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.

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)

t. 1. Problemy vospitanii︠a︡ vsestoronne razvitoĭ lichnosti. Dukhovnyĭ mir shkolʹnika. Metodika vospitanii︠a︡ kollektiva.--t. 2. Formirovanie Kommunisticheskikh ubezhdeniĭ molodogo pokolenii︠a︡. Kak vospitat nastoi︠a︡shchego cheloveka. Sto sovetov uchiteli︠u︡.--t. 3. Serdt︠s︡e otdai︠u︡ deti︠a︡m. Rozhdenie grazhdanina. Pisʹma k synu.--t. 4. Pavlyshskai︠a︡ sredni︠a︡i︠a︡ shkola. Razgovor s molodym direktorom shkoly.--t. 5. Statʹi.

t. 1. Serdt︠s︡e otdai︠u︡ deti︠a︡m. Rozhdenie grazhdanina.--t. 2. Pavlyshskai︠a︡ sredni︠a︡i︠a︡ shkola.

t. 1. Problemy vykhovanni︠a︡ vsebichno rozvynenoï osobystosti. Dukhovnyĭ svit shkoli︠a︡ra. Metodika vykhovanni︠a︡ kolektyvu -- t. 2. Formuvanni︠a︡ komunistychnykh perekonanʹ molodoho pokolinni︠a︡. I︠A︡k vykhovaty spravz︠h︡ni︠u︡ li︠u︡dynu. Sto porad uchytelevi -- t. 3. Sert︠s︡e viddai︠u︡ diti︠a︡m. Narodz︠h︡enni︠a︡ hromadi︠a︡nyna. Lysty do syna -- t. 4. Pavlysʹka seredni︠a︡ shkola. Rozmova z molodym dyrektorom -- t. 5. Statti.

Science maps are visual representations of the structure and dynamics of scholarly knowl­edge. They aim to show how fields, disciplines, journals, scientists, publications, and scientific terms relate to each other. Science mapping is the body of methods and techniques that have been developed for generating science maps. This entry is an introduction to science maps and science mapping. It focuses on the conceptual, theoretical, and methodological issues of science mapping, rather than on the mathematical formulation of science mapping techniques. After (...) a brief history of science mapping, we describe the general procedure for building a science map, presenting the data sources and the methods to select, clean, and pre-process the data. Next, we examine in detail how the most common types of science maps, namely the citation-based and the term-based, are generated. Both are based on networks: the former on the network of publications connected by citations, the latter on the network of terms co-occurring in publications. We review the rationale behind these mapping approaches, as well as the techniques and methods to build the maps. We also present less-common types of science maps, including co-authorship networks, interlocking editorship networks, maps based on patents’ data, and geographic maps of science. Moreover, we consider how time can be represented in science maps to investigate the dynamics of science. We also discuss some epistemological and sociological topics that can help in the interpretation, contextualization, and assessment of science maps. Then, we present some possible applications of science maps in science policy. In the conclusion, we point out why science mapping may be interesting for all the branches of meta-science, from knowl­edge organization to epistemology. (shrink)