Analog SFF, July-August 2007

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Analog SFF, July-August 2007 Page 9

by Dell Magazine Authors


  Reply to Objection 1. William of Conches wrote, “[They say] ‘We do not know how this is, but we know that God can do it.’ You poor fools! God can make a cow out of a tree, but has He ever done so? Therefore show some reason why a thing is so, or cease to hold that it is so."

  Aquinas wrote that reason could be applied to theology, but revelation was forbidden to philosophy. His insistence that faith and reason were both independent and in concord was influential.

  Reply to Objection 2. To paraphrase the objection: The formal cause of falling bodies is an inner nature called “gravity” possessed by matter, but the nature of gravity can only be known through the behavior of falling bodies. (Newton agreed [Principia Mathematica, General Scholium].) Likewise, in evolution, reproductive success is due to an inner nature called “fitness,” but fitness can be known only through reproductive success. These explanations are as circular as Aristotle's brittle nature of glass, but are not discarded on those grounds.

  In Aristotelian terms, the nature of an object cannot be fully known unless four aitia are understood. The static aitia (Matter and Form) explain a thing's being; the dynamic aitia (Agent and End) explain a thing's becoming (i.e., motion/change). Only Agent (effective cause) is a “cause” in the modern sense; so the objection is merely that formal causes are not efficient causes, which of course they are not.

  The medievals recognized that extension was common to all objects, and to this they gave the name of “prime matter,” which possesses dimension, but no substantial form. Substantial form actuates prime matter to a specific nature: the form of oxygen, the form of a dog. All dogs share the substantial form of a dog, but differ in color, size, etc. These latter are called accidental forms or accidents. For details on natures and Aristotelian natural philosophy, see Wallace.

  Formal causes did not disappear simply because they were disregarded any more than logic disappeared because the Renaissance deemphasized it. Now that we call them “atomic structures,” “genomes,” and the like, formal causes are better understood. When Feynman said, “Electrons behave ... in exactly the same way as photons; they are both screwy, but in exactly the same way,” he was recognizing that both species share a substantial form. Oxygen and carbon consist of identical matter (neutrons, protons, electrons), but possess different natures because of their formal arrangements. An electron in a carbon atom does not behave as a free electron; rather, its behavior is controlled by the form of the carbon atom as a whole. When we say that glass breaks because of its “amorphous atomic structure,” we cite a formal cause, not an efficient one. The amorphous structure doesn't make the glass break; it's what makes the glass breakable. (And we still don't know how: 3rd International Workshop on the Flow and Fracture of Advanced Glasses). Similarly, the formal cause of a dog is its “genome,” while its efficient causes are the chemical and biological reactions that “unpack” and express that genome “in a manner harmonious to its environment."

  The importance of “emergent properties” and “self-organization” in modern science—inherent in Aristotelian formalism—suggests that rejection of Aristotle's second aition may have been premature.

  Reply to Objection 3. Final causes are sometimes called “purposes,” but telos or “End” need not be consciously purposeful. A falling rock does not intend to minimize its gravitational potential; a species does not plan to become more fit for its niche; a puppy does not strive to become an adult dog. But each will move toward these natural ends, provided they “run true to form.” Potential functions and strange attractors are teleological. Considering their importance in modern physics—and the difficulties in applying efficient causes alone to quantum entanglement—rejection of telos may also have been premature.

  * * * *

  Article 2. Whether the medievals distinguished primary from secondary qualities, assigning the latter to the perceptions of the subject.

  Objection 1. It would seem they did not because the distinction derives from atomism, which Aristotle rejected as self-contradictory. The medievals held that an apple is red, or round, or tart, or falls with a rectilinear motion onto Newton's head without any sense that these were not all equally objective properties.

  On the contrary, Oresme [Traité du ciel et du monde] writes, “One cannot demonstrate by any [sense] experience whatever that the heavens are moved with daily movement, because ... if an observer is in the heavens and sees the earth clearly, the earth would seem to be moved; and if the observer were on the earth, the heavens would seem to be moved. The sight is not deceived in this, because it senses nothing except movement. But if it is relative to any such body, this judgment is made by the senses from inside that body, as Witelo stated in his Perspectiva; and such senses are often deceived..."

  First, the distinction must be made. Galileo [Il Saggitore] says, “tastes, odors, colors, etc., so far as their objective existence is concerned, are nothing but mere names for something which resides exclusively in our sensitive body, so that if the perceiving creatures were removed, all of these qualities would be annihilated and abolished from existence.” These were called “subjective,” or “secondary” qualities. Length, weight, position, etc., without which Galileo found it impossible to imagine an object, were called “objective,” or “primary” qualities.

  Atomism supposed that all phenomena were due to the “shape, arrangement, and motion” of identical, invisible particles. Hence, only mathematical qualities like length or weight could “really” exist in the object. Since we cannot assemble a red apple from an arrangement of colorless particles, color [and other secondary qualities] must be an effect of the extended matter on the subject's mind.

  I answer that natural philosophy tried to explain the world as perceived by humans and this commitment to empiricism compelled scholastics to consider color, sound, etc. as real. The medievals conceived prime matter as formless but possessing extension, that is, possessing only primary, objective qualities. They further approached subject/object duality in perspectiva and in nominalism.

  The medieval science of perspectiva combined the physics of light, mirrors, and lenses with the biology of the eye and the psychology of perception. The difference between Kepler's Optics and Witelo's Perspectiva, Smith explains, lies not in their geometric analysis of image formation on the retina—identical in both books—but in that Kepler was analyzing light while the perspectivists were analyzing sight.

  In Thomistic psychology, an apple's redness has real, “extensive” existence in the object. Light, by reflection, transmits the form of redness to the brain, creating an image with “intensive” existence in the subject. But extensive/intensive is not the same as objective/subjective. The medievals believed the senses were impressed by something real in the object. The apple really is red, and would remain red, even if no one saw it.

  In the debate over universals, nominalism distinguished entities having real existence from mere names (nomines). This chair and that chair have real existence, but the species “chair” is only a convenient term that supposits in a sentence for any and all particular chairs. William of Ockham justified this using his famous razor to “erase” unnecessary entities, reducing them to “mere names.” Galileo's claim that secondary qualities are “mere names” followed this tradition.

  Atomism nudged philosophers away from Aristotle toward Plato's ideal forms; viz., abstract mathematical properties and geometric arrangements of invisible particles. This disconnected science from empiricism, making science, literally, almost sense-less. Berkeley took one step further, proposing that even primary qualities were subjective, which aroused Samuel Johnson to his famous contrapuntal refutation. But Berkeley may have been on to something. Ask Schrödinger's cat.

  Furthermore, if redness is only a subjective impression produced in the individual mind, it is impossible to speak of two people seeing the same “red.” Subject/object dualism thus subverts the very idea of a knowable objective world. Yet, the simplified world of positivism, though severely bat
tered nowadays by quantum theory, may have been necessary for the adolescence of Science.

  Reply to Objection 1. The medieval realists agreed with the atomists that matter was granular, but disagreed on the nature of the granules: Their minima naturalia were “the least natural parts [of a body] which mingle and interact.” Minimists did not make the primary/secondary distinction because their version of least particles did not require it.

  Atomist particles are indivisible ("atomos"), not only in practice but in principle. They are made of identical stuff, differing only in size and shape, and do not possess the secondary qualities of the macroscopic body they comprise, such as color.

  Minimist particles are divisible, though there is a smallest quantity of each substance beyond which the form of the substance can not be sustained. The minima of water is the smallest particle of water. Divided further, it ceases to be water and becomes ... oh, let's say, hydrogen and oxygen. Minimae are as different as the substances they form and do possess the secondary qualities of the macroscopic body they comprise.

  If “indivisibles” have shapes, Aristotle countered, then they have parts, and are divisible, a contradiction. Indeed, modern science supports Aristotle: atoms do consist of parts: electrons, protons, and neutrons, and we have actually learned how to divide them in practice. Protons in turn are composed of quarks; and quarks are ... When Dalton re-imagined the atom, he argued that the atoms of different substances, e.g., gold and silver, had different properties, as the minimists had always claimed. His biggest opponents were die-hard orthodox atomists!

  So, the modern concept of atom, greatly influenced by minimism, is a far cry from the identical corpuscles that forced subject/object dualism on Galileo, Descartes, and Hume. A minimist “atomic” theory might not need to separate the observer from the observed.

  * * * *

  Article 3. Whether medieval natural philosophers used deliberate and recordable observation and experiment.

  Objection 1. It would seem otherwise becauseGalileo [Dialogues on the Two Chief Systems of the World] causes Simplicio the Aristotelian to say, “You have made me see the matter so plainly and palpably, that if Aristotle's text were not contrary to it ... I would be forced to admit it to be true.” Thus, the medievals relied on texts and authorities rather than on observation of nature.

  On the contrary, Pierre of Maricourt [Epistola de magnete] writes, “an investigator diligent in the use of his own hands ... will in a short time correct an error which he would never do in eternity by his knowledge of natural philosophy and mathematics alone.” Roger Bacon [Opus maius] writes, “Nature reveals herself more readily under the vexations of art than when allowed to go her own way.” Likewise Albertus Magnus [De vegetabilibus et plantis] states, “Experiment is the only safe guide” and often adds, “I was there and saw for myself."

  I answer that medieval natural philosophers were careful observers of nature and often cited evidentia naturalis to support their determinations, but these observations were seldom quantified and more often cited common experiences than deliberate experiments. Bacon determined that light was faster than sound because he saw a distant blacksmith swinging a hammer before he heard the clang. Buridan's formulation of Newton's first law was inspired by his observation of a millstone that continued to roll after the gears were disengaged. But neither recorded times or distances. There were exceptions—Theodoric of Fribourg's explanation of the rainbow, Merle's weather data, astronomy in general—but for the most part, the medievals lacked the instruments needed to obtain useful measurements. Measuring distance or weight was simple, but time was problematical and temperature, force, etc. was beyond them. However, their reliance on observation was a large and important step.

  Robert Grosseteste has been called the father of the experimental method. He combined the procedures of “resolution and composition” to demonstrate natural laws: First, analyze the components of a phenomenon and induce a principle or reason (propter quid); then deduce the logical consequences of that principle and seek evidence to verify or contradict them. This is recognizably Galileo's “demonstrative regress."

  Laying the philosophical foundations for the provability of natural laws was no small thing; but Aristotelians were wary of deliberate experiments. Substances possess inner principles that inform their development “in a manner harmonious with their environment,” and the purpose of Science is to understand how those forms work. By imposing artificial conditions, an experiment interferes with the natural environment and hence with understanding the principles. (For example, a genome may express itself differently under different environmental cues.)

  Magicians, more interested in practical results than in hidden principles, did conduct experiments, dubbed “natural magic.” ("Magic” meant that the inner principles were hidden [occult], not necessarily that they were supernatural.) But alchemy had no academic standing, and no institutional base. When Pope John XXII called a conference of magicians and natural philosophers to ask whether magic had any foundation, the alchemists answered yes; the scientists no.

  While natural philosophers reasoned about motion—often correctly—they did not apply their conclusions to the actual motions of real objects. Buridan explained motion (L., momentum) by an impetus proportional to the “weight and speed” of the body—and even applied it to planetary motions; but he made no calculations for actual millstones or planets. Again, measurement was a problem: impetus theory implied that bodies in motion were heavier than at rest, but gravitas in decendendo could not be weighed without interfering with its speed. The alchemist-magicians, on the other hand, developed no significant interest in counting or measuring, or in making occult principles manifest. It was all rule-of-thumb. Experimental science was born of the marriage of philosophy and magic; but in the Middle Ages, they were just engaged in heavy petting.

  Reply to Objection 1. Galileo was employing satire, not factual reporting. We have no record of an actual Aristotelian arguing in such a way. By Galileo's day, rhetorical persuasion had replaced syllogistic proof as the object of reason.

  Albertus Magnus [De mineralibus] had rebutted Galileo four hundred years early, “The aim of natural science is not simply to accept the statements of others, but to investigate the causes that are at work in nature.” Adelard of Bath, Anselm of Canterbury, and others wrote likewise, and Grosseteste, Buridan, or Oresme often modified Aristotle or called him wrong on many points. Granted, as Duhem notes, the Italian scholastics of Galileo's day had reacted against the Paris school; but we mustn't assume this applies to medieval scholasticism.

  Scholastics could not refer readers to a source and page for an argument because hand-made books lacked consistent pagination. Rather than repeat an argument at length, they offered a quote. The reader was expected already to know the rest. This was as close to footnote, reference, or hyperlink as they could get, but it gives modern readers the impression of an appeal to authority.

  * * * *

  Article 4. Whether natural philosophers used mathematics as a privileged tool for disclosing nature.

  Objection 1. It would seem not, because Aristotle warned against the use of mathematics in physics. (The mathematical features of objects are accidental, not essential, and the behavior of objects is best explained by their essences.) And the medievals followed Aristotle in all things.

  Objection 2. Furthermore, physics is about changing things while mathematics is about unchanging things. But principles explain the matter only if they are homogeneous with it. Therefore, following Aristotle, medievals did not use mathematics for science.

  On the contrary, Robert Grosseteste wrote “nothing can be understood in natural philosophy and empirical investigation without mathematics.” By about 1320, says White, “regularity, mathematically predictable relationships, [and] facts quantitatively measurable, were looming larger in man's picture of the universe."

  I answer that the medieval Latins pioneered the use of mathematics to prove propositions in physics. (This
was very different from the calculation of land areas or planetary cycles.) But to do so, they faced an enormous hurdle: most Greek mathematics was unknown to them. The Romans had never translated it, having little interest in math beyond surveying [of conquered land] and accounting [of loot and booty]. “In mathematics,” writes Mahoney, “to succeed the Romans was to succeed to nothing...” Beyond Euclid's Elements, little was available. Medieval scholars had to learn from scratch—and without teachers. It was all Greek to them.

  Consequently, the Latins often violated Greek rules of geometry—"at times quite creatively,” says Mahoney. Their purposes were practical, not theoretical: to clarify geometric references in Aristotle and elsewhere, to do the math required by the “exact sciences” (astronomy, statics, perspectiva, music), or to improve measurement instruments and practices. For example, Dominic de Clavasio [Practica geometria] wrote, “The ratio of the circumference of any circle to its diameter is a triple sesquiseptimate [ratio], or thereabouts, because there is no definite demonstrated ratio ... I do not speak demonstratively, but only to teach how to find the area such that no sensible error remains.” He knew pi was irrational, but 22/7 was “good enough for all practical purposes."

  Aquinas had distinguished three degrees of abstraction: The physics of material objects is prior to the mathematics of ideal objects, and both are prior to and underlie the metaphysics of their being. Further, he distinguished qualities from their quantitative extensions, e.g., heat from temperature, raising the “exact sciences” (straddling the physics/ mathematics border) to the status of Science. This eventually led to quantitative physics, the 14th century's radical break with Aristotle.

  During the 14th century, mathematical thinking became embedded in natural philosophy. Oresme developed graphical displays of “longitude and latitude” (x and y), and geometrical methods for summing series and integrating linear functions, and analytical geometry stirred in its cradle. His geometrical proof of the Mean Speed Theorem was good enough that Galileo used it unchanged three hundred years later. It symbolized an important milestone: a proposition in physics was demonstrated by a mathematical analysis.

 

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