It was shown in [3] (see also [5]) that there is a duality between the category of bounded distributive lattices endowed with a join-homomorphism and the category of Priestley spaces endowed with a Priestley relation. In this paper, bounded distributive lattices endowed with a join-homomorphism, are considered as algebras and we characterize the congruences of these algebras in terms of the mentioned duality and certain closed subsets of Priestley spaces. This enable us to characterize the simple and subdirectly irreducible algebras. (...) In particular, Priestley relations enable us to characterize the congruence lattice of the Q-distributive lattices considered in [4]. Moreover, these results give us an effective method to characterize the simple and subdirectly irreducible monadic De Morgan algebras [7].The duality considered in [4], was obtained in terms of the range of the quantifiers, and such a duality was enough to obtain the simple and subdirectly irreducible algebras, but not to characterize the congruences. (shrink)

In the last decades, research in science mapping has delivered several powerful techniques, based on citation or textual analysis, for charting the intellectual organization of research fields. To map the social network underlying science and scholarship, by contrast, science mapping has mainly relied on one method, co-authorship analysis. This method, however, suffers from well-known limitations related to the practice of authorship. Moreover, it does not perform well on those fields where multi-authored publications are rare. In this study, a new method (...) for mapping the social structure of research fields is advanced, based on the analysis of the acknowledgments of academic publications. We first discuss the standard account of the function of acknowledgments in scholarly communication, then we introduce a new interpretative framework in which the acknowledgments are intended as positioning signals exchanged by researchers. Next, we provide the formal definition of the four acknowledgments-based networks that stand at the core of the method, and we test it on a humanities field, analytic philosophy. Results show that acknowledgement-based networks allow to reconstruct the fine-grained social structure of analytic philosophy from different perspectives. Furthermore, by comparing the citation-based maps of the field with the acknowledgments-based networks, it permits to shed light on the relationship between the intellectual and social layer of analytic philosophy. We conclude by presenting practical limitations of the method and by sketching some further research lines. (shrink)

The author elucidates the ontological basis of elementary mathematical theories and thereby assesses their certainty as a foundation for the more complex theories of modern mathematics, such as mathematical analysis and set theory. He adduces arguments in favor of the position of Frege, who held that geometry can provide a sufficiently broad and certain foundation for mathematics.

This book offers an unprecedented quantitative portrait of analytic philosophy focusing on two seemingly marginal features of philosophical texts: citations and acknowledgements in academic publications. Originating from a little network of philosophers based in Oxford, Cambridge, and Vienna, analytic philosophy has become during the Twentieth century a thriving philosophical community with thousands of members worldwide. Leveraging the most advanced techniques from bibliometrics, citations and acknowledgments are used in this book to shed light on both the epistemology and the sociology of (...) this philosophical field, illuminating the intellectual trajectory of analytic philosophy as well as the social characteristics of the analytic community. Special attention is dedicated to the last forty years, providing insights into a phase of analytic philosophy which is still understudied by historians of philosophy. In the eight chapters of the book, readers will find not only numerous quantitative investigations and technical explanations, but also a robust theoretical framework and epistemological reflections on the strengths and limitations of quantitative methods for the study of philosophy. With its strong interdisciplinary appeal, this book will engage a wide range of scholars, including historians of philosophy seeking new methodologies, analytic philosophers interested in a new look at their discipline, and scholars in digital humanities, bibliometrics, and quantitative studies of science, who will find many innovative techniques for investigating disciplinary fields. (shrink)