For the Glory of Athens: Xenophon’s Hipparchikos <Logos>, a technical treatise and instruction manual on ideal leadership

Xenophon’s Peri hippikes <technees>, “On Horsemanship,” and the Hipparchikos <logos>, “the Cavalry Commander”, writings which can be regarded as technical works with a didactic purpose, are almost unknown. Xenophon was interested in problems of leadership and the exercise of power (For the titles of the both writings and the analogous supplementary terms “technees” and “logos” compare Breitenbach, 1966, 1761. Angled brackets are used by modern editors of ancient texts as text-critical signs and are inserted here because “peri hippikes” and “hipparchikos” are adjectives and cannot stand alone; “technees” and “logos” are supplied as absent, but implied, substantives. The conventional signs “<>” clarify this supplementary act for the modern reader.). The “Cavalry Commander” (ca. 365 B.C.) intended for the instruction of potential hipparchs (calvary commanders) is simultaneously political and didactic and technical; in this text, categories of leadership that had been developed in earlier works are combined in a powerful manner. Xenophon constructed “leaders” as exempla (“examples”) of correct behaviour; military and political theory are synthesised. The Hipparchikos logos, as a didactic work, aims to produce specialists who master their techné (“art” or “skill”), to develop their ideal qualities. Both texts are directed at an Athenian society, in which the cavalry had lost their significance and pride as a result of recent political turbulence. Xenophon hoped to reform the cavalry for the benefit of Athens. The basic question of the didactic work is: how can I become the best hipparch, how can I go beyond simply filling the office, and instead develop it for the well-being of the polis and thus serve the city? The art of leadership consists in dealing with subordinates in such a manner that they obey and follow voluntarily—still an innovative and modern approach today.     

Why be regular? Part II

We provide a novel perspective on “regularity” as a property of representations of the Weyl algebra. In Part I, we critiqued a proposal by Halvorson [2004, “Complementarity of representations in quantum mechanics”, Studies in History and Philosophy of Modern Physics 35 (1), pp. 45–56], who advocates for the use of the non-regular “position” and “momentum” representations of the Weyl algebra. Halvorson argues that the existence of these non-regular representations demonstrates that a quantum mechanical particle can have definite values for position or momentum, contrary to a widespread view. In this sequel, we propose a justification for focusing on regular representations, pace Halvorson, by drawing on algebraic methods.     

Scrutinizing thing knowledge

In his book Thing Knowledge Davis Baird argues that our accustomed understanding of knowledge as justified true beliefs is not enough to understand progress in science and technology. To be more accurate he argues that scientific instruments are to be seen as a form of “objective knowledge” in the sense of Karl Popper.I want to examine if this idea is plausible. In a first step I want to show that this proposal implies that nearly all man-made artifacts are materialized objective knowledge. I argue that this radical change in our concept of knowledge demands strong reasons and that Baird does not give them. I take a look at the strongest strand of arguments of Baird's book—the arguments from cognitive autonomy—and conclude that they do not suffice to make Baird's view of scientific instruments tenable.     

Why Be regular?, part I

We provide a novel perspective on “regularity” as a property of representations of the Weyl algebra. We first critique a proposal by Halvorson [2004, “Complementarity of representations in quantum mechanics”, Studies in History and Philosophy of Modern Physics 35 (1), pp. 45–56], who argues that the non-regular “position” and “momentum” representations of the Weyl algebra demonstrate that a quantum mechanical particle can have definite values for position or momentum, contrary to a widespread view. We show that there are obstacles to such an intepretation of non-regular representations. In Part II, we propose a justification for focusing on regular representations, pace Halvorson, by drawing on algebraic methods.     

The goal of explanation

I defend the claim that understanding is the goal of explanation against various persistent criticisms, especially the criticism that understanding is not truth-connected in the appropriate way, and hence is a merely psychological (rather than epistemic) state. Part of the reason why understanding has been dismissed as the goal of explanation, I suggest, is because the psychological dimension of the goal of explanation has itself been almost entirely neglected. In turn, the psychological dimension of understanding—the Aha! experience, the sense that a certain explanation “feels right”, and so on—has been conspicuously overemphasized. I try to correct for both of these exaggerations. Just as the goal of explanation includes a richer psychological—including phenomenological—dimension than is generally acknowledged, so too understanding has a stronger truth connection than is generally acknowledged.     

Theories of Newtonian gravity and empirical indistinguishability

In this essay, I examine the curved spacetime formulation of Newtonian gravity known as Newton–Cartan gravity and compare it with flat spacetime formulations. Two versions of Newton–Cartan gravity can be identified in the physics literature—a “weak” version and a “strong” version. The strong version has a constrained Hamiltonian formulation and consequently a well-defined gauge structure, whereas the weak version does not (with some qualifications). Moreover, the strong version is best compared with the structure of what Earman (World enough and spacetime. Cambridge: MIT Press) has dubbed Maxwellian spacetime. This suggests that there are also two versions of Newtonian gravity in flat spacetime—a “weak” version in Maxwellian spacetime, and a “strong” version in Neo-Newtonian spacetime. I conclude by indicating how these alternative formulations of Newtonian gravity impact the notion of empirical indistinguishability and the debate over scientific realism.     

Pluto and the platypus: An odd ball and an odd duck - On classificatory norms

Many astronomers seem to believe that we have discovered that Pluto is not a planet. I contest this assessment. Recent discoveries of trans-Neptunian Pluto-sized objects do not militate for Pluto's expulsion from the planets unless we have prior reason for not simply counting these newly-discovered objects among the planets. I argue that this classificatory controversy — which I compare to the controversy about the classification of the platypus — illustrates how our classificatory practices are laden with normative commitments of a distinctive kind. I conclude with a discussion of the relevance of such “norm-ladenness” to other controversies in the metaphysics of classification, such as the monism/pluralism debate.     

Proposition II (Book I) of Newton’s <Emphasis Type="Italic">Principia</Emphasis>

After preparing the way with comments on evanescent quantities and then Newton’s interpretation of his second law, this study of Proposition II (Book I)— Proposition II Every body that moves in some curved line described in a plane and, by a radius drawn to a point, either unmoving or moving uniformly forward with a rectilinear motion, describes areas around that point proportional to the times, is urged by a centripetal force tending toward that same point. —asks and answers the following questions: When does a version of Proposition II first appear in Newton’s work? What revisions bring that initial version to the final form in the 1726 Principia? What, exactly, does this proposition assert? In particular, what does Newton mean by the motion of a body “urged by a centripetal force”? Does it assert a true mathematical claim? If not, what revision makes it true? Does the demonstration of Proposition II persuade? Is it as convincing, for example, as the most convincing arguments of the Principia? If not, what revisions would make the demonstration more persuasive? What is the importance of Proposition II, to the physics of Book III and the mathematics of Book I?     

(Mis)Understanding scientific disagreement: Success versus pursuit-worthiness in theory choice

Scientists often diverge widely when choosing between research programs. This can seem to be rooted in disagreements about which of several theories, competing to address shared questions or phenomena, is currently the most epistemically or explanatorily valuable—i.e. most successful. But many such cases are actually more directly rooted in differing judgments of pursuit-worthiness, concerning which theory will be best down the line, or which addresses the most significant data or questions. Using case studies from 16^th-century astronomy and 20^th-century geology and biology, I argue that divergent theory choice is thus often driven by considerations of scientific process, even where direct epistemic or explanatory evaluation of its final products appears more relevant. Broadly following Kuhn's analysis of theoretical virtues, I suggest that widely shared criteria for pursuit-worthiness function as imprecise, mutually-conflicting values. However, even Kuhn and others sensitive to pragmatic dimensions of theory ‘acceptance’, including the virtue of fruitfulness, still commonly understate the role of pursuit-worthiness—especially by exaggerating the impact of more present-oriented virtues, or failing to stress how ‘competing’ theories excel at addressing different questions or data. This framework clarifies the nature of the choice and competition involved in theory choice, and the role of alternative theoretical virtues.     

Seepage,objectivity, and climate science

Based on the disproportionate amount of attention paid by climate scientists to the supposed global warming hiatus, it has recently been argued that contrarian discourse has “seeped into” climate science. While I agree that seepage has occurred, its effects remain unclear. This lack of clarity may give the impression that climate science has been compromised in a way that it hasn't—such a conclusion should be defended against. To do this I argue that the effects of seepage should be analyzed in terms of objectivity. I use seven meanings of objectivity to analyze contrarian discourse's impact on climate science. The resulting account supports the important point that climate science has not been compromised in a way that invalidates the conclusions its scientists have drawn, despite the reality of seepage having occurred.     

Klein-Weyl's program and the ontology of gauge and quantum systems

We distinguish two orientations in Weyl's analysis of the fundamental role played by the notion of symmetry in physics, namely an orientation inspired by Klein's Erlangen program and a phenomenological-transcendental orientation. By privileging the former to the detriment of the latter, we sketch a group(oid)-theoretical program—that we call the Klein-Weyl program—for the interpretation of both gauge theories and quantum mechanics in a single conceptual framework. This program is based on Weyl's notion of a “structure-endowed entity” equipped with a “group of automorphisms”. First, we analyze what Weyl calls the “problem of relativity” in the frameworks provided by special relativity, general relativity, and Yang-Mills theories. We argue that both general relativity and Yang-Mills theories can be understood in terms of a localization of Klein's Erlangen program: while the latter describes the group-theoretical automorphisms of a single structure (such as homogenous geometries), local gauge symmetries and the corresponding gauge fields (Ehresmann connections) can be naturally understood in terms of the groupoid-theoretical isomorphisms in a family of identical structures. Second, we argue that quantum mechanics can be understood in terms of a linearization of Klein's Erlangen program. This stance leads us to an interpretation of the fact that quantum numbers are “indices characterizing representations of groups” ((Weyl, 1931a), p.xxi) in terms of a correspondence between the ontological categories of identity and determinateness.     

Rehabilitating the regulative use of reason: Kant on empirical and chemical laws

In his Kritik der reinen Vernunft, Kant asserts that laws of nature “carry with them an expression of necessity” (A159/B198). There is, however, widespread interpretive disagreement regarding the nature and source of the necessity of empirical laws of natural sciences in Kant's system. It is especially unclear how chemistry—a science without a clear, straightforward connection to the a priori principles of the understanding—could contain such genuine, empirical laws. Existing accounts of the necessity of causal laws unfortunately fail to illuminate the possibility of non-physical laws. In this paper, I develop an alternative, ‘ideational’ account of natural laws, according to which ideas of reason necessitate the laws of some non-physical sciences. Chemical laws, for instance, are grounded on ideas of the elements, and the chemist aims to reduce her phenomena to these elements via experimentation. Although such ideas are beyond the possibility of experience, their postulation is necessary for the achievement of reason's theoretical ends: the unification and explanation of the cognitions of science.     

Novelty,coherence, and Mendeleev’s periodic table

Predictivism is the view that successful predictions of “novel” evidence carry more confirmational weight than accommodations of already known evidence. Novelty, in this context, has traditionally been conceived of as temporal novelty. However temporal predictivism has been criticized for lacking a rationale: why should the time order of theory and evidence matter? Instead, it has been proposed, novelty should be construed in terms of use-novelty, according to which evidence is novel if it was not used in the construction of a theory. Only if evidence is use-novel can it fully support the theory entailing it. As I point out in this paper, the writings of the most influential proponent of use-novelty contain a weaker and a stronger version of use-novelty. However both versions, I argue, are problematic. With regard to the appraisal of Mendeleev’ periodic table, the most contentious historical case in the predictivism debate, I argue that temporal predictivism is indeed supported, although in ways not previously appreciated. On the basis of this case, I argue for a form of so-called symptomatic predictivism according to which temporally novel predictions carry more confirmational weight only insofar as they reveal the theory’s presumed coherence of facts as real.     

On the time reversal invariance of classical electromagnetic theory

David Albert claims that classical electromagnetic theory is not time reversal invariant. He acknowledges that all physics books say that it is, but claims they are “simply wrong” because they rely on an incorrect account of how the time reversal operator acts on magnetic fields. On that account, electric fields are left intact by the operator, but magnetic fields are inverted. Albert sees no reason for the asymmetric treatment, and insists that neither field should be inverted. I argue, to the contrary, that the inversion of magnetic fields makes good sense and is, in fact, forced by elementary geometric considerations. I also suggest a way of thinking about the time reversal invariance of classical electromagnetic theory—one that makes use of the invariant four-dimensional formulation of the theory—that makes no reference to magnetic fields at all. It is my hope that it will be of interest in its own right, Albert aside. It has the advantage that it allows for arbitrary curvature in the background spacetime structure, and is therefore suitable for the framework of general relativity. The only assumption one needs is temporal orientability.     

The relative facts interpretation and Everett's note added in proof

In the published version of Hugh Everett III's doctoral dissertation, he inserted what has become a famous footnote, the “note added in proof”. This footnote is often the strongest evidence given for any of various interpretations of Everett (the many worlds, many minds, many histories and many threads interpretations). In this paper I will propose a new interpretation of the footnote. One that is supported by evidence found in letters written to and by Everett; one that is suggested by a new interpretation of Everett, an interpretation that takes seriously the central position of relative states in Everett's pure wave mechanics: the relative facts interpretation. Of central interest in this paper is how to make sense of Everett's claim in the “note added in proof” that “all elements of a superposition (all “branches”) are “actual,” none any more “real” than the rest.”     

Reichenbach on causality in 1923: Scientific inference,coordination, and confirmation

In The Theory of Relativity and A Priori Knowledge (1920b), Reichenbach developed an original account of cognition as coordination of formal structures to empirical ones. One of the most salient features of this account is that it is explicitly not a top-down type of coordination, and in fact it is crucially “directed” by the empirical side. Reichenbach called this feature “the mutuality of coordination” but, in that work, did not elaborate sufficiently on how this is supposed to work. In a paper that he wrote less than two years afterwards (but that he published only in 1932), “The Principle of Causality and the Possibility of its Empirical Confirmation” (1923/1932), he described what seems to be a model for this idea, now within an analysis of causality that results in an account of scientific inference. Recent reassessments of his early proposal do not seem to capture the extent of Reichenbach's original worries. The present paper analyses Reichenbach's early account and suggests a new way to look at his early work. According to it, we perform measurements, individuate parameters, collect and analyse data, by using a “constructive” approach, such as the one with which we formulate and test hypotheses, which paradigmatically requires some simplicity assumptions. Reichenbach's attempt to account for all these aspects in 1923 was obviously limited and naive in many ways, but it shows that, in his view, there were multiple ways in which the idea of “constitution” is embodied in scientific practice.     

Norton's material theory of analogy

In his book, The Material Theory of Induction, Norton argues that the quest for a universal formal theory or ‘schema’ for analogical inference should be abandoned. In its place, he offers the “material theory of analogy”: each analogical inference is “powered” by a local fact of analogy rather than by any formal schema. His minimalist model promises a straightforward, fact-based approach to the evaluation and justification of analogical inferences. This paper argues that although the rejection of universal schemas is justified, Norton's positive theory is limited in scope: it works well only for a restricted class of analogical inferences. Both facts and quasi-formal criteria have roles to play in a theory of analogical reasoning.     

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).