In our lives, we aim to achieve welfare for ourselves, that is, to live good lives. But we also have another, more impartial perspective, where we aim to balance our concern for our own welfare against a concern for the welfare of others. This is a perspective of justice. Nils Holtug examines these two perspectives and the relations between them.

In the present paper we introduce a constructive theory of nonstandard arithmetic in higher types. The theory is intended as a framework for developing elementary nonstandard analysis constructively. More specifically, the theory introduced is a conservative extension of HAω + AC. A predicate for distinguishing standard objects is added as in Nelson's internal set theory. Weak transfer and idealisation principles are proved from the axioms. Finally, the use of the theory is illustrated by extending Bishop's constructive analysis with infinitesimals.

The contributors to the volume are: Richard Arneson, Linda Barclay, Thomas Christiano, Nils Holtug, Susan Hurley, Kasper Lippert-Rasmussen, Dennis McKerlie, ...

When formalizing mathematics in constructive type theories, or more practically in proof assistants such as Coq or Agda, one is often using setoids. In this note we consider two categories of setoids with equality on objects and show, within intensional Martin-Löf type theory, that they are isomorphic. Both categories are constructed from a fixed proof-irrelevant family F of setoids. The objects of the categories form the index setoid I of the family, whereas the definition of arrows differs. The first category (...) has for arrows triples →F)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\,\rightarrow \,F)$$\end{document} where f is an extensional function. Two such arrows are identified if appropriate composition with transportation maps makes them equal. In the second category the arrows are triples 2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^2)$$\end{document} where R is a total functional relation between the subobjects F,F↪Σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F, F \hookrightarrow \Sigma $$\end{document} of the setoid sum of the family. This category is simpler to use as the transportation maps disappear. Moreover we also show that the full image of a category along an E-functor into an E-category is a category. (shrink)

In a previous paper we constructed a full and faithful functor ℳ from the category of locally compact metric spaces to the category of formal topologies . Here we show that for a real-valued continuous function f, ℳ factors through the localic positive reals if, and only if, f has a uniform positive lower bound on each ball in the locally compact space. We work within the framework of Bishop constructive mathematics, where the latter notion is strictly stronger than point-wise (...) positivity. (shrink)

A new foundation for constructive nonstandard analysis is presented. It is based on an extension of a sheaf-theoretic model of nonstandard arithmetic due to I. Moerdijk. The model consists of representable sheaves over a site of filter bases. Nonstandard characterisations of various notions from analysis are obtained: modes of convergence, uniform continuity and differentiability, and some topological notions. We also obtain some additional results about the model. As in the classical case, the order type of the nonstandard natural numbers is (...) a dense set of copies of the integers. Every standard set has a hyperfinite enumeration of its standard elements in the model. All arguments are carried out within a constructive and predicative metatheory: Martin-Löf's type theory. (shrink)

According to the Harm Principle, roughly, the state may coerce a person only if it can thereby prevent harm to others. Clearly, this principle depends crucially on what we understand by harm. Thus, if any sort of negative effect on a person may count as a harm, the Harm Principle will fail to sufficiently protect individual liberty. Therefore, a more subtle concept of harm is needed. I consider various possible conceptions and argue that none gives rise to a plausible version (...) of the Harm Principle. Whether we focus on welfare, quantities of welfare or qualities of welfare, we do not arrive at a plausible version of this principle. Instead, the concept of harm may be moralized. I consider various ways this may be done as well as possible rationales for the resulting versions of the Harm Principle. Again, no plausible version of the principle turns up. I also consider the prospect of including the Harm Principle in a decision-procedure rather than in a criterion of rightness. Finally, in light of my negative appraisal, I briefly discuss why this principle has seemed so appealing to liberals. (shrink)

Dahlbäck, Forsblad and Hydén argue that conversational remembering in the real‐world must be acknowledged as an interactional practice grounded in and bound to the communicative actions produced by the interlocutors. They illustrate the complexity of those processes by referring to their own fieldwork examining older adults’ prospective memory within their homes (Dahlbäck, Kristiansson, & Stjernberg, 2013) and propose alternative methodologies (e.g., scenarios design) to increase collaborations between ethnographic and experimental memory researchers.

F. P. Ramsey was a remarkably creative and subtle philosopher who in the briefest of academic careers made significant contributions to logic, philosophy of mathematics, philosophy of language and decision theory. His few published papers reveal him to be a figure or comparable importance to Russell, Carnap and Wittgenstein in the history of analytical philosophy. This book was the first critical study of Ramsey's work, offering a thorough exposition and interpretation of his ideas, setting the ideas in their historical context, (...) and assessing their significance for contemporary research. The study is intended to complement the reissue of Ramsey's papers edited by Professor Hugh Mellor. (shrink)

This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett’s and Dag Prawitz’ philosophical motivations and give precise characterisations of the crucial notions of harmony and stability, placed in the context of proving normalisation results in systems of natural deduction. I point out a problem for defining the meaning of negation in this framework and prospects for an account of the meanings of (...) modal operators in terms of rules of inference. (shrink)

In order to explain several discrepancies between the gene-recombination phenomena in phages and in higher organisms, we assume that theT 2 phage, after entering the bacterium, divides in three parts corresponding to the three “chromosomes' whichHershey andRotman have traced in this phage. The three parts are supposed to be able to divide further by rupture or by the action of other “chromosome fragments”. Each fragment is supposed able to reproduce inside the bacterium as a more or less independent unit and (...) before lysis of the bacterium the various parts are assumed to reunite in complete sets of genes each forming a new phage.After discussing the experimental facts supporting these assumptions, we show that the assumptions are in perfect agreement with the theory of the symbiosis of genes, a theory which seems necessary in order to explain the ability of the “chromosome-fragments” to reunite into complete phages.Also the problems arising with respect to the sexual reproduction in bacteria is discussed under the point of view of the symbiosis theory. The assumption is made that the hereditary material is transduced from bacterium to bacterium by ultramicroscopic virus-like particles “genophores”. In several lysogenic bacteria the genophores are supposed still able to act as parasites instead of symbiontes towards some other sensitive bacteria. The experimental facts supporting this assumption are analyzed, and new experimental tests suggested. (shrink)

This is a comprehensive introduction to the history of Western Philosophy from the Pre-Socratics to Twentieth Century thought. In addition to all the key figures, the book covers figures whose contributions have so far been overlooked, such as Vico, Montesquieu, Durkheim and Weber. Along with in-depth discussion of the philosophical movements, Skirbekk and Gilje also discuss the natural sciences, the establishment of the Humanities, Socialism and Fascism, Psychoanalysis, and the rise of the social sciences. _History of Western Thought_ is an (...) ideal introduction to philosophy and the sociological and scientific structures that have shaped modern day philosophy. (shrink)

Berichte zur Wissenschaftsgeschichte, EarlyView.

For Hannah Arendt, the public is the realm where individuals show themselves to their fellow human beings. They do this by relating to each other through speaking and acting together. Both speaking and acting are only possible if men acknowledge each other as independent, autonomous individuals but at the same time keep a common interest, a reference point for their speaking and acting together. In or- der to recognize each other as equal yet unique, individuals must gain distance – to (...) themselves, to others and to the objects they speak of. They are only able to do this in public. Helmuth Plessner has developed a concept of publicity which ensures the individual’s »right to distance«. This »right to distance« can contribute to a better understanding of Hannah Arendt’s often misinterpreted separation of the private from the public realm and furthermore allows a better understanding of how Arendt envisioned a culture within which the political can be established. (shrink)

First-order logic with dependent sorts, such as Makkai's first-order logic with dependent sorts (FOLDS), or Aczel's and Belo's dependently typed (intuitionistic) first-order logic (DFOL), may be regarded as logic enriched dependent type theories. Categories with families (cwfs) is an established semantical structure for dependent type theories, such as Martin-Löf type theory. We introduce in this article a notion of hyperdoctrine over a cwf, and show how FOLDS and DFOL fit in this semantical framework. A soundness and completeness theorem is proved (...) for DFOL. The semantics is functorial in the sense of Lawvere, and uses a dependent version of the Lindenbaum-Tarski algebra for a DFOL theory. Agreement with standard first-order semantics is established. Applications of DFOL to constructive mathematics and categorical foundations are given. A key feature is a local propositions-as-types principle. (shrink)

The strength of a slippery slope argument is a matter of some dispute. Some see it as a reasonable argument pointing out what probably or inevitably follows from adopting some practice, others see it as essentially a fallacious argument. However, there seems to be a tendency emerging to say that in many cases, the argument is not actually fallacious, although it may be unsubstantiated. I shall not try to settle this general discussion, but merely seek to assess the strength of (...) the slippery slope argument applied to human gene therapy. The structure of my argument will be the following. First, I shall distinguish between three different versions of the slippery slope argument; two logical versions and an empirical one. Next, I will address human gene therapy in terms of each of the three versions, partly relying on slippery slope arguments against this practice that have already surfaced in the literature. I shall argue that neither version pulls through. The logical versions fail primarily because relevant distinctions can be made between different uses of gene therapy, contrary to what the proponents of the arguments claim. The empirical version fails because there seems to be no evidence supporting the claim that we shall in fact slide down the slope if we engage in gene therapy, and because if we accepted the conclusion that we should not allow gene therapy on the basis of the empirical argument, we should have to make very far-reaching and undesirable modifications in health care in general, in order to be consistent. Or at least so I shall argue. (shrink)

Normative ethics usually presupposes background accounts of human agency, and although different ethical theorists might have different pictures of human agency in mind, there is still something like a standard account that most of mainstream normative ethics can be understood to rest on. Ethical theorists tend to have Rational Man, or at least some close relative to him, in mind when constructing normative theories. It will be argued here that empirical findings raise doubts about the accuracy of this kind of (...) account; human beings fall too far short of ideals of rationality for it to be meaningful to devise normative ideals within such a framework. Instead, it is suggested, normative ethics could be conducted more profitably if the idea of unifying all ethical concerns into one theoretical account is abandoned. This disunity of ethical theorizing would then match the disunited and heuristic-oriented nature of our agency. (shrink)

In bilateral logic formulas are signed by + and –, indicating the speech acts assertion and denial. I argue that making an assumption is also speech act. Speech acts cannot be embedded within other speech acts. Hence we cannot make sense of the notion of making an assumption in bilateral logic. Attempts to solve this problem are considered and rejected.

This chapter examines autonomism. Autonomism is roughly the view that an artwork’s ethical properties do not bear on its aesthetic or artistic value. The author sketches some of the view’s history before describing various versions of it defended over the last quarter-century. These are divided into ‘radical’, ‘robust’, and ‘moderate’ forms of autonomism. The author considers the strengths and weaknesses of each. The author also devotes some space to the ‘interactionist’ views against which contemporary autonomism is typically opposed. In doing (...) so, he considers the so-called ‘qua problem’ at some length, as well its bearing on these various autonomist positions. (shrink)

Ian Rumfitt has proposed systems of bilateral logic for primitive speech acts of assertion and denial, with the purpose of ‘exploring the possibility of specifying the classically intended senses for the connectives in terms of their deductive use’ : 810f). Rumfitt formalises two systems of bilateral logic and gives two arguments for their classical nature. I assess both arguments and conclude that only one system satisfies the meaning-theoretical requirements Rumfitt imposes in his arguments. I then formalise an intuitionist system of (...) bilateral logic which also meets those requirements. Thus Rumfitt cannot claim that only classical bilateral rules of inference succeed in imparting a coherent sense onto the connectives. My system can be extended to classical logic by adding the intuitionistically unacceptable half of a structural rule Rumfitt uses to codify the relation between assertion and denial. Thus there is a clear sense in which, in the bilateral framework, the difference between classicism and intuitionism is not one of the rules of inference governing negation, but rather one of the relation between assertion and denial. (shrink)

This is only a very short essay on negation and harmony in philosophical logic. If you buy it anyway, you'll help me pay the bills and I'll be able to write longer things.

Emergence is a universal phenomenon that can be defined mathematically in a very general way. This is useful for the study of scientifically legitimate explanations of complex systems, here defined as hyperstructures. A requirement is that the observation mechanisms are considered within the general framework. Two notions of emergence are defined, and specific examples of these are discussed.

In this paper we present and study a categorical formulation of the W-types of Martin-Löf. These are essentially free term algebras where the operations may have finite or infinite arity. It is shown that W-types are preserved under the construction of sheaves and Artin gluing. In the proofs we avoid using impredicative or nonconstructive principles.

We develop a constructive version of nonstandard analysis, extending Bishop's constructive analysis with infinitesimal methods. A full transfer principle and a strong idealisation principle are obtained by using a sheaf-theoretic construction due to I. Moerdijk. The construction is, in a precise sense, a reduced power with variable filter structure. We avoid the nonconstructive standard part map by the use of nonstandard hulls. This leads to an infinitesimal analysis which includes nonconstructive theorems such as the Heine-Borel theorem, the Cauchy-Peano existence theorem (...) for ordinary differential equations and the exact intermediate-value theorem, while it at the same time provides constructive results for concrete statements. A nonstandard measure theory which is considerably simpler than that of Bishop and Cheng is developed within this context. (shrink)

In this paper, I'll present a general way of "reading off" introduction/elimination rules from elimination/introduction rules, and define notions of harmony and stability on the basis of it.