Newton’s notion and practice of unification

In this paper I deal with a neglected topic with respect to unification in Newton’s Principia. I will clarify Newton’s notion (as can be found in Newton’s utterances on unification) and practice of unification (its actual occurrence in his scientific work). In order to do so, I will use the recent theories on unification as tools of analysis (Kitcher, Salmon and Schurz). I will argue, after showing that neither Kitcher’s nor Schurz’s account aptly capture Newton’s notion and practice of unification, that Salmon’s later work is a good starting point for analysing this notion and its practice in the Principia. Finally, I will supplement Salmon’s account in order to answer the question at stake.     

Does Kant have a pre-Newtonian picture of force in the balance argument? An account of how the balance argument works

In this paper, I discuss whether the Metaphysical Foundations of Natural Science version of Kant’s argument that space-filling matter requires both attractive and repulsive forces betrays a pre-Newtonian picture of forces as Warren (2010) argues. More generally, I discuss Kant’s overall strategy for securing the possibility of space-filling matter and I describe what motivates Kant to think of the argument in the way, I believe, he does. Ultimately, I argue that Kant’s argument does not suggest a pre-Newtonian picture of forces. Along the way, I discuss the status of quantity of matter and the nature of forces in the Dynamics chapter of that work so as to better clarify what is at work in the balance argument.     

Hegel and Naturphilosophie

Against current non-metaphysical interpretations, I argue that Naturphilosophie is central to Hegel’s philosophy. This is so for three reasons. First, it was crucial to Hegel’s program to create a holistic culture. Second, Naturphilosophie is pivotal to absolute idealism, Hegel’s characteristic philosophical doctrine. Third, the idea of organic development, so central to Naturphilosophie, is pervasive throughout Hegel’s system. This idea is essential to Hegel’s concepts of spirit, dialectic, and identity-in-difference. Finally, I take issue with the neo-Kantian critique of Hegel’s Naturphilosophie on the grounds that it fails to appreciate the underlying motive behind Hegel’s system: the attempt to resolve the aporia of Kant’s epistemology.     

‘The long-lost truth’: Sir Isaac Newton and the Newtonian pursuit of ancient knowledge

In the 1720s the antiquary and Newtonian scholar Dr. William Stukeley (1687-1765) described his friend Isaac Newton as ‘the Great Restorer of True Philosophy’. Newton himself in his posthumously published Observations upon the prophecies of Daniel, and the Apocalypse of St. John (1733) predicted that the imminent fulfilment of Scripture prophecy would see ‘a recovery and re-establishment of the long-lost truth’. In this paper I examine the background to Newton’s interest in ancient philosophy and theology, and how it related to modern natural philosophical discovery. I look at the way in which the idea of a ‘long-lost truth’ interested others within Newton’s immediate circle, and in particular how it was carried forward by Stukeley’s researches into ancient British antiquities. I show how an interest in and respect for ancient philosophical knowledge remained strong within the first half of the eighteenth century.     

Francesco Patrizi’s two books on space: geometry, mathematics, and dialectic beyond Aristotelian science

Francesco Patrizi was a competent Greek scholar, a mathematician, and a Neoplatonic thinker, well known for his sharp critique of Aristotle and the Aristotelian tradition. In this article I shall present, in the first part, the importance of the concept of a three-dimensional space which is regarded as a body, as opposed to the Aristotelian two-dimensional space or interval, in Patrizi’s discussion of physical space. This point, I shall argue, is an essential part of Patrizi’s overall critique of Aristotelian science, in which Epicurean, Stoic, and mainly Neoplatonic elements were brought together, in what seems like an original theory of space and a radical revision of Aristotelian physics. Moreover, I shall try to show Patrizi’s dialectical method of definition, his geometrical argumentation, and trace some of the ideas and terms used by him back to Proclus’ Commentary on Euclid. This text of Proclus, as will be shown in the second part of the article, was also important for Patrizi’s discussion of mathematical space, where Patrizi deals with the status of mathematics and redefines some mathematical concepts such as the point and the line according to his new theory of space.     

The intelligibility of motion and construction: Descartes’ early mathematics and metaphysics, 1619-1637

I argue for an interpretation of the connection between Descartes’ early mathematics and metaphysics that centers on the standard of geometrical intelligibility that characterizes Descartes’ mathematical work during the period 1619 to 1637. This approach remains sensitive to the innovations of Descartes’ system of geometry and, I claim, sheds important light on the relationship between his landmark Geometry (1637) and his first metaphysics of nature, which is presented in Le monde (1633). In particular, I argue that the same standard of clear and distinct motions for construction that allows Descartes to distinguish ‘geometric’ from ‘imaginary’ curves in the domain of mathematics is adopted in Le monde as Descartes details God’s construction of nature. I also show how, on this interpretation, the metaphysics of Le monde can fruitfully be brought to bear on Descartes’ attempted solution to the Pappus problem, which he presents in Book I of the Geometry. My general goal is to show that attention to the standard of intelligibility Descartes invokes in these different areas of inquiry grants us a richer view of the connection between his early mathematics and philosophy than an approach that assumes a common method is what binds his work in these domains together.     

Incommensurability reconsidered

In his later writings Kuhn reconsidered his earlier account of incommensurability, clarifying some aspects, modifying others, and explicitly rejecting some of his earlier claims. In Kuhn’s new account incommensurability does not pose a problem for the rational evaluation of competing scientific theories, but does pose a problem for certain forms of realism. Kuhn maintains that, because of incommensurability, the notion that science might seek to learn the nature of things as they are in themselves is incoherent. I develop Kuhn’s new account of incommensurability, respond to his anti-realist argument, and sketch a form of realism in which the realist aim is a pursuable goal.     

Radical mathematical Thomism: beings of reason and divine decrees in Torricelli’s philosophy of mathematics

Evangelista Torricelli (1608-1647) is perhaps best known for being the most gifted of Galileo’s pupils, and for his works based on indivisibles, especially his stunning cubature of an infinite hyperboloid. Scattered among Torricelli’s writings, we find numerous traces of the philosophy of mathematics underlying his mathematical practice. Though virtually neglected by historians and philosophers alike, these traces reveal that Torricelli’s mathematical practice was informed by an original philosophy of mathematics. The latter was dashed with strains of Thomistic metaphysics and theology. Torricelli’s philosophy of mathematics emphasized mathematical constructs as human-made beings of reason, yet mathematical truths as divine decrees, which upon being discovered by the mathematician ‘appropriate eternity’. In this paper, I reconstruct Torricelli’s philosophy of mathematics—which I label radical mathematical Thomism—placing it in the context of Thomistic patterns of thought.     

Emilie du Châtelet’s Institutions de physique as a document in the history of French Newtonianism

This paper discusses the contribution of Madame Du Châtelet to the reception of Newtonianism in France prior to her translation of Newton’s Principia. It focuses on her Institutions de physique, a work normally considered for its contribution to the reception of Leibniz in France. By comparing the different editions of the Institutions, I argue that her interest in Newton antedated her interest in Leibniz, and that she did not see Leibniz’s metaphysics as incompatible with Newtonian science. Her Newtonianism can be seen to be in the course of development between 1738 and 1742 and it was shaped by contemporary French debates (for example the vis viva controversy) and the achievement of French Newtonians like Maupertuis in confirming his theories. Her Institutions therefore is linked to the same drive to disseminate Newtonianism undertaken by popularisations such as Voltaire’s Elements de la philosophie de Newton and Algarotti’s Newtonianismo per le dame.     

Newton’s substance monism, distant action, and the nature of Newton’s empiricism: discussion of H. Kochiras “Gravity and Newton’s substance counting problem”

This paper is a critical response to Hylarie Kochiras’ “Gravity and Newton’s substance counting problem,” Studies in History and Philosophy of Science 40 (2009) 267-280. First, the paper argues that Kochiras conflates substances and beings; it proceeds to show that Newton is a substance monist. The paper argues that on methodological grounds Newton has adequate resources to respond to the metaphysical problems diagnosed by Kochiras. Second, the paper argues against the claim that Newton is committed to two speculative doctrines attributed to him by Kochiras and earlier Andrew Janiak: i) the passivity of matter and ii) the principle of local causation. Third, the paper argues that while Kochiras’ (and Janiak’s) arguments about Newton’s metaphysical commitments are mistaken, it qualifies the characterization of Newton as an extreme empiricist as defended by Howard Stein and Rob DiSalle. In particular, the paper shows that Newton’s empiricism was an intellectual and developmental achievement that built on non trivial speculative commitments about the nature of matter and space.     

Naturalized epistemology, or what the Strong Programme can’t explain

In this paper I argue that the Strong Programme’s aim to provide robust explanations of belief acquisition is limited by its commitment to the symmetry principle. For Bloor and Barnes, the symmetry principle is intended to drive home the fact that epistemic norms are socially constituted. My argument here is that even if our epistemic standards are fully naturalized—even relativized—they nevertheless can play a pivotal role in why individuals adopt the beliefs that they do. Indeed, sometimes the fact that a belief is locally endorsed as rational is the only reason why an individual holds it. In this way, norms of rationality have a powerful and unique role in belief formation. But if this is true then the symmetry principle’s emphasis on ‘sameness of type’ is misguided. It has the undesirable effect of not just naturalizing our cognitive commitments, but trivializing them. Indeed, if the notion of ‘similarity’ is to have any content, then we are not going to classify as ‘the same’ beliefs that are formed in accordance with deeply entrenched epistemic norms as ones formed without reflection on these norms, or ones formed in spite of these norms. My suggestion here is that we give up the symmetry principle in favor of a more sophisticated principle, one that allows for a taxonomy of causes rich enough to allow us to delineate the unique impact epistemic norms have on those individuals who subscribe to them.     

Forces and causes in Kant’s early pre-Critical writings

This paper considers Kant’s conception of force and causality in his early pre-Critical writings, arguing that this conception is best understood by way of contrast with his immediate predecessors, such as Christian Wolff, Alexander Baumgarten, Georg Friedrich Meier, Martin Knutzen, and Christian August Crusius, and in terms of the scientific context of natural philosophy at the time. Accordingly, in the True estimation Kant conceives of force in terms of activity rather than in terms of specific effects, such as motion (as unnamed Wolffians had done). Kant’s explicit arguments in the Nova dilucidatio for physical influx (in the guise of the principle of succession) are directed primarily against the conception of grounds and existence held by Wolff, Baumgarten, and Meier, and only secondarily against Leibniz (by asserting the priority of bodies over mind rather than vice versa). Finally, Kant’s reconciliation of the infinite divisibility of space and the unity of monads in the Physical monadology is designed to respond to objections that could be raised naturally by Wolff and Baumgarten.     

On the sources and implications of Carnap’s Der Raum

Der Raum, Carnap’s earliest published work, finds him largely a follower of Husserl. In particular, he holds a distinctively Husserlian conception of the synthetic a priori—a view, I will suggest, paradigmatic of what he would later reject as ‘metaphysics’. His main purpose is to reconcile that Husserlian view with the theory of general relativity. On the other hand, he has already broken with Husserl, and in ways which foreshadow later developments in his thought. Especially important in this respect is his use of Hans Driesch’s Ordnungslehre.     

Is Newton a ‘radical empiricist’ about method?

Recently, some Newton scholars have argued that Newton is an empiricist about metaphysics—that ideally, he wants to let advances in physical theory resolve either some or all metaphysical issues. But while proponents of this interpretation are using ‘metaphysics’ in a very broad sense, to include the ‘principles that enable our knowledge of natural phenomena’, attention has thus far been focused on Newton’s approach to ontological, not epistemological or methodological, issues. In this essay, I therefore consider whether Newton wants to let physical theory bear on the very ‘principles that enable our knowledge’. By examining two kinds of argument in the Principia, I contend that Newton can be considered a methodological empiricist in a substantial respect. I also argue, however, that he cannot be a ‘radical empiricist’—that he does not and cannot convert all methodological issues into empirical issues.     

Signs, toy models, and the a priori: from Helmholtz to Wittgenstein

The Marburg neo-Kantians argue that Hermann von Helmholtz’s empiricist account of the a priori does not account for certain knowledge, since it is based on a psychological phenomenon, trust in the regularities of nature. They argue that Helmholtz’s account raises the ‘problem of validity’ (Gültigkeitsproblem): how to establish a warranted claim that observed regularities are based on actual relations. I reconstruct Heinrich Hertz’s and Ludwig Wittgenstein’s Bild theoretic answer to the problem of validity: that scientists and philosophers can depict the necessary a priori constraints on states of affairs in a given system, and can establish whether these relations are actual relations in nature. The analysis of necessity within a system is a lasting contribution of the Bild theory. However, Hertz and Wittgenstein argue that the logical and mathematical sentences of a Bild are rules, tools for constructing relations, and the rules themselves are meaningless outside the theory. Carnap revises the argument for validity by attempting to give semantic rules for translation between frameworks. Russell and Quine object that pragmatics better accounts for the role of a priori reasoning in translating between frameworks. The conclusion of the tale, then, is a partial vindication of Helmholtz’s original account.     

Kuhn, Popper, and the Superconducting Supercollider

The demise of the Superconducting Supercollider (SSC) is often explained in terms of the strain that it placed on the federal budget of the United States, and change in national security interests with the end of the Cold War. Recent work by Steve Fuller provides a framework to re-examine this episode in epistemological terms using the work of Kuhn and Popper. Using this framework, it is tempting to explain the demise as resulting from the overly Kuhnian character of its proponents, who supposedly argued for its construction by appealing to the importance of testing the predictions of a specific paradigm (i.e. the Standard Model). On this reading, the SSC case appears as an example of how Kuhn’s paradigm-driven view of science was invoked to keep science closed and autonomous from society. I argue that the SSC episode should not be viewed as giving support to the displacement of Kuhn’s view of science for Popper’s, and that such a displacement is detrimental to the project of integrating discussion on science into the public sphere. Drawing upon Rouse and Wimsatt, I argue that understanding paradigms as practices blunts some criticisms against Kuhn’s model, and that his model should play an important epistemological role in the aforementioned project.     

On Popper’s strong inductivism (or strongly inconsistent anti-inductivism)

It is generally accepted that Popper‘s degree of corroboration, though “inductivist” in a very general and weak sense, is not inductivist in a strong sense, i.e. when by ‘inductivism’ we mean the thesis that the right measure of evidential support has a probabilistic character. The aim of this paper is to challenge this common view by arguing that Popper can be regarded as an inductivist, not only in the weak broad sense but also in a narrower, probabilistic sense. In section 2, first, I begin by briefly characterizing the relevant notion of inductivism that is at stake here; second, I present and discuss the main Popperian argument against it and show that in the only reading in which the argument is formally it is restricted to cases of predicted evidence, and that even if restricted in this way the argument is formally valid it is nevertheless materially unsound. In section 3, I analyze the desiderata that, according to Popper, any acceptable measure for evidential support must satisfy, I clean away its ad-hoc components and show that all the remaining desiderata are satisfied by inductuvist-in-strict-sense measures. In section 4 I demonstrate that two of these desiderata, accepted by Popper, imply that in cases of predicted evidence any measure that satisfies them is qualitatively indistinguishable from conditional probability. Finally I defend that this amounts to a kind of strong inductivism that enters into conflict with Popper’s anti-inductivist argument and declarations, and that this conflict does not depend on the incremental versus non-incremental distinction for evidential-support measures, making Popper’s position inconsistent in any reading.     

What’s right about Carnap, Neurath and the Left Vienna Circle thesis: a refutation

This paper rejects as unfounded a recent criticism of research on the so-called left wing of the Vienna Circle and the claim that it sported a political philosophy of science. The demand for ‘specific, local periodized claims’ is turned against the critic. It is shown (i) that certain criticisms of Red Vienna’s leading party cannot be transferred to the members of the Circle involved in popular education, nor can criticism of Carnap’s Aufbau be transferred to Neurath’s unified science project; (ii) that neither with regard to Carnap nor to Neurath does the criticism raise points that either engage with the thesis proposed or stand up to closer scrutiny; (iii) that the main thesis attacked is just what I had warned the claim that the Vienna Circle had a political philosophy of science should not be understood as. The question whether theirs is ‘political enough’ today can and should be discussed without distortion of the historical record.