Science, Logic, and Mathematics

The aim of this paper is to reconstruct the logical structure of Melissus philosophy, building on Laks Most’s translation and Barnes’ seminal work on the Samian. This will allow us to shed some light on the subtle argumentations of Melissus. On top of that, we frame Melissus’ metaphysics employing modern logical instruments. On one side, this reformulation makes clear a few assumptions hidden in the deductions made by the Samian; on the other side, our paper shows that contemporary analytic metaphysics (...) has forerunners dating back 2500 years. (shrink)

The concept of a chemical element is foundational within the field of chemistry, but there is wide disagreement over its definition. Even the International Union for Pure and Applied Chemistry (IUPAC) claims two distinct definitions: a species of atoms versus one which identifies chemical elements with the simple substances bearing their names. The double definition of elements proposed by the International Union for Pure and Applied Chemistry contrasts an abstract meaning and an operational one. Nevertheless, the philosophical aspects of this (...) notion are not fully captured by the IUPAC definitions, despite the fact that they were crucial for the construction of the Periodic Table. Although rich scientific literature on the element and the periodic table exists as well as a recent growth in the philosophy of chemistry, scholars are still searching for a definitive answer to this important question: What is an element? (shrink)

Determinism fails easily if spacetimes with points removed from the spacetime manifold are taken to be physically reasonable representations of a way the world could be according to classical general relativity. I discuss a recently proposed condition for determining which spacetimes have holes—epistemic hole freeness—and show that epistemic hole freeness gives the correct verdict in some non-globally hyperbolic spacetimes with a closed subset removed, certain spacetimes with genuinely indeterministic features count as having an epistemic hole, which implies that the requirement (...) of epistemic hole freeness enforces a form of determinism, and there is a large class of spacetimes that intuitively are radically indeterministic and unphysical due to containing a hole, but are free from epistemic holes. I show that a few natural ways of remedying are not satisfactory. (shrink)

Drawing on ‘interpretational’ accounts of scientific representation, I argue that the use of so-called ‘toy models’ provides no particular philosophical puzzle. More specifically; I argue that once one gives up the idea that models are accurate representations of their targets only if they are appropriately similar, then simple and highly idealized models can be accurate in the same way that more complex models can be. Their differences turn on trading precision for generality, but, if they are appropriately interpreted, toy models (...) should nevertheless be considered accurate representations. A corollary of my discussion is a novel way of thinking about idealization more generally: idealized models may distort features of their targets, but they needn’t misrepresent them. (shrink)

It is often thought that the vindication of experimental work lies in its capacity to be revelatory of natural systems. I challenge this idea by examining laboratory experiments in ecology. A central task of community ecology involves combining mathematical models and observational data to identify trophic interactions in natural systems. But many ecologists are also lab scientists: constructing microcosm or ‘bottle’ experiments, physically realizing the idealized circumstances described in mathematical models. What vindicates such ecological experiments? I argue that ‘extrapolationism’, the (...) view that ecological lab work is valuable because it generates truths about natural systems, does not exhaust the epistemic value of such practices. Instead, bottle experiments also generate ‘understanding’ of both ecological dynamics and empirical tools. Some lab work, then, aids theoretical understanding, as well as targeting hypotheses about nature. 1Introduction2Trophic Interactions and Observational Techniques3Cryptic Dynamics in Bottle Experiments4Extrapolationism 4.1Ecological possibility and actuality4.2Ecological heterogeneity5Understanding 5.1The epistemic good of understanding5.2Bottle experiments as understanding-generators5.3How understanding travels6Conclusion. (shrink)

This article demonstrates that non-mechanistic, dynamical explanations are a viable approach to explanation in the special sciences. The claim that dynamical models can be explanatory without reference to mechanisms has previously been met with three lines of criticism from mechanists: the causal relevance concern, the genuine laws concern, and the charge of predictivism. I argue, however, that these mechanist criticisms fail to defeat non-mechanistic, dynamical explanation. Using the examples of Haken et al.’s model of bimanual coordination, and Thelen et al.’s (...) dynamical field model of infant perseverative reaching, I show how each mechanist criticism fails once the standards of Woodward’s interventionist framework are applied to dynamical models. An even-handed application of Woodwardian interventionism reveals that dynamical models are capable of producing genuine explanations without appealing to underlying mechanistic details. 1Introduction2Interventionism and Mechanistic Explanation 2.1Causal relevance and ideal interventions2.2Invariance2.3Explanation3Covering-Laws and Dynamical Explanation 3.1Dynamical models3.2Covering-law explanation3.3Prediction4Causal Relevance 4.1The causal relevance concern4.2Intervening on dynamical models4.3Test case I: The Haken–Kelso–Bunz model4.4Test case II: Dynamical field model5Genuine Laws 5.1The genuine laws concern5.2Using invariance in place of laws5.3Test case I: The Haken–Kelso–Bunz model5.4Test case II: Dynamical field model6Prediction 6.1Predictivism6.2Crude and invariant prediction7Interventionist Criticism of the Haken–Kelso–Bunz Model8Dynamical Explanation8Conclusion. (shrink)

This article highlights a use of analogies in science that so far has received relatively little systematic discussion: providing reasons for pursuing a model or theory. Using the development of the liquid drop model as a test case, I critically assess two extant pursuit worthiness accounts: that analogies justify pursuit by supporting plausibility arguments and that analogies can serve as a guide to potential theoretical unification. Neither of these fit the liquid drop model case. Instead, I develop an alternative account, (...) based on the idea that analogies facilitate the transfer of a well-understood modelling strategy to a new domain. 1Introduction2Case Study: The Development of the Liquid Drop Model3Plausibility Accounts 3.1Bartha on plausibility and analogical inference3.2Plausibility and the drop analogy4Analogies as a Guide to Unification5Generative Accounts 5.1Analogy-based modelling strategies5.2Did analogies play a merely generative role?6A New Pursuit Worthiness Account of Analogies 6.1Transferring understanding-with through analogies6.2Understanding-with and the liquid drop model7Conclusion. (shrink)

Probably the most dramatic historical challenge to scientific realism concerns Arnold Sommerfeld’s derivation of the fine structure energy levels of hydrogen. Not only were his predictions good, he derived exactly the same formula that would later drop out of Dirac’s 1928 treatment. And yet the most central elements of Sommerfeld’s theory were not even approximately true: his derivation leans heavily on a classical approach to elliptical orbits, including the necessary adjustments to these orbits demanded by relativity. Even physicists call Sommerfeld’s (...) success a ‘miracle’, which rather makes a joke of the so-called ‘no miracles argument’. However, this can all be turned around. Here I argue that the realist has a story to tell vis-à-vis the discontinuities between the old and the new theory, leading to a realist defence based on sufficient continuity of relevant structure. 1Introduction2No Realist Commitment Required?3Enter the Physicists4A New Approach to the Non-relativistic Success5Relativity and Spin6Structure and Realist Commitment7Conclusion. (shrink)

According to Ian Hacking, some human kinds are subject to a peculiar type of classificatory instability: individuals change in reaction to being classified, which in turn leads to a revision of our understanding of the kind. Hacking’s claim that these ‘human interactive kinds’ cannot be natural kinds has been vehemently criticized on the grounds that similar patterns of instability occur in paradigmatic examples of natural kinds. I argue that the dialectic of the extant debate misses the core conceptual problem of (...) human interactive kinds. The problem is not that these kinds are particularly unstable but ‘capricious’—their members behave in wayward, unexpected manners that defeats existing theoretical understanding. The reason for that, I argue, is that human interactive kinds are often ‘hybrid kinds’ consisting of a base kind and an associated status, which makes mechanisms that support patterns of change and stability systematically difficult to understand and predict. 1Introduction2The Extant Discussion 2.1Hacking’s account of interactive kinds2.2Classificatory feedback in non-human kinds3Natural kinds and Ontological Instability 3.1Understanding instability3.2The problem of stabilizing feedback3.3Summary4Capricious Kinds 4.1Biased conceptualization4.2Studying social status5Conclusion. (shrink)

This article shows a clear sense in which general relativity allows for a type of ‘machine’ that can bring about a spacetime structure suitable for the implementation of ‘supertasks’. 1Introduction2Preliminaries3Malament–Hogarth Spacetimes4Machines5Malament–Hogarth Machines6Conclusion.

The polarity of light and dark in the treatment of the Newtonian spectrum and the inverse spectrum is studied further and the validity of heterogeneity of light and darkness in relation to Goethe’s views is examined. In order to clarify the reality of the “darkness rays”, the experimentum crucis is re-evaluated. It is shown that the commonly accepted analysis contains assumptions in the choice of the spectrum and background, which mask the inherent dynamic of the spectrum. The relation between colour (...) and wavelength is re-examined with respect to the immutability and specific refrangibility of colour. It is then shown that both these properties are approximations that apply under the specific conditions that have later become standardized in spectroscopy, leading to a consensus regarding the relation of wavelength to colours of one particular spectrum. This consensus has resulted in the study of colour diverging into spectroscopy and colour physiology. As an alternative, the basis of the dichotomy postulated by Müller is studied, leading to the realization that the resolution of this dichotomy was begun by Goethe with the idea of turbidity. A further study shows that turbidity resolves the apparent incompatibility of light and dark. (shrink)

The authors describe the context and need for, and three methods to achieve a paradigm normalization in space research and space programming for the coming changes to the human species wrought by human enhancements. They explore the relevance of the longstanding nature of human enhancements, which reach back into prehistory, and new future capacities that will render humans able to withstand the rigors of microgravity, the monotony of spaceflight, and the extremes of off-world environments. The authors draw together a wide (...) range of transformative changes to the human genome, human strength, physiology, and cognition that are now perceived as distinct, into a single set of options that must be tested, evaluated, and vetted by both space medicine boards and the public. The backflow of technology from space enterprises to the earthbound human species will make many beneficial changes to our species and the next ones on the human line. These changes have already begun. (shrink)

This dissertation examines several of the problems that Hilbert discovered in the foundations of mathematics, from a metalogical perspective. The problems manifest themselves in four different aspects of Hilbert’s views: (i) Hilbert’s axiomatic approach to the foundations of mathematics; (ii) His response to criticisms of set theory; (iii) His response to intuitionist criticisms of classical mathematics; (iv) Hilbert’s contribution to the specification of the role of logical inference in mathematical reasoning. This dissertation argues that Hilbert’s axiomatic approach was guided primarily (...) by model theoretical concerns. Accordingly, the ultimate aim of his consistency program was to prove the model-theoretical consistency of mathematical theories. It turns out that for the purpose of carrying out such consistency proofs, a suitable modification of the ordinary first-order logic is needed. To effect this modification, independence-friendly logic is needed as the appropriate conceptual framework. It is then shown how the model theoretical consistency of arithmetic can be proved by using IF logic as its basic logic. Hilbert’s other problems, manifesting themselves as aspects (ii), (iii), and (iv)—most notably the problem of the status of the axiom of choice, the problem of the role of the law of excluded middle, and the problem of giving an elementary account of quantification—can likewise be approached by using the resources of IF logic. It is shown that by means of IF logic one can carry out Hilbertian solutions to all these problems. The two major results concerning aspects (ii), (iii) and (iv) are the following: (a) The axiom of choice is a logical principle; (b) The law of excluded middle divides metamathematical methods into elementary and non-elementary ones. It is argued that these results show that IF logic helps to vindicate Hilbert’s nominalist philosophy of mathematics. On the basis of an elementary approach to logic, which enriches the expressive resources of ordinary first-order logic, this dissertation shows how the different problems that Hilbert discovered in the foundations of mathematics can be solved. (shrink)

Many formulations of scientific realism include some commitment to metaphysical realism. On the other hand, authors like Schlick, Carnap and Putnam held forms of scientific realism coupled with metaphysical antirealism. So we might ask: do scientific realists really need MR? or is MR already implied by SR, so that SR is actually incompatible with metaphysical antirealism? And if MR must really be added to SR, why is that so? And which additional arguments scientific realists need to support it? After reviewing (...) and classifying a number of different kinds of realisms, metaphysical and not, I answer that SR and MR are logically independent of each other, so that there is no logical inconsistency in holding SR while rejecting MR. However, I argue that the “no miracle” argument not only is the “ultimate” argument for SR, but by the same token it also supports MR. Therefore one cannot effectively defend SR without also subscribing to MR, but this can be done at no additional argumentative cost. I show this by discussing not only the standard version of the NMA, but also three more versions which are not usually considered as such in the literature. (shrink)

We examine the role of category representations for decision-making in real-life tasks. To this end, we empirically examine how people categorize kitchen objects and make use of categories when storing objects in a kitchen. We then compare two computational models and their ability to represent the participants’ mental models. We discuss the advantages and disadvantages of the models and point the way to further research.

Antinomy basically as an inherent structural tension from within the reason between rational willing toward the unconditioned and rational thinking necessarily conditioned by the rule of understanding plays a negative role in and for Kant's system to critically compass reason in limiting itself within the possibility of real experience. In Husserl, under the banner of one all-encompassing reason, antinomy takes a modified form of an ontological incommensurability between two essentially separable regions of being, i.e., between the ideal and the real; (...) such ontological antinomy now takes up the place of an apriori condition for the possibility of meaning for Husserl. Representing a peculiar hierarchical ontological relation through which a lawful power flows, Husserlian antinomy plays an essentially affirmative-political function. In this paper, I will analyze the constructive antinomic structure of phenomenological being relation in contrast to Kantian restrictive antinomy and discuss its political implication. (shrink)

Ethical research on human subjects requires that subjects, if they have the capacity to do so, give free and informed consent to participate in the trials in which they are enrolled. This requirement, which is commonly referred to as the principle of informed consent, was prominently endorsed by the authors of the Belmont Report in 1978, and it remains widely accepted today. Yet while the principle of informed consent is by now almost universally accepted, the responsibilities that it imposes on (...) those who conduct research on human subjects is a more contentious matter. New challenges to securing informed consent have emerged since the publication of the Belmont Report, and responding to these challenges requires... (shrink)

The ethical principles articulated in the Belmont Report and the regulatory oversight of research based on those principles seem to have served society well. Before Belmont, there were numerous egregious violations of research ethics. Since Belmont, there seem to be fewer—though good data are lacking.A central pillar of the Belmont framework is that a bright line must be drawn between medical practice and biomedical research. The Report stated that to qualify as practice, the following conditions must be satisfied: the purpose (...) of an intervention is to provide diagnosis, preventive treatment, or therapy; the intervention is designed solely to enhance the well-being of an individual... (shrink)

There is a long history of Western scientists conducting medical research in other countries. Indeed, one of the first recorded cases of the use of a consent form for research volunteers comes from Walter Reed’s studies of the transmission of yellow fever in American-occupied Cuba at the turn of the 20th century. But in the 1960s and ’70s, the volume of international clinical research was low relative to the present. The scandals that prompted the creation of the National Commission for (...) the Protection of Human Subjects of Biomedical and Behavioral Research were all domestic: the Tuskegee syphilis study, the Willowbrook State School hepatitis experiment, the Jewish Chronic Disease... (shrink)

The Belmont Report, issued in 1979 by the US National Commission for the Protection of Human Subjects of Biomedical and Behavioral Research, is a landmark document providing guidance on the ethics of research involving human subjects. It is divided into three sections: “Boundaries between practice and research; “Basic ethical principles” ; and “Applications of these principles with respect to informed consent, assessment of risks and benefits, and selection of subjects.”While the Belmont Report has enduring significance, the landscape of biomedical research (...) has changed in important ways over the past 40 years. Additionally, a large and growing body of... (shrink)

The Belmont Report has had an enormous influence on the ethics of biomedical research over the last several decades. It has served as a philosophical foundation for federal regulations governing human subjects research, and its principles are well known to individuals across the research enterprise. Given the outsized influence Belmont has enjoyed as a core document in bioethics, it is worth reminding ourselves of the historical context in which it came to be. In this article, we examine the societal forces (...) that helped bring about the Belmont Report and that shaped its conception of ethical research. In turn, we set the stage for discussions on whether Belmont remains applicable as the research enterprise... (shrink)