This paper defends a version of J. H. Randall’s thesis that modern empiricism is rooted in the Scholastic regressus method epitomized by Jacopo Zabarella in De Regressu (1578). Randall’s critics note that the empirical practice of Galileo and his contemporaries does not follow Zabarella. However, Zabarella’s account of the regressus is imprecise, which permitted an interpretation introducing empirical hypothesis testing into the framework. The discourse surrounding Galileo’s lunar observations in Sidereus Nuncius (1610) suggests that both Galileo and his interlocutors amended the regressus method in this way, such that a developmental narrative links Scholastic logic to Galilean science.
One of the distinctive features of modern science is a commitment to empiricism—a fundamental expectation that theoretical hypotheses will survive encounters with observations. Those that comport with the theory’s explanations and predictions confirm the theory. Anomalous observations that do not fit theoretical expectations disconfirm it. Moreover, experiments can be contrived to generate observations that might serve to confirm or disconfirm a theory. Philosophers of science may disagree as to how exactly all of this is supposed to work, but the basic empiricist expectation almost goes without saying. To deny it is to rule one’s self out of the bounds of the scientific enterprise.
Strange as it might seem to modern readers, empiricism in this guise was not always a feature of attempts to understand the natural world. It was not a prominent feature of Scholastic Aristotelianism, the preeminent philosophical tradition of the pre-modern era. The Scholastics held that it was possible to attain certain knowledge—scientia—about the natural world without a commitment to empirical adequacy in the face of specific observations. This is not to say that Scholastic natural philosophy was not at all empirical, as we shall see. Yet, in the view of Scholastic philosophers, individual experiences typically could not confirm or disconfirm a theory. Consequently, there was little point in appealing to discrete observations or devising experimental tests to establish grounds for accepting or rejecting theoretical hypotheses (Schmitt 1969; McMullin 1978; Dear 1987; Dear 1995).
This raises a historical question: how did natural philosophers come to value empiricism in the modern sense? When did observations become probative? Naturally, this is a complicated question that has long exercised scholars. Much of the relevant literature, however, focuses on northern Europe in the middle-to-late seventeenth and eighteenth centuries, and especially on the influence of Francis Bacon and Baconian thought. Certainly, Baconianism is an essential feature of the broader story, especially regarding inductive confirmation of theories, but empiricism of a sort also emerged outside and prior to the Baconian sphere of influence. One finds, in particular, that Galileo and his interlocutors considered specific observations as reasons to reject theoretical hypotheses at the beginning of the seventeenth century. That is, they took incompatible observations as disconfirmations of a theory.
This essay attempts to illuminate this cisalpine Baconianism avant la lettre, employing the debates surrounding Galileo’s lunar observations as a paradigmatic example. In that debate, both Galileo and his opponents used particular observations—as opposed to general experience—to discriminate between competing theoretical hypotheses. Anomalous observations discounted possible explanations in favor of an alternative. This shows that eliminative empiricism (for lack of a better term)1 was an agreed-upon method by the time Galileo and his opponents entered the lists. This narrows the framing question to the use of observations as disconfirmations in Galileo’s milieu. That is, how did Galileo and his contemporaries make observations probative—at least negatively—in the pursuit of natural science?
One thread of an answer links empirical hypothesis testing to Aristotelian Scholastic logic, which was already undergoing significant reconsideration during the sixteenth century. In particular, the “demonstrative regress” or regressus had been incorporated into the logic curriculum by which Galileo and his contemporaries were schooled. The regressus method reconfigured the relationship between theoretical explanations and observed effects. Yet regressus also inserted an ambiguity into the understanding of this relationship, in the form of the negotiatio intellectus. Though an essential step in regressus, there was no consensus as to how the negotiatio was supposed to proceed. The discriminatory use of observations could be seen as a natural way to resolve this ambiguity. Thus, the regressus method suggested a novel methodology in natural science that admitted observations as epistemic grounds for accepting and rejecting theories. Hence, Scholastic Aristotelian resistance to the probity of individual experiences was partly overcome by developments within the tradition of Scholastic Aristotelianism itself.
The regressus method has been an object of scholarly attention for a long time. In 1940, John Herman Randall, following Ernst Cassirer’s earlier suggestion, famously asserted that, with the addition of mathematics, it could be counted as the methodology of modern science (Cassirer 1906, pp. 134–41; Randall 1940, esp. p. 205; Randall 1961).2 Subsequent authors harshly criticized Randall’s view, showing that his radical claim had to be tempered, at least, if any connection between regressus and modern science was to be retained. In particular, Randall’s critics emphasized dissimilarities between Galileo’s method and Zabarella’s, concluding that the former was not the latter (Gilbert 1963; Schmitt 1969; Jardine 1976; Wisan 1978).3 This can be granted, but it does not preclude the possibility that Galileo’s method was a development of Zabarella’s. As discussed below, William Wallace and others have documented that Galileo and his contemporaries were at least well-acquainted with regressus (Wallace 1984, 1988, 1992a, 1992b).4 Thus, even if Randall’s original claim overreached, it might nevertheless be possible to show that regressus contributed to modern, Galilean science.5
The present essay is an attempt to modulate Randall’s claim along these lines. I aim to establish a more limited, yet more precise connection between Scholastic logic and Galilean-style empiricism by closely examining uses of the regressus by those in Galileo’s intellectual orbit, including—but not limited to—Galileo himself. Galileo’s deployment of a regressus-like argument, and his interlocutors’ responses in kind, shows that the method, and the eliminative empiricism associated with it, had entered the natural scientific discourse of Galileo and his contemporaries. In this regard, Galileo’s work represents the development of natural scientific discourse more generally.6
The discussion begins by briefly stating the problem—the Aristotelian emphasis on certainty and what is generally known to be the case stands opposed to argumentative appeals to specific observations. The regressus theory is then explained, using the authoritative De Regressu (1578) by the Paduan Scholastic Jacopo Zabarella. This discussion highlights the ambiguity surrounding one stage of the regressus method—the so-called negotiatio intellectus. Two successive interpretive moves are then proposed. First, the ambiguous role of the negotiatio in a regressus can be filled by a process that discriminates between competing causal hypotheses. Second, one means of discriminating hypotheses is empirically testing them against observations. In this way, empirical hypothesis testing can be inserted into the regressus method. Next, the paper examines Galileo’s arguments in Sidereus Nuncius (1610) and a response, the De Phoenomenis in Orbe Lunae (1612) by the Aristotelian professor of natural philosophy Giulio Cesare La Galla. The examination reveals the use of empirical hypothesis testing to complete regressus demonstrations. In other words, the texts offer evidence that regressus was indeed interpreted empirically in the discourse surrounding Galileo’s lunar discoveries. The paper then closes with a discussion of further implications of this analysis.
2. Stating the Problem
In traditional Aristotelianism, the aim of natural philosophy is certain knowledge—scientia—of natural phenomena. One seeks a thorough and indubitable understanding of natural facts. This is achieved once the causal order of nature is expressed in a logical order of deductions. As Aristotle puts it in the Posterior Analytics, an ideal scientific demonstration (apodeixis) is a syllogism that expresses the causal necessity of the fact to be known. Such a demonstration shows “that the explanation because of which the object is is its explanation, and that it is not possible for this to be otherwise” (Posterior Analytics I.2, 71b10–12; Aristotle 1984, p. 1:115). In natural science, then, the logical necessity of the demonstration reflects the causal necessity inherent in the natural world—its certainty derives from the inviolability of causal principles. Natural knowledge is thus tied to the way causes determine what must be.
This insistence upon demonstrative certainty distances scientific knowledge from observations. Since they are the basis of causal explanation, Aristotelian scientia is derived from necessary universals—what must be and is generally known to be the case—rather than contingent particulars. Discrete experiences, even in aggregate, do not yield the kind of necessary universal that might be the basis of a proper scientific demonstration. Consider Posterior Analytics I.31:
Nor can one understand through perception. For even if perception is of what is such and such, and not of individuals, still one necessarily perceives an individual and at a place and at a time, and it is impossible to perceive what is universal and holds in every case; for that is not an individual at a time; for then it would not be universal … The universal is valuable because it makes clear the explanation; hence universal demonstration is more valuable than perception … (Posterior Analytics I.31, 87b29-99a6; Aristotle 1984, p. 1:144)
This is not to say that Aristotelian natural philosophy was not empirical. Aristotle himself wrote lengthy treatises reporting observations of phenomena, especially on biological topics. Moreover, “nothing is in the intellect that was not first in the senses” (nihil est in intellectu quod non sit prius in sensu) was an oft-quoted dictum of Aquinas (De Veritate, q. 2 art. 3 arg. 19).8 What this meant, though, was that experiences are the basis of knowledge, not that they are themselves scientific. For example, by general experience of dogs, birds, fish, etc., one first comes to an understanding of “animal,” and only then sets about demonstrating what necessarily follows from the universal concept of “animal” thus acquired. Observations are propaedeutic, not constitutive, of scientific knowledge.9
It follows that particular observations have minimal value in the methodology of traditional Aristotelian science. On the one hand, one cannot gain knowledge of dogs by studying Fido. On the other hand, one cannot reject a scientific principle on the basis of an observed counterexample. Natural causes are sometimes frustrated by accidental impediments (Wallace 1974). Hence, singular counterexamples only indicate that something is wrong with the particular case; they do not refute what is known to be true universally. A shorn, three-legged sheep does not show that a sheep is not a furry, four-legged animal. Consequently, observations are not the basis of scientific knowledge, nor can they disprove established scientia. Traditional Aristotelian methodology provides no obvious way to test a theory against observations of individual cases (Dear 1987, p. 145). As a general rule, therefore, Aristotelian natural philosophers did not seek empirical confirmation or disconfirmation of their theories. General experience and the testimony of authorities were enough to establish what was known.
In the Dialogue on the Two Chief World Systems (Dialogo), Galileo notes this attitude to comedic effect:
One day I was at the home of a very famous doctor in Venice, where many persons came on account of their studies, and others occasionally came out of curiosity to see some anatomical dissection performed by a man who was truly no less learned than he was a careful and expert anatomist. It happened on this day that he was investigating the source and origin of the nerves, about which there exists a notorious controversy between the Galenist and Peripatetic doctors. The anatomist showed that the great trunk of nerves, leaving the brain and passing through the nape, extended down the spine and then branched out through the whole body, and that only a single strand as fine as a thread arrived at the heart. Turning to a gentleman whom he knew to be a Peripatetic philosopher, and on whose account he had been exhibiting and demonstrating everything with unusual care, he asked this man whether he was at last satisfied and convinced that the nerves originated in the brain and not in the heart. The philosopher, after considering for awhile, answered: “You have made me see this matter so plainly and palpably that if Aristotle’s text were not contrary to it, stating clearly that the nerves originate in the heart, I should be forced to admit it to be true” (Galilei  1967, pp. 107–8).
Galileo’s charming anecdote reads as caricature, but it does illustrate the issue. Galileo is parodying something, and the humor depends on his audience’s recognition of the target. The question, then, is how did someone like Galileo come to see the Scholastic attitude toward observations as worthy of ridicule? Conversely, how did Galileo and his peers come to see particular experiences as negatively probative? How, that is, did observations become evidence against theories?
3. An Empirical Interpretation of Regressus
As one might suspect, Galileo was not being entirely charitable when he penned the story of the Venetian doctor. In fact, Scholastic Aristotelian authors were concerned about the role of observations in natural science. This was primarily a consequence of the promotion of the medical arts to the status of scientific discipline and the associated foundation of medical faculties in Renaissance universities. Galenic medicine valued observation, especially in the process of diagnosis, and this generated a need to reconcile medical method with Aristotelian natural philosophy. Humanism’s elevation of the status of human sensory powers also reinforced this need. Thus, Scholastic scientific methodology had undergone significant emendation in the generations prior to Galileo and remained in flux even during his lifetime.10
As we have seen, traditional Aristotelian method generated knowledge of phenomena by demonstrating them from already established causes. But philosophers had begun to wonder how it might be possible to discover a cause that was not already known. Some suggested supplementing the traditional demonstration from causes to effects with a prior inference from the observed effects to the unknown causes. Scholastic logicians thus began to develop a method that inferred from observed effects to an unknown cause, and then from that same cause back to the observed effects, in a way that somehow avoided mere circularity. This was called demonstration by regressus. Pietro d’Abano, writing in the fourteenth century, was the first to use the term, but the theory’s heyday was in the late sixteenth-century, especially at the University of Padua—famous, not incidentally, for its medical faculty.
The leading expositor of regressus theory was the Paduan professor Jacopo Zabarella, whose 1578 De Regressu was its best-known statement. Consider Zabarella’s description of regressus:
Regressus … is between cause and effect, when they reciprocate and the effect is more known to us than the cause. For since progressing always has to be from what is more known to us, we first demonstrate unknown cause from known effect; then, the cause [now] known, we regress from it to demonstrate the effect, with the result that we know scientifically what it is on account of (ut sciamus propter quid est). (Zabarella  2013b, p. 359)
As an extended illustration, Zabarella considers an example drawn from Aristotle’s Physics.13 Here is the quia:
Where there is generation, there is underlying subject matter there;
In natural body there is generation;
Therefore, in natural body, there is matter. (Zabarella  2013b, p. 373)
However, argues Zabarella, one cannot immediately regress and demonstrate the propter quid. The knowledge of the cause—matter—produced by the quia is merely “confused”:
The knowledge of the major premise is nothing but confused, because, granted that the predicate [i.e., matter] is the cause of the subject [i.e., generation], nevertheless it is not known as cause. For we know that every change has underlying subject matter—not as an effect of the matter itself, but as perpetually conjoined to the underlying subject matter. … And thus it happens that knowledge of this conclusion too is confused, because we discover and know only that matter belongs to natural body but do not know its characteristics, nature, and definition. … That the known thing itself exists, makes nothing clear except that there is a cause—though not as its cause, because it is not known as an effect of that cause, but only as something never separable from it. (Zabarella  2013b, pp. 375–7)
Determining the nature and operation of the cause requires an intermediate step between the quia and the propter quid.
And so, the first procedure, which is from effect to cause, having been performed, before we go back from it [i.e., the cause] to the effect, it is necessary that there intercede some third intermediate effort by which we are led into distinct knowledge of that cause, which was known only confusedly (confusè tantùm). Some, knowing that this is necessary, call it negotiation of the understanding (negotiatio intellectus). We can call it a mental examination of the cause (examen ipsius causae mentale) or a mental consideration (consideratio mentalis). (Zabarella  2013b, pp. 378–79)
Finally, the necessity uncovered by the negotiatio yields the propter quid:
Where there is matter, there is generation;
In natural body, there is matter;
Therefore, in natural body, there is generation.15
So, to summarize, a regressus consists of three inferential moves. First, one infers from the observed effect to the cause confusedly known (causa confusè cognita) by a demonstratio quia, which establishes only that a cause is associated with the effect. Second, one performs a negotiatio intellectus that results in a cause distinctly known (causa distinctè cognita); i.e., a comprehensive understanding of its nature and operation. Third, one deduces by a demonstratio propter quid from the cause distinctly known to the effect, which is thus scientifically demonstrated. Following this method, one can discover new items of scientific knowledge from observed effects, including the causes of effects not previously understood.
The negotiatio is, of course, the crucial step in regressus. On the one hand, it separates the quia from the propter quid, thereby preventing regressus from falling into mere circularity. On the other hand, the negotiatio uncovers the causal necessity by which the cause is known distinctly. Since such necessity is the benchmark of scientia, the negotiatio is where the real work of discovery is done. So, what is a negotiatio, exactly? How is it supposed to work? In fact, this is not at all clear. Zabarella says as much:
What sort of thing this mental consideration is and how it is done, I have not seen made clear by anyone. For even though some say that this intermediate negotiation of [the] understanding is interposed, they nevertheless have not shown how we are led by means of it into distinct knowledge of the cause and what the power of this negotiation is. We will do something much worth the work, therefore, if we say something about this. (Zabarella  2013b, p. 379)16
Generally, what Zabarella “says about this” is that the transition from confused to distinct knowledge of the cause is achieved by a “mental consideration”—his own term for the negotiatio. By holding a thing up to the intellect, the mind can intuitively grasp its essential attributes, including its causality. The mind is “prepared” for this examination by the demonstratio quia, “For when we know beforehand that something is in a thing, we can track down and discover something else in it” (Zabarella  2013b, p. 379). How one makes this final transition, recognizing this essential causality as the cause of that effect, and thus moving from confused to distinct knowledge, is never quite explained. Even for Zabarella, the important moment of knowledge acquisition remains ineffable.17
The negotiatio was thus something of a mystery, even to its expositors (Mikkeli 1992, pp. 97–100; Wallace 1995, p. 93). Yet by the same token, it was a palimpsest onto which many different modes of reasoning could be impressed. Authors using regressus could carry out the negotiatio in several ways and still meet the methodological expectations of their audience. And here is the important point: one natural way to interpret the negotiatio is as a process of hypothesis elimination. On this reading, the “confused knowledge” of the cause refers to a range of distinct possible causes in which each might explain the effect. These are identified by the quia as features of the phenomena associated with the effect in question. The negotiatio then serves to eliminate alternative hypotheses until the actual cause is identified—the cause distinctly known. Furthermore, one way of eliminating hypothetical alternatives is by testing them against the observations. In other words, by manipulating the Scholastic method of regressus, authors could introduce observations into scientific inquiry. I will argue below that Galileo and his peers achieved this result, such that a kind of eliminative empiricism became an accepted means of demonstration in natural science.
In the meantime, though, it is worth noting details of Zabarella’s discussion of the negotiatio that might support an empirical (re-)interpretation. Consider Zabarella’s contrast between “confused” and “distinct” knowledge. Neither De Regressu nor the more general De Methodis (1578) offer clear definitions of these terms of art. When they are first introduced in the De Methodis, Zabarella merely offers “imperfect” and “perfect”—i.e., incomplete and completed knowledge—as synonyms (Zabarella  2013a, p. 49).18 Elsewhere, as we have already seen, Zabarella defines distinct knowledge as knowledge of “why it is” derived from a demonstratio propter quid (Zabarella  2013a, p. 247; Zabarella  2013b, p. 371). While these explicit definitions are not particularly helpful, it seems that Zabarella is appealing implicitly to standard Scholastic terminology derived from a distinction in Aquinas and its elaboration by Thomas Cajetan (Aquinas, Summa Theologica, pt. 1 q. 85 art. 3; Cajetan 1572, pp. 5–7; Cajetan 1964, pp. 19–22, 40–2; Pasnau 2002, pp. 318–29). In this tradition, one has confused knowledge when one knows a universal without knowing what makes it that universal.19 So, for instance, one has confused knowledge when one knows what “man” is without knowing that something is a man on account of being a rational animal—i.e., the definition of “man.” Putting this into the context of causal reasoning, Zabarella seems to indicate that “confused knowledge of the cause” is knowledge of the cause as the conditions coextensive (“perpetually conjoined”) with the effect, while “distinct knowledge of the cause” is knowledge of the particular causal features (“characteristics, nature, and definition”) that bring the effect about and thus make the conditions the cause.
Zabarella’s discussion then suggests an empirical eliminative method. He says that a negotiatio might include a “comparison of the discovered cause with the effect by means of which it is discovered.” This will lead “little by little to knowledge of the characteristics of the former thing, and, once one characteristic has been discovered, we are helped to discover another, until finally we know that this is the cause of that effect” (Zabarella  2013b, pp. 379–81).20 In light of the last terminological point, a possible reading of this “comparison of the discovered cause with the effect” is an enumeration of the possible causal conditions—taken together as the “cause confusedly known”—in light of the observed phenomena. In this way, successive possible theories about the nature and operation of the cause are ruled out by checking them against observations, and one is led “little by little to knowledge” of the particular, actual cause—the “cause distinctly known.”
This is not meant to assert that empirical hypothesis testing is what Zabarella himself had in mind. As noted above, he seems to think that a negotiatio can be carried out by mere “mental examination,” without empirical considerations. Nevertheless, the ambiguity surrounding the negotiatio accommodated and even encouraged a range of possible interpretations, and the tradition of Zabarellan logic was marked by more flux than stability.21 The interpretation suggested here is not exclusive of others. The point is merely that those attempting to use regressus might have reasonably interpreted it as involving empirical hypothesis testing.22 If so, then regressus offers an avenue to empiricism in the modern sense. It remains to be seen if Galileo and his contemporaries followed that path.
Note in passing that it might be tempting to read the demonstratio quia as a precursor of modern inductivism. It is, after all, a logical progression from particular observations to general causal principles. However, the connection is tenuous. In a quia, as seen in the examples below, individual instances are not individually connected to the cause, followed by an inductive generalization over those instances. Rather, the observed effects are gathered together before any causal hypothesis is tendered. The association between cause and effects then comes all at once, cognized out of the collective whole, not through the individual instances. The general experience of the effects, not particular observations, is the ground of the inference. Moreover, the possible causes might be antecedently known independently of the observations. Thus, individual observations do not offer confirmation. In this way, the quia more resembles traditional Aristotelian methods than modern (Baconian) induction. Naturally, modern inductivism likely grew out of the quia, but the connection is not as clear as it at first might seem (Wallace 1995, pp. 91–2).
4. Using Regressus: Earthshine
Thanks to the work of William Wallace, we know that the regressus method was widely known in Galileo’s intellectual context. Zabarella’s De Regressu appeared in 1578, when Galileo was fourteen. Moreover, regressus theory was already a part of the curriculum in Italian universities—indeed, throughout Europe (Wallace 1984, ch. 1; Sgarbi 2013). In particular, it was standardly taught as the primary demonstrative strategy in natural philosophical discourse, wherein one must infer causes from effects, in the logic and physics courses of the Collegio Romano, to which Galileo had close connections (Wallace 1984, ch. 3; Wallace 1997).23 In fact, as a young professor starting out at Pisa, Galileo penned a set of logical questions, modeled on lecture notes from Paulus Vallius’s course at the Collegio Romano. The last question addressed in the manuscript, “Is there a demonstrative regress [regressus demonstrativus]?” is eventually answered affirmatively. So Galileo not only knew of the method, but was prepared to teach it (Wallace 1992b, ch. 1).24 As a mathematics professor he probably had little opportunity to do so, of course.25 But if regressus was known to Galileo, who was by no means a scholar of philosophy or logic, then one can assume the same is true of his university-educated audience.
Galileo never explicitly mentions regressus in the Sidereus Nuncius, but there are strong circumstantial reasons to suppose that he is using the method. It is not surprising that he does not explicitly discuss his method, since the book’s subject is astronomy, not logic.26 Moreover, this was Galileo’s first major publication, reporting the remarkable discoveries he made with his improved telescope. It was likewise the first of Galileo’s publications aimed at a wide audience—“all seekers of true philosophy” (omnes verae Philosophiae cupidos) (Galilei 1610, p. 7r). He saw the book as a ticket to fame and position; rightly so, as it turned out. On the strength of the book, Galileo was able to negotiate the position of chief mathematician and philosopher to the Grand Duke of Tuscany. But this goes to show that Galileo was aiming his discourse, at least in part, at natural philosophers versed in Aristotelian logic, not just the mathematicians and engineers he had hitherto engaged with. So, when Galileo offers “to assign causes” (causam assignare) in the text, it is reasonable to suppose he is conscientiously calling upon the standard method of doing so in natural science, so as to gain a hearing from his intended readers (Galilei 1610, p. 14r).27 In any case, there are discussions in the treatise that hew very closely to regressus.28
The clearest example is Galileo’s discussion of earthshine—the “secondary light” that dimly illuminates the part of the moon not directly lit by the sun. This, he admits, was not a recently discovered effect, but since it is related to the other phenomena described in the text, he repeats the “explanation and declaration of the cause” he had devised “many years ago” (Galilei  1989, p. 53).29 This begins with a description of the observed effect:
When, both before and after conjunction, the Moon is found not far from the Sun, she offers to our sight not only that part of her globe that is adorned with shining horns, but also a thin, faint periphery that is seen to outline the circle of the dark part (that is, the part turned away from the Sun) … But if we examine the matter more closely, we will see not only the extreme edge of the dark part shining with a faint brightness, but the entire face of the Moon—that part, namely, that does not yet feel the brightness of the Sun—made white by some not inconsiderable light. (Galilei  1989, p. 53)
The natural philosopher, of course, enquires after the cause of this effect, and there are several associated phenomena that might be responsible:
This marvelous brightness has caused no small astonishment to those applying themselves to philosophy, and some have put forward one reason and some another as the cause to be assigned to it. Some have said that it is the intrinsic and natural brightness of the Moon herself; others that it is imparted to it by Venus, or by all the stars; and yet others have said that it is imparted by the Sun who penetrates the Moon’s vast mass with his rays. (Galilei  1989, p. 54)
This inference to a range of possibilities constitutes Galileo’s demonstratio quia. Each proposed cause is something that is universally associated with the effect in question. Whenever the moon displays its secondary light, Venus, the stars, and the Sun all shine, and the Earth reflects sunlight, as is obvious during the daytime. So all of these phenomena are “perpetually conjoined” to the secondary light. Moreover, one of them must be the cause of the effect since they exhaust the concurrently observed sources of light bright enough to cause the effect. Thus, one knows that these possibilities, taken together, are the cause of the effect—collectively, they are the “cause confusedly known.” It remains, then, to settle upon the actual cause from among the possibilities; i.e., by a negotiatio.
Hence, by a comparison with observed phenomena, Galileo proceeds to eliminate possible causes.
But such proposals [prolata] are refuted with little difficulty and shown to be false [ac falsitatis evincuntur]. For if this light were either the Moon’s own or gathered from the stars, she would retain it and show it especially during eclipses. When she is placed in a very dark sky. This is not borne out by experience, however [quòd tamen adversatur experientiae], for the light that appears in the Moon during an eclipse is much weaker, somewhat reddish, and almost coppery, while this light is brighter and whiter. (Galilei 1610, p. 14v; Galilei  1989, p. 54)
Other observations rule out the Sun as the cause of the secondary light.
But it is equally inconceivable that this light is due to the Sun, who with his light penetrates and fills the solid body of the Moon. For it would never be diminished, since a hemisphere of the Moon is always illuminated by the Sun except at the moment of a lunar eclipse. Yet the light is diminished when the Moon hastens toward quadrature and is entirely dimmed when she has gone beyond quadrature. (Galilei  1989, p. 55)
Finally, the light cannot be coming from Venus:
To declare, on the other hand, that this light is imparted by Venus is so childish as to be unworthy of an answer. For who is so ignorant as not to know that near conjunction and with the sextile aspect it is entirely impossible for the part of the Moon turned away from the Sun to be seen from Venus? (Galilei  1989, p. 55)
In any case, only one possible cause remains—light reflected from the Earth:
Since, therefore, this secondary light is not intrinsic and proper to the Moon, and is borrowed neither from any star nor from the Sun, and since in the vastness of the world [mundi; i.e., cosmos] no other body therefore remains except the Earth, I ask what are we to think? What are we to propose—that the lunar body or some other dark and gloomy body is bathed by light from the Earth? But what is so surprising about that? In an equal and grateful exchange the Earth pays back the Moon with light equal to that which she receives from the Moon …. (Galilei  1989, p. 55)
But the identification of the cause enables a more complete understanding of the secondary light. Given the known cause, one can go on to deduce the effect, including details not previously recognized. This is the demonstratio propter quid.
Let us expound the matter more clearly. [Rem clarius aperiamus.] … In its various aspects to the Sun and Earth, the Moon receives more or less light by reflection from the Earth as she faces a larger or smaller part of the illuminated terrestrial hemisphere. For the relative positions of those two globes are always such that at those times when the Earth is most illuminated by the Moon the Moon is least illuminated by the Earth, and vice versa. (Galilei 1610, pp. 15r–16r; Galilei  1989, pp. 55–7, slightly altered)
The final propter quid completes the regressus. From the appearance of the secondary light of the Moon, Galileo infers that the cause is among the concurrent sources of sufficient light. Using empirical observations to test the possibilities, he eliminates them until he settles on the Earth as the source of the light. And on that assumption, Galileo demonstrates how the secondary light is produced. Of course, the important point for our purposes is that empirical testing has been inserted into the negotiatio phase of the demonstrative method. Yet an educated reader, schooled in the latest Aristotelian method, would recognize the exposition as at least formally valid. Galileo has offered a causal demonstration, including empirical tests of hypothetical causes, that comports with Zabarella’s Scholastic logic and yields scientific knowledge of the effect.
5. Using Regressus: Lunar Mountains
The phenomenon of earthshine threatened Aristotelian cosmology and favored Copernicanism by making the Earth luminous and active, comparable to the other celestial bodies. Yet its significance paled in comparison to Sidereus Nuncius’s other startling reports, especially the Jovial satellites and Galileo’s discovery that the surface of the Moon is seen to be not “smooth, even, and perfectly spherical, as the great crowd of philosophers have believed about this and other heavenly bodies, but, on the contrary, to be uneven, rough, and crowded with depressions and bulges” (Galilei  1989, p. 40). As Galileo indicates, this is a momentous conclusion, since it contradicts the orthodox Aristotelian position that the Moon, like all the celestial objects, is a perfect, incorruptible sphere. Moreover, a mountainous Moon lends significant support to heliocentrism, because if a corruptible, imperfect Moon can inhabit the celestial realm, then it seems that a corruptible, imperfect Earth might do so, as well. Thus, the Moon’s mountainousness (montuosità) posed a stark challenge to Aristotelian cosmology and was met with resistance. While Galileo’s own use of regressus to establish the existence of lunar mountains is not as clear as in the case of earthshine, the significance for the present discussion is that Galileo’s argument and his opponents’ responses both insert observations as empirical hypothesis tests into the regressus structure. This is further evidence that the regressus could be and was interpreted empirically by Galileo’s time.
Galileo’s discussion seems to adhere to the method, if somewhat obliquely. He first reports several telescopic observations of the Moon’s appearance. These include the fact that the terminator—the line of separation between the sunlit and darkened sides of the Moon’s face—is “uneven, rough, and very sinuous” (Galilei  1989, p. 40). In addition, bright spots are seen on the dark side of the terminator, completely separated from the general illumination, while dark spots can be seen on the light side. Moreover, the appearance of these spots changes, even over the course of a few hours. For instance, in a waxing Moon, the bright spots will grow in size and eventually merge with the sunlit part of the lunar face. Galileo then suggests that these appearances are caused by a mountainous lunar surface. This demonstratio quia proceeds by comparison with terrestrial experience. Considering the growing bright spots, for example, Galileo writes: “And we have an almost entirely similar sight on Earth, around sunrise, when the valleys are not yet bathed in light but the surrounding mountains facing the Sun are already seen shining with light” (Galilei  1989, p. 41). General experience shows that such changing and merging illuminated spots are associated with mountains, and this is sufficient to suggest that mountains exist on the Moon (Ariew 1984; Shea 2000; Wilson 2001; Spranzi 2004).
The negotiatio phase of the discussion in the Sidereus Nuncius does not take the form of an empirical discrimination between hypothetical causes since Galileo does not consider causes of the changing spots other than lunar montuosità. Still, Galileo does insert consideration of observations that might serve as an empirical refutation of his own view. The extreme periphery of the visible Moon (i.e., its limb) is seen to be “exactly round and circular, and not jagged with prominences and depressions” (Galilei  1989, p. 48). This presents “opportunity for serious doubt,” (Galilei  1989, p. 48) since the mountains near the limb should make it appear rough and uneven. To allay the doubt, Galileo offers two possible explanations. First, the Moon might be so mountainous near its visible extremities that the appearances of the mountaintops join together into what looks, from the side, like an undifferentiated plateau, as “in a billowy sea the high tips of the waves appear stretched out in the same plane, even though between the waves there are very many troughs and gulfs” (Galilei  1989, p. 49). Second, the Moon might be enveloped by an atmosphere that prevents the surface of the limb from being clearly seen. (Since it is observed obliquely, more atmosphere would be interposed between the observer and the limb than between the observer and the central parts of the Moon.) As it happens, neither excuse is particularly successful in circumventing objections, as we will see. However, it is worth noting once again that Galileo gives—in the middle phase of his argument—consideration to discrete observations that might function as a test of hypotheses generated by the demonstratio quia.
Galileo’s apparent regressus is completed by a mathematical “demonstration” (Galilei 1610, p. 13r; Galilei  1989, p. 51) of the extreme height of the lunar mountains. Given that some of the changing spots are sometimes seen to be separated from the terminator by more than a twentieth of the moon’s diameter, Galileo calculates that the height of the mountains producing those spots must exceed four Italian miles. Again, this does not quite fit the archetype of a demonstratio propter quid, since it deduces particular features of the cause from particular features of the effect, rather than the other way around. On the other hand, the demonstration does reveal the necessary connection between particular features of the observed effects, the spots’ distance from the terminator, with particular features of the proposed cause, the heights of the lunar mountains. Indeed, the necessity is here mathematical. So, this inference does extend the reader’s understanding of the effect from knowledge of the nature and operation of the cause, as one would expect from a propter quid.
While Galileo’s own discussion might not be a perfect example of regressus, the method can be seen clearly in some of his opponents’ arguments against the montuosità of the Moon. Galileo does not consider an alternative cause of the Moon’s rugged appearance, but Aristotelian natural philosophers offered one in order to defend the smoothness of the celestial spheres. A consensus coalesced around the possibility that the Moon’s aetherial substance varied in its optical properties. This was an extension of a standard explanation of the varying appearances in the heavens (Miller 2013). The view held that there was only one celestial substance—the aether—but that parts of the aether could differ in their accidental luminescence. “Rare” aether could absorb and re-emit light; while “dense” aether remained dark and transparent. For example, the planets were thought to be orbs of rare aether embedded in otherwise dense aetherial spheres, through which the rest of the heavens, including the fixed stars, could be seen. This, moreover, was the usual explanation of the obvious superficial variations we call the Man in the Moon, which can be seen by the naked eye. The Moon, it was said, consists of a mixture of dense and rare aether, which gives it an uneven appearance, even though it is actually smooth and homogenous, just as a uniform, polished sphere of marble exhibits veins of light and dark (La Galla 1612; La Galla  1892, p. 89).
Galileo’s newly observed spots, of course, are not the “large and ancient spots” (Galilei  1989, p. 40) of the Man in the Moon, which do not vary over the course of a few hours. But natural philosophers could amend the old theory by holding that the variation in the optical properties of the lunar aether extended in three dimensions, into the body of the Moon. For example, in his 1611 Contro il Moto della Terra, Galileo’s frequent antagonist Ludovico Delle Colombe describes how the Moon might be a smooth sphere of transparent aether containing an uneven core of opaque aether, “like a big ball of the clearest crystal, inside of which a little earth is formed of white enamel, with forests, valleys, and mountains.” Since the earth-bound observer sees through the transparent aether to the opaque aether within, the moon would appear “unequal, toothed, and mountainous, even if it is not” (Delle Colombe 1892, p. 287).30 Accidental variations in the rarity and density of the lunar aether might account for Galileo’s observations and still maintain the homogeneous nature and perfect sphericity of the Moon. For Galileo and his interlocutors alike, the dialectical situation thus demanded a negotiatio to decide between the two candidate causes, montuosità and variation in optical density. Yet, just as Galileo had used observations as tests of competing theories, so too could his Aristotelian opponents.
One rejoinder to the Sidereus Nuncius by Julio Cesare La Galla, professor of philosophy at La Sapienza, illustrates the methodological commonality, even while defending a Peripatetic theory of the moon. De Phoenomenis in Orbe Lunae explicitly refers to the parts of regressus in drawing a contrast between astronomical (i.e., Galileo’s) and physical (his own) reasoning.
Indeed, in [their] speculations about celestial motions and phenomena, mathematicians [i.e., astronomers] do not proceed to demonstration propter quid—that is, from cause to effect—but to demonstration quia—from effect to cause. Wherefore once the observations of motions and phenomena are collected, then, supposing these, they seek to find and assign causes that suffice to conform to them [the observations], as we said. For it is enough that from these [causes], a fixed proportion preserves the apparent motions. (La Galla  1892, pp. 338–9)31
The regressus structure is apparent in La Galla’s text. It begins by repeating and confirming “the experiments—that is to say, the observations—of the lunar orb made by Doctor Galilei and very faithfully recounted in the little book named Sidereus Nuncius” (La Galla  1892, p. 325).34 La Galla then follows Galileo’s own demonstratio quia. He admits that the observed phenomena might be associated with unevenness on the Moon’s surfaces. That is, lunar montuosità could cause the observed effects. He is even willing to say that he would himself hold Galileo’s opinion to be probable, if there were no other, more valid reasons to believe otherwise (La Galla  1892, p. 379).35
However, La Galla points out that there is another possible cause that might account for the observed effects—variation in optical clarity.
Hence, I argue: if the variable substance with a smooth and even surface (without multiplying bodies), is the cause of the same phenomenal variety that is seen in the rest of the Moon, [i.e.] in the larger Lunar spots; then the same variability of substance can be said to be the cause of the variation in the illuminated part of the moon.… Thus, this variability between clear and opaque, of which the whole body of the moon is an admixture, is assumed, as we will declare below. (La Galla  1892, pp. 379–80)36
To proceed, then, La Galla offers a negotiatio that settles on one of the possibilities as the “cause distinctly known.” La Galla, it goes without saying, comes down on the side of the Aristotelians, attributing the observations to variations in clarity and opacity. In so doing, La Galla appeals to the usual theses about the perfection of the heavens, drawn from the usual authorities, especially Aristotle.
However, La Galla also inserts observations into the argument, by using Galileo’s against him. Specifically, he points out that, if the Moon is really mountainous, then the limbs of the Moon should be “uneven and toothed” (inaequalis ac dentatus) (La Galla  1892, p. 380). Yet the circumference of the Moon is seen to be circumscribed by a “perfectly continuous and entirely even line” (perfecte continua atque omnino aequali linea) (La Galla  1892, p. 380). La Galla is not swayed by Galileo’s attempts to explain away the smoothness of the moon’s limbs. The lunar mountains cannot be so densely and evenly distributed such that their peaks form an apparent plateau, for then the terminator would also be smooth and even (since the Sun “sees” a hemisphere of the Moon just as we do). And there cannot be a lunar atmosphere, since an atmosphere is created by vaporous exhalations, of which the celestial aether is not capable. Thus, lunar montuosità is not compatible with the observations, and can be rejected. La Galla, that is, uses empirical hypothesis testing against Galileo.
In the final section of his treatise, La Galla completes the regressus by “demonstrating” the observed phenomena on the “supposition” of variations in the optical density of the lunar substance (La Galla  1892, p. 389).37 He explains that transparent aether will appear dark, since it is not pervaded and illuminated by incipient light. Thus, if a transparent part of the moon extends into the illuminated hemisphere, it will appear dark. And this, for instance, will produce a terminator that “may seem unequal, even sinuous or tuberous” (inaequalis videatur, ac sinuosa vel tuberosa) (La Galla  1892, p. 389). Likewise, La Galla explains how variations in optical properties account for all of Galileo’s other observations. This discussion functions as the propter quid, deducing the observed effects from the nature of the cause and how it operates.
Admittedly, La Galla’s reasoning is not convincing. In fact, La Galla’s own preferred cause, opacity and density, is threatened by the same liminal observations. (If the waviness of the terminator and the changing spots are caused by variations in clarity and opacity of the Moon’s body, a Galilean might ask, then why do we not see the Moon’s circumference to be interrupted by invisible sections of transparent aether?) Hence, La Galla’s first rejoinder to Galileo’s account of the observed lunar circumference would refute his own position, while his second clearly begs the question, since it supposes that the celestial aether is perfect and unchanging. But the point here is not to evaluate the relative merits of La Galla’s argument, but to notice that he, like Galileo, uses observation to discriminate between possible causes in the course of a negotiatio.
Incidentally, Galileo characteristically had the last word in this debate. In the Dialogo, published in 1632, eight years after La Galla’s death, Galileo has the Aristotelian character Simplicio claim against his own representative, Salviati, that,
The appearances you [Salviati] speak of, the mountains, rocks, ridges, valleys, etc., are all illusions. I have heard it strongly maintained in public debates against these innovators that such appearances belong merely to the unevenly dark and light parts of which the moon is composed inside and out. We see the same thing occur in crystal, amber, and many perfectly polished precious stones, where, from the opacity of some parts and the transparency of others, various concavities and prominences appear to be present. (Galilei  1967, p. 70)
I say, then, that this argument of yours is too general, and since you do not apply it to all the appearances, one by one, which are seen on the moon and which incline me and others to hold it to be mountainous, I do not believe that you could find anyone who would be content with such a view. (Galilei  1967, p. 86)
What is significant here is that both Galileo and his Aristotelian opponent saw the situation as demanding a negotiatio that discriminated between possible causes of the observed effects—montuosità versus variations in rarity and density. And the discrimination effecting the negotiatio could be achieved by reference to empirical observations. Both sides of the dispute, that is, admitted empirical hypothesis testing as part of regressus.39
Pace Randall, regressus is not the modern scientific method. But the precise working of regressus, especially the negotiatio, was not entirely settled in the time leading up to Galileo. Discriminating between possible causes by testing them against observations was one way to achieve the ends of the negotiatio, and at least Galileo and La Galla seem to have found it fitting. Yet taking that step inserted empirical hypothesis testing into an accepted methodology of natural philosophy. It made observations function as reasons in the pursuit of scientific knowledge.
I have not surveyed the entirety of Galileo’s corpus for his methodological pronouncements, and I have not tried to establish that Galileo was committed to anything beyond the rhetorical usefulness of regressus. Yet, if this account is even partially correct, it might help explain other features of Galileo’s work. In the first place, it is a short step from using observations to rule out possible causes to contriving situations in which to subject hypotheses to empirical tests. The empirical interpretation of regressus could thus have been a motivation for Galileo’s extensive and creative use of experiments, both real and imaginary. Galileo often proposes experiments, the outcome of which is meant to decide between alternative hypotheses. The experiment functions as a negotiatio. As he puts it in the Dialogo, one can “make an experiment [esperienza] and then … decide according to the result” (Galilei  1967, p. 43).40 On this interpretation, Galileo’s experimentalism has roots in Scholastic logic.41
At the same time, this account helps explain why so many of the experiments Galileo proposes are merely imagined, or even impossible to achieve.42 If the point of appealing to an experiment is to fulfill the role of a negotiatio, then all is needed is a way to exclude hypotheses. If imagining an experimental condition, and consequently recognizing the necessity of one outcome, is sufficient to settle on one out of a range of alternatives, then the execution of the experiment is superfluous. Galileo does not claim, for example, to have carried out his famous ship experiment, involving a ball dropped from a mast. This is meant to show that bodies conserve motion impressed upon them, so the ball will fall at the foot of the mast whether the ship moves or not. Rather than describing the outcome, though, Galileo asserts that “Without experiment, I am sure, that the effect will happen as I tell you, because it must happen that way” (Galilei  1967, p. 145).43 This, and other unperformed experiments, are effective guides to reason, and decide the issue in favor of inertia as a causal principle. The negotiatio is malleable, and an imagined observation serves as well as a real one.
Finally, one last caveat. While I have endeavored to salvage some of Randall’s thesis, the remainder must still be supplemented. Regressus is not the whole story of early-modern empiricism. Regressus only permitted the discriminatory use of observations within the logical strictures of an accepted method. There must be some explanation of why Galileo and his peers chose to follow this interpretive path. And here one can appeal to the many other intellectual traditions that exerted influence on Galileo and others. For instance, the traditions of practical mathematics and the mixed sciences also contributed to experimentalism, especially in the person of Galileo himself.44 Moreover, the eliminitave empiricism that emerged from the negotiatio eventually merged with other empiricist developments. There is, of course, the aforementioned later contributions of Baconian inductivism, which motivated the positive use of observation as evidence in favor of theories. A complete history of modern empiricism must follow many strands.
The term is chosen to echo “eliminative induction,” used to characterize aspects of Bacon’s method (Schwartz 2017).
See also Edwards 1960, p. 283.
Schmitt (1969) and Jardine (1976), in particular, contrast early modern experimentalism with the regressus. Their argument is that Galileo used particular observations to test hypotheses, while Zabarella only appealed to experience in general, so the latter could not have influenced the former. What follows is an attempt to weaken this contrast by suggesting a path from regressus to an experimental method.
Wallace’s close reading of Galileo’s early logical manuscripts is not matched in his attempts to locate Galileo’s use of regressus in his later scientific work (Wallace 1992a, chs. 5–6; Laird 1997, p. 258). That is, in part, what I intend to do here. Others have also connected the regressus to non-Galilean contexts—including Italian vernacular logics, Harvey, Hobbes, and British empiricism (Edwards 1983; Schmitt 1983; Sgarbi 2013; Hattab 2014; Sgarbi 2014).
Consequently, and unlike much of the relevant literature, this essay is not specifically about Galileo, and takes no position on Galileo’s mature commitment to the method. Indeed, as I indicate below, the regressus cannot be the whole story.
The precise role of empirical observation in Scholastic natural philosophy is subject to some scholarly dispute. Even though there are several counterexamples, the emphasis on demonstration and certainty (over probability) generally discouraged empirical research among philosophers (Schmitt 1969; McMullin 1978; Dear 1987; Jardine 1988; Dear 1995; Daston 1998).
Apropos the discussion below, see La Galla  1892, p. 350.
Bayer (1997) details the Aristotelian root of this attitude.
The term was intended to translate Aristotle’s “apodeixis tou hoti.”
Translating Aristotle’s “apodeixis tou dioti.”
See also South (2005).
This syllogism is implied by the text, but does not explicitly appear (Zabarella  2013b, p. 385).
Zabarella’s near-contemporary Alessandro Piccolomini was even more strident: “Others, who follow Averroës and defend his opinion, trying to expound the aforementioned method, are forced to suppose some (as they call it) negotiatio after the first progression. However much I pondered it, I have never understood what this might mean” (Aliqui, qui Averroi addicti sunt, ut eius sententiam defendant, ita praedictam rationem cona[n]tur solvere, ut coacti ponant quamdam (ut ipsi dicunt) negociationem post primum processum, quam ego ponderans nunq[uam] intellexi, quid sibi vellet) (Piccolomini 1565, p. 80v).
See also Zabarella ( 2013a, p. 2:103): “In a mind considering something, therefore, the essential connection shines forth [elucescit] by means of the thing itself, not by means of something else.” In this regard, Zabarella is following Thomist epistemology. The “illumination” of the object is provided by the agent intellect and ultimately dependent on God’s grace (Mikkeli 1992, p. 104).
Zabarella here clarifies that knowledge can be “absolutely” perfect—such as the knowledge a natural philosopher ought to have about metals—and perfect “by what is characteristic of and the nature of the discipline”—such as the knowledge that suffices for a copper-worker to practice his art. In other words, one can have “distinct” knowledge if one comprehends the nature of the thing to the extent appropriate to the discipline, which is “absolute” when one comprehends the nature in its entirety.
For the sake of simplicity, I am here eliding Cajetan’s distinction between “actual” and “virtual” confused knowledge. Since Zabarella explicitly seeks the “definition” of the cause, I take him to be concerned with the former, which is explained in the text above. The latter obtains when one knows the universal qua genus without knowing its species, as when one knows what “animal” is without knowing the kinds of animals there are.
See also Zabarella ( 2013a, p. 203).
Along similar lines, Sgarbi (2013, pp. 9–10) argues that the rise of empiricism in the British Isles can similarly be “understood as a series of betrayals and re-elaborations of Zabarella’s methodological and epistemological doctrines.”
McMullin (1978) argues that the use of a hypothetico-deductive method of observation to confirm or disconfirm hypotheses is antithetical to the syllogistic method of Aristotelian science, since the latter confers necessity on the causal explanation, while the former does not. Since Galileo appears to employ both syllogistic and hypothetico-deductive methods, McMullin concludes, he has two incompatible concepts of science. On the contrary, I am suggesting, the two concepts are compatible, if one supposes that the hypothetico-deductive elimination of hypotheses is inserted into the negotiatio phase of the syllogistic method.
On the mixed verdicts regarding non-regressive methods in natural philosophy, see Kuhn (1997).
There are some terminological and textual differences between Zabarella’s view of regressus and the account given by Galileo in his manuscripts, though these are not germane to the present discussion. For a detailed comparison, see de Jong (1989).
Galileo asserted that his arguments proceed “by sense experience and by necessary demonstration” (sensata esperienza et per necessaria dimostrazione) in a 1611 letter (1890–1909, p. 11:142). Catering to his audience in this way does not imply Galileo was himself committed to the regressus method, and one can remain agnostic about his mature views. The point is just that his use of the regressus demonstrates its wider acceptance.
Aristotle’s blithe assumption, noted above, that causal necessity actually can be expressed by logical necessity has been a source of much difficulty for historical and contemporary authors alike. For one thing, it led to a tangle of terminological distinctions in medieval and renaissance methodological treatises, which has in turn confused the literature surrounding Galileo. Regressive progressions from consequent to cause or principle and back again were called, in addition to ‘quia’ and ‘propter quid’, ‘resolution’ and ‘composition’, and ‘analysis’ and ‘synthesis’, with varying degrees of synonymy. The latter pair was specifically used in mathematics—one source is Pappus (Hintikka and Remes 1974, pp. 8–10; Wisan 1974, p. 117)—to refer to a procedure by which a conclusion is assumed in order to discover the (independently known) principle from which it is derived, and then actually proven from that principle—but see Gilbert (1960, p. 35). Jardine (1976), especially, has argued that Galileo’s method was more akin to this mathematical procedure than to regressus. However, even in Galileo’s own time, there was a dispute de certitudine mathematicarum about whether premises are causally productive of conclusions in mathematical proofs. That is, whether the logic of mathematics reflects the causal structure of the world (and thus meets the Aristotelian standard of scientific demonstration) (De Pace 1993; Mancosu 1996). On the one hand, if mathematical premises are taken to be causal, then the distinction between regressus, resolution-composition, and analysis-synthesis is largely terminological, since all refer to inferences from effect to cause and cause to effect. On the other hand, if mathematical analysis-synthesis expresses merely logical necessity, then this is clearly not what Galileo is doing, since his “demonstrations” are explicitly causal. By the same token, one can resist interpretations of Galileo that see his project as natural historical rather than natural philosophical; e.g., Jalobeanu (2014).
Lubet hoc loco alterius cuiusdam Lunaris apparitionis admiratione dignae causam assignare, quae licet à nobis non recens, sed multis abhinc annis observata sit, nonnullisque familiaribus amicis, & discipulis ostensa, explicata, atque per causam declarata; quia tamen eius observatio Perspicilli ope facilior redditur, atque evidentior, non incongruè hoc in loco reponendam esse duxi; […] (Galilei 1610, p. 14r).
[E] perciò, non si vedendo l’altre parti di quel corpo che lo fanno sferico, rotondo e liscio (perchè, essendo rare, non reflettono il raggio del Sole nè si fanno luminose), appar che egli sia ineguale, dentato e montuoso, se bene non è. Essemplo manifesto ne sia il vedere, che se altri piglia una palla grande di chiarissimo cristallo, dentro a cui sia formato di smalto bianco una picciola Terra con selve, valli e monti, al Sole esposta verso il Cielo assai lontana dall’occhi di chi vi guarda dentro, quella palla non apparisce altramente sferica e liscia, ma ineguale e montuosa, e adombrata là dove non dà il Sole, perchè la parte transparente di quel cristallo non è visibile, terminando la vista in quelle facendole apparir colorate […].
Neque aliquis est ex mathematicis adeo stultus, qui veram illam existimet, quamvis illa utantur fere omnes, ut certam apparentiae syderum atque motuum rationem reddant. Non enim mathematici, in speculationibus coelestium motuum et phoenomenûm, demonstratione propter quid processerunt, a causa scilicet ad effectum, sed demonstratione quia, ab effectu ad causam; quare primum observationes motuum et phoenomenûm constituerunt, deinde, his suppositis, causas indagare et assignare conati sunt, quae illis convenienter sufficiunt, ut diximus; satis enim est, ut ex illis certa apparentium motuum ratio constet.
Proposui vero hanc disputationem physice, non mathematice, habere.
Opinio igitur circa haec sensibilia, et falsa et vera esse potest, prout decipientis aut non decipientis sensus iudicium sequitur, aut rationis recte ratiocinantis ope corrigitur vel destituitur: opinio enim, cum infima rationalis animae pars sit, sensui et rationi contermina, ambobus iungi potest.
Ut vero ordine aggrediamur, primum quidem experimenta atque, ut ita dicam, observationes a D. Gallilaeo factas in orbe Lunae fidelissima historia, ut in libello, cui nomen Sydereus Nuntius, extractae sunt […] in medium afferam et proponam.
Ob has igitur et alias rationes, quas fuse et dilucide satis attulit D. Gallileus ex suis observationibus in Sydereo Nuncio, quas etiam nos recitavimus initio nostrae disputationis; ego satis probabilem reputarem hanc sententiam, nisi aliquibus aliis rationibus, his forsitan validioribus, pro contraria suaderer. Ac primo, frustra fit per plura quod potest fieri per pauciora et aeque bene: sed absque his montibus et vallibus, bene possumus assignare et afferre rationem observatorum phoenomenûm, ut infra, Deo iuvante, demonstrabimus; ergo frustra est, hos montes et valles ponere.
Quare aliam assignat D. Gallileus harum macularum antiquarum causam; nempe, heterogeneam ac dissimilarem substantiam, quam causare dicit, non modo maiores illas obscuras maculas, verum etiam minores quasdam, veluti areolas clariores, inter obscuras dispersas. Quare ita arguo: si dissimilaris substantia in superficie leni et aequali, absque multiplicatione corporum, hanc eamdem varietatem phoenomenûm, quae in reliqua Luna videntur, causare valet in maioribus Lunae maculis; ergo eadem dissimilaris substantiae ratio eamdem phoenomenûm varietatem in illuminata Lunae parte causare poterit. Consequentia est necessaria: nam non est maior ratio, cur substantia Lunae, ubi maiores videntur maculae, magis dissimilaris sit, quam ubi lucida apparet; cum haec dissimilaritas sumatur penes perspicuum et opacum, ex quibus totum Lunaris globi corpus admixtum est, ut infra declarabimus.
His autem suppositis, non erit impossibile, absque montibus et convallibus omnia observata in Luna phoenomena demonstrare.
For further discussion, see Hamou (1999, ch. 2).
See also the later discussion by the Capuchin Valeriano Magni (1643, pp. 62–64), who argues that one may proceed from “obscure” to “clearer” cognition of a thing either by argument or by observation, and uses the telescopic discovery of lunar mountains and valleys as an example of the latter. (Thanks to Tomáš Nejeschleba for pointing out this connection.)
Bisognerebbe poterla fare una tale esperienza, e poi secondo l’evento giudicare … (Galilei 1890–1909, p. 7:169).
In a well-known letter to Fortunio Liceti, written in 1640 near the end of his life, Galileo avers that he has always been a Peripatetic in method (Galilei 1890–1909, p. 18:248; Wallace 1992a, p. 295). However, in the same letter, he emphasizes that he means by this the use of experience to refute theories: “Among the secure means of finding truth is to put experience before any reasoning, since we are sure that it, at least covertly, will contain the falsehood [of the argument]; it not being possible that a sensory experience is contrary to the truth. And this is a well esteemed precept of Aristotle” (Tra le sicure maniere per conseguire la verità è l’anteporre l’esperienze a qualsivoglia discorso, essendo noi sicuri che in esso, almanco copertamente, sarà contenuta la fallacia, non [es]sendo possibile che una sensata esperienza sia contraria al vero e questo è pure precetto stimatissimo da Aristotile) (Galilei 1890–1909, p. 18:249).
This feature of Galileo’s work famously led Koyré (1966) to posit that Galileo made no experiments at all.
Io senza esperienza son sicuro che l’effetto seguirà come vi dico, perchè così è necessario che segua (Galilei 1890–1909, p. 7:171).
This paper is partly the result of work supported by the NEH Summer Institute “Between Medieval and Early Modern, Philosophy from 1300–1700.” Anonymous referees made crucial contributions, for which I am very grateful. I am also thankful for the feedback from audiences in Hanover (NH), Alba Iulia, Minneapolis, and Padua.