Initial Axioms Research Articles

Pragmatism in Education: Philosophical Foundations and Pedagogical Practice

The subject of this article is the ideas in the field of philosophy and practice of education, proposed by the founders of pragmatism: C. Pierce, W. James, J. Dewey, R. Rorty. The concepts of these authors gave rise to one of the most successful philosophies of education, which has been and is being subjected to considerable criticism, but is still in demand and demonstrating effectiveness. The article analyzes the initial axioms of the philosophy of pragmatism and the principles on which, according to the philosophers-authors, this educational model should work. The modern criticism of pragmatism in English-language literature is also touched upon. Attention to the philosophy of pragmatism in education seems justified due to the search for a better educational model that is taking place in Russia today. The scientific novelty of the article lies in the analysis of the key philosophical principles of the educational model of pragmatism along with practical recommendations, as well as in the attention paid to Ch. Pierce and the place, significance, of his ideas in the educational model of pragmatism. Traditionally Ch. Pierce is taken out of the brackets when writing about pragmatism in education. Much more attention is paid to the ideas of W. James, J. Dewey, R. Rorty, while Peirce's prolegomena seem fundamentally significant in understanding pragmatism as a philosophy of education. The author discusses the current controversy around the relevance of pragmatism as a philosophy of education, about its strengths and weaknesses. It is concluded that pragmatism as a philosophy of education carries useful principles associated with consensual practices, critical thinking, dialogue, increased attention to experience and an active cognitive position, and therefore can be used as a counterweight to destructive (commercialization, deprofessionalization) trends in education.

Эволюция систем расселения в аспекте классической теории центральных мест

Considering the features of the evolutionary development of central places' systems, we establish that, contrary to the prevailing point of view, in the general case there is no pronounced relationship between the share of urban population and the number of central places of a lower hierarchy level subordinate to the central place of a given level. Moreover, the axiom of the theory, stating the heterogeneous distribution of only the urban population, should be replaced by the following: “Space is homogeneous and isotropic in all respects, with the exception of the distribution of the entire population or part of it.” Thus, the existence of central systems without rural population does not contradict the theory itself in its classic version. The evolution of central places' systems within an infinite lattice takes place by sequentially filling the hierarchy levels (increasing the value of the K -parameter for a given level), interrupted by the appearance of subsystems (increasing the number of hierarchy levels with constant K )—at least after filling the second and the fifth levels. The article substantiates the possibility of considering the isolated sections of the lattice. In this regard, the axiom of the “rational” consumer behavior can be considered excessive, and the postulate of the infinity of space is rejected. Only two initial axioms—on the polymorphism of central places' systems and on the most compact “packaging” of their parts—can be considered unshakable.

Explicit Treatment of Non-Michaelis-Menten and Atypical Kinetics in Early Drug Discovery*.

Biological systems are highly regulated. They are also highly resistant to sudden perturbations enabling them to maintain the dynamic equilibrium essential to sustain life. This robustness is conferred by regulatory mechanisms that influence the activity of enzymes/proteins within their cellular context to adapt to changing environmental conditions. However, the initial rules governing the study of enzyme kinetics were mostly tested and implemented for cytosolic enzyme systems that were easy to isolate and/or recombinantly express. Moreover, these enzymes lacked complex regulatory modalities. Now, with academic labs and pharmaceutical companies turning their attention to more-complex systems (for instance, multiprotein complexes, oligomeric assemblies, membrane proteins and post-translationally modified proteins), the initial axioms defined by Michaelis-Menten (MM) kinetics are rendered inadequate, and the development of a new kind of kinetic analysis to study these systems is required. This review strives to present an overview of enzyme kinetic mechanisms that are atypical and, oftentimes, do not conform to the classical MM kinetics. Further, it presents initial ideas on the design and analysis of experiments in early drug-discovery for such systems, to enable effective screening and characterisation of small-molecule inhibitors with desirable physiological outcomes.

Методология юриспруденции в контексте парадигм научной рациональности

The article examines the methodological problems of jurisprudence, caused by a change in the paradigms of scientific rationality and corresponding to the level of conceptual structures. This level is characterized by problems of understanding the qualitative evolution of knowledge, as well as an appeal to a more abstract, rather than objective, level of understanding of reality. The named level, usually called philosophical, can be based on two genetically different axioms, namely philosophy, including the philosophy of the phenomenon being studied, as well as the philosophy and epistemology of science. At the same time, the difference in the initial axioms determines the difference in the final conclusions for an apparent terminological similarity. At present, philosophy in jurisprudence is mainly represented by postmodernism; the philosophy of law searches for the demarcation line between the philosophical-legal and theoretical-legal knowledge; the philosophy and epistemology of science that has developed within the framework of natural sciences is aimed at analyzing the foundations of models of scientific rationality, applicable, in particular, to the socio-humanitarian sphere. The legal distancing from classical rationality is represented by two main directions: the overcoming of classical rationality and appeal to the synergy and nonlinear dynamics. For the understanding of the law is enough selection of classical and post-classical type of rationality, while the conjugate with the state of knowledge of social management issues should be allocated classical, non-classical and post-nonclassical types of rationality. The postnonclassical paradigm (synergetics) allows us to consider the existence of unique (historical) open unstable nonlinear hierarchical dynamic complex, attractive self-developing subject systems, included in the sociocultural context, under external chaos and interacting with other subjects and subject systems. As a result, the 
 state and law conceptualized as dynamic organic selfregulating non-equilibrium systems, and in the subject field of law include the idea of philosophy, nonlinear dynamics and mathematical simulation of evolutionary and catastrophic processes that transforms the object and the subject of law and includes in it a number of qualitatively new methodological orientations.

Conditional probability and improper priors

ABSTRACTAccording to Jeffreys improper priors are needed to get the Bayesian machine up and running. This may be disputed, but usage of improper priors flourish. Arguments based on symmetry or information theoretic reference analysis can be most convincing in concrete cases. The foundations of statistics as usually formulated rely on the axioms of a probability space, or alternative information theoretic axioms that imply the axioms of a probability space. These axioms do not include improper laws, but this is typically ignored in papers that consider improper priors.The purpose of this paper is to present a mathematical theory that can be used as a foundation for statistics that include improper priors. This theory includes improper laws in the initial axioms and has in particular Bayes theorem as a consequence. Another consequence is that some of the usual calculation rules are modified. This is important in relation to common statistical practice which usually include improper priors, but tends to use unaltered calculation rules. In some cases, the results are valid, but in other cases inconsistencies may appear. The famous marginalization paradoxes exemplify this latter case.An alternative mathematical theory for the foundations of statistics can be formulated in terms of conditional probability spaces. In this case, the appearance of improper laws is a consequence of the theory. It is proved here that the resulting mathematical structures for the two theories are equivalent. The conclusion is that the choice of the first or the second formulation for the initial axioms can be considered a matter of personal preference. Readers that initially have concerns regarding improper priors can possibly be more open toward a formulation of the initial axioms in terms of conditional probabilities. The interpretation of an improper law is given by the corresponding conditional probabilities.

Research on Context-aware Web Service Composition based on the Fluent Calculus

With the exponential growth in available web services and diversity of user needs, automatic web service selection and composition techniques have attracted the attention of many researchers. This paper presents a fluent calculus-based, context-aware web service composition model. The model uses an artificial intelligence (AI) planning-based web service composition technique, which translates web service composition problems into AI planning problems, and then achieves target goals by acquisition and reasoning using existing environmental knowledge. We first construct a model for service, service context, and service composition on the basis of the fluent calculus theory. Then, we extend the basic axioms of the fluent calculus (initial state and state update axioms) to describe context information, an approach that endows context-aware ability to the fluent calculus-based web service composition. Furthermore, we implement a fluent calculus-based, context-aware web service composition model using a fluent calculus executor or FLUX in a digital tourism service scenario. The experimental results show that the proposed model has context-aware capability and exhibits better performance in service composition.

Improper Priors Are Not Improper

It is well known that improper priors in Bayesian statistics may lead to proper posterior distributions and useful inference procedures. This motivates us to give an elementary introduction to a theoretical frame for statistics that includes improper priors. Axioms that allow improper priors are given by a relaxed version of Kolmogorov’s formulation of probability theory. The theory of conditional probability spaces formulated by Renyi is closely related, but the initial axioms and the motivation differ. One consequence of the axioms is a general Bayes theorem which gives proper posterior distributions, and furthermore, the theory also gives a convenient frame for formulation of non-Bayesian statistical models. The results are in particular relevant for the current usage of improper priors in Markov chain Monte Carlo methods, and for methods for simulation from conditional distributions given sufficient statistics. This theory gives an alternative to ad hoc arguments without an underlying theory, and removes apparent paradoxes. Readers who acknowledge the need for a theoretical basis for statistical inference including improper priors are urged to consider the theory of conditional probability spaces as presented here.

A constructive method of establishing the validity of the theory of systems with non-retaining constraints

The formal axiomatic approach to establishing the validity of the theory of constrained systems has obvious disadvantages: the source of the initial axioms (such as the Befreiungsprinzip and the conditions for constraints to be ideal) remains unclear. A constructive method is proposed for establishing the validity of the main principles of the dynamics of unilaterally constrained systems (including systems with collisions). The idea of the method is related to the analysis of physical methods for realising constraints (stiff systems, anisotropic viscosity, and apparent additional masses). This approach yields simple equations of motion, suitable for the entire time interval and more accurately incorporating the actual dynamics. Several problems of the mechanics of oscillatory systems with collisions are solved by the method. In particular, conditions are determined for the stability of periodic oscillatory modes and a study is made of the evolution of motion with inelastic collisions when the coefficient of restitution is close to unity. Total integrability is established and a qualitative analysis is presented of the problem of parabolic billiards in a uniform force field.