Fundamental assumptions behind qualitative modelling are critically considered and some inherent problems in that modelling approach are outlined. The problems outlined are due to the assumption that a sufficient set of symbols representing the fundamental features of the physical world exists. That assumption causes serious problems when modelling continuous systems. An alternative for intelligent system building for cases not suitable for qualitative modelling is proposed. The proposed alternative combines neural networks and quantitative modelling.

Stationary spacetimes containing a black hole have several properties akin to those of atoms. For instance, such spacetimes have only three classical degrees of freedom, or observables, which may be taken to be the mass, the angular momentum, and the electric charge of the hole. There are several arguments supporting a proposal originally made by Bekenstein that quantization of these classical degrees of freedom gives an equal spacing for the horizon area spectrum of black holes. We review some of these (...) arguments and introduce a specific Hamiltonian quantum theory of black holes. Our Hamiltonian quantum theory gives, among other things, a discrete spectrum for the classical observables, and it produces an area spectrum which is closely related to Bekenstein's proposal. We also present a foamlike model of horizons of spacetime. In our model spacetime horizon consists of microscopic Schwarzschild black holes. Applying our Hamiltonian approach to this model we find that the entropy of any horizon is one quarter of its area. (shrink)

We study the computational complexity of the model checking problem for quantifier-free dependence logic ${(\mathcal{D})}$ formulas. We characterize three thresholds in the complexity: logarithmic space (LOGSPACE), non-deterministic logarithmic space (NL) and non-deterministic polynomial time (NP).

J.S. Mill's plural voting proposal in Considerations on Representative Government presents political theorists with a puzzle: the elitist proposal that some individuals deserve a greater voice than others seems at odds with Mill's repeated arguments for the value of full participation in government. This essay looks at Mill's arguments for plural voting, arguing that, far from being motivated solely by elitism, Mill's account is actually driven by a commitment to both competence and participation. It goes on to argue that, for (...) Mill, much of the value of political participation lies in its unique ability to educate the participants. That ability to educate is not, however, a product of participation alone; rather, for Mill, the true educative benefits of participation obtain only when competence and participation work together in the political sphere. Plural voting, then, is a mechanism for allowing Mill to take advantage of the educative benefits that arise from the intersection of competence and participation. (shrink)

The book deals with the reception and critique of symbolic logic among German-speaking philosophers at the turn of the 20th century. The first part discusses the period from the late 1870s up to the end of the 19th century. The main issue is the arrival of the Boolean algebra of logic in Germany and Austria. It examines also the reasons why Gottlob Frege was so unsuccessful in his attempts to draw the attention of philosophers to his logicist programme. The second (...) part deals with the first two decades of the 20th century. Its main topic of inquiry is the reception of Bertrand Russell's and Louis Couturat's ideas in the German-speaking world. In particular, it concentrates on the relationship between Russell and neo-Kantians. (shrink)

Thomas J.J. Altizer is one of the most important theologians of the twentieth and early twenty-first centuries, and all radical theology must pass through and be conversant with his work and the historical significance of his earlier contributions. This chapter presents Altizer’s essential ideas in a straightforward and accessible manner and provides a guide for the beginning reader.

J.N. Findlay was a South African philosopher who published from the late 1940s into the 1980s. He had a prestigious international academic career, holding many academic posts around the world. This article uses a textual comparative approach and focuses on Findlay’s Gifford Lecture at St Andrews University between 1965 and 1970. The objective of the article is to highlight the extent to which Findlay’s philosophical writings were influenced by Mahāyāna Buddhism. Although predominantly a Platonist, Findlay drew influence from Asian philosophy (...) and religion, particularly Mahāyāna Buddhism. In these lectures, he applies the metaphor of the Platonic Cave to investigate Hegelian and Husserlian approaches to knowledge. Though he was a leading Hegel and Husserl scholar, his reading of these two philosophers is strongly influenced by Mahāyāna Buddhism, resulting in a unique mystical interpretation of these two philosophers. Revisiting Findlay’s writings is significant for two reasons; firstly, he investigated Buddhism prior to the Asian religions being included in Religious Studies departments’ purview in South African universities, and secondly, his interpretation of two prominent Western philosophers along Buddhist lines provides an early attempt at decolonising the predominance of Western philosophical views of knowledge.Contribution: This contribution forms part of a larger collection of essays investigating philosophical works that have had a significant impact on the study of religion. This contribution investigates the Buddhist influence on J.N. Findlay’s philosophical readings of Husserl and Hegel. (shrink)

If Wittgenstein's later account of language is applied to music, what seems to follow is a version of musical formalism. This is to say that the meaning of music is constituted by the rules of a given system of music, and the understanding of music is the ability to follow these rules. I argue that, while this view may seem unattractive at the outset, Wittgenstein actually held this view. Moreover, his later notion of a rule gives us resources to answer (...) some of the traditional criticisms directed against formalism. (shrink)