Since the discovery of incommensurability in ancient Greece, arithmeticism and geometricism constantly switched roles. After ninetieth century arithmeticism Frege eventually returned to the view that mathematics is really entirely geometry. Yet Poincaré, Brouwer, Weyl and Bernays are mathematicians opposed to the explication of the continuum purely in terms of the discrete. At the beginning of the twenty-first century ‘continuum theorists’ in France (Longo, Thom and others) believe that the continuum precedes the discrete. In addition the last 50 years witnessed (...) the revival of infinitesimals (Laugwitz and Robinson—non-standard analysis) and—based upon category theory—the rise of smooth infinitesimal analysis and differential geometry. The spatial whole-parts relation is irreducible (Russell) and correlated with the spatial order of simultaneity. The human imaginative capacities are connected to the characterization of points and lines (Euclid) and to the views of Aristotle (the irreducibility of the continuity of a line to its points), which remained in force until the ninetieth century. Although Bolzano once more launched an attempt to arithmetize continuity, it appears as if Weierstrass, Cantor and Dedekind finally succeeded in bringing this ideal to its completion. Their views are assessed by analyzing the contradiction present in Grünbaum’s attempt to explain the continuum as an aggregate of unextended elements (degenerate intervals). Alternatively a line-stretch is characterized as a one-dimensional spatial subject, given at once in its totality (as a whole) and delimited by two points—but it is neither a breadthless length nor the (shortest) distance between two points. The overall aim of this analysis is to account for the uniqueness of discreteness and continuity by highlighting their mutual interconnections exemplified in the nature of a line as a one-dimensional spatial subject, while acknowledging that points are merely spatial objects which are always dependent upon an extended spatial subject. Instead of attempting to reduce continuity to discreteness or discreteness to continuity, a third alternative is explored: accept the irreducibility of number and space and then proceed by analyzing their unbreakable coherence. The argument may be seen as exploring some implications of the view of John Bell, namely that the “continuous is an autonomous notion, not explicable in terms of the discrete.” Bell points out that initially Brouwer, in his dissertation of 1907, “regards continuity and discreteness as complementary notions, neither of which is reducible to each other.”. (shrink)

Some of the commentators on Intricate Ethics complain of my method. One finds the main ideas ‘Kammouflaged’ because the relevant causal distinctions are so fine-grained and the cases that illustrate them so numerous. Some say that they do not have the intuitions about many cases that I have, that I concoct dubious and ad hoc distinctions and invest them with moral significance; I am Ptolemaic in that new crystalline spheres and epicycles are constantly being added in an attempt to fix (...) the appearances. (shrink)

Bioethical Prescriptions collects F.M. Kamm's articles on bioethics -- revised for publication in book form -- which have appeared over the last 25 years and which have made her among the most widely-respected philosophers working in this field.

In Intricate Ethics, Kamm questions the moral importance of some non-consequentialist distinctions and then introduces and argues for the moral importance of other distinctions. The first section discusses nonconsequentialist ethical theory and the trolley problem; the second deals with the notions of moral status and rights; the third takes up the issues of responsibility and complicity and the possible moral significance of distance; and the fourth section analyzes the views of others in the non-consequentialist and consequentialist camps.

Ethics for Enemies comprises three original philosophical essays on torture, terrorism, and war. F. M. Kamm deploys ethical theory in her challenging new treatments of these most controversial practical issues. First she considers the nature of torture and the various occasions on which it could occur, in order to determine why it might be wrong to torture a wrongdoer held captive, even if this were necessary to save his victims. In the second essay she considers what makes terrorism wrong--whether it (...) is the intention to harm civilians, rather than harm to them being 'collateral damage,' or something else--and whether terrorism is always wrong. The third essay discusses whether having a right reason, in the sense of a right intention, is necessary in order for a war to be just. Kamm then examines ways in which the harms of war can be proportional to the achievement of the just cause and other goods that war can bring about, so as to make the declaration of war permissible. (shrink)

I begin by reconsidering the arguments of John Taurek and Elizabeth Anscombe on whether the number of people we can help counts morally. I then consider arguments that numbers should count given by F. M. Kamm and Thomas Scanlon, and criticism of them by Michael Otsuka. I examine how different conceptions of the moral method known as pairwise comparison are at work in these different arguments and what the ideas of balancing and tie-breaking signify for decision-making in various types of (...) cases. I conclude by considering how another moral method that I call virtual divisibility functions and what it helps reveal about an argument by Otsuka against those who do not think numbers count. (shrink)

Temporal Logic: From Ancient Ideas to Artificial Intelligence deals with the history of temporal logic as well as the crucial systematic questions within the field. The book studies the rich contributions from ancient and medieval philosophy up to the downfall of temporal logic in the Renaissance. The modern rediscovery of the subject, which is especially due to the work of A. N. Prior, is described, leading into a thorough discussion of the use of temporal logic in computer science and the (...) understanding of natural language. Temporal Logic: From Ancient Ideas to Artificial Intelligence thus interweaves linguistic, philosophical and computational aspects into an informative and inspiring whole. (shrink)

In this paper two models for movement of respiratory gases in the insect trachea are presented. One model considers the tracheal system as a single flexible compartment while the other model considers the trachea as a single flexible compartment with gas exchange. This work represents an extension of Ben-Tal’s work on compartmental gas exchange in human lungs and is applied to the insect tracheal system. The purpose of the work is to study nonlinear phenomena seen in the insect respiratory system. (...) It is assumed that the flow inside the trachea is laminar, and that the air inside the chamber behaves as an ideal gas. Further, with the isothermal assumption, the expressions for the tracheal partial pressures of oxygen and carbon dioxide, rate of volume change, and the rates of change of oxygen concentration and carbon dioxide concentration are derived. The effects of some flow parameters such as diffusion capacities, reaction rates and air concentrations on net flow are studied. Numerical simulations of the tracheal flow characteristics are performed. The models developed provide a mathematical framework to further investigate gas exchange in insects. (shrink)

This book is a philosophical discussion of moral, legal, and medical issues related to aging, dying, and death. One of its aims is to decide whether and when it might make sense to not resist or bring about the end of one's life. To answer this question it considers views about meaning in life and what makes life worth living. It also evaluates recent attempts to help the general public plan in advance for the end of life. It also considers (...) whether or not physician-assisted suicide is morally permissible and if it should be legalized. (shrink)

Feature selection is a widely studied technique whose goal is to reduce the dimensionality of the problem by removing irrelevant features. It has multiple benefits, such as improved efficacy, efficiency and interpretability of almost any type of machine learning model. Feature selection techniques may be divided into three main categories, depending on the process used to remove the features known as Filter, Wrapper and Embedded. Embedded methods are usually the preferred feature selection method that efficiently obtains a selection of the (...) most relevant features of the model. However, not all models support an embedded feature selection that forces the use of a different method, reducing the efficiency and reliability of the selection. Neural networks are an example of a model that does not support embedded feature selection. As neural networks have shown to provide remarkable results in multiple scenarios such as classification and regression, sometimes in an ensemble with a model that includes an embedded feature selection, we attempt to embed a feature selection process with a general-purpose methodology. In this work, we propose a novel general-purpose layer for neural networks that removes the influence of irrelevant features. The Feature-Aware Drop Layer is included at the top of the neural network and trained during the backpropagation process without any additional parameters. Our methodology is tested with 17 datasets for classification and regression tasks, including data from different fields such as Health, Economic and Environment, among others. The results show remarkable improvements compared to three different feature selection approaches, with reliable, efficient and effective results. (shrink)

Why is death bad for us, even on the assumption that it involves the absence of experience? Is it worse for us than prenatal nonexistence? In this first volume of the two-volume Morality, Mortality, Kamm begins by considering these questions, critically examining some answers other philosophers have given. The book examines specifically what differences between persons are relevant to the distribution of any scarce resource, discussing for example, the distribution of bodily organs for transplantation.

Zeller argued that the ‘innumerable worlds’ mentioned in accounts of Anaximander's system must be an endless succession of single worlds, not an unlimited number of coexistent worlds scattered through infinite space, some always coming into being while others are passing away. Zeller pointed out that a succession of single worlds is grounded in the principles of the system. ‘Things perish into that from which they had their birth… according to the order of Time,’ a cycle of birth, existence, and destruction. (...) A world ends, and the living divine stuff begets a new world to take its place. On the other hand, there is much in the system to contradict the idea of coexistent worlds. Anaximander's successors, Anaximenes, Anaxagoras, and Diogenes, show that this idea is not a necessary consequence of the unlimitedness of the original world-stuff. Nothing in the appearances of Nature suggests it. Anaximander is a monistic hylozoist, whereas Democritus is a pluralist with his innumerable independent atoms producing, by similar processes, independent world-systems in different parts of an infinite void. (shrink)

In this article, I first compare positions I have taken in the past and those taken by Peter Singer on how the allocation of life-saving resources should be affected by the aggregation of expected quality of life, quantity of life, and need, both within the life of a person and across persons . I then reexamine the specific issue of whether and why differences in expected years of life and quality of life that a scarce resource can provide a disabled (...) and a nondisabled person should affect our allocation decisions. I attend to how the use of the veil of ignorance bears on this issue and also how the conclusions I reach differ in certain ways from my past positions. (shrink)

This article considers the possible relation between the idea of parity and some past work on the allocation of scarce resources. Parity of value is first connected with the idea of some goods being irrelevant in interpersonal comparisons. The notion of moral parity is introduced to describe the recognition that people who are moral equals (even when they are not on a par in terms of value) as not substitutable. The relation between a Separability Test and nonsubstitutability of persons is (...) considered. These ideas are then used to discuss various cases in which one must choose to whom to provide medical assistance, including whether and when to distinguish morally between a disabled and a nondisabled person. (shrink)

This article begins by comparing terror and death and then focuses on whether killing combatants and noncombatants as a mere means to create terror, that is in turn a means to winning a war, is ever permissible. The role of intentions and alternative acts one might have done is examined in this regard. The second part of the article begins by criticizing a standard justification for causing collateral (side effect) deaths in war and offers an alternative justification that makes use (...) of the idea of group liability. (shrink)

Abortion bans have been characterized as cruel especially in not allowing exceptions for rape or incest. The article first examines one approach to morally justifying bans based on the Doctrine of Double Effect (DDE) which distinguishes morally between killing or letting die intending death versus doing so only foreseeing death. It then presents some criticisms of the implications of the DDE but also argues that what the doctrine permits helps provide a ground for the permissibility of abortions even if the (...) fetus is a person. Whether there are limits on applying this argument is also considered. In conclusion, the article considers whether and why not permitting exceptions to bans for rape and incest is cruel and whether cruelty is a ground for opposition to bans. (shrink)

Peter Unger’s book has both substantive and methodological aims. Substantively, it aims to prove the following four claims in the following order: we must, in general, suffer great losses of property to prevent suffering and death; we may, in general, impose such losses on others for the same goals; we may, in general, kill others to prevent more deaths; and we must, in general, kill ourself to prevent more deaths. Methodologically, it aims to show that intuitive judgments about cases that (...) would be presented as evidence against the four substantive claims—the standard technique of nonconsequentialists arguing against consequentialists—are worthless because we can construct cases that generate the opposite intuitive judgment; further, we can show that the factors that distinguish the cases yielding such different intuitions are not morally significant; and hence, we must decide which judgments are correct by consulting such general moral values as the importance of reducing suffering and death. Thus, Unger offers an error theory of nonconsequentialist restrictions on harming others and prerogatives not to make large sacrifices to aid. This error theory is based on the psychological effects of morally insignificant factors. (shrink)