We present an axiomatic framework for nonstandard analysis-the Nonstandard Class Theory which extends von Neumann-Godel-Bernays Set Theory by adding a unary predicate symbol St to the language of NBG means that the class X is standard) and axioms-related to it- analogs of Nelson's idealization, standardization and transfer principles. Those principles are formulated as axioms, rather than axiom schemes, so that NCT is finitely axiomatizable. NCT can be considered as a theory of definable classes of Bounded Set Theory by V. Kanovei (...) and M. Reeken. In many aspects NCT resembles the Alternative Set Theory by P. Vopenka. For example there exist semisets in NCT and it can be proved that a set has a standard finite cardinality iff it does not contain any proper subsemiset. Semisets can be considered as external classes in NCT. Thus the saturation principle can be formalized in NCT. (shrink)
A remarkable phenomenon in our present-day culture has been the broad interest shown in the history of Russian thought, which is continually, and sometimes even from unexpected quarters, showing itself to be of topical interest. Recently, and particularly in connection with the publication of the works of N. F. Fedorov, there has been an exchange of opinions in the pages of various journals with regard to the essence of his philosophical views, revealing not merely conflicting, but in a number of (...) cases mutually exclusive assessments of those views. (shrink)
We develop an axiomatic set theory — the Theory of Hyperfinite Sets THS— which is based on the idea of the existence of proper subclasses of large finite sets. We demonstrate how theorems of classical continuous mathematics can be transfered to THS, prove consistency of THS, and present some applications.
The problem of the relationship between formal logic and philosophy, which arose when formal logic arose, continues to concern both Soviet and foreign philosophers and logicians. Interest in this problem is traceable to a number of factors, among which, it should be noted at the outset, is the appearance of dialectical, logic. With the emergence of dialectical logic, the question of the relationship of formal logic to philosophy is posed anew. No matter how we approach the question of the subject (...) matter of dialectical logic, there is no doubt of the fact that, being logic, it is concerned with the investigation of philosophical problems. It follows that logic is at the same time philosophy or, at least, a portion of philosophy. (shrink)
Environmentalists consider invasions by exotic species of plants and animals to be one of the most serious environmental problems we face today, as well as one of the leading causes of biodiversity loss. We argue that in order to develop and enact sensible policies, it is crucial to consider two philosophical questions: What exactly makes a species native or exotic, and What values are at stake? We focus on the first of these two questions, and offer some preliminary suggestions with (...) regard to the second. Through a series of case studies, we show that it is not always clear whether a species is native or exotic. We identify five possible criteria that could be used for distinguishing natives from exotics. Rather than identifying one of these criteria as the 'correct' one, we suggest that the concepts of 'native' and ' exotic ' function more like what some philosophers have called cluster concepts. That is, there are several characteristics that are typical of native species, and a corresponding set of characteristics that are typical of exotic species. None of these characteristics is either necessary or sufficient for identifying a species as either native or exotic. We then identify several of the values that are at stake in dealing with exotic species, and we suggest that policies need to avoid being overly simplistic. (shrink)
The book deals with the notion of Downward Causation from a wide array of perspectives, including physics, biology, psychology, social science, communication studies, text theory, and philosophy. The book includes proponents as well as opponents discussing the validity of the notion.
The improvement of man, of his ideological and political, occupational, and moral qualities, is a most important condition for success in the building of communism. The socialization of the new man as a creatively active, spiritually rich, and harmoniously developed personality is a goal in our Party's program. It is becoming increasingly obvious that the process of socialization means much more than familiarizing a person with the ideological principles and norms of behavior of a citizen of developed socialist society. Socrates (...) long ago was astounded by the illogic of the man who knew what was good but did what was bad. (shrink)
In speaking of the reasons for the appearance of semantics, certain writers note the following three problems the solution of which demanded semantic analysis: 1) the problem of antinomies; 2) the problem of refining and explaining the basic concepts of formalized logic and mathematics; and 3) the problem of the complete formalization of logic.
By the "logic of scientific knowledge," or simply "the logic of science" we mean the discipline in philosophy concerned with the application of the techniques and methods of logic to scientific knowledge. In studying certain aspects of the logic of scientific knowledge it is possible to employ successfully not only the methods of dialectical logic but those of formal logic. It is the latter that will be the special concern of the present article.
1. The Commentariolum Petitionis is not in the Codex Mediceus of Cicero's correspondence with his brother Quintus, but it appears at the end of the letters to Quintus in the other manuscripts. It starts in the normal manner of a letter and is, or purports to be, a collection of tips on canvassing set in the particular context of M. Cicero's consular candidature in 64: a composition of his brother Quintus. It is printed as no. 12 in Tyrrell and Purser's (...) collection of Cicero's Letters. (shrink)
This collection of essays is concerned with the present world struggle between totalitarianism and the western heritage of freedom. Its contributors are well-known economists, sociologists, philosophers and political scientists from the United States and Europe. It is dedicated "to the moral and intellectual struggle against communism and an analysis of our own democratic institutions." The purpose of the book is both clarification and inspiration. The essays cover such subjects as the nature of freedom in the West, the common patrimony of (...) America and Europe, the role of the masses in representative democracy, intellectualism and political impotence.--V. G. P. (shrink)
This English version of Van Riet's well-known L'épistémologie thomiste makes readily available, for the first time to students in this country, a comprehensive survey of developments in neo-Thomism from the middle of the nineteenth century to the middle of the twentieth. It is an indispensable reference work to a significant movement in contemporary philosophy. Volume I brings the reader to the year 1920 with the contributions of Maritain and Garrigou-Lagrange. Presumably, Volume II will make available the remainder of Van Riet's (...) study, that is, to the year 1946.—V. J. P. (shrink)