Winthrop Parkhurst, W. J. Kingsland, Jr; Infinity and the Infinitesimal, The Monist, Volume 35, Issue 4, 1 October 1925, Pages 633–666, https://doi.org/10.5840/.

The starting point of the present study is to investigate which environmental factors play a role in the media behavior of ethnic minority youth. To what extent do socio-demographic characteristics influence ownership and use of the media? We also address the role of religion, cultural origin and the cultural distance between ethnic minority youth and indigenous Dutch youth. Three numerically important groups of ethnic minority youth are discussed: Turks, Moroccans and Surinamese. In a survey conducted among Turkish, Moroccan and Surinamese (...) youth aged between 12 and 19, residing in the Netherlands, we investigated which environmental factors play a role in the media behavior of ethnic minority youth. A control group of indigenous Dutch youth was established and likewise exposed to the variables under study. (shrink)

SummaryA feature of mid-nineteenth century scientific debates in France on the subject of plant nutrition was the rivalry, at times acrimonious, between Jean Baptiste Boussingault and Georges Ville. It started in 1848 when Ville was demonstrator to Boussingault, who held one of the two chairs of agriculture at the Conservatoire des Arts et Métiers. A study of their disputes serves to illustrate their mutual incompatibility, exacerbated by the patronage extended to Ville by his step-brother, Louis Napoléon Bonaparte, afterwards Napoléon III. (...) Their disputes were not merely the result of personal differences but also accompanied the development of two concepts of plant nutrition, namely the rôle of atmospheric nitrogen. and its possible assimilation by plants, and the chemical nature of plant nutrients, especially nitrates and phosphates. (shrink)

There exist important deductive systems, such as the non-normal modal logics, that are not proper subjects of classical algebraic logic in the sense that their metatheory cannot be reduced to the equational metatheory of any particular class of algebras. Nevertheless, most of these systems are amenable to the methods of universal algebra when applied to the matrix models of the system. In the present paper we consider a wide class of deductive systems of this kind called protoalgebraic logics. These include (...) almost all (non-pathological) systems of prepositional logic that have occurred in the literature. The relationship between the metatheory of a protoalgebraic logic and its matrix models is studied. The following results are obtained for any finite matrix model U of a filter-distributive protoalgebraic logic : (I) The extension U of is finitely axiomatized (provided has only finitely many inference rules); (II) U has only finitely many extensions. (shrink)

W. J. Mander presents a history of metaphysics in nineteenth-century Britain. He traces the story of the development and interplay of three great schools of thought, the agnostics, the empiricists, and the idealists, and their different responses to the idea of an ultimate but unknowable way that things really are in themselves.

This paper is based on Lectures 1, 2 and 4 in the series of ten lectures titled “Algebraic Structures for Logic” that Professor Blok and I presented at the Twenty Third Holiday Mathematics Symposium held at New Mexico State University in Las Cruces, New Mexico, January 8-12, 1999. These three lectures presented a new approach to the algebraization of deductive systems, and after the symposium we made plans to publish a joint paper, to be written by Blok, further developing these (...) ideas. That project was still incomplete when Blok died. In fact, there is no indication that he had prepared a draft of the paper, and we do not know what new material he intended to include. I am therefore not in a position to complete the project as he had envisioned it. So, I have settled for the more limited objective of presenting the material from the three lectures, leaving to others the task of adapting the techniques used there to more general situations. (shrink)

W. J. Mander provides a brief introduction to and critical assessment of the thought of the greatest of the British Idealist philosophers, F. H. Bradley (1846-1924), whose work has been largely neglected in this century. After a general introduction to Bradley's metaphysics and its logical foundations, Mander shows that much of Bradley's philosophy has been seriously misunderstood. Mander argues that any adequate treatment of Bradley's thought must take full account of his unique dual inheritance from the traditions of British empiricism (...) and Hegelian rationalism. The scholarship of recent years is assessed, and new interpretations are offered of Bradley's views about truth, predication, and relations, and of his arguments for idealism. (shrink)

Modal logics are studied in their algebraic disguise of varieties of so-called modal algebras. This enables us to apply strong results of a universal algebraic nature, notably those obtained by B. Jonsson. It is shown that the degree of incompleteness with respect to Kripke semantics of any modal logic containing the axiom □ p → p or containing an axiom of the form $\square^mp \leftrightarrow\square^{m + 1}p$ for some natural number m is 2 ℵ 0 . Furthermore, we show that (...) there exists an immediate predecessor of classical logic (axiomatized by $p \leftrightarrow \square p$ ) which is not characterized by any finite algebra. The existence of modal logics having 2 ℵ 0 immediate predecessors is established. In contrast with these results we prove that the lattice of extensions of S4 behaves much better: a logic extending S4 is characterized by a finite algebra iff it has finitely many extensions and any such logic has only finitely many immediate predecessors, all of which are characterized by a finite algebra. (shrink)