The meaning of πλασμαтιкό<Emphasis Type="Italic">ν</Emphasis> in Diophantus’ <Emphasis Type="Italic">Arithmetica</Emphasis>

Three problems in book I of Diophantus’ Arithmetica contain the adjective plasmatikon, that appears to qualify an implicit reference to some theorems in Elements, book II. The translation and meaning of the adjective sparked a long-lasting controversy that has become a nonnegligible aspect of the debate about the possibility of interpreting Diophantus’ approach and, more generally, Greek mathematics in algebraic terms. The correct interpretation of the word, a technical term in the Greek rhetorical tradition that perfectly fits the context in which it is inserted in the Arithmetica, entails that Diophantus’ text contained no (implicit) reference to Euclid’s Elements. The clause containing the adjective turns out to be a later interpolation, that cannot be used to support any algebraic interpretation of the Arithmetica.     

A new analytical framework for the understanding of Diophantus’s Arithmetica I–III

This study is the foundation of a new interpretation of the introduction and the three first books of Diophantus’s Arithmetica, one that opens the way to a historically correct contextualization of the work. Its purpose, as indicated in the title, is to renew the traditional discussion on the methods of problem-solving used by Diophantus, through the detailed exposition of a new analytical framework that aims to give an account of the coherence and progressive nature of the material included in the three first books of the Arithmetica. One outcome of this new ‘toolbox’ is a new conspectus of the problems and solutions contained in the latter, which is presented in appendix. The first part of the article clarifies, as a necessary preliminary, the key notions and terminology underlying our analysis. Among these new concepts is the notion of “method of invention,” which accounts in general for any way, by which “positions” (hypostaseis) are used in the Arithmetica. The next part proposes a complete inventory of the various methods of invention found in the three first books. Finally the last part presents the above mentioned conspectus and proposes a series of preliminary conclusions that can be drawn from it.     

Scientific realism bit by bit: part I. Kitcher on reference

In this paper, I consider Kitcher’s (1993) account of reference for the expressions of past science. Kitcher’s case study is of Joseph Priestley and his expression ‘dephlogisticated air’. There is a strong intuitive case that ‘dephlogisticated air’ referred to oxygen, but it was underpinned by very mistaken phlogiston theory, so concluding either that dephlogisticated air referred straightforwardly or that it failed to refer both have unpalatable consequences. Kitcher argues that the reference of such terms is best considered relative to each token—some tokens refer, and others do not. His account thus relies crucially on how this distinction between tokens can be made good—a puzzle I call the discrimination problem. I argue that the discrimination problem cannot be solved. On any reading of Kitcher’s defence of the distinction, the grounds provided are either insufficient or illegitimate. On the first reading, Kitcher violates the principle of humanity by making Priestley’s referential success a matter of the mental contents of modern speakers. The second reading sidesteps the problem of beliefs by appealing to mind-independent facts, but I argue that these are insufficient to achieve reference because of the indeterminacy introduced by the qua problem. On the third and final reading, Priestley’s success is given by what he would say in counterfactual circumstances. I argue that even if there are facts about what Priestley would say, and there is reason for doubt, there is no motivation to think that such facts determine how Priestley referred in the actual world.     

Putting the Indices into practice: censoring science in early modern Portugal

ABSTRACT

During the sixteenth and seventeenth centuries, the Inquisition was the institution most invested in the censorship of printed books in the Portuguese empire. Besides publishing the Indices of Forbidden Books, the Holy Office was also responsible for overseeing their implementation and ensuring their efficacy in preventing the importation, reading, and circulation of banned books. Overall, the sixteenth-century Indices condemned 785 authors and 1081 titles, including 52 authors and 85 titles of medicine, natural history, natural philosophy, astronomy, chronology, cosmography, astrology, and divinatory arts. By looking at the largest collection of early modern scientific books in Portugal, I will argue that a closer inspection of marginalia and ownership, and the establishment of a typology of expurgations is essential for the comprehension of the actual practices and the mechanisms of censorship. By examining the material evidence of censorship, in order to reconstruct expurgation practices, this paper reveals the processes and effectiveness of ecclesiastical control in the Portuguese Inquisition and highlights the differences between what inquisitors wrote in the Indices and what others put into practice.     

Primitive actimoterigian fishes can synthesize ascorbic acid

Amphibians and reptiles evolved with the capacity to synthesize ascorbic acid. Some higher vertebrates, like bats, guinea pigs, primates, and humans have lost the microsomal enzyme gulonolactone oxidase, and in cases of ascorbic acid deficiency suffer from symptoms of scurvy. The question of whether the capacity to synthesize ascorbate is also present in lower vertebrates could throw light on the evolution of this pathway. In order to find out whether ascorbic acid synthesis took place in two primitive Actinopterigian fish, the paddlefish (Polydon spathula) and the white sturgeon (Acipenser transmontanus) were fed with a scorbutogenic diet or diet(s) supplemented with a graded level of ascorbic acid. We found no growth depression nor external symptoms of scurvy, which would be pronounced in modern bony fishes (Teleostei) under similar conditions. The tissue level of ascorbate in both these primitive species indicated that vitamin C in intestine and liver is not depleted when fed a scorbutogenic diet. Gulonolactone oxidase activity was found in the kineys of the Actinopterigian fishes. Thus, I question the accepted evolutionary pathway for ascorbic acid biosynthesis in lower vertebrates and suggest that the modern bony fishes,Teleostei, lost their ability to express the gulonolactone oxidase genes after they had separated during the Silurian from their common ancestor with the coelacanths (Latimeria) and Dipnoi.     

Formation of buds in leaves ofAtropa belladonna L. in the in vitro culture

Zusammenfassung Blattmaterial vonAtropa belladonna vermag unter geeigneten Bedingungen ganze Pflanzen zu regenerieren. Ausgangspunkt der Knospenbildung ist das Pallisadenparenchym.

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Acknowledgements: I wish to thank the head of the Department of General Botany Prof.A. Szweykowska for the facilities and critical reading of this report.     

In vitro production of haploid plants from pollen grains ofAtropa belladonna L.

Zusammenfassung Pollen aus Antheren vonAtropa belladonna verschiedener Reifestadien können unter geeigneten in vitro Kulturbedingungen zu haploiden, diploiden oder triploiden Pflanzen heranwachsen.

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Acknowledgments. I wish to thank the head of the Departmente of General Botany Prof.A. Szweykowska for the facilities and critical reading of this report.     

Publishing and the classics: Paley’s Natural theology and the nineteenth-century scientific canon

This article seeks a new way to conceptualise the ‘classic’ work in the history of science, and suggests that the use of publishing history might help avoid the antagonism which surrounded the literary canon wars. It concentrates on the widely acknowledged concept that the key to the classic work is the fact of its being read over a prolonged period of time. Continued reading implies that a work is able to remain relevant to later generations of readers, and, although some of this depends upon the openness of the original text, much more depends on the actions of subsequent publishers and editors in repackaging the work for later audiences.This is illustrated through an examination of the long publishing history of William Paley’s Natural theology (1802). Over the course of the century, Natural theology was read as a work of gentlemanly natural theology, as a work which could be used in a formal or informal education in science, and as a work of Christian apologetic. These transformations occurred because of the actions of the later publishers and editors who had to make the work suit the current interests of the literary marketplace. Comparisons are made to Constitution of man, Vestiges of the natural history of creation and Origin of species.     

What We Can Learn from a Diagram: The Case of Aristarchus's On The Sizes and Distances of the Sun and Moon

By using the example of a single proposition and its diagrams, this paper makes explicit a number of the processes in effect in the textual transmission of works in the exact sciences of the ancient and medieval periods. By examining the diagrams of proposition 13 as they appear in the Greek, Arabic, and Latin traditions of Aristarchus's On the Sizes and Distances of the Sun and Moon, we can see a number of ways in which medieval, and early modern, scholars interpreted their sources in an effort to understand and transmit canonical ancient texts. This study highlights the need for modern scholars to take into consideration all aspects of the medieval transmission in our efforts to understand ancient practices.     

The genesis of a mediaeval historian: Pierre Duhem and the origins of statics

Contrary to what might be expected given a religious or other motivation, Pierre Duhem's interest in mediaeval science was the result of his surprise encounter with Jordanus de Nemore while working on Les origines de la statique in the late autumn of 1903. Historical assumptions common among physicists at that time may explain this surprise, which occasioned a frantic search for more mediaeval precursors for Renaissance mechanics. It also raised serious historiographical problems that threatened even his methodological views, until they were resolved in his To save the phenomena of 1908.     

Descartes’s changing mind

Descartes is always concerned about knowledge. However, the Galileo affair in 1633, the reactions to his Discourse on method, and later his need to reply to objections to his Meditations provoked crises in Descartes’s intellectual development the import of which has not been sufficiently recognized. These events are the major reasons why Descartes’s philosophical position concerning how we know and what we may know is radically different at the end of his life from what it was when he began. We call this later position Descartes’s epistemic stance and contrast it with his earlier methodological, metaphysical realism. Yet Descartes’s epistemic views cannot be separated from other aspects of his work, for example, his views concerning God, causality, metaphysics, and the nature of science. A further meta-implication is that serious errors await any scholar who cites early Cartesian texts in support of late Cartesian positions, or who uses later texts in conjunction with early ones to support a reading of Descartes’s philosophy.     

Euler's invention of integral transforms

Euler invented integral transforms in the context of second order differential equations. He used them in a fragment published in 1763 and in a chapter of Institutiones Calculi Integralis (1769). In introducing them he made use of earlier work in which a concept akin to the integral transform is implicit. It would, however, be reading too much into that earlier work to see it as contributing to the theory of the integral transform. Other work sometimes cited in this context in fact has different concerns.     

Ptolemy and the meta-helikôn

In his Harmonics, Ptolemy constructs a complex set of theoretically ‘correct’ forms of musical scale, represented as sequences of ratios, on the basis of mathematical principles and reasoning. But he insists that their credentials will not have been established until they have been submitted to the judgement of the ear. They cannot be audibly instantiated with the necessary accuracy without the help of specially designed instruments, which Ptolemy describes in detail, discussing the uses to which each can be put and cataloguing its limitations. The best known of these instruments is the monochord, but there are several more complex devices. This paper discusses one such instrument which is known from no other source, ancient or modern, whose design was prompted by the geometrical construction known as the helikôn. It has several remarkable peculiarities. I examine its design, its purposes, and the merits and shortcomings which Ptolemy attributes to it. An appendix describes an instrument I have built to Ptolemy’s specifications (possibly the first of its kind since the second century bc), in an attempt to find out how satisfactorily such a bizarre contraption will work; and it explains how various practical problems can be resolved.     

Hippocrates’ complaint and the scientific ethos in early modern England

Among the elements of the modern scientific ethos, as identified by R.K. Merton and others, is the commitment of individual effort to a long-term inquiry that may not bring substantial results in a lifetime. The challenge this presents was encapsulated in the aphorism of the ancient Greek physician, Hippocrates of Kos: vita brevis, ars longa (life is short, art is long). This article explores how this complaint was answered in the early modern period by Francis Bacon’s call for the inauguration of the sciences over several generations, thereby imagining a succession of lives added together over time. However, Bacon also explored another response to Hippocrates: the devotion of a ‘whole life’, whether brief or long, to science. The endorsement of long-term inquiry in combination with intensive lifetime involvement was embraced by some leading Fellows of the Royal Society, such as Robert Boyle and Robert Hooke. The problem for individuals, however, was to find satisfaction in science despite concerns, in some fields, that current observations and experiments would not yield material able to be extended by future investigations.     

Theophrastus on Lyngurium: Medieval and Early Modern Lore from the Classical Lapidary Tradition

The ancient philosopher Theophrastus (c. 371-285 BC) described a gemstone called lyngurium, purported to be solidified lynx urine, in his work De lapidibus ('On Stones'). Knowledge of the stone passed from him to other classical authors and into the medieval lapidary tradition, but there it was almost always linked to the 'learned master Theophrastus'. Although no physical example of the stone appears to have been seen or touched in ancient, medieval, or early modern times, its physical and medicinal properties were continually reiterated and elaborated as if it did 'exist'. By the seventeenth century, it began to disappear from lapidaries, but with no attempt to explain previous authors' errors since it had never 'existed' anyway. In tracing the career of lyngurium, this study sheds some light on the transmission of knowledge from the classical world to the Renaissance and the changing criteria by which such knowledge was judged.     

The five problems of irreversibility

Thermodynamics has a clear arrow of time, characterized by the irreversible approach to equilibrium. This stands in contrast to the laws of microscopic theories, which are invariant under time-reversal. Foundational discussions of this “problem of irreversibility” often focus on historical considerations, and do therefore not take results of modern physical research on this topic into account. In this article, I will close this gap by studying the implications of dynamical density functional theory (DDFT), a central method of modern nonequilibrium statistical mechanics not previously considered in philosophy of physics, for this debate. For this purpose, the philosophical discussion of irreversibility is structured into five problems, concerned with the source of irreversibility in thermodynamics, the definition of equilibrium and entropy, the justification of coarse-graining, the approach to equilibrium and the arrow of time. For each of these problems, it is shown that DDFT provides novel insights that are of importance for both physicists and philosophers of physics.     

“Will someone say exactly what the H-theorem proves?” A study of Burbury's Condition A and Maxwell's Proposition II

Summary Many historians of science recognize that the outcome of the celebrated debate on Boltzmann's H-Theorem, which took place in the weekly scientific journal Nature, beginning at the end of 1894 and continuing throughout most of 1895, was the recognition of the statistical hypothesis in the proof of the theorem. This hypothesis is the Stosszahlansatz or hypothesis about the number of collisions. During the debate, the Stosszahlansatz was identified with another statistical hypothesis, which appeared in Proposition II of Maxwell's 1860 paper; Burbury called it Condition A. Later in the debate, Bryan gave a clear formulation of the Stosszahlansatz. However, the two hypotheses are prima facie different. Burbury interchanged them without justification or even warning his readers. This point deserves clarification, since it touches upon subtle questions related to the foundation of the theory of heat. A careful reading of the arguments presented by Burbury and Bryan in their various invocations of both hypotheses can clarify this technical point. The Stosszahlansatz can be understood in terms of geometrical invariances of the problem of a collision between two spheres. A byproduct of my analysis is a clarification of the debate itself, which is apparently obscure.     

Reconsidering the Fresnel–Maxwell theory shift: how the realist can have her cake and EAT it too

This paper takes another look at a case study which has featured prominently in a variety of arguments for rival realist positions. After critically reviewing the previous commentaries of the theory shift that took place in the transition from Fresnel’s ether to Maxwell’s electromagnetic theory of optics, it will defend a slightly different reading of this historical case study. Central to this task is the notion of explanatory approximate truth, a concept which must be carefully analysed to begin with. With this notion properly understood, it will be finally argued, the popular Fresnel–Maxwell case study points towards a novel formulation of scientific realism.