Galileo and the Language of Mathematics
The sixteenth century is widely seen as witnessing a reconfiguration of the notion of natural philosophy. In part, this was due to increasing concern about the evidential basis of Aristotelian natural philosophy, which appeared to many to have tempered Aristotle’s empirical instincts, leading to a petrification of his philosophical system. Aristotelianism was often treated as a definitive interpretation of the natural world, rather than as a provisional account of the nature of the world which was to be augmented and corrected in the light of a continuing engagement with the natural order. A growing interest emerged in expanding knowledge empirically—for example, by observing nature in newly discovered parts of the globe, or by making increasingly accurate observations of the natural world. In this chapter, we shall reflect on the importance of such empirical observations of the heavens, particularly the movement of the planets against the background of fixed stars.
The heavens have always fascinated human beings,1 not least because they create a mind-expanding sense of what Albert Einstein described as ‘rapturous amazement’.2 Yet alongside this affective impact of the night sky, many recognized its utility. In Babylonian times, the study of the heavens was seen as practically important (for example, in the prediction of solar and lunar eclipses),3 while in ancient Egypt it served to predict the annual flooding of the Nile or allow the correct orientation of temples.4 Others were intrigued by the more cognitive questions it raised. The movements of the five ‘wandering stars’ (Greek: planētes) against the background of seemingly changeless ‘fixed stars’ were observed with particular interest. What were they? And how could their slightly irregular movements across the sky be explained?
The model of planetary motion developed by Claudius Ptolemy of Alexandria in the second century achieved widespread acceptance. In his Amalgest, Ptolemy argued that the observed patterns of motion of the planets could be explained, and their future movements predicted, in terms of a series of nested circular orbits around the earth. Although this model is often described as ‘forced’ or ‘contrived’ by its modern critics, it is very difficult to sustain these criticisms in the light of the measurements of planetary positions available to Ptolemy at this time.5 Ptolemy’s planetary theory is ‘strictly empirical’, setting out a rigorous mathematical derivation of numerical parameters based on observations, aiming to ‘preserve the phenomena’.6
Ptolemy’s account of planetary motions remains the best theoretical approximation to the observational data before Johannes Kepler’s model of the early seventeenth century. Perhaps its greatest achievement was to demonstrate that a fixed and constant framework could be discerned behind what seemed like somewhat irregular planetary motions. It is important not to judge Ptolemy in the light of today’s more precise observational knowledge, but rather to adopt a historical approach which tries to understand ‘how and why Ptolemy and his successors formulated the problems the way they did’, and how successful this formulation was in accounting for the observable phenomena of their time, ‘within the restrictions of their ability to observe’.7
So did Ptolemy’s mathematical planetary model—or others that might arise to displace it—aim to explain the real world, or was the role of such mathematical models essentially to describe and accurately predict planetary motions? Many classical and medieval writers considered that the substances of nature did not conform to the abstractive precision that was characteristic of mathematics,8 and that the deductive structure of mathematical demonstration could not adequately capture the complex causal relationships among natural bodies.9 Aristotle had raised concerns about the mixing of disciplines on the grounds that qualities that might be essential from the perspective of one discipline might be considered accidental from another disciplinary perspective.10 While Aristotle was satisfied that mathematics could be mixed in an acceptable manner with astronomy, optics, and harmonics, he did not consider it could be mixed with physics.11
One of the most interesting debates on the interpretation of Ptolemy on this point took place in the city of Toledo in Moorish Spain during the twelfth century, when Islamic philosophers discussed the status of his model.12 The Toledan school of astronomy offered an instrumentalist approach to Ptolemy, where others preferred a realist interpretation.13 This debate also highlighted the role of natural philosophy as an interpretation, not simply an aggregation, of observations.14 European intellectuals of the sixteenth and seventeenth centuries increasingly came to understand the study of both the Bible and nature as mutually illuminating hermeneutical exercises.15
In this chapter, we shall consider the interpretative natural philosophy which emerged from the works of the three leading astronomers of the early modern period: Copernicus, Kepler, and Galileo. We begin by considering Nicolaus Copernicus’s proposal for a heliocentric understanding of planetary motion.
Ptolemy’s account of the relation of the planets, earth, sun, and moon secured wide acceptance for nearly a thousand years. Yet not all were persuaded. A treatise of Martianus Capella (fl. c.475), which attracted little attention at the time of its composition, began to be studied seriously with the emergence of the great cathedral schools of learning in the ninth century.16 Capella argued that Ptolemy was correct in asserting that Mars, Jupiter, and Saturn orbited the earth; the observational data suggested, however, that Mercury and Venus orbited the sun. Capella’s work was known to the Polish astronomer Nicolaus Copernicus, and appears to have played a significant role in the position Copernicus set out in his De Revolutionibus orbium coelestium (‘On the Revolutions of Heavenly Orbs’, 1543). By then, scholars such as Johannes Regiomontanus had raised significant concerns relating to many core assumptions of medieval astronomy, creating an environment that was open to reconsideration of traditional approaches.17
Although Copernicus himself carried out some observational work, his main contribution to the development of natural philosophy lay in re-evaluating existing data from a different perspective.18 Copernicus’s earliest discussion of planetary theory, known as the Commentariolus, probably dates from 1514. In this work, Copernicus noted the views of Capella, and appears to have been stimulated to extend this earlier writer’s approach.19 Bernard Goldstein’s careful reconstruction of Copernicus’s evolving heliocentrism is based on three core assumptions, all of which are stated clearly in the Commentariolus:
Copernicus’s mature statement of his theory, set out in his posthumously published work De Revolutionibus, envisaged six planets (one of which is the earth) rotating around the sun.21 The earth, Copernicus asserted, moved in a circular orbit at constant speed, where the other planets moved in eccentrically placed orbits in non-uniform speed. The closer a planet was to the sun, the faster it moved. The earth was the sole exception to this rule; although it had an eccentric orbit, it was nevertheless held to move at a constant speed.
The ‘logic of discovery’ underlying Copernicus’s heliocentric model of the solar system remains unclear.22 What was the fundamental motivating factor which led him to make this proposal, given that it failed to offer more accurate observational predictions in comparison with the older Ptolemaic model?23 To put the matter bluntly, the traditional geocentric Ptolemaic cosmology and the ‘new-fangled heliocentric Copernican arrangement’ predicted ‘essentially the same planetary positions’.24 Copernicus’s new theory might have seemed to be more elegant and economical at the qualitative level; closer examination, however, revealed a deeper quantitative complexity that compromised this simplicity.25
In November 1572 the Danish astronomer Tycho Brahe observed that a new star had appeared in the constellation of Cassiopeia. Using a sextant and cross-staff as measuring instruments, he was able to determine that the star was located among the ‘fixed stars’, which Aristotle had declared to be perfect and unchanging.26 It was an important observation, which raised concerns about the reliability of some core assumptions of Aristotle’s natural philosophy. Yet for our purposes, the importance of Tycho’s increasingly precise observational instrumentation relates to his determination of the daily positions of planets.27 Tycho’s observations were made using instruments such as his ‘equatorial armillary’, completed in 1585—perhaps the last such instrument constructed which did not make use of the optical technology later used in telescopes.28
Tycho accumulated a vast repository of accurate determinations of the positions of the planets, particularly Mars. These observations, widely agreed to be the most accurate and comprehensive in pre-telescopic astronomy, needed to be interpreted using a model of the planetary system. Noticing increasing disparities between his observations of planetary locations and those predicted by the Copernican model,29 Tycho proposed an alternative model, according to which the five planets rotated around the sun, which in turn rotated around the earth.30 While this hybrid model is often interpreted as a conservative attempt to hold on to the traditional Ptolemaic model of the solar system, Tycho’s own account suggests that the model was a response to the failure of Copernicus’s new system to offer a good fit with the observational data. Given that the competing hypotheses offered by Copernicus and Tycho seemed to be observationally equivalent, those trying to adjudicate between rival theoretical claims often seemed to depend on non-empirical considerations in coming to a decision, such as their apparent metaphysical implications, or their theological foundations or consequences.31
Up to this point, Tycho had enjoyed the patronage of the Danish monarchy. However, Tycho fell out of favour with Christian IV, and was forced to leave Denmark in 1597. The Habsburg emperor Rudolf II welcomed him to Prague, and helped him to set up an observatory at a manor house at nearby Benatky, situated on high ground, and offering a clear view of the horizon in every direction.32 There, he was joined by a rising star in the world of astronomy, Johannes Kepler, whose Mysterium cosmographicum (‘The Mystery of the Universe’, 1596) attracted international attention, partly on account of its explicit acceptance of the Copernican theory, but also because of the elegance of its central theme of ‘nested spheres’ enfolding geometrical solids, such as the cube, tetrahedron, and dodecahedron.33 Following Tycho’s death in 1601, Kepler became Imperial Mathematician in Prague, and gained access to Tycho’s observational data, accumulated during his time in Denmark. These observations would be the foundation of his Rudolphine Tables, published in 1627, which predicted the positions of all the planets. Yet they also proved to be of critical importance in his philosophical reflections on the structure of the solar system.
Despite the cultural and religious disruptions caused by the Protestant Reformation, there was continuing interest in the study of the natural world throughout the regions which adopted Protestantism.34 By the 1560s, the two major constituencies within the emerging Protestant tradition, traditionally referred to as ‘Lutheranism’ and ‘Calvinism’, had developed their own distinct theological frameworks which were hospitable towards the natural philosophies of the period. Calvinism achieved such an accommodation through its distinction between the ‘natural knowledge of God’ and a ‘revealed knowledge of God’,35 where Lutheranism relocated the field of natural philosophy within its theological dialectic between ‘law’ and ‘gospel’.36 Like Albertus Magnus in the thirteenth century, the Lutheran theologian Philip Melanchthon made a critically important distinction between the truths of revelation, and those which resulted from natural inquiry. This development created a conceptual space that was hospitable to natural philosophers such as Kepler.37
After Tycho’s death, Kepler began to engage the problem of planetary motion, aiming to make sense of Tycho’s accumulated observations of the position of the planet Mars. Whatever theory he derived would have to agree with the planetary positions that were actually observed, and so carefully tabulated by Tycho. Using a process of fitting by trial and error, which Newton later considered to be ‘rife with compromises and unsupported opportunistic assumptions’,38 Kepler came to the conclusion that Mars orbited the sun in an ellipse.39 While this hypothesis fitted the observational data, it remains unclear how Kepler arrived at this conclusion, in that this does not appear to have been a totally reliable inference from the observational evidence.40 Kepler could not have established an elliptical orbit on the basis of these observations alone, in that ‘the uncertainty in the data is too great to plot out the points geometrically and fit a curve through them.’41 But Kepler was looking for more than empirical correspondence, thus ‘preserving the phenomena’; he was looking for ‘plausible physical explanations for his astronomical hypotheses’.42
So why did Mars orbit the sun elliptically? In the Mysterium cosmographicum Kepler suggested this was due to some efficient force emanating from the sun; in the Astronomia nova (1609), this is put down to some virtus motrix. This latter idea was based on Kepler’s reading of William Gilbert’s De magnete (1600), which led him to suggest that some form of magnetic force existed between the planets and the sun, which resulted in some kind of orbital equilibrium.43
Kepler also corrected a problem with Copernicus’s model of planetary motion, which rested on the assumption, apparently carried over from Ptolemy, that the earth moved in a circular orbit at constant speed. Tycho’s observations of the position of the planet Mars were so detailed and accurate that Kepler was able to show, using Tycho’s records for observations of Mars that were precisely 687 days (the orbital period of Mars) apart, that the earth also moved in an elliptical orbit.
What are now known as ‘Kepler’s three laws of planetary motion’ may be set out as follows, summarizing the basic patterns that Kepler had identified through close examination of the Tychonian observational records:44
The important point, so easily overlooked, is that these ‘laws’ are summaries of what Kepler observed, and was able to represent mathematically; they are not themselves explanations, but are actually observations that themselves require explanation. Why, for example, is the square of the period of any planet proportional to the cube of the semi-major axis of its orbit?45
Kepler himself was not satisfied with inductions from pure observation, believing that there must exist a physical explanation for these general principles, grounded in some deeper ordering within nature which might not be entirely accessible to human reasoning. He offered a plausible causal explanation of planetary motion based on a rectilinearly oriented magnetic force. Although Kepler was somewhat vague about the details, and was clearly uneasy about the concept of some kind of magnetic force acting at a distance,46 he nevertheless believed that the observed behaviour of the planets was best explained in terms of forces at work within the physical structure of the universe.47 In the end, of course, Newton would later offer a better explanation, based on the concepts of inertia and universal gravitation.
Kepler’s contribution to the mathematization of natural philosophy is of enormous significance. His success in the mathematization of the solar system encouraged the growing trend to see mathematics as the language of the natural world. ‘Although astronomy had always been deemed a mathematical science, few in the early sixteenth century would have envisioned a reduction of physics – that is, of nature as motion and change – to mathematics.’48 Yet our concern here is not with documenting the details of Kepler’s mathematical success, but rather with reflecting on its wider importance, especially in relation to a reframing of the enterprise of natural philosophy. Why does mathematics seem able to describe some fundamental structures of the universe? As we shall see, this question would be developed further by Galileo and others.
Kepler’s achievement was to reconceive the world of the planets as part of the natural order. To appreciate this point, we need to step into the bygone imagined world of the Renaissance, bifurcated into two domains by Luna, the moon. In his classic study The Discarded Image, C. S. Lewis offers an explanation of the significance of this division:
At Luna we cross in our descent the great frontier which I have so often had to mention; from aether to air, from heaven to nature, from the realm of gods (or angels) to that of daemons, from the realm of necessity to that of contingence, from the incorruptible to the corruptible. Unless this great divide is firmly fixed in our minds, every passage in Donne and Drayton or whom you will that mentions translunary or sublunary will lose its intended force.49
As Lewis rightly observes, the ‘sublunary world’ of Aristotelian natural philosophy constituted ‘Nature in the strict sense’. With the erosion of the artificial Aristotelian bifurcation of what we now take to be ‘nature’ as a whole, the scope of natural philosophy was significantly extended and enriched.50
A consequence of this development needs to be highlighted. Some popular accounts of the rise of Copernicanism suggest that it was resisted because it was seen to challenge any privileged status for humanity or the earth as the centre of things.51 This is a somewhat modernist view, which is not sufficiently attentive to the Aristotelian intellectual framework which was so influential in the sixteenth century and beyond. Given the Aristotelian dichotomy between the perfection of the heavens and the imperfection of the sublunar regions, to relocate the earth in the realm of the heavens significantly enhanced its status. John Wilkins, an early English advocate of Copernicanism, reported that one of the most common objections he had encountered to the Copernican system was that it elevated human beings above their proper station.52
Two themes in Kepler’s natural philosophy require further discussion, in the light of its place in our overall project of reflection and recovery of natural philosophy. Kepler is an important witness to what some might now consider to be an inappropriate transgression of disciplinary boundaries, but which appeared to Kepler himself as natural and legitimate moves within a wider understanding of knowledge. Every natural philosophy is shaped by a wider framework of understanding; in the case of Kepler, this was framed by a Lutheran understanding of the place of a knowledge of nature, and a Trinitarian understanding of the nature of God.53 Kepler did not see these as competing, but rather wove them into his overall vision of the purpose and place of natural philosophy, enfolding domains of knowledge which might now seem disconnected, yet were to him aspects of a greater whole.
Kepler’s mathematical metaphysics was based on the informing theological belief that God had created the natural world according to certain ‘archetypes’ expressed through an essentially geometric order. For Kepler, the human mind, which bears the ‘image of God’,54 is shaped in such a manner that sensitizes it to patterns within the created order, and their potential implications. In his Harmonices Mundi (‘The Harmony of the World’, 1619), Kepler argued that, since geometry had its origins in the mind of God, it was only to be expected that the created order would conform to its patterns, and that humanity was endowed with faculties intended to allow these archetypal patterns to be discerned.
In that geometry is part of the divine mind from the origins of time, even from before the origins of time (for what is there in God that is not also from God?) has provided God with the patterns for the creation of the world, and has been transferred to humanity with the image of God.55
This leads to the second point of interest. The reader of Kepler’s main works—especially Harmonices Mundi—is struck by its pervasive theme of harmony, in which the universe is perceived to possess an archetypal pattern which is ‘mathematical in nature and aesthetic in character’.56 The use of the musical concept of ‘harmony’ is critically important here, not simply as an analogy for cosmic order, but as a fundamental aspect of that ordering, and the capacity of humanity to recognize it. Kepler himself suggested that the movements of the heavens could be understood as an ‘everlasting polyphony’—a harmony which, though not audible, was certainly intelligible.57 The complex interconnections that Kepler recognizes between music, mathematics, aesthetics, and astronomy has significant roots in the classical tradition, being seen as having some deeper rooting in the structures of the cosmos.58
For Kepler, the notion of harmony did not merely assist natural philosophy in interpreting the world; it offered a pattern for its relationship which called out to be put into action—in other words, to make the structures of the social world parallel the harmony of the natural world. The motif of ‘harmony’ can be shown to inform Kepler’s scientific, theological, and political thinking at a time of social upheaval and communal tensions.59 This point is of wider importance, as Kepler himself appreciated. As Daniel Chua has pointed out in an important study of the musician Vincenzo Galilei (the father of Galileo Galilei), musical harmony was seen in this cultural context as holding everything together within the ‘great chain of being’, so that music ‘was not simply an object in the natural world, but the rational agent of enchantment itself’.60 Kepler’s reflections on the ‘harmony of the world’ reflect a perception of the interconnections of astronomy, music, and mathematics that reaches back to the Hellenic era,61 and was consolidated through the inclusion of these fields in the medieval university quadrivium.62 Kepler clearly saw an association—whether intuited or culturally acquired—between these multiple disciplines, and incorporated these into his natural philosophy.
Kepler’s contributions to natural philosophy chiefly take the form of reflections on Tycho Brahe’s astronomical observations, undertaken with the naked eye. Although Kepler made significant contributions to the understanding of optics,63 he did not use telescopes to augment natural human vision, or reflect on the issues of interpretation that arose from this technological extension of the range of the human eye. In turning to consider the contributions of Galileo Galilei, we are confronted with a question that has become of increasing importance in modern philosophy of science: the question of the observability of nature.64
While Galileo made significant contributions to the development of the Copernican theory, and is regularly cited in discussions about the relation of science and religion,65 his significance for the purposes of this present study lies in his use of the telescope to study the heavens. This optical instrument extended the range of human vision beyond its natural limits, allowing access to a greater horizon of entities and events.66 The invention of the telescope is generally dated to 1608. It is known that several Dutch telescopes had been distributed in Italy between May and August 1609.
A year later, Galileo constructed his own telescope, and used it to study the heavens.67 It was a small instrument by today’s standards.68 Galileo may not have been the first to use such an instrument to observe the heavens; he was, however, able to interpret his observations in ways that significantly advanced discussion of important issues in natural philosophy. Galileo was a good artist, and was able to draw the patterns of light and shade that he observed on the face of the moon,69 as well as note the dense starfields of the Milky Way, and the changing positions of the four faint starlike objects he observed close to the planet Jupiter between December 1609 and January 1610.
Each of these three sets of observations deserves closer attention. The first set related to the moon. Galileo’s telescope disclosed that the face of the moon was not perfectly smooth, thus calling into question the Aristotelian belief that the celestial bodies, such as the moon, were perfect. Although most accounts of this discovery report that Galileo ‘observed mountains on the moon’,70 this simple statement needs to be nuanced significantly. What Galileo actually observed were two dimensional patterns of light and shade; he interpreted these as lunar mountains and valleys. Galileo used a sophisticated analogical argument, embodying Renaissance theories of perspective,71 which allowed him to conclude that these changing patterns of light and dark on the surface of the moon were evidence for the existence of mountains and valleys, analogous to those found on earth.72
The second set of observations related to the Milky Way and Ptolemaic nebulae—such as the fuzzy patch of light in the constellation of Cancer, now known as ‘Messier 44’. In every case, objects that seemed ‘nebulous’ turned out to consist of individual stars, which could be resolved individually through the increased light-gathering power of Galileo’s telescope. Galileo rightly concluded that certain objects that appeared to be misty patches of light were actually made up of individual stars; yet he seems to have wrongly believed that all such patches of nebulae could be resolved in this way. As is well known, the eighteenth-century British astronomer John Herschel changed his mind on the idea of ‘nebulosity’, initially believing that such patches of light were simply ‘clusters of stars in disguise’, and would be resolved into individual stars by sufficiently powerful telescopes, before realizing that some such objects could not be resolved in this way.73
The third set of observations concerned the planet Jupiter which appeared as a disc rather than as a point of light when seen through a telescope. What attracted Galileo’s attention, however, were four stars arranged in a straight line close to the planet Jupiter, which changed their positions nightly. What Galileo observed were four starlike objects whose positions changed over time with respect to Jupiter; Galileo then interpreted these four objects as moons that were orbiting the planet.74
At that time, debates about the solar system focused on two rival models: Kepler’s view that the earth and other planets orbited the sun, initially set out in his Mysterium cosmographicum (1596) and refined in Harmonices Mundi (1619), and Tycho Brahe’s modified geocentric cosmology, set out in his 1588 work De mundi aetherei recentioribus phaenomeni (‘Concerning Recent Phenomena in the Celestial World’, 1588). Once he had concluded that these starlike objects were best understood as moons orbiting Jupiter, Galileo realized that this interpretation had important implications for the evaluation of Kepler’s model in relation to Tycho’s. He therefore published his findings, with appropriate illustrations, in his pamphlet Siderius Nuncius (‘Starry Messenger’) in March 1609. Galileo named these four moons ‘the Medicean Stars’ in honour of his former student Cosimo of Medici; in the end, however, the four names proposed by Simon Marius in 1614—Europa, Io, Ganymede and Callisto—found wider acceptance.75
Galileo’s discovery subverted a classic objection to Kepler’s heliocentric model: the uniqueness of the earth in possessing a moon. In the Ptolemaic and Tychonian models, the moon was only one of a number of bodies to orbit the earth; according to Kepler, the moon was the only object to orbit the earth. This exceptionalism was seen by some critics as indicating that Kepler’s system was implausible. Galileo’s demonstration that Jupiter also possessed satellites indicated that the earth was not alone in this respect. Other observations confirming Kepler’s model followed after the publication of Siderius Nuncius. In December 1610, Galileo observed the changing phases of the planet Venus, very similar to those of the moon. For Galileo, these phases only made sense within the context of a Copernican model of the solar system, in which Venus orbited the sun.
Galileo’s application of the telescope to extend discussion of the themes of natural philosophy was paralleled several decades later by the use of the microscope to disclose a hitherto unobserved biological world. This led the English natural philosopher John Wilkins to remark that ‘’tis certain that our senses are extreamly disproportioned for comprehending the whole compasse and latitude of things.’76 Other natural philosophers of this age, such as Margaret Cavendish, were, however, apprehensive of substituting artificial technology for natural human vision.77 The point remains important today; the philosopher of science Bas van Fraassen continues to express concerns about transgression of the limits of human vision, noting its implications for a realist account of the natural world.78
Yet Galileo is of importance to the development of natural philosophy in another way—the suggestion that mathematics is the language of nature.79 This point is made clearly in his defence of natural philosophy over and against humanly constructed philosophies. In arguing that natural philosophy is grounded in the natural order, rather than being a human invention, Galileo turns to consider the language in which this natural philosophy is written.
[Natural philosophy] is written in this grand book – I mean the universe – which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to comprehend a single word of it.
Galileo here draws on the Renaissance metaphor of ‘God’s Two Books’—nature and the Christian Bible—which share the same author, but take different forms.80 To read either requires knowledge of the languages in which it is written, and the appropriate hermeneutical tools to make sense of it.81 The Bible was written in Hebrew and Greek; the natural order is written in the ‘language of mathematics’.
Galileo’s statement that the book of nature is written in mathematical language is open to several interpretations. It might, for example, be construed as an affirmation of the intellectual autonomy of natural philosophy,82 or perhaps of the accountability of the natural philosopher to the objectivities under consideration. Yet Galileo’s approach is more naturally to be interpreted as a simple statement of mathematical realism, holding that ‘mathematical entities are ontologically independent from us and that the physical world has a mathematical structure.’83 Yet the implications are clear: to understand nature, one must master its language.
Natural philosophy is thus a human response to the ‘book of nature’ which is more trustworthy and secure than other philosophical or theological approaches.84 The problem is that lex divina, being disclosed through a text, requires interpretation—and it is often difficult to secure closure on such interpretative disputes. But lex natura transcends such disputes; there is only one way of interpreting nature, so that the matter can be resolved.85 Having already insisted that natural philosophy is something discovered or discerned, not invented, Galileo then makes an interpretative move which further privileges the natural philosopher. The ‘Book of Scripture’, Galileo suggests, is accessible to everyone on account of divine self-accommodation in revelation; yet this leads to interpretative pluralism and uncertainty.86 The ‘Book of Nature’ is only accessible and intelligible to those who are mathematically competent, in that it offers no accommodation to those who are unwilling or unable to learn its mathematical language. If nature is to disclose its wisdom, there is a significant restrictive entry barrier.87
The importance of this point is best appreciated by considering Francis Bacon’s critique of the specialist trade guilds and the universities, both of which he considered to have erected inappropriate barriers to the wider social dissemination of knowledge and wisdom. Bacon was particularly critical of ‘the exclusivity both of the guilds, where practical information is esoteric by virtue of keeping knowledge or techniques within a trade or profession to which access is then restricted, and of the universities, where an esoteric and often convoluted language renders information inaccessible to all but those accepted into the university system’.88 Galileo’s vigorous defence of the necessity of mathematical literacy on the part of natural philosophers pointed towards natural philosophy becoming the preserve of an educated social elite.
The significance of this point is perhaps best appreciated by reading a popular work of natural theology, which was widely copied and circulated in the Iberian peninsula during the sixteenth century. In his Liber naturae sive creaturarum (‘Book of Nature and the Creatures’) the Catalan writer Raymond de Sebonde (c.1385–1436) spoke of the importance of the accessibility of knowledge of God through contemplation of the natural world for those who were unable to read, or did not have access to the Bible or theological works.89 While Galileo did not deny that most could appreciate the beauty and wonder of the natural world, the task of understanding it properly was restricted to those with the necessary mathematical tools.
We now turn to consider the experimental natural philosophies that emerged in England during the earlier modern period, focusing on Francis Bacon, Robert Boyle, and Isaac Newton.