Theorems of arithmetic are used, perhaps essentially, to reach conclusions about the natural world. This applicability can be explained in a natural way by analogy with the applicability of statements of law to the world. ;In order to carry out an ontological argument for my thesis, I assume the existence of universals as a working hypothesis. I motivate a theory of laws according to which statements of law are singular statements about scientific properties. Such statements entail generalizations about instances of (...) those properties. My task, then, is to show that theorems of arithmetic, in application, are similar to statements of law in this respect. On the basis of my working hypothesis, I argue that there are inclining reasons to think that cardinal numbers are scientific properties whose instances occur in the natural world. The works of Mill, Frege and Benacerraf play central roles in these arguments. ;In general, I urge that there are no conclusive epistemological or ontological factors which preclude arithmetical truths from being laws of nature. Consequently, I think we can extend any semantic theory which is adequate for statements of law to theorems of arithmetic. This would apply even to a theory of predication which does not involve commitment to universals. So, to the degree that my argument succeeds with the working hypothesis, it also supports the unconditioned thesis that arithmetical truths are laws of nature. (shrink)

At the turn of the century, Gottlob Frege and Edmund Husserl both participated in the discussion concerning the foundations of logic and mathematics. Since the 1960s, comparisons have been made between Frege's semantic views and Husserl's theory of intentional acts. In quite recent years, new approaches to the two philosophers' views have appeared. This collection of articles opens with the first English translation of Dagfinn Føllesdal's early classic on Husserl and Frege of 1958. The book brings together a number of (...) new contributions by well-known authors and gives a survey of recent developments in the field. It shows that Husserl's thought is coming to occupy a central role in the philosophy of logic and mathematics, as well as in the philosophy of mind and cognitive science. The work is primarily meant for philosophers, especially for those working on the problems of language, logic, mathematics, and mind. It can also be used as a textbook in advanced courses in philosophy. (shrink)

Call a family F of subsets of a set E inductive if ∅ ∈ F and F is closed under unions with disjoint singletons, that is, if ∀X∈F ∀x∈E–X(X ∪ {x} ∈ F]. A Frege structure is a pair (E.

Throughout his life, Hegel showed great interest in physics and mathematics. His most sustained, surviving treatment of Euclidean geometry is his early work ‘Geometrische Studien’, which he completed while he was a private tutor [Hoffmeister] in Frankfurt, shortly before leaving for Jena to join Schelling.GSis not easy reading, but despite that, it seems to me that Hegel presents in it a remarkably erudite as well as interesting and insightful critique of geometry. He investigates some of the themes from the foundations (...) of geometry, in particular from the first book of theElements of Euclid. Like the mathematical philosophies of Kant and Frege, Hegel's understanding of geometry is conceptually based, but unlike them, it is also grounded in the classical Greek philosophy of mathematics, which achieved its definitive expression in Proclus's great commentary onEuclid 1. Much of this classical philosophy of geometry is forgotten nowadays, under the influence of the great modern mathematical philosophers. In my view, it well deserves reconsideration, especially since, as illustrated by Gödel's incompleteness theorems, modern mathematical philosophy has failed in its attempt to ground mathematics within the framework of formal systems.Much ofGShas not survived, and what remains is condensed and fragmentary. It seems that originally, Hegel covered all of the propositions ofEuclid 1rather than just the 14 propositions that are covered in what remains of the originalGS. I have given detailed treatment ofGStogether with related material in Hegel's Jena dissertation elsewhere. The objective of the present paper is to introduce the translation ofGS. (shrink)

Pace Perry, wondering whether perceived things are identical is thinking about them, for Hume, with no thought of perceptions of them. Hume is not a proto-Fregean; Hume's Difficulty is not a version of Frege's Puzzle. Pace Falkenstein, wondering about an identity is not wondering whether clearly distinct things--stages, surfaces, names--are connected in some way. Pace Garrett, wondering about the identity of an observed object is wondering whether it is really one or two things, not whether there is one F or (...) two Fs. Second, Humean consciousness is apperception, not immediate awareness. Third, Hume finds nothing with epistemic merit. (shrink)

Veterinarians play an essential role in the animal-based food chain. They are professionally responsible for the health of farm animals to secure food safety and public health. In the last decades, food scandals and zoonotic disease outbreaks have shown how much animal and human health are entangled. Therefore, the concept of One Health is broadly promoted within veterinary medicine. The profession embraces this idea that the health of humans, animals and the environment is inextricably linked and supports the related call (...) for transdisciplinary collaboration. Especially in zoonotic disease control, the benefits of the cooperation between veterinarians and human doctors seem evident. However, applying a One Health approach also makes moral problems explicit. For instance, how should veterinarians deal with situations in which measures to protect public health negatively affect animal health? This creates a conflict of professional responsibilities. To deal with such moral problems and to strengthen the veterinarian’s position, the starting point is a holistic perspective on One Health. We will argue for an ‘encapsulated health’ argument: the best way to safeguard human health is to promote the health of animals and the environment. This also holds for the responsibility of the veterinary profession: to serve public health, the central responsibility of veterinarians should be to be experts in animal health and welfare. We elaborate this point by using a case study on the role of the veterinary profession in antimicrobial resistance policies in the Netherlands. (shrink)

Why did Hume drop sympathy as a key concept of his moral philosophy, and why—on the other hand—did Smith make it into the ‘didactic principle’ of his Theory of Moral Sentiments? These questions confront us with the basic issue of ethical theory concerning human nature. My point in dealing with these questions is to show what views of human nature their respective choices involved. And my procedure will be to take a close look at the revisions they made to their (...) ethical theories to bring out the contrasting aspects of their views of human nature. (shrink)

The report entitled An Analysis of the Canadian Research and Development System for Agriculture/Food which was presented to the Science Council of Canada in July, 1991 contains many far-reaching recommendations for revisions of the research and educational components of the Agriculture/Food System in Canada. The report calls for research of holistic and interdisciplinary nature. It calls for determination of research priorities by broadly constituted committees which would include reporesentaitves heretofore not included in the process of decisionmaking regarding scientific research. In (...) addition, it calls for restructuring of the agricultural education system. The Co-editors of this Journal, believe that these recommendations should be wildely discussed and, therefore, requested publication of the Executive Summary of this Report. (shrink)