), 53--iii.

(82.) "Proper Time," accessed February 2, 2011, http://en.wikipedia.org/wiki/Proper_ time.

(83.) It is important to remember that if the clock itself is falling freely, the oscillations are a uniform rotation of the pendulum.

(84.) Stephen Barr, Modern Physics and Ancient Faith (Notre Dame: University of Notre Dame Press, 2003), 228.

(85.) "The philosophical implications of quantum mechanics, and their theological consequences, thus come not from the result of physical experiments, but from the philosophical premises inherent in the various formulations. The Copenhagen interpretation is based on positivism, so it is not surprising that causality is denied and physics is reduced to the correlation of sense impressions. If on the other hand, one adopts a realist position, one is thus free to believe that physical reality is a strictly determined system that we only partly understand." P. E. Hodgson, "Interpretations of Quantum Mechanics," Science and Belief in the Nuclear Age (Naples, FL: Sapientia Press, 2005), 206.

(86.) Barr, Modern Physics, 228.

(87.) Hodgson, "Interpretations," 177.

(88.) Erwin Schrodinger, "An Undulatory Theory of the Mechanics of Atoms and Molecules," Physical Review 28(6) (1926): 1049-70.

(89.) Werner Heisenberg, "Uber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik," Z.furPhys. 43 (1927): 172-98.

(90.) "Uncertainty Principle," accessed July 27, 2012, http://abyss.uoregon.edu/~js/21st _century_science/lectures/lec 14.html.

(91.) L. E. Ballentine, "The Statistical Interpretation of Quantum Mechanics," Reviews of Modern Physics 42:358.

(92.) P. E. Hodgson, "Relevance of Quantum Mechanics," Science and Belief in the Nuclear Age (Naples, FL: Sapientia Press, 2005), 217.

(93.) See Stanley L. Jaki, "Determinism and Reality," in Patterns or Principles and Other Essays (Bryn Mawr, PA: Intercollegiate Studies Institute, 1995).

(94.) Hawking, Universe, 59.

(95.) John F. Wippel, The Metaphysical Thought of Thomas Aquinas: From Finite Being to Uncreated Being (Washington, DC: Catholic University of America Press, 2000), 61.

(96.) Artigas, Knowing Things for Sure: Science and Truth, 12.

(97.) Ibid., 18.

(98.) Mariano Artigas, Filosofia de la Ciencia (Pamplona: EUNSA, 1999), 202.

(99.) Artigas, Filosofia de la Ciencia, 1999), 89.

(100.) Ibid., 199.

(101.) Ibid., 197.

(102.) Fabro, God in Exile, 1125.

(103.) Stanley L. Jaki, Science and Religion: A Primer (Pinckney, MI: Real View Books, 2004), 28.
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