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Jan Woleński

Abstract

The paper discusses the concept of adequacy central for Pertażycki’s methodology. According to Petrażycki any valuable scientific theory should be adequate, that is, neither limping (to broad with respect its actual scope) nor jumping (too narrow with respect to its actual scope). Consequently, adequacy of a theory is a stronger condition than its truth. Every adequacy theory is true, but not conversely. However, there is problem, because scientific laws are conditionals (implications). This suggests that adequacy is too strong conditions, because the consequence of an implication has a wider scope than its antecedent. Thus, laws should have the form of equivalence. The paper shows how model-theoretic characterization of theories allows to recognize truth and adequacy, consistently with Petrażycki’s claims.

Open access

Ravi Shanker Dubey, Anil Sharma and Monika Jain

Abstract

Elliptic-type integral plays a major role in the study of different problems of physics and technology including fracture mechanics. Many papers have been written for various families of elliptic-type integrals. Due to their applications here, we are presenting an organized study of certain generalized family of incomplete elliptic integral. The obtained results are basic in nature have various generalizations. While using the fractional integral operator of Riemann-Liouville type, we found several obvious hyper geometric representations. Which are further used to originate many definite integrals relating to their modules and amplitude of elliptic type generalized incomplete integrals.

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Nuri Celik

Abstract

In this article, we introduce some examples of cubic rank transmuted distributions proposed by Granzatto et al. (2017). The statistical aspects of the introduced distributions such as probability density functions, hazard rate functions and reliability functions are studied. The maximum likelihood estimation method is used in order to estimate the parameters of interest. Finally, real data examples are applied for the illustration of these distributions.

Open access

M. Darus and Saumya Singh

Abstract

In the present paper, we introduce and investigate two new subclasses QΣ(n; y;k) and BΣ(n;β;k) of bi-valent functions in the unit disk U. For functions belonging to the classes QΣ(n;y;k) and BΣ(n;β;k), we obtain estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3|.

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Adil Rashid, Tariq Rashid Jan, Akhtar Hussain Bhat and Z. Ahmad

Abstract

There are diverse lifetime models available to the researchers to predict the uncertain behavior of random events but at times they fail to provide adequate fit for some complex and new data sets. New probability distributions are emerging as lifetime models to meet this ever growing demand of modeling complex real world phenomena from different sciences with better efficiency. Here, in this manuscript we shall compose Ailamujia distribution with that of power series distribution. This newly developed distribution called Ailamujia power series distribution reduces to four new special lifetime models on simple specific function parametric setting. Apart from this some important mathematical properties in the form of propositions will also be discussed. Furthermore, characterization and some statistical properties that include mgf, moments, and parameter estimation have also been discussed. Finally, the potency of newly proposed model has been analyzed statistically and graphically and it has been established from the statistical analysis that newly proposed model offers a better fit when it comes to model some lifetime data set.

Open access

Elena Lisanyuk and Evelina Barbashina

Abstract

In this paper we discuss L. Petrażycki’s idea of norm as a normative relation and show its repercussions in two perspectives connected to each other, in the legal theory in the framework of which it was originally introduced and where its role was straightforward, and in logic where it played a shadowy role of a fresh idea which in his expectation would have been the core of the novel logical theories capable of modelling reasoning in law and morals. We pay attention to the scholarly environment in which Petrażycki has proposed those ideas and to the unlucky fate of his academic legacy which is now being rediscovered.

Open access

Andrzej Waleszczyński, Michał Obidziński and Julia Rejewska

Abstract

The characteristic asymmetry in the attribution of intentionality in causing side effects, known as the Knobe effect, is considered to be a stable model of human cognition. This article looks at whether the way of thinking and analysing one scenario may affect the other and whether the mutual relationship between the ways in which both scenarios are analysed may affect the stability of the Knobe effect. The theoretical analyses and empirical studies performed are based on a distinction between moral and non-moral normativity possibly affecting the judgments passed in both scenarios. Therefore, an essential role in judgments about the intentionality of causing a side effect could be played by normative competences responsible for distinguishing between normative orders.

Open access

Adrian Mróz

Abstract

he process of decision making is predictable and irrational according to Daniel Ariely and other economic behaviorists, historians, and philosophers such as Daniel Kahneman or Yuval Noah Harari. Decisions made anteriorly can be, but don’t have to be, present in the actions of a person. Stories and shared belief in myths, especially those that arise from a system of human norms and values and are based on a belief in a “supernatural” order (religion) are important. Because of this, mass cooperation amongst strangers is possible.

Open access

Andrew Schumann

Abstract

In decision making quite often we face permanently changeable and potentially infinite databases when we cannot apply conventional algorithms for choosing a solution. A decision process on infinite databases (e.g. on a database containing a contradiction) is called troubleshooting. A decision on these databases is called creative reasoning. One of the first heuristic semi-logical means for creative decision making were proposed in the theory of inventive problem solving (TIPS) by Genrich Altshuller. In this paper, I show that his approach corresponds to the so-called content-generic logic established by Soviet philosophers as an alternative to mathematical logic. The main assumption of content-genetic is that we cannot reduce our thinking to a mathematical combination of signs or to a language as such and our thought is ever cyclic and reflexive so that it contains ever a history.

Open access

Abbas Pak

Abstract

Fisher information is of key importance in estimation theory. It is used as a tool for characterizing complex signals or systems, with applications, e.g. in biology, geophysics and signal processing. The problem of minimizing Fisher information in a set of distributions has been studied by many researchers. In this paper, based on some rather simple statistical reasoning, we provide an alternative proof for the fact that Gaussian distribution with finite variance minimizes the Fisher information over all distributions with the same variance.