The empirical basis of equilibrium: Mach, Vailati, and the lever

About a century ago, Ernst Mach argued that Archimedes’s deduction of the principle of the lever is invalid, since its premises contain the conclusion to be demonstrated. Subsequently, many scholars defended Archimedes, mostly on historical grounds, by raising objections to Mach’s reconstruction of Archimedes’s deduction. In the debate, the Italian philosopher and historian of science Giovanni Vailati stood out. Vailati responded to Mach with an analysis of Archimedes’s deduction which was later quoted and praised by Mach himself. In this paper, my objective is to show that the debate can be further advanced, as Mach indicated, by reframing it in terms of the empirical vs. the logical dimensions of mechanics. In this way, I will suggest, the debate about Archimedes’s deduction can be resolved in Mach’s favour.     

On the epistemological foundations of the law of the lever

In this paper I challenge Paolo Palmieri’s reading of the Mach—Vailati debate on Archimedes’ proof of the law of the lever. I argue that the actual import of the debate concerns the possible epistemic (as opposed to merely pragmatic) role of mathematical arguments in empirical physics, and that construed in this light Vailati carries the upper hand. This claim is defended by showing that Archimedes’ proof of the law of the lever is not a way of appealing to a non-empirical source of information, but a way of explicating the mathematical structure that can represent the empirical information at our disposal in the most general way.     

Mach and Hertz’s mechanics

The place of Heinrich Hertz’s The principles of mechanics in the history of the philosophy of science is disputed. Here I critically assess positivist interpretations, concluding that they are inadequate.There is a group of commentators who seek to align Hertz with positivism, or with specific positivists such as Ernst Mach, who were enormously influential at the time. Max Jammer is prominent among this group, the most recent member of which is Joseph Kockelmans. I begin by discussing what Hertz and Mach had to say about one another, and I specify certain respects in which their views are indeed similar. I then go on to detail their differences, looking at Hertz’s attitude to the atomic theory, to the mechanical world-view, to simplicity, to unobservables and metaphysics, and his objections to Newtonian forces. I conclude that the positivist interpretation of Hertz’s mechanics significantly overplays its similarities to Mach’s views.     

Picturing the moon: Hevelius’s and Riccioli’s visual debate

This article investigates the maps of the moon produced in the mid-seventeenth century by Jesuit Giambattista Riccioli (1598-1671) and Johannes Hevelius (1611-1687), whose cartographic projects competed for widespread acceptance. Although Hevelius’s Selenographia (1647) was applauded for its many detailed, self-engraved pictures of the moon, his cartography and proposed nomenclature were supplanted by Riccioli’s as offered in Almagestum novum (1651), in spite of the latter’s simplistic pictures and promotion of geocentric cosmology. Exploring this paradox through pictorial analysis, three types of images common to both Selenographia and Almagestum novum are compared, employing an analytical tool developed by Svetlana Alpers in The art of describing (1983). A focus on this debate exposes the tensions evoked by new technologies of vision and competing cultures of visual epistemology in seventeenth-century astronomy. As both selenographers grappled with questions about the role of representation and what kinds of knowledge could be generated visually, the successes and failures of their competing projects present implications for the course of visual astronomy, as well as for our understanding of the use of ‘visual technologies’ in a period of controversy.     

Response to one point in Gingras’s review of Gravity’s shadow

Yves Gingras says of my book Gravity’s shadow that it is too long, the style is poor, and in its 870 pages there is nothing new that is not to be regretted. Gingras’s purity of vision would be a cause for congratulation were it not for the appalling implications of one of his claims. For the sake of the future of social science—indeed for the sake of the future of civilisation—it is impossible to leave unchallenged the idea that respondents, who don’t like to see their use of data questioned, are to be commended when they withhold those data from public scrutiny.     

Reception and discovery: the nature of Johann Wilhelm Ritter’s invisible rays

Ultraviolet radiation is generally considered to have been discovered by Johann Wilhelm Ritter in 1801. In this article, we study the reception of Ritter’s experiment during the first decade after the event—Ritter’s remaining lifetime. Drawing on the attributional model of discovery, we are interested in whether the German physicists and chemists granted Ritter’s observation the status of a discovery and, if so, of what. Two things are remarkable concerning the early reception, and both have to do more with neglect than with (positive) reception. Firstly, Ritter’s observation was sometimes accepted as a fact but, with the exception of C. J. B. Karsten’s theory of invisible light, it played almost no role in the lively debate about the nature of heat and light. We argue that it was the prevalent discourse based on the metaphysics of Stoffe that prevented a broader reception of Ritter’s invisible rays, not the fact that Ritter himself made his findings a part of his Naturphilosophie. Secondly, with the exception of C. E. Wünsch’s experiments on the visual spectrum, there was no experimental examination of the experiment. We argue that theorizing about ontological systems was more common than experimenting, because, given its social and institutional situation, this was the appropriate way of contributing to physics. Consequently, it was less clear in 1810 than in 1801 what, if anything, had been discovered by Ritter.     

John Dalton’s puzzles: from meteorology to chemistry

Historical research on John Dalton has been dominated by an attempt to reconstruct the origins of his so-called “chemical atomic theory”. I show that Dalton’s theory is difficult to define in any concise manner, and that there has been no consensus as to its unique content among his contemporaries, later chemists, and modern historians. I propose an approach which, instead of attempting to work backward from Dalton’s theory, works forward, by identifying the research questions that Dalton posed to himself and attempting to understand how his hypotheses served as answers to these questions. I describe Dalton’s scientific work as an evolving set of puzzles about natural phenomena. I show how an early interest in meteorology led Dalton to see the constitution of the atmosphere as a puzzle. In working on this great puzzle, he gradually turned his interest to specifically chemical questions. In the end, the web of puzzles that he worked on required him to create his own novel philosophy of chemistry for which he is known today.     

I s

Richard Arthur (2006) and I (Savitt, 2009) proposed that the present in (time-oriented) Minkowski spacetime should be thought of as a small causal diamond. That is, given two timelike separated events p and q, with p earlier than q, we suggested that the present (relative to those two events) is the set I⁺(p)∩I^-(q). Mauro Dorato (2011) presents three criticisms of this proposal. I rebut all three and then examine two more plausible criticisms of the Arthur/Savitt proposal. I argue that these criticisms also fail.     

Pierre Duhem’s good sense as a guide to theory choice

This paper examines Duhem’s concept of good sense as an attempt to support a non rule-governed account of rationality in theory choice. Faced with the underdetermination of theory by evidence thesis and the continuity thesis, Duhem tried to account for the ability of scientists to choose theories that continuously grow to a natural classification. I will examine the concept of good sense and the problems that stem from it. I will also present a recent attempt by David Stump to link good sense to virtue epistemology. I will argue that even though this approach can be useful for the better comprehension of the concept of good sense, there are some substantial differences between virtue epistemologists and Duhem. In the light of this reconstruction of good sense, I will propose a possible way to interpret the concept of good sense, which overcomes the noted problems and fits better with Duhem’s views on scientific method and motivation in developing the concept of good sense.     

John Venn’s opposition to probability as degree of belief

John Venn is known as one of the clearest expounders of the interpretation of probability as the frequency of a particular outcome in a potentially unlimited series of possible events. This view he held to be incompatible with the alternate interpretation of probability as a measure of the degree of belief that would rationally be held about a certain outcome based upon the reliability of testimony and other prior information. This paper explores the reasons why Venn may have been so opposed to the degree-of-belief interpretation and suggests that it may have been a way for him to resolve a conflict in his own mind between his ideas of proper scientific methods of inference and the religious beliefs that he held as a young man.     

An appraisal of Mendeleev’s contribution to the development of the periodic table

Historians and philosophers of science generally conceptualize scientific progress to be dichotomous, viz., experimental observations lead to scientific laws, which later facilitate the elaboration of explanatory theories. There is considerable controversy in the literature with respect to Mendeleev’s contribution to the origin, nature, and development of the periodic table. The objectives of this study are to explore and reconstruct: a) periodicity in the periodic table as a function of atomic theory; b) role of predictions in scientific theories and its implications for the periodic table; and c) Mendeleev’s contribution: theory or an empirical law? The reconstruction shows that despite Mendeleev’s own ambivalence, periodicity of properties of chemical elements in the periodic table can be attributed to the atomic theory. It is argued that based on the Lakatosian framework, predictions (novel facts) play an important role in the development of scientific theories. In this context, Mendeleev’s predictions played a crucial role in the development of the periodic table. Finally, it is concluded that Mendeleev’s contribution can be considered as an “interpretative” theory which became “explanatory” after the periodic table was based on atomic numbers.     

Popper’s response to Dingle on special relativity and the problem of the observer

Dingle contended that Einstein’s special theory of relativity was physically impossible for the simple reason that it required clocks to be simultaneously faster and slower than each other. McCrea refuted Dingle using an operationalist argument. An operational response did not satisfy Popper, who wrote an unpublished essay to counter Dingle’s claim. Popper developed an analysis that avoided operationalism by using a system of coinciding clocks, contending that this system showed that special relativity withstood Dingle’s criticism that it was not a symmetrical and consistent physical theory. However, Popper mistakenly included an asymmetric calculation in his analysis. Once this is corrected, the amended result supports Dingle’s position. Popper went on to argue that to avoid determinism, special relativity had to be reconciled with absolute time; this too supports Dingle. Popper’s failure to refute Dingle calls into question his claim that ‘the observer’ is superfluous to special relativity.     

How to tell causes from effects: Kant’s causal theory of time and modern approaches

I attempt a reconstruction of Kant’s version of the causal theory of time that makes it appear coherent. Two problems are at issue. The first concerns Kant’s reference to reciprocal causal influence for characterizing simultaneity. This approach is criticized by pointing out that Kant’s procedure involves simultaneous counterdirected processes—which seems to run into circularity. The problem can be defused by drawing on instantaneous processes such as the propagation of gravitation in Newtonian mechanics. Another charge of circularity against Kant’s causal theory was leveled by Schopenhauer. His objection was that Kant’s approach is invalidated by the failure to deliver non-temporal criteria for distinguishing between causes and effects. I try to show that the modern causal account has made important progress toward a successful resolution of this difficulty. The fork asymmetry, as based on Reichenbach’s principle of the common cause, provides a means for the distinction between cause and effect that is not based on temporal order (if some preconditions are realized).     

Pierre Duhem’s epistemic aims and the intellectual virtue of humility: a reply to Ivanova

David Stump (2007) has recently argued that Pierre Duhem can be interpreted as a virtue epistemologist. Stump’s claims have been challenged by Milena Ivanova (2010) on the grounds that Duhem’s ‘epistemic aims’ are more modest than those of virtue epistemologists. I challenge Ivanova’s criticism of Stump by arguing that she not distinguish between ‘reliabilist’ and ‘responsibilist’ virtue epistemologies. Once this distinction is drawn, Duhem clearly emerges as a ‘virtue-responsibilist’ in a way that complements Ivanova’s positive proposal that Duhem’s ‘good sense’ reflects a conception of the ‘ideal scientist’. I support my proposal that Duhem is a ‘virtue-responsibilist’ by arguing that his rejection of the possibility of our producing a ‘perfect theory’ reflects the key responsibilist virtue of ‘intellectual humility’.     

Kant’s dynamical theory of matter in 1755, and its debt to speculative Newtonian experimentalism

This paper explores the scientific sources behind Kant’s early dynamical theory of matter in 1755, with a focus on two main Kant’s writings: Universal Natural History and Theory of the Heavens and On Fire. The year 1755 has often been portrayed by Kantian scholars as a turning point in the intellectual career of the young Kant, with his much debated conversion to Newton. Via a careful analysis of some salient themes in the two aforementioned works, and a reconstruction of the scientific sources behind them, this paper shows Kant’s debt to an often overlooked scientific tradition, i.e. speculative Newtonian experimentalism. The paper argues that more than the Principia, it was the speculative experimentalism that goes from Newton’s Opticks to Herman Boerhaave’s Elementa chemiae via Stephen Hales’ Vegetable Staticks that played a central role in the elaboration of Kant’s early dynamical theory of matter in 1755.     

Locke’s construction of the idea of power

I explain Locke’s account of the origin of our idea of power, showing that it concerns the idea of the disposition to act or change, and that this idea is constructed out of the ideas of action or change. I also show how Locke could have modified his account to avoid Hume’s criticism and argue that his neglect to do so reflects a studied neglect of taxonomy, an ambiguity in the notion of capacity, and complications in Locke’s conception of simple ideas. A comparison of the two empiricists reveals that not only do they disagree about the role of reason in the origin of our idea of power, but they are also talking about different ideas. Within the framework of Locke’s account of the origin of the idea of power, I explain why he believes that bodies only provide us with an obscure idea of active power. I conclude by defending his insight that there is a deep connection between the ability to predict and the idea of power.     

Mathematical instrumentalism, Gödel’s theorem, and inductive evidence

Mathematical instrumentalism construes some parts of mathematics, typically the abstract ones, as an instrument for establishing statements in other parts of mathematics, typically the elementary ones. Gödel’s second incompleteness theorem seems to show that one cannot prove the consistency of all of mathematics from within elementary mathematics. It is therefore generally thought to defeat instrumentalisms that insist on a proof of the consistency of abstract mathematics from within the elementary portion. This article argues that though some versions of mathematical instrumentalism are defeated by Gödel’s theorem, not all are. By considering inductive reasons in mathematics, we show that some mathematical instrumentalisms survive the theorem.     

Duhem’s theory of mixture in the light of the Stoic challenge to the Aristotelian conception

The bulk of Duhem’s writing which bears on the understanding of mixtures suggests he adopted an Aristotelian position which he opposed only to the atomic view. A third view from antiquity—that of the Stoics—seems not to be taken into account. But his lines of thought are not always as explicit as could be wished. The Stoic view is considered here from a perspective which Duhem might well have adopted. This provides a background against which his somewhat unorthodox Aristotelianism might be understood.