Daniel Garber

Leibniz and the Foundations of Physics: The Middle Years

Leibniz must appear as something of a paradox to the reader of the recent literature on his thought (i.e., that written after the seminal work of Russell and Couturat). The Leibniz who appears in the commentaries is almost invariably Leibniz the logician/metaphysician, concerned to argue for a world of individual substances, later monads, mind-like, immortal, containing all and reflecting all, concerned to argue that this is all there is to our world and to every other possible world. But, on the other hand, most of us know, if only dimly, that Leibniz was a physicist of some note in his day, and, as such, was concerned with the determination of the basic laws that govern the bodies of everyday experience, the same problem that worried Galileo, Descartes, Huygens, and Newton. But what status could the science of physics possibly have for a philosopher who, like Leibniz, seems to hold a metaphysics so distant from our common-sense conceptions of the world of physics? The perplexity is greater still when one finds, even in the standard works of Leibniz’s metaphysical corpus, like the Discourse on Metaphysics, numerous remarks to the effect that his metaphysics is intended to ground the true physics! What possible connection could there be between Leibniz’s metaphysical conception of what there really Is in the world, and his physics?

On the Emergence of Probability

The modern theory of probability is usually dated from the second half of the 17th century. The famous Pascal-Fermat correspondence of 1654 began a rapid advance in the subject, and by the completion of Jacob Bernoullis Ars Conjectandi (published posthumously in 1713, but written and discussed long before) one can say that the subject has more or less fully emerged. This of course raises an important historical question: what factors are responsible for the sudden growth of the theory of probability? Why did it happen when it did? In this paper we will examine an answer to this question recently put forward by Ian Hacking. In his book The Emergence of Probability,1 Hacking proposes that the sudden development of the theory of probability is to be explained by an important conceptual change in the way people thought about chance and evidence. The claim, in brief, is that the modern theory of probability emerged when it did because it was not until the middle of the 17th century that we possessed the modern concept of probability. We believe that Hacking is wrong. After presenting an outline of his thesis and the principal arguments that he offers for it, we will show that Hackings explanation for the sudden activity in the theory of probability cannot be correct, since many of the concepts that Hacking believes constitute the core of our modern notion of probability were present long before the mid- 17th century. We will argue instead for a different explanation, one that accounts for the history of the theory of probability without appeal to radical conceptual revolution.

On the Frontlines of the Scientific Revolution: How Mersenne Learned to Love Galileo

Marin Mersenne was central to the new mathematical approach to nature in Paris in the 1630s and 1640s. Intellectually, he was one of the most enthusiastic practitioners of that program, and published a number of inuential books in those important decades. But Mersenne started his career in a rather different way. In the early 1620s, Mersenne was known in Paris primarily as a writer on religious topics, and a staunch defender of Aristotle against attacks by those who would replace him by a new philosophy. In this essay, I would like to examine Mersennes changing attitude toward Galileo. In the early 1620s, Mersenne lists Galileo among the innovators in natural philosophy whose views should be rejected. However, by the early 1630s, less than a decade later, Mersenne has become one of Galileos most ardent supporters. How, then, did Mersenne learn to love Galileo?

Learning from the past: Reflections on the role of history in the philosophy of science

In recent years philosophers of science have turned away from positivist programs for explicating scientific rationality through detailed accounts of scientific procedure and turned toward large-scale accounts of scientific change. One important motivation for this was better fit with the history of science. Paying particular attention to the large-scale theories of Lakatos and Laudan I argue that the history of science is no better accommodated by the new large-scale theories than it was by the earlier positivist philosophies of science; both are, in their different ways, parochial to our conception of rationality. I further argue that the goal of scientific methodology is not explaining the past but promoting good scientific practice, and on this the large-scale methodologies have no obvious a priori advantages over the positivist methodologies they have tried to replace.

The mathematical realm of nature

MATHEMATICS, MECHANICS, AND METAPHYSICS At the beginning of what we now call the scientific revolution, Nicholas Copernicus (1473-1543) displayed on the title page of De revolutionibus (1543) Platos ban against the mathematically incompetent: ‘Let no one enter who is ignorant of geometry’. He repeated the notice in the preface, cautioning that ‘mathematics is written for mathematicians’. Although Isaac Newton posted no such warning at the front of the Principia a century and a half later, he did insist repeatedly that the first two books of the work treated motion in purely mathematical terms, without physical, metaphysical, or ontological commitment. Only in the third book did he expressly draw the links between the mathematical and physical realms. There he posited a universal force of gravity for which he could offer no physical explanation but which, as a mathematical construct, was the linchpin of his system of the world. ‘It is enough’, he insisted in the General Scholium added in 1710, ‘that [gravity] in fact exists.’ No less than the De revolutionibus , the Principia was written by a mathematician for mathematicians. Behind that common feature of the two works lies perhaps the foremost change wrought on natural philosophy by the scientific revolution. For 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. Fewer still would have imagined the analysis of machines as the medium of reduction, and perhaps none would have accorded ontological force to mathematical structure.

Descartes and the Scientific Revolution: Some Kuhnian Reflections

Important to Kuhns account of scientific change is the observation that when paradigms are in competition with one another, there is a curious breakdown of rational argument and communication between adherents of competing programs. He attributed this to the fact that competing paradigms are incommensurable. The incommensurability thesis centrally involves the claim that there is a deep conceptual gap between competing paradigms in science. In this paper I argue that in one important case of competing paradigms, the Aristotelian explanation of the properties of bodies in terms of matter and form as opposed to the Cartesian mechanist paradigm, where the properties of bodies are explained on the model of machines, there was no such conceptual gap: the notion of a machine was as fully intelligible on the Aristotelian paradigm as it was on the Cartesian. But this does not mean that the debate between the two sides was conducted on purely rational terms. Rational argument breaks down not because of Kuhnian incommensurability, I argue, but because of other cultural factors separating the two camps.

Remarks on the Pre-history of the Mechanical Philosophy

The mechanical (or corpuscular philosophy) has been well-established as a historiographical category for some years now. While it certainly began as an actor’s category, it has slipped into being something else, a kind of broad catch-all category that is taken to include most of those who opposed the Aristotelian philosophy of the schools throughout the entire seventeenth century, part of a broad master narrative about the demise of the scholastic Aristotelian philosophy of the schools and the rise of modern mathematical and experimental science, the titanic intellectual clash that gave birth to modernity.

The occultist tradition and its critics

THE SOURCES AND STATUS OF THE OCCULT PHILOSOPHY IN THE EARLY SEVENTEENTH CENTURY One of the first members of Romes Accademia dei Lincei, established in 1603 to advance the understanding of natural philosophy, was Giambattista Della Porta, Galileos colleague in the renowned Roman society and his rival in the development of the telescope. Four decades before, Della Porta had founded his own Accademia dei Secreti della Natura, only to see it fail when the Inquisition called him up on charges of sorcery. He died in 1615, 1ong after publishing his Magia naturalis libri IV in Naples in 1558; a much enlarged edition followed in 1589, commanding enough interest through the seventeenth century to support many Latin and vernacular printings. Readers of the English version (London, 1658) learned in the first chapter that ‘Magick is taken amongst all men for Wisdom, and the perfect knowledge of natural things: and those are called Magicians, whom… the Greeks call Philosophers’. This overture to a treatise on magic was commonplace in its own time and had been familiar since antiquity, but when Della Porta called magicians philosophers, he struck a note that jars modern ears. ‘There are two sorts of Magick’, he explained; ‘the one is infamous… because it hath to do with soul spirits and… Inchantments… and this is called Sorcery…. The other Magick is natural…. The most noble Philosophers… call this knowledge the very… perfection of natural Sciences’. In other words, the good natural magic that Della Porta traced to Pythagoras, Plato, Aristotle, andother philosophical worthies was not the evil demonic magic that ‘all learned and good men detest’.

Proposition and judgement

CATEGORICAL PROPOSITIONS Seventeenth-century logicians commonly adhered to the usual distinction between two operations of the mind: on the one hand, simple conceptions, through which things are apprehended that, as categorematic terms, are capable of becoming the subject and the predicate of a categorical proposition; on the other, acts of predication, by which the contents of simple apprehensions are combined into a propositional complex that is a suitable potential object of assent or dissent. Although at the propositional level acts of predication and judgement will often coincide, authors were aware that there are good reasons to distinguish merely apprehensive propositions from judicative propositions. The former are states of affairs that are presented to the mind without any commitment to truth or falsity, whereas the latter actually have judicative or assertive force. Notwithstanding the predominant tendency to stick to the traditional division into incomplex concepts and propositional complexes, there were also factors at work which made for blurring of that fundamental distinction. One of them was Descartess use of the word idea for both the categorematic elements of a proposition and the proposition itself, as the object of judgement. Spinoza went even farther by explicitly declaring that at bottom a particular idea and a particular act of affirming or denying are one and the same thing. When, for example, the mind affirms that the sum of the three angles of a triangle is equal to two right angles, that affirmation cannot exist or be thought without the idea of a triangle.

Monads on My Mind

Daniel Garber (Princeton University, USA), in Monads on my Mind shows that monads were very much on Leibniz’s mind in the late 1690s. In these crucial years between about 1695 and 1700, Leibniz was beginning to work out the details of the monadology, what monads are, and how they are to function as the ultimate building-blocks of his metaphysics. In this essay, Daniel Garber looks carefully at the development of the argument in those years, as Leibniz’s view was undergoing what has to be regarded as a major shift. He begins by reviewing what he takes to be Leibniz’s position in what he has called his middle years, the years between the late 1670s and the mid-1690s, before monads, when Leibniz’s view of the world was grounded in corporeal substances. He then traces at least one of the paths by which monads came into Leibniz’s world during those important years of transition.