Logical Relativism Through Logical Contexts

We advance an approach to logical contexts that grounds the claim that logic is a local matter: distinct contexts require distinct logics. The approach results from a concern about context individuation, and holds that a logic may be constitutive of a context or domain of application. We add a naturalistic component: distinct domains are more than mere technical curiosities; as intuitionistic mathematics testifies, some of the distinct forms of inference in different domains are actively pursued as legitimate fields of research in current mathematics, so, unless one is willing to revise the current scientific practice, generalism must go. The approach is advanced by discussing some tenets of a similar argument advanced by Shapiro, in the context of logic as models approach. In order to make our view more appealing, we reformulate a version of logic as models approach following naturalistic lines, and bring logic closer to the use of models in science.

On Idealizations and Models in Science Education

Idealizations are omnipresent in science. However, to date, science education research has paid surprisingly little attention to the use of idealizations in fostering students’ model competence and understanding of the nature of science (NOS). The starting point for the theoretical reflection in this paper is that insufficient consideration of idealizations in the science classroom can lead to learning difficulties. The following discussions should help to clarify the terms idealization and model and their relationship to each other. An example is drawn from physics. At least two cases can apply when considering model usage in the classroom. In the first case, to understand an observed phenomenon, a model (as a representation) of the situation to be explained is constructed. At this point, it is necessary to perform idealization. Seemingly, this step is still neglected in much of the science education literature but is well addressed in the philosophy of science. In the second case, existing models to work with are introduced, perhaps alongside a real experimental situation. This approach is called working with models in science education. This paper focuses primarily on the first case. Against the background of model building, a positioning and conceptual approximation of idealizations take place. To organize the idealization process, a framework of several categories of idealization adopted from science philosophy is offered. The framework is intended to stimulate explicit reflection about how models are constructed. The construction of a model by idealization is illustrated through an example from geometrical optics. Finally, the considerations presented are discussed in the context of the literature, and suggested research topics are provided.

Metaphors as models: Towards a typology of metaphor in ancient science

Metaphors play a crucial role in the understanding of science. Since antiquity, metaphors have been used in technical texts to describe structures unknown or unnamed; besides establishing a terminology of science, metaphors are also important for the expression of concepts. However, a concise terminology to classify metaphors in the language of science has not been established yet. But in the context of studying the history of a science and its concepts, a precise typology of metaphors can be helpful. Metaphors have a lot in common with models in science, as has been observed already. In this paper, therefore, I suggest a typology of metaphor in ancient science to fill this terminological gap by using concepts applied to the classification of models in science, as coined by Rom Harré. I propose to differentiate between homeoconceptual metaphors (with the same conceptual frame between source and target) and paraconceptual metaphors (mapped via a different conceptual frame). Furthermore, functional and structural aspects of metaphors in ancient science are taken into account. Case studies from ancient texts displaying metaphors in ancient science are presented and classified following the outlined typology of metaphors.

On the integral transform of Mittag-Leffler-type functions with applications

In this article, we study certain results connected with a generalized Mittag-Leffler function. A generalized Mittag-Leffler function operator of Laplace and Sumudu conversions are investigated and some applications of the recognized results are also deduced as corollaries in this article. The outcomes of the present study are valuable in solving fractional order mathematical models in science, mathematics, finance and technology where the Mittag-Leffler function arises in a natural manner.

Modeller i kjemiundervisning - et eksempel på hvordan de kan bidra til læring og feillæring

We discuss the use of analogical models in science education using examples from online learning resources. We have conducted a teaching program for a group of 7th grade pupils and a group of science teacher students, and the main theme of this program is the use of models in chemistry. Specifically, we study the effect of an analogical model that is designed to promote understanding of the properties of molecules, related to a paper chromatography experiment. Our research indicates that analogical models can be a useful tool to convey understanding of abstract concepts and non-visible phenomena, but they hold serious pitfalls that can lead to misunderstandings amongst students if not used in a proper manner. These findings are in line with other studies. Our data indicate that respondents` knowledge about molecular properties may have increased after participating in this teaching program. However, both groups of respondents consistently used wrong properties to explain the paper chromatography experiment. Conversation transcripts and respondents` models indicate that these misconceptions are enhanced by the analogical model they were given to work with during the teaching program. Based on our findings, we give some advice for how to best present analogies in the classroom.

Boolean Networks Models in Science and Engineering

As a generalization of other notions like cellular automata or Kauffman networks appeared in the last quarter of the twentieth century, the notion of Boolean networks has undergone a special development in recent decades [...]

The Analogical Model of Cognitive Principles and Its Significance for the Dialogue between Science and Theology

Analogical models in science enable us to understand unobservable theoretical entities. We need this basic understanding, even in the case of mental phenomena, where multiple cognitive principles are involved. In this article, we suggest an analogical model of cognition that incorporates basic insights from the philosophies of science and theology, which could serve as a point of contact for the dialogue between science and theology. For this purpose, we presuppose six stages of understanding and the existence of six different theoretical cognitive principles that have their own characteristics, which coincide with some Biblical characters, theological reflections and scientific approaches to finding the truth. The choice of the analogical model and the cognitive principles is justified with their ability to organize, structure and make sense of different segments of scientific and theological knowledge, which otherwise seem confused, unrelated and without structure. The analogical model gives us a big picture of their relations and confirms the ability of the observable macroworld and phenomenological experience to assist us in understanding the realities that, at first sight, seem incomprehensible.