Instruments of Music,Instruments of Science: Hermann von Helmholtz's Musical Practices,his Classicism,and his Beethoven Sonata

The young Hermann Helmholtz, in an 1838 letter home, declared that he always appreciated music much more when he played it for himself. Though a frequent concert-goer, and celebrated for his highly influential 1863 work on the physiological basis of music theory, Die Lehre von den Tonempfindungen, it is likely that Helmholtz's enduring engagement with music began with his initial, personal experience of playing music for himself. I develop this idea, shifting the discussion of Helmholtz's work on sound sensation back to its origins, and examine the role of his material interaction with musical instruments and music itself. In his sound sensation studies, Helmholtz understood sound as an external, physical object. But Helmholtz also conceived of sound in musical terms. Further, Helmholtz's particular musical tastes as well as his deeply personal interaction with musical instruments allowed him to reconcile his conception of sound as physical object with his conception of sound as music. Helmholtz's physiological theory of sound sensation was both the product of and constitutive of how he heard and created sound. I argue that Helmholtz himself was the embodied reconciliation of his physiological theory of sound sensation and his belief that musical aesthetics were historically and culturally contingent.     

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.     

Essentially narrative explanations

This essay argues that narrative explanations prove uniquely suited to answering certain explanatory questions, and offers reasons why recognizing a type of statement that requires narrative explanations crucially informs on their assessment. My explication of narrative explanation begins by identifying two interrelated sources of philosophical unhappiness with them. The first I term the problem of logical formlessness and the second the problem of evaluative intractability. With regard to the first, narratives simply do not appear to instantiate any logical form recognized as inference licensing. But absent a means of identifying inferential links, what justifies connecting explanans and explanandum? Evaluative intractability, the second problem, thus seems a direct consequence. This essay shows exactly why these complaints prove unfounded by explicating narrative explanations in the process of answering three interrelated questions. First, what determines that an explanation has in some critical or essential respect a narrative form? Second, how does a narrative in such cases come to constitute a plausible explanation? Third, how do the first two considerations yield a basis for evaluating an explanation offered as a narrative? Answers to each of these questions include illustrations of actual narrative explanations and also function to underline attendant dimensions of evaluation.     

British Acoustics and its Transformation from the 1860s to the 1910s

Between the 1860s and the 1910s, British acoustics was transformed from an area of empirical research into a mathematically organized field. Musical motives—improving musical scales and temperaments, making better musical instruments, and understanding the nature of musical tones—were among the major driving forces of acoustical researchers in nineteenth-century Britain. The German acoustician, Helmholtz, had a major impact on British acousticians who also had extensive interactions with American and French acousticians. Rayleigh's acoustics, reflecting all these features, bore remarkable fruit in his treatise The Theory of Sound, which successfully subjected empirical acoustics to analytical mathematics. His accomplishments made British acoustics a subfield of physics, thus distinguishing it from the ‘new acoustics’ in early twentieth-century America.     

Fresnel's laws,ceteris paribus

This article is about structural realism, historical continuity, laws of nature, and ceteris paribus clauses. Fresnel's Laws of optics support Structural Realism because they are a scientific structure that has survived theory change. However, the history of Fresnel's Laws which has been depicted in debates over realism since the 1980s is badly distorted. Specifically, claims that J. C. Maxwell or his followers believed in an ontologically-subsistent electromagnetic field, and gave up the aether, before Einstein's annus mirabilis in 1905 are indefensible. Related claims that Maxwell himself did not believe in a luminiferous aether are also indefensible. This paper corrects the record. In order to trace Fresnel's Laws across significant ontological changes, they must be followed past Einstein into modern physics and nonlinear optics. I develop the philosophical implications of a more accurate history, and analyze Fresnel's Laws' historical trajectory in terms of dynamic ceteris paribus clauses. Structuralists have not embraced ceteris paribus laws, but they continue to point to Fresnel's Laws to resist anti-realist arguments from theory change. Fresnel's Laws fit the standard definition of a ceteris paribus law as a law applicable only in particular circumstances. Realists who appeal to the historical continuity of Fresnel's Laws to combat anti-realists must incorporate ceteris paribus laws into their metaphysics.     

Bayesian pseudo-confirmation,use-novelty,and genuine confirmation

According to the comparative Bayesian concept of confirmation, rationalized versions of creationism come out as empirically confirmed. From a scientific viewpoint, however, they are pseudo-explanations because with their help all kinds of experiences are explainable in an ex-post fashion, by way of ad-hoc fitting of an empirically empty theoretical framework to the given evidence. An alternative concept of confirmation that attempts to capture this intuition is the use novelty (UN) criterion of confirmation. Serious objections have been raised against this criterion. In this paper I suggest solutions to these objections. Based on them, I develop an account of genuine confirmation that unifies the UN-criterion with a refined probabilistic confirmation concept that is explicated in terms of the confirmation of evidence-transcending content parts of the hypothesis.     

On reading Newton as an Epicurean: Kant,Spinozism and the changes to the Principia

This paper argues for three distinct, albeit mutually illuminating theses: first it explains why well informed eighteenth-century thinkers, e.g., the pre-critical Immanuel Kant and Richard Bentley would have identified important aspects of Newton’s natural philosophy with (a species of modern) Epicureanism. Second, it explores how some significant changes to Newton’s Principia between the first (1687) and second (1713) editions can be explained in terms of attempts to reframe the Principia so that the charge of “Epicureanism” can be deflected. In order to account for this, the paper discusses the political and theological changes in the wake of the Glorious Revolution (1688); Bentley plays a non-trivial role in these matters. Third, the paper argues that there is an argument in Kant’s (1755) Universal Natural History and Theory of the Heavens that undermines a key claim of Newton’s General Scholium that was used to discredit Spinozism by Clarke in A demonstration of the being and attributes of God.     

Nicolas Béguelin and his search for a crucial experiment on the nature of light (1772)

In the second half of the eighteenth century a lively debate was going on in Germany about the nature of light. One important contribution to this discussion, namely a paper by Nicolas Béguelin, is studied in this article. In his essay, Béguelin compared the Newtonian emission theory of light and the wave theory of Leonhard Euler. Whereas others opted for one of the two theories by invoking arguments or authorities, Béguelin made a systematic search for experiments which he hoped would settle the dispute. Two of these experiments were most original. The first, which Béguelin himself performed, concerned light rays grazing a glass surface. For several reasons it did not have the impact it deserved. The second one was a thought experiment which was meant to illustrate a major tenet of the wave theory, that is, the analogy between light and sound. An analysis is given of these two experiments, and it is shown that neither of them brought the debate to an end.     

A novel mechanism for jumping in the indian ant<Emphasis Type="Italic">Harpegnathos saltator</Emphasis> (Jerdon) (Formicidae,Ponerinae)

The Indian antHarpegnathos saltator may be unique among insects in using its jumping capacity not only as an escape mechanism but also as a normal means of locomotion, and for catching its prey in flight. High-speed cinematography used to analyse the various phases of the jump suggests thatHarpegnathos employs a novel jumping mechanism to mediate these behaviours: namely the synchronous activation of its middle and hindlegs. Electrophysiological recordings from muscles or nerves in pairs of middle and hindlegs show remarkably synchronous activity during fictive jumping, supporting the synchronous activation hypothesis.Harpegnathos is not the only ant to jump, and a cladistic analysis suggests that jumping behaviour evolved independently three times during ant evolutionary history.     

Leibniz’s syncategorematic infinitesimals

In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s mature interpretation was fully in accord with the Archimedean Axiom: infinitesimals are fictions, whose treatment as entities incomparably smaller than finite quantities is justifiable wholly in terms of variable finite quantities that can be taken as small as desired, i.e. syncategorematically. In this paper I explain this syncategorematic interpretation, and how Leibniz used it to justify the calculus. I then compare it with the approach of Smooth Infinitesimal Analysis, as propounded by John Bell. I find some salient differences, especially with regard to higher-order infinitesimals. I illustrate these differences by a consideration of how each approach might be applied to propositions of Newton’s Principia concerning the derivation of force laws for bodies orbiting in a circle and an ellipse. “If the Leibnizian calculus needs a rehabilitation because of too severe treatment by historians in the past half century, as Robinson suggests (1966, 250), I feel that the legitimate grounds for such a rehabilitation are to be found in the Leibnizian theory itself.”—(Bos 1974–1975, 82–83).      

Local reduction in physics

A conventional wisdom about the progress of physics holds that successive theories wholly encompass the domains of their predecessors through a process that is often called “reduction.” While certain influential accounts of inter-theory reduction in physics take reduction to require a single “global” derivation of one theory׳s laws from those of another, I show that global reductions are not available in all cases where the conventional wisdom requires reduction to hold. However, I argue that a weaker “local” form of reduction, which defines reduction between theories in terms of a more fundamental notion of reduction between models of a single fixed system, is available in such cases and moreover suffices to uphold the conventional wisdom. To illustrate the sort of fixed-system, inter-model reduction that grounds inter-theoretic reduction on this picture, I specialize to a particular class of cases in which both models are dynamical systems. I show that reduction in these cases is underwritten by a mathematical relationship that follows a certain liberalized construal of Nagel/Schaffner reduction, and support this claim with several examples. Moreover, I show that this broadly Nagelian analysis of inter-model reduction encompasses several cases that are sometimes cited as instances of the “physicist׳s” limit-based notion of reduction.     

The National Science Foundation and philosophy of science's withdrawal from social concerns

At some point during the 1950s, mainstream American philosophy of science began increasingly to avoid questions about the role of non-cognitive values in science and, accordingly, increasingly to avoid active engagement with social, political and moral concerns. Such questions and engagement eventually ceased to be part of the mainstream. Here we show that the eventual dominance of ‘value-free’ philosophy of science can be attributed, at least in part, to the policies of the U.S. National Science Foundation's “History and Philosophy of Science” sub-program. In turn, the sub-program's policies were set by logical empiricists who espoused value-free philosophy of science; these philosophers' actions, we also point out, fit a broad pattern, one in which analytic philosophers used institutional control to marginalize rival approaches to philosophy. We go on to draw on existing knowledge of this pattern to suggest two further, similar, contributors to the withdrawal from value-laden philosophy of science, namely decisions by the editors of Philosophy of Science and by the editors of The Journal of Philosophy. Political climate was, we argue, at most an indirect contributor to the withdrawal and was neither a factor that decided whether it occurred nor one that was sufficient to bring it about. Moreover, we argue that the actions at the National Science Foundation went beyond what was required by its senior administrators and are better viewed as part of what drove, rather than as what was being driven by, the adoption of logical empiricism by the philosophy of science community.     

The Philosopher's conception of Mathesis Universalis from Descartes to Leibniz

In Descartes, the concept of a ‘universal science’ differs from that of a ‘mathesis universalis’, in that the latter is simply a general theory of quantities and proportions. Mathesis universalis is closely linked with mathematical analysis; the theorem to be proved is taken as given, and the analyst seeks to discover that from which the theorem follows. Though the analytic method is followed in the Meditations, Descartes is not concerned with a mathematisation of method; mathematics merely provides him with examples. Leibniz, on the other hand, stressed the importance of a calculus as a way of representing and adding to what is known, and tried to construct a ‘universal calculus’ as part of his proposed universal symbolism, his ‘characteristica universalis’. The characteristica universalis was never completed—it proved impossible, for example, to list its basic terms, the ‘alphabet of human thoughts’—but parts of it did come to fruition, in the shape of Leibniz's infinitesimal calculus and his various logical calculi. By his construction of these calculi, Leibniz proved that it is possible to operate with concepts in a purely formal way.     

Scientific progress without increasing verisimilitude: In response to Niiniluoto

First, I argue that scientific progress is possible in the absence of increasing verisimilitude in science's theories. Second, I argue that increasing theoretical verisimilitude is not the central, or primary, dimension of scientific progress. Third, I defend my previous argument that unjustified changes in scientific belief may be progressive. Fourth, I illustrate how false beliefs can promote scientific progress in ways that cannot be explicated by appeal to verisimilitude.     

Arte rates reguntur: Nautical handbooks in antiquity?

Given the huge number of technical handbooks on multifarious subjects, ranging from astronomy and music to rhetoric, horticulture, and cooking, the absence of ancient nautical handbooks comes as a surprise. Such handbooks did exist in antiquity in some form, likely having been written in the period of the Hellenistic boom of technical texts, but disappearing at some later point, perhaps around the third or fourth century AD. This disappearance could be due to a number of reasons, suggesting that the tastes and needs of the audience(s) for nautical technai were changing. These nautical handbooks may have been superseded by more specialized works, such as treatises on astronomy and mathematics, geography and periploi, and naval tactics, which may have been regarded as being of greater use than an interdisciplinary book on sailing. From a purely aesthetic perspective, many readers will probably not feel inclined to bemoan the loss of all ancient handbooks on navigation, as they will have looked similar to the periploi, containing many imperatives, short main clauses in hypotaxis, and many numerals.     

Nagel on reduction

This paper attempts a critical reappraisal of Nagel's (1961, 1970) model of reduction taking into account both traditional criticisms and recent defenses. This model treats reduction as a type of explanation in which a reduced theory is explained by a reducing theory after their relevant representational items have been suitably connected. In accordance with the deductive-nomological model, the explanation is supposed to consist of a logical deduction. Nagel was a pluralist about both the logical form of the connections between the reduced and reducing theories (which could be conditionals or biconditionals) and their epistemological status (as analytic connections, conventions, or synthetic claims). This paper defends Nagel's pluralism on both counts and, in the process, argues that the multiple realizability objection to reductionism is misplaced. It also argues that the Nagel model correctly characterizes reduction as a type of explanation. However, it notes that logical deduction must be replaced by a broader class of inferential techniques that allow for different types of approximation. Whereas Nagel (1970), in contrast to his earlier position (1961), recognized the relevance of approximation, he did not realize its full import for the model. Throughout the paper two case studies are used to illustrate the arguments: the putative reduction of classical thermodynamics to the kinetic theory of matter and that of classical genetics to molecular biology.     

Maxwell's role in turning the concept of model into the methodology of modeling

This is a contribution towards a history and philosophy of modeling in its early stages in electromagnetism. In 1873, James Clerk Maxwell (1831–1879) hinted at the methodology of modeling at the end of his Treatise on Electricity and Magnetism. We focus on Maxwell's impact on physicists who immediately followed him, specifically Oliver Lodge (1851–1940) and George Francis FitzGerald (1851–1901). We begin with the role that the scientific concept of model played in the late nineteenth century, as assessed by Ludwig Boltzmann (1844–1906). We then discuss the role of hypothesis as a methodology, the appeal to (dynamical) illustration, and the way Maxwell applied model and working model in his studies of electromagnetism. We show that for Maxwell these key terms were kept distinct, but Lodge did not maintain these distinctions and, in this regard, FitzGerald followed Lodge. Notwithstanding Lodge's influence, Fitzgerald modified Maxwell's theory based on the mechanical model he designed, thereby implicitly taking the first step towards modeling. This methodology consists in drawing consequences from the (mechanical) model to the (electrodynamic) theory and modifying the latter in light of the functioning of the former. At the core of our argument is the thesis that it was a methodological novelty to move from the concept of model to the methodology of modeling. The introduction of modeling as a new methodology into physics in the late nineteenth century was a major event which deserves proper recognition.     

Kant's universal conception of natural history

Scholars often draw attention to the remarkably individual and progressive character of Kant's Universal Natural History and Theory of the Heavens (1755). What is less often noted, however, is that Kant's project builds on several transformations that occurred in natural science during the seventeenth and eighteenth centuries. Without contextualising Kant's argument within these transformations, the full sense of Kant's achievement remains unseen. This paper situates Kant's essay within the analogical form of Newtonianism developed by a diverse range of naturalists including Georges Buffon, Albrecht von Haller and Thomas Wright. It argues that Kant's universal conception of natural history can be viewed within the free-thinking and anti-clerical movement associated with Buffon. This does not mean, however, that it breaks from the methodological rules of Newtonianism. The claim of this paper is that Kant's essay contributes to the transformation of natural history from a logical system of classification to an explanation for the physical diversity of natural products according to laws.     

Integrating mechanistic explanations through epistemic perspectives

Talk of levels is ubiquitous in philosophy, especially in the context of mechanistic explanations spanning multiple levels. The mechanistic conception of levels, however, does not allow for the kind of integration needed to construct such multi-level mechanistic explanations integrating observations from different scientific domains. To address the issues arising in this context, I build on a certain perspectival aspect inherent in the mechanistic view. Rather than focusing on compositionally related levels of mechanisms, I suggest analyzing the situation in terms of epistemic perspectives researchers take when making scientific observations. Characterizing epistemic perspectives along five dimensions allows for a systematic analysis of the relations the scientific observations made from these different epistemic perspectives. This, in turn, provides a solid foundation for integrating the mechanistic explanations that are based on the scientific observations in question.