§36. The Method of Mechanics
In 1612, Galileo offered the public his first contribution to experimental natural philosophy, a small treatise explaining why some things float and others sink when placed on water.
Aristotelians met the work with a hot counterattack, competing to make Galileo’s experiments look ridiculous and his conclusions obviously false. Except they were not. Galileo argued that floating was entirely a matter of relative density, but his opponents were convinced that shape had something to do with it. Shape seemed to matter because a flat object can float which sinks when made into a ball, though behind that observation lay the decisive consideration that water must resist division, which would produce the void their natural philosophy disavowed. In this argument their whole system was at stake, while Galileo had only his experiments and calculations, with nothing more to lose than a reputation for ingenuity.97His procedure was nothing like the method practiced by Galileo’s prestigious colleagues in natural philosophy, whose signature Padua approach was the method of analysis and synthesis as developed from Hippocrates to Galen and married to Aristotelian syllogistic by Grosseteste. It was not a good match; the two methods were never meant to work together. What Plato called “the method of medicine” and described as a good way to “determine the nature of something” was, first, to decide whether the object is simple or complex. If simple, investigate its power, what it can act on and what acts on it. If complex, enumerate the forms and resolve each till you finally reach simples. Galen confirmed the method’s Hippocratic pedigree (§6). On a separate track, Aristotle in Posterior Analytics distinguished two sorts of demonstration. One demonstrated the cause from given present fact, the other demonstrated the effect, given knowledge of the cause.98
The Hippocratics had introduced a method of inquiry, Aristotle a method of demonstration, and though these are different goals, a history of efforts insistently links them.
Already in late antiquity Chalcidius, in his Latin translation and commentary on Plato’s Timaeus (the only work of Plato’s to survive Roman collapse and enjoy continuous readership in Europe), described as resolutio syllogisms moving from things evident to the senses up to causes and principles, and as compositio syllogisms descending from principles to effects. Arabic commentary cemented Hippocratic resolution-composition and Aristotle’s two types of demonstration.Method was not a preoccupation of Thomas Aquinas or Duns Scotus. They accept Aristotle’s idea that the intellectual mind enjoys the power to grasp principles and causes. For the Renaissance natural philosophers at Padua this was a discredited “myth of the given.” “It is significant,” John Herman Randall writes, “that at no time do the Paduan Aristotelians attribute any such perceptive power to intellect.” Instead of an inexplicable epagoge or intuitive cognition, the scientific certainty of natural knowledge depends on the method by which it is obtained. It was in this context that a relatively flexible Hippocratic canon for natural inquiry became obsessively encumbered with Aristotelian syllogistic. Following what Paduans called the regressus method, the natural philosopher is obliged to construct two syllogisms, one tortured into accommodating the resolution of effects to simples with simple causes, the other a no less tormented effort to reproduce in syllogistic the compositional, synthetic moment when the empirically educed cause is shown to explain the effect.99
One would like an example of this method at work, but as a scholar ruefully admits, for all the discussion the topic provoked, actual examples of regressus reasoning are very difficult to find in these authors. “It is almost impossible to catch a regressus theorist employing regressus in his own investigations.” It taxes credulity to think this procedure could be a method of discovery and not just a way of tidying up the results, yet its most resourceful proponent, Jacopo Zabarella, insists that “the end of the resolutive method is discovery (inventio) rather than science.” In a work devoted to the method, Zabarella says, “Method is an intellectual instrument producing knowledge of the unknown from the known.... Method has the force of inference, and connects this with that.” What Zabarella calls methodus is a syllogistic logic for what Alexandrian physicians called indicative signs.
A favorite example was sweat indicating invisible pores in the skin. Zabarella wants a method or logic for this sign, like the Epicurean canonic (§19), but one adequate to the demonstrations required for Aristotelian scientia.100Aristotle was interested in proof, not discovery. The Paduans are interested in inquiry and view principles as no more than conjectures. “That something is a cause can never be so certain as that an effect exists; for the existence of the effect is known to the senses. That it is the cause remains conjectural.” Experience for Zabarella involves trained observations under experimental conditions, and he insists on the value of a creative hypothesis. “If we form some hypothesis (praenoscimus) about the matter, we are able to search out and discover something else in it; where we form no hypothesis at all, we shall never discover anything.” His effort to bring experience into natural- philosophical discovery can almost be called empiricism, except that the ruling tendency of his thought is to corroborate the position of Aristotle. If Aristotle is understood, nature is understood, but accurate understanding of Aristotle is the primary task. With Galileo the situation is entirely different.101
Around the time Zabarella writes, in the mid-sixteenth century, works of Alexandrian mathematics were being newly translated and published. Zabarella has no interest in this material, but Galileo studied it sedulously, declaring himself a disciple of Archimedes. He is not impressed by regressus as a method of discovery, mocking its circular syllogisms, and voicing the suspicion that those who claim to rely on them first assure themselves of their conclusion by experiment and observation, then dress it up in the regressus for show. Nobody discovers by reasoning like that. Galileo urges the superiority of geometric methods, convinced that they promise a new way of discovery—not mere observation, not generalization or abstraction from common experience, and definitely not a syllogistic regressus.
Instead, we isolate and examine a typical phenomenon in order, first, to intuitively dissect the simple elements in terms of which it can be translated into mathematics, resolving qualitative, sensible phenomenon into quantitative combinations, then proceeding to demonstrate the complex phenomenon from those elements suitably mathematized.102The problem with regressus is its compulsive syllogistic, not the Hippocratic method commentators tried to graft onto Aristotle’s theory of demonstration. The Hippocratic canon says, assume that the phenomenon is complex and that it is an effect; assume that its causes can be isolated through observation and manipulation; then demonstrate your success in this analysis by the power to produce or destroy the effect at will. It is because of this balance of reason and experience mutually controlled that Galen described the method as qualified experience. Strapped in syllogisms, the model is worse than stilted, but restored to its analytical simplicity it was a supple method of discovery for Galileo, whose “mechanical” (mathematical) way of solving problems became the model for natural philosophy in the century before Newton.103
For the demonstration to attain the last degree of certainty, Galileo (like Galen and Roger Bacon) requires verification by experiment to confirm that the hypothesized mechanism actually operates in nature. Galileo wants to “consider the phenomena of bodies falling with an acceleration such as actually occurs in nature and to make this definition of accelerated motion exhibit the essential features of observed accelerated motions.” He says that sciences like his, “which apply mathematical demonstrations to physical conclusions,” must “confirm their principles with sensory experiments that are the foundation of all the resulting structures,” an experimental empiricism reiterated in a late letter, where he says that “giving priority to some experience over any reasoning whatsoever is one of the sure ways of pursuing the truth”104