The article deals with historical dynamics of implicit and intuitive elements of mathematical knowledge. The author describes historical dynamics of implicit and intuitive elements and discloses a historical and evolutionary mechanism of building up mathematical knowledge. Each requirement to increase the level of theoretical rigor in mathematics is historically realized as a three-stage process. The first stage considers some general conditions of valid mathematical knowledge recognized by the mathematical community. The second one reveals the level of theoretical rigor increasing, while (...) the third one is characterized by explication of the hidden lemmas. A detailed discussion of historical substantiation of the basic algebra theorem is conducted according to the proposed technique. (shrink)

In the article, questions from the field of philosophy of mathematics are studied. The author is driven by the need to achieve a balance between the philosophy of science and the history of science in formation of concepts of the science development. In this regard, the author justifies the reliance on the methodology of implicit knowledge, combined with the epistemology principle of criticism in studying the development of mathematics as the most expedient and effective. The author expresses the necessity of (...) criticizing the methodology of counterexamples typical for mathematical empiricism declared by I. Lakatos. In the article, an explanation of the concept of implicit knowledge, as well as the examples from mathematics are given. The author believes that application of the concept of implicit knowledge in philosophical and mathematical terms allows us to reveal the unique specificity of mathematical science deeper. The author concludes that it is necessary to recognize the fundamental importance of the methodology of implicit knowledge for the epistemology, as well as for the development of philosophy and methodology of science in general. (shrink)

The article is devoted to the nature of the topological intuition and disclosure of the specifics of topological heuristics in the framework of philosophical theory of knowledge. As we know, intuition is a one of the support categories of the theory of knowledge, the driving force of scientific research. Great importance is mathematical intuition for the solution of non-standard problems, for which there is no algorithm for such a solution. In such cases, the mathematician addresses the so-called heuristics, built on (...) the basis of guesswork, obtained by intuition. The author substantiates the conclusion that topological intuition significantly specific compared to a traditional mathematical intuitions of Euclidean geometry. Today topology is a rapidly developing field of modern mathematics, integrates nicely with other sections of mathematical science. In its most general form of the topology can be defined as the branch of mathematics that studies the properties of spatial figures, does not change under deformations. The topological intuition is an instrument for development of topology on the basis of typological heuristics, which is the result of applying topological intuition to the objects topology. The author demonstrates in detail providing with the examples the specificity of topological heuristics and establishes its interconnection with Euclidean geometry. The author draws the conclusion about the fundamentality of topological intuition, and that it, perhaps, is primary in relation to traditionally understood mathematical intuition. (shrink)

Recent work in the ontology of music suggests that we will avoid confusion if we distinguish between two kinds of question that are typically posed in music ontology. Thus, a distinction has been made between fundamental ontology and higher-order ontology. The former addresses questions about the basic metaphysical options from which ontologists choose. For instance, are musical works types, indicated types, classes of particulars, or some other kind of entity? Higher-order ontology addresses the question of what lies ‘at the centre’ (...) of a specific form of music, such as rock or jazz—or perhaps classical music. The argument of this essay is, first, that a close examination of the best efforts in two of these territories shows that they have the effect of pressing the music in each sphere into implausible Procrustean beds. Second, it is argued that the general question that higher-order ontologies pose, that is, ‘What work-kind is it that lies at the centre of a given kind of music, F?’ is a question based on a mistaken but seductive assumption, namely that the concept of the work of F has actual application. In fact, these concepts—upon which higher-order ontology depends—are mere artefacts of philosophy. The question is also addressed why the assumption is so seductive. Finally, the question finally is posed about what, if anything, is implied from the foregoing about the traditional ontology of classical music. (shrink)

L B Daniels; Some Comments on ‘Value in Education’ by Johanna Burgess1, Journal of Philosophy of Education, Volume 8, Issue 2, 30 May 2006, Pages 237–250, https.

In "But Is It Art?", B. R. Tilghman argues in effect that art's necessary paracriticism on other areas of human activity and interest follows from the condition that artistic and aesthetic perceptions are matters of experiencing aspects. However, aspect-seeing is so common in many avenues of human endeavor that it fails to justify a special artistic paracriticism. The realm of art has a language which must be understood in its own right, as is the case for any social realm which (...) dominates a portion of language as a whole. (shrink)

Heidegger''s conception of death as an attitude toward life, overlooked in current literature on death and dying, offers potential for deepening our understanding of the care of non-critically ill patients. By breaking away from the notion of death as an event distinct from life and viewing it as an anticipated possibility at every moment of life, Heidegger provides insight into our attempts to evade death through our fundamental attitudes and value commitments, which in turn determine our behavior and actions. When (...) combined with a method of application — the Nietzschean principle of reversal — these insights permit the understanding of diverse types of human mentality confronted with significant situations. Among the most important applications of these conceptions is to persons in need of medical care, and the resultant types, which are sampled as hypothetical cases, carry important implications for the sensitive care and psychosocial management of non-terminally ill patients. (shrink)

Any comprehensive theory of narrative must accommodate both the justificational and the creative elements of narrative, the activities leading to narrative, and reflections upon the finished product. This examination of four levels of theory reveals the incompleteness of most extant theories, including those of Hayden White and Ricoeur. The four levels are: 1. narrative discourse and temporal language; 2. narrative and historical constructions; 3. narrative objects or stories; and 4. narrative functions and purposes. We remain far from our goal of (...) achieving a comprehensive theory. However, by placing theories and partial theories within a metatheoretical framework, we can see more clearly their nature, ramifications, and limits, thereby differentiating between the contributions and the philosophical fads. (shrink)

An enormous amount of philosophical literature gets published nowadays. Some of it is good; some is fit only for pulping. We get into the habit not so much of reading as of glancing through the torrent that pours down on us. But sometimes special conditions arise. It so happened that I was forced to spend about a month in the hospital. I took with me the book Evolutionary Epistemology and the Logic of the Social Sciences: K. Popper and His Critics (...) [Evoliutsionnaia epistemologiia i logika sotsial'nykh nauk. K. Popper i ego kritiki] . I attentively read it through and without any irony I can say that I felt "legitimate pride and deep satisfaction." Legitimate pride for philosophy and deep satisfaction with the content of the book. And although readers of Problems of Philosophy [Voprosy filosofii] have already had the opportunity of reading a review of this book , I would like to return to it and make in passing a number of points about Popper's philosophy in general. (shrink)

It is argued that ideas and theories often evolve into preconceptions of our perceptions. Such evolution is implicit in Heidegger's notion of truths of alethia. The description of this process holds implications for the traditional givenness of humans for themselves in terms of the changabllity of absolute presuppositions. Among the implications are 1. the insufficiency of the historical mode for explaining changes in human self-perception; 2. the inadequacy of radical subjectivism and environmentalism; 3. a radical contingency and complexity to the (...) course of human conceptualization; and 4. the awareness that human efforts can influence alterations in preconceptions. The influence of modern brain theory is subject to these conditions. (shrink)