This paper analyses the relationship between Hobbes's theory of language and his theory of science and method. It is shown that Hobbes, at least in his Computatio sive Logica (1655), deviates in some measure from the traditional (Aristotelian) model of language. In this model speech is considered to be a fairly unproblematic expression of thought, which itself is independent of language. Basing himself on a nominalist account of universals, Hobbes states that the demonstration or assertion of universal propositions presupposes speech (...) (more especially, the use of names as marks). This insight turns out to be essential for Hobbes's (rationalist) view of scientific method. (shrink)

In this article, we will first give a historic overview of the concept of benefit sharing and its appearance in official agreements, particularly with respect to crop genetic resources. It will become clear that, at present, benefit sharing is primarily considered as an instrument of compensation or exchange, and thus refers to commutative justice. However, we believe that such a narrow interpretation of benefit sharing disregards, and even undermines, much of its (historical) content and potency, especially where crop genetic resources (...) are concerned. We argue that benefit sharing should not be based merely on commutative justice but rather on a broader model that is also grounded in the concept of distributive justice. This has repercussions for the application of benefit sharing, which we try to clarify by distinguishing between downstream and upstream benefit sharing. Upstream benefit sharing is not so much inspired by compensation for actions done, or the distribution downstream of benefits developed, but by the idea of shared decision‐making on the research and development of resources fundamental to human welfare. Going upstream in the research process of crop genetic resources, and determining research agendas and improving crops according to the needs of the poor, benefit sharing may well be a tool to contribute to world food security and global justice. We concretize our ideas on upstream benefit sharing by introducing a set of criteria that determine the success of consultations on agricultural research agenda setting. (shrink)

In angiosperms cytoplasmic DNA is typically passed on maternally through ovules. Genes in the mtDNA may cause male sterility. When male-sterile (female) cytotypes produce more seeds than cosexuals, they pass on more copies of their mtDNA and will co-occur with cosexuals with a neutral cytotype. Cytoplasmic gynodioecy is a well-known phenomenon in angiosperms, both in wild and crop plants. In some conifer families (e.g. Pinaceae) mitochondria are also maternally inherited. However in some other families (e.g. Taxaceae and Cupressaceae) mtDNA is (...) paternally inherited through the pollen. With paternal mtDNA inheritance, male cytotypes that produce more pollen than cosexuals are expected to co-occur with cosexuals. This is uncharted territory. An ESS model shows that the presence of male cytotypes selects for more female allocation in the cosexual, i.e. for sexual specialisation. An allele that switches sex from male to female can then invade. This leads to rapid loss of the neutral cytotype of the cosexual, fixation of the male cytotype and dioecy with 50% males and 50% females. The models suggest that paternal inheritance of mtDNA facilitates the evolution dioecy. Consistent with this hypothesis the Pinaceae are 100% monoecious, while dioecy is common in the Taxaceae family and in the genus Juniperus (Cupressaceae). However, no reliable data are yet available on both mode of inheritance of mtDNA and gender variation of the same species. When cosexuals benefit from reproductive assurance (high selfing rate, low inbreeding depression, low fertilisation) they maintain themselves next to males and females. This predicted pattern with three sex types present in the same population is observed in conifers in nature. (shrink)

This study argues that contemporary theology needs a reconceptualised form of metaphysical theology to readdress this question of universality. In order to develop such a new metaphysical theology, de Jong turns to the work of Karl Rahner and Edward Schillebeeckx. Presenting a new perspective on their theological methods, he demonstrates that these theologians employ a dialectical interplay of hermeneutical and metaphysical arguments yielding a modest theological metaphysics. Crucially, these thinkers recognise that acknowledging hermeneutical conditions does not need to end (...) in particularism. Instead, Rahner and Schillebeeckx argue that the infinite variety of particular human experiences can act as potential encounters with the universally self-revealing God. Retrieving these modest forms of theological metaphysics reminds contemporary theology that it is possible to think about universality from within particularity. Balancing the intelligible and mysterious nature of God, Rahner and Schillebeeckx show how a modest theological metaphysics contains its own self-critical hermeneutical disciplining. This renewed understanding about the earlier use of metaphysics opens up new avenues of thought for fundamental theologians that do not want to shy away from the difficult question of the universality of God. (shrink)

Automated technologies and robots make decisions that cannot always be fully controlled or predicted. In addition to that, they cannot respond to punishment and blame in the ways humans do. Therefore, when automated cars harm or kill people, for example, this gives rise to concerns about responsibility-gaps and retribution-gaps. According to Sven Nyholm, however, automated cars do not pose a challenge on human responsibility, as long as humans can control them and update them. He argues that the agency exercised in (...) automated cars should be understood in terms of human–robot collaborations. This brief note focuses on the problem that arises when there are multiple people involved, but there is no obvious shared collaboration among them. Building on John Danaher’s discussion of command responsibility, it is argued that, although Nyholm might be right that autonomous cars cannot be regarded as acting on their own, independently of any human beings, worries about responsibility-gaps and retribution-gaps are still justified, because it often remains unclear how to allocate or distribute responsibility satisfactorily among the key humans involved after they have been successfully identified. (shrink)

Throughout more than two millennia philosophers adhered massively to ideal standards of scientific rationality going back ultimately to Aristotle’s Analytica posteriora . These standards got progressively shaped by and adapted to new scientific needs and tendencies. Nevertheless, a core of conditions capturing the fundamentals of what a proper science should look like remained remarkably constant all along. Call this cluster of conditions the Classical Model of Science . In this paper we will do two things. First of all, we will (...) propose a general and systematized account of the Classical Model of Science. Secondly, we will offer an analysis of the philosophical significance of this model at different historical junctures by giving an overview of the connections it has had with a number of important topics. The latter include the analytic-synthetic distinction, the axiomatic method, the hierarchical order of sciences and the status of logic as a science. Our claim is that particularly fruitful insights are gained by seeing themes such as these against the background of the Classical Model of Science. In an appendix we deal with the historiographical background of this model by considering the systematizations of Aristotle’s theory of science offered by Heinrich Scholz, and in his footsteps by Evert W. Beth. (shrink)

Prenatal screening for foetal abnormalities such as Down's syndrome differs from other forms of population screening in that the usual aim of achieving health gains through treatment or prevention does not seem to apply. This type of screening leads to no other options but the choice between continuing or terminating the pregnancy and can only be morally justified if its aim is to provide meaningful options for reproductive choice to pregnant women and their partners. However, this aim should not be (...) understood as maximizing reproductive choice per se. Only if understood as allowing prospective parents to avoid suffering related to living with (a child with) serious disorders and handicaps can prenatal screening be a publicly or collectively funded programme. The alternative of moving prenatal testing outside the healthcare system into the private sector is problematic, as it makes these tests accessible only to those who can afford to pay for it. New developments in prenatal screening will have to be assessed in terms of whether and to what extent they either contribute to or undermine the stated aim of providing meaningful options for reproductive choice. In the light of this criterion, this article discusses the introduction of the new non‐invasive prenatal test (NIPT), the tendency to widen the scope of follow‐up testing, as well as the possible future scenarios of genome‐wide screening and ‘prenatal personalised medicine’. The article ends with recommendations for further debate, research and analysis. (shrink)

In this series of papers, I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Paper I (de Jong in Arch Hist Exact Sci 73:1–37, 2019) was devoted to a study of system A theory of the outer planets. In this second paper, I will study system A theory of the planet Venus. All presently known ephemerides of Venus appear to have been written after 200 BC so that (...) the development of system A theory of Venus may have been a late development. On the other hand, there are several earlier texts in which the motion of Venus, going from one synodic phenomenon to the next one, is parametrized in quite some detail. At least six computational systems of Venus are known of which only two, systems A0 and A3, are genuine type-A systems. Both are based on the hypothesis that in exactly 1151 years Venus experiences 720 synodic phenomena of the same kind and that after this period of 1151 years Venus returns to exactly the same position in the sky. This period relation was probably derived from the observational fact that after 8 years Venus returns to a position in the zodiac that falls on average 2.5° short of its previous position. The study of the Babylonian planetary theory of Venus presented here will be primarily based on the system A3 theory of Venus because it is the most complete of the two systems. The parameters of the four step functions characterizing the system A3 model of the first and last appearances of Venus are known from previous studies of tablet BM 32599 (ACT 1050). Based on a database of synthetic observations of the first and last appearances (morning first, morning last, evening first and evening last) and the two stationary points (morning station and evening station) of Venus between 315 BC and 50 BC, I first discuss the observational material from the point of view of a Babylonian astronomer. This involves deriving synodic time intervals and synodic arcs from the observed dates and longitudes of Venus. Both vary with the position of Venus in the zodiac. This variation shows up most purely in the synodic arcs and synodic time intervals of Venus at its stations. The variation pattern of the synodic arcs and of the synodic time intervals at the first and last appearances of Venus differ considerably because they are strongly affected by atmospheric extinction and by the ecliptic latitude of Venus. A comparison of predictions of the first and last appearances of Venus computed according to system A3 with observations in the synthetic database shows that the models provide fairly accurate fits to the observations of evening last and morning first with typical standard deviations of about 2° but rather poor fits to the observations of morning last and evening first with typical standard deviations of about 7° and 4°. Quite surprisingly, it turns out that the morning first A3 model fits the observed longitudes of Venus at its stations almost perfectly, with standard deviations of about 1°. This suggests that observations of the stations of Venus must have been available to the Babylonian astronomer(s) who constructed the system A3 model of Venus and who computed the longitudes of Venus at its first and last appearances preserved in tablet BM 32599. This is quite puzzling because observations of the stations of Venus were definitely not part of the standard observing program of the Babylonian astronomers as we know it from the Astronomical Diaries. To resolve this problem, I propose that observations could have been made by some individual astronomer for his own use but that these observations never became part of the tradition of what was regularly observed and recorded in the Astronomical Diaries. It turns out that 25 years of observations of Venus (here illustrated for the years 203 BC to 178 BC) is sufficient for the construction of a system A model that perfectly fits the variation of the synodic arcs of Venus at its stations. By combining observed time intervals and known velocities of Venus, observations over this limited timespan can also be used to construct longitudes of Venus at its first and last appearances from previous known positions of Venus based on Normal Stars passages or from known positions at its stations. This is the only way in which positions of Venus at its first and last appearances can be determined because at its first and last appearances the sky is too bright for Normal Stars to be visible. I propose that the Babylonian system A3 models of Venus were based on longitudes constructed in this way. I finally suggest that the tablet, of which BM 32599 is the remainder, was filled line by line starting with a set of initial values in the bottom left-hand corner of the tablet and that the choice of these initial values was based on an observation of Venus at its evening station when it was exceptionally close to the Normal Star η Piscium in February 179 BC. Based on this choice of initial conditions, the tablet covers the years 403 BC to 170 BC and it may have been composed around 170 BC. It was probably computed with the purpose of creating a raster of longitudes with mazes of about 2.5° that could be used to predict future positions of Venus at its first or last appearance once a position at a previous first or last appearance was available. (shrink)

Countries, companies and farming communities are increasingly involved in issues of sharing and protecting plant genetic resources, (traditional) knowledge and technologies. Intellectual Property Rights and Access and Benefit-Sharing policies currently regulate the transfer and usage of much of this genetic material, information and related production, which is employed in multiple research projects involving public research institutes. Strikingly, not much is known about how these institutes deal with the transfer and usage regulations. And what, furthermore, are their responsibilities while serving a (...) civil society in which there is such a range of diverging interests in and opinions about such regulations? In order to shed more light on these questions, two public research institutes will here be studied, the International Potato Centre in Peru and Wageningen University & Research Centre in the Netherlands. These institutes are both heavily involved in research into genetic resources, knowledge and technologies related to the potato, and work together with a wide spectrum of stakeholders that have a direct interest in the sharing and/or protection of these resources. The two institutes are continuously weighing up the various stakeholder interests in their attempts to strike a balance between policies geared towards sharing and those aimed at protection. It will be argued that public research institutes must dare to share, and that they need to develop new ways of sharing and protecting in order to adhere to their mission and best serve the public interest. (shrink)

The Movement of Showing investigates the idea, shared by Derrida, Hegel and Heidegger, that the value of their thought is not found in its results or conclusions, but in its "movement." All three describe the heart of their work in terms of a pathway, development, or movement rather than in terms of its propositions or conclusions. This seems to deprive their thought of a solid ground, and indeed deconstruction in particular is often criticized in this way. Johan de Jong (...) argues that this is a structural vulnerability that is both its weakness and the source of its value, tracing Derrida's indirect method from his early to later works, and considering his engagements with Hegel and Heidegger. His analysis locates an affinity among Hegel, Heidegger and Derrida in a shared distrust of externality and, against the grain of some Levinasian commentaries, argues that Derrida's indirectness results in an ethics of complicity. The Movement of Showing answers a central question that many polemics about continental philosophy and postmodernism revolve around concerning how, methodologically, one can philosophize responsibly. It shows the difference between critique and polemics, and why simply taking up a position for or against is insufficient in order to think responsibly. (shrink)

Several studies have focused on the effects of corporate social responsibility fit on external stakeholders’ evaluations of CSR activities, attitudes towards companies or brands, and behaviors. The results so far have been contradictory. A possible reason may be that the concept of CSR fit is more complicated than previously assumed. Researchers suggest that there may be different types of CSR fit, but so far no empirical research has focused on a typology of CSR fit. This study fills this gap, describing (...) a qualitative content analysis of the congruence between six organizations and their various CSR activities. Ten annual reports and CSR reports were analyzed, and 102 specific CSR activities were identified. The results show that two levels of fit must be distinguished: based on the means for and the intended ends of the CSR activity. Furthermore, six different types of fit were found, focusing on products and services, production processes, environmental impact, employees, suppliers, and geographical location. Considering the above variety of fit possibilities, the findings emphasize the role of CSR communication as a means of creating fit perceptions. (shrink)

This paper concentrates on some aspects of the history of the analytic-synthetic distinction from Kant to Bolzano and Frege. This history evinces considerable continuity but also some important discontinuities. The analytic-synthetic distinction has to be seen in the first place in relation to a science, i.e. an ordered system of cognition. Looking especially to the place and role of logic it will be argued that Kant, Bolzano and Frege each developed the analytic-synthetic distinction within the same conception of scientific rationality, (...) that is, within the Classical Model of Science: scientific knowledge as cognitio ex principiis . But as we will see, the way the distinction between analytic and synthetic judgments or propositions functions within this model turns out to differ considerably between them. (shrink)

In this study I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Although no texts are preserved in which the Babylonians tell us how they did it, from the surviving Astronomical Diaries we have a fairly complete picture of the nature of the observational material on which the scholars must have based their theory and from which they must have derived the values of the defining parameters. Limiting the (...) discussion to system A theory of the outer planets Saturn, Jupiter and Mars, I will argue that the development of Babylonian planetary theory was a gradual process of more than a century, starting sometime in the fifth century BC and finally resulting in the appearance of the first full-fledged astronomical ephemeris around 300 BC. The process of theory formation involved the derivation of long “exact” periods by linear combination of “Goal–Year” periods, the invention of a 360° zodiac, the discovery of the variable motion of the planets and the development of the numerical method to model this as a step function. Longitudes of the planets in the Babylonian zodiac could be determined by the scholars with an accuracy of 1° to 2° from observations of angular distances to Normal Stars with known positions. However, since the sky is too bright at first and last appearances of the planets and at acronychal rising for nearby stars to be visible, accurate longitudes as input for theoretical work could only be determined when the planets were near the stationary points in their orbits. In this study I show that the Babylonian scholars indeed based their system A modeling of the outer planets on planetary longitudes near stations, that their system A models of Saturn and Jupiter provided satisfactory results for all synodic phenomena, that they realized that their system A model of Mars did not produce satisfactory results for the second station so that separate numerical schemes were constructed to predict the positions of Mars at second station from the model at first station, and finally that their system A model for Mars provided quite poor predictions of the longitude of Mars at first and last appearances over large stretches of the zodiac. I further discuss ways in which the parameters of the system A models may have been derived from observations of the outer planets. By analyzing contemporaneous ephemerides from Uruk of four synodic phenomena of Jupiter from the second century BC, I finally illustrate how the Babylonian scholars may have used observations of Normal Star passages of planets to choose the initial conditions for their ephemerides. (shrink)

Paternalism has attracted new defenders in recent years. Such defenders typically either downplay the normative significance of autonomy or deny that we are sufficiently rational for paternalistic interventions to be objectionable.1 Both of these argumentative strategies constitute challenges to John Stuart Mill’s influential anti-paternalistic ‘harm principle’, which states that coercive interference with the liberty of competent adults is justifiable only if such interference prevents harm to non-consenting third parties (Mill, p. 23).2 In this journal, Wilkinson has provided a novel, provocative (...) defence of paternalism in the medical context—one that (provisionally) accepts rather than challenges Mill’s harm principle.3 Wilkinson’s argument is complex. But he begins with Parfit’s influential account of personal identity.4 According to Parfit, Alice at T1 can be the same person as Alice at T2, but the extent to which Alice at T1 and Alice at T2 are similar depends on the extent to which there are ‘chains’ of strong psychological connections between Alice at T1 and Alice at T2. Strong psychological connections, in turn, are mental states such as intentions or beliefs, or psychological traits. For example, if Alice at T2 remembers very little about herself the day before, and the day before that, all the way to Alice at T1, Alice at T2 has completely different psychological traits than Alice at T1—for example, Alice at T1 was courageous, whereas Alice at T2 is cowardly—then Alice at T1 and Alice at T2 are distinct persons. If the harm principle is correct and Alice is autonomous, it is permissible to interfere with Alice’s liberty only if it prevents harm to some non-consenting third party. But if we accept Parfit’s view on personal identity, then a novel defence of paternalistic intervention emerges: Alice at T2 may well be a distinct person from Alice at T1. So, …. (shrink)

The advent of new genetic and genomic technologies may cause friction with the principle of respect for autonomy and demands a rethinking of traditional interpretations of the concept of informed consent. Technologies such as whole‐genome sequencing and micro‐array based analysis enable genome‐wide testing for many heterogeneous abnormalities and predispositions simultaneously. This may challenge the feasibility of providing adequate pre‐test information and achieving autonomous decision‐making. At a symposium held at the 11th World Congress of Bioethics in June 2012 (Rotterdam), organized by (...) the International Association of Bioethics, these challenges were presented for three different areas in which these so‐called ‘new genetics’ technologies are increasingly being applied: newborn screening, prenatal screening strategies and commercial personal genome testing. In this article, we build upon the existing ethical framework for a responsible set‐up of testing and screening offers and reinterpret some of its criteria in the light of the new genetics. As we will argue, the scope of a responsible testing or screening offer should align with the purpose(s) of testing and with the principle of respect for autonomy for all stakeholders involved, including (future) children. Informed consent is a prerequisite but requires a new approach. We present preliminary and general directions for an individualized or differentiated set‐up of the testing offer and for the informed consent process. With this article we wish to contribute to the formation of new ideas on how to tackle the issues of autonomy and informed consent for (public) healthcare and direct‐to‐consumer applications of the new genetics. (shrink)

It is not easy being green, but it does beg the question: Does being green pay off on the bottom-line? Unfortunately, that question of becoming ISO 14001 to reap financial benefit remains widely unanswered. In particular, corporate practice is interested in how environmental management impacts firms’ finance through top-line impact, bottom-line impact, or both—as this paves the way for an investment of environmental management. As current findings are mixed, our study tracks financial performance of publicly traded US firms between 1996 (...) and 2005 to test whether ISO 14001 leads to improved financial performance. Employing a rigorous event-study approach, we compare certified firms to different control groups based on several matching criteria that include industry, size, and/or ROA. In the short run, ISO 14001 certification makes only a minor impact on the bottom-line, according to our results. However, these same results show a significant financial improvement over the long haul with ISO 14001 certification. Additionally, this long-term improvement also makes a significant improvement in top-line performance. Thus, we conclude that environmental management pays off along both dimensions. (shrink)

One of Heidegger’s enduring concerns was to develop an original meditation on the meaning of the present. Integral to this attempt is his critique of the understanding of the bein...

Besides offering opportunities in both clinical and non-clinical domains, the application of novel neuroimaging technologies raises pressing dilemmas. ‘Responsible Research and Innovation’ (RRI) aims to stimulate research and innovation activities that take ethical and social considerations into account from the outset. We previously identified that Dutch neuroscientists interpret “responsible innovation” as educating the public on neuroimaging technologies via the popular press. Their aim is to mitigate (neuro)hype, an aim shared with the wider emerging RRI community. Here, we present results of (...) a media-analysis undertaken to establish whether the body of articles in the Dutch popular press presents balanced conversations on neuroimaging research to the public. We found that reporting was mostly positive and framed in terms of (healthcare) progress. There was rarely a balance between technology opportunities and limitations, and even fewer articles addressed societal or ethical aspects of neuroimaging research. Furthermore, neuroimaging metaphors seem to favour oversimplification. Current reporting is therefore more likely to enable hype than to mitigate it. How can neuroscientists, given their self-ascribed social responsibility, address this conundrum? We make a case for a collective and shared responsibility among neuroscientists, journalists and other stakeholders, including funders, committed to responsible reporting on neuroimaging research. (shrink)

Prenatal screening pathways, as nowadays offered in most Western countries consist of similar tests. First, a risk‐assessment test for major aneuploides is offered to pregnant women. In case of an increased risk, invasive diagnostic tests, entailing a miscarriage risk, are offered. For decades, only conventional karyotyping was used for final diagnosis. Moreover, several foetal ultrasound scans are offered to detect major congenital anomalies, but the same scans also provide relevant information for optimal support of the pregnancy and the delivery.Recent developments (...) in prenatal screening include the application of microarrays that allow for identifying a much broader range of abnomalities than karyotyping, and non‐invasive prenatal testing (NIPT) that enables reducing the number of invasive tests for aneuploidies considerably. In the future, broad NIPT may become possible and affordable.This article will briefly address the ethical issues raised by these technological developments. First, a safe NIPT may lead to routinisation and as such challenge the central issue of informed consent and the aim of prenatal screening: to offer opportunity for autonomous reproductive choice. Widening the scope of prenatal screening also raises the question to what extent ‘reproductive autonomy’ is meant to expand. Finally, if the same test is used for two different aims, namely detection of foetal anomalies and pregnancy‐related problems, non‐directive counselling can no longer be taken as a standard. Our broad outline of the ethical issues is meant as an introduction into the more detailed ethical discussions about prenatal screening in the other articles of this special issue. (shrink)

Vardanyan's theorem states that the set of PA-valid principles of Quantified Modal Logic, QML, is complete Π0 2. We generalize this result to a wide class of theories. The crucial step in the generalization is avoiding the use of Tennenbaum's Theorem.

Inleiding in de moderne logica - met name de syllogistiek - bedoeld voor zelfstudie en inleidende academische cursussen.

Mediation is a process in which two parties agree to resolve their dispute by negotiating over alternative solutions presented by a mediator. In order to construct such solutions, the mediator brings more information and knowledge, and, if possible, resources to the negotiation table. In order to do so, the mediator faces the challenge of determining which information is relevant to the current problem, given a vast database of knowledge. The contribution of this paper is the automated mediation machinery to resolve (...) this issue. We define the concept of a Mediation Problem and show how it can be described in Game Description Language. Furthermore, we present an algorithm that allows the mediator to efficiently determine which information is relevant to the problem and collect this information from the negotiating agents. We show with several experiments that this algorithm is much more efficient than the naive solution that simply takes all available knowledge into account. (shrink)

“Fair and equitable benefit-sharing” is one of the objectives of the UN Convention on Biological Diversity and the FAO International Treaty on Plant Genetic Resources for Food and Agriculture. In essence, benefit-sharing holds that countries, farmers, and indigenous communities that grant access to their plant genetic resources and/or traditional knowledge should share in the benefits that users derive from these resources. But what exactly is understood by “fair” and “equitable” in this context? Neither term is defined in the international treaties. (...) A complicating factor, furthermore, is that different motivations and perspectives exist with respect to the notion of benefit-sharing itself. This paper looks at six different approaches to benefit-sharing that can be extracted from the current debates on “Access and Benefit-Sharing.” These approaches form the basis of a philosophical reflection in which the different connotations of “fair and equitable” are considered, by analyzing the main principles of justice involved. Finally, the various principles are brought together in order to draw some conclusions as to how a fair and equitable benefit-sharing mechanism might best be realized. This results in several recommendations for policymakers. (shrink)

Where the possibility of metaphysics as a science is concerned, Kant assigns the exact sciences the function of an exemplar; for these disciplines have long been well established on "the secure path of a science." Accordingly, in the Prolegomena Kant explicitly addresses the question "How is metaphysics possible as a science?" by way of the questions "How is pure mathematics possible?" and "How is pure natural science possible?" Moreover, all these questions arise directly out of the main transcendental question: "How (...) are synthetic judgments a priori possible?" The deplorable situation of the metaphysics of the day would have been entirely attributable to misappraisal of this central transcendental question. (shrink)

In this series of papers I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Papers I and II were devoted to system A theory of the outer planets and of the planet Venus. In this third and last paper I will study system A theory of the planet Mercury. Our knowledge of the Babylonian theory of Mercury is at present based on twelveEphemeridesand sevenProcedure Texts. Three computational systems of (...) Mercury are known, all of system A. System A1is represented by nineEphemeridescovering the years 190 BC to 100 BC and system A2by twoEphemeridescovering the years 310 to 290 BC. System A3is known from aProcedure Textand from Text M, anEphemerisof the last evening visibility of Mercury for the years 424 to 403 BC. From an analysis of the Babylonian observations of Mercury preserved in theAstronomical DiariesandPlanetary Textswe find: (1) that dates on which Mercury reaches its stationary points are not recorded, (2) that Normal Star observations on or near dates of first and last appearance of Mercury are rare (about once every twenty observations), and (3) that about one out of every seven pairs of first and last appearances is recorded as “omitted” when Mercury remains invisible due to a combination of the low inclination of its orbit to the horizon and the attenuation by atmospheric extinction. To be able to study the way in which the Babylonian scholars constructed their system A models of Mercury from the available observational material I have created a database of synthetic observations by computing the dates and zodiacal longitudes of all first and last appearances and of all stationary points of Mercury in Babylon between 450 and 50 BC. Of the data required for the construction of an ephemeris synodic time intervals Δt can be directly derived from observed dates but zodiacal longitudes and synodic arcs Δλ must be determined in some other way. Because for Mercury positions with respect to Normal Stars can only rarely be determined at its first or last appearance I propose that the Babylonian scholars used the relation Δλ = Δt −3;39,40, which follows from the period relations, to compute synodic arcs of Mercury from the observed synodic time intervals. An additional difficulty in the construction of System A step functions is that most amplitudes are larger than the associated zone lengths so that in the computation of the longitudes of the synodic phases of Mercury quite often two zone boundaries are crossed. This complication makes it difficult to understand how the Babylonian scholars managed to construct System A models for Mercury that fitted the observations so well because it requires an excessive amount of computational effort to find the best possible step function in a complicated trial and error fitting process with four or five free parameters. To circumvent this difficulty I propose that the Babylonian scholars used an alternative more direct method to fit System A-type models to the observational data of Mercury. This alternative method is based on the fact that after three synodic intervals Mercury returns to a position in the sky which is on average only 17.4° less in longitude. Using reduced amplitudes of about 14°–25° but keeping the same zone boundaries, the computation of what I will call 3-synarc system A models of Mercury is significantly simplified. A full ephemeris of a synodic phase of Mercury can then be composed by combining three columns of longitudes computed with 3-synarc step functions, each column starting with a longitude of Mercury one synodic event apart. Confirmation that this method was indeed used by the Babylonian astronomers comes from Text M (BM 36551+), a very early ephemeris of the last appearances in the evening of Mercury from 424 to 403 BC, computed in three columns according to System A3. Based on an analysis of Text M I suggest that around 400 BC the initial approach in system A modelling of Mercury may have been directed towards choosing “nice” sexagesimal numbers for the amplitudes of the system A step functions while in the later final models, dating from around 300 BC onwards, more emphasis was put on selecting numerical values for the amplitudes such that they were related by simple ratios. The fact that different ephemeris periods were used for each of the four synodic phases of Mercury in the later models may be related to the selection of a best fitting set of System A step function amplitudes for each synodic phase. (shrink)