Karolina Tytko

This paper presents a new interpretation of Dedekind’s philosophy of mathematics, based on an analysis of a selected part of his mathematical practice. The article consists of three parts. In the first part, I describe selected interpretations of Dedekind’s philosophy of mathematics, such as fictionalism, creationism, or realism on the one hand, and the ontology of the intentional object or structuralism on the other. In the second part, I introduce the tools and methods that I use in the third part of the article, such as Giaquinto’s proposed use of visual thinking in mathematical practice, as well as the socio-historical perspective of the development of mathematical knowledge. I also explain why a perspective of the philosophy of mathematical practice is useful here. In the last part of the article, I analyze how Dedekind introduced two number systems and present a new and original suggestion for the interpretation of his philosophy.The main object of the research is Dedekind’s mathematical texts and the mathematical concepts and objects they describe, but I also try to reinterpret the non-mathematical statements contained in these texts. Finally, I argue that in addition to certain “technical” arguments that can be made against fictionalism, realism, and creationism in Dedekind’s case, the interpretation presented herecan also be used as an argument from the perspective of cognitive psychology and the socio-historical perspective of mathematical practices.

The launch of ChatGPT in November 2022 and the possibility of using this for free by Internet users was undoubtedly a groundbreaking event that had a huge impact on various areas of life. Focusing on education, and especially on the Prussian model of teaching in Poland, one can be tempt ed to compare this phenomenon to the Big Bang. Almost a year after the debut of ChatGPT, as public awareness of this tool grows, a new model of education is slowly emerging from the “post-explosion matter”. This article aims to draw attention to the challenges posed by the AI era to education, and in a broader perspective – to social epistemology and the social responsibility of science. The paper briefly discusses AI tools, including generative language models. It also analyzes the pros and cons associated with their use by society, especially by students, with a partic ular focus on ChatGPT. The article presents a preliminary analysis of the openness of the Prus sian model of education to the adoption and adaptation of generative models of artificial intelligence. Areas have been indicated which may be changed so profoundly that it will be necessary to redefine the goals, methods and relationships accompanying the educational process. As an example, the relationship between student and teacher is considered. The main advantages and disadvantages of using generative models in education are discussed, thus justifying the need to introduce systemic changes in this area.

In this paper, we aim to show that studies on the new epistemology of mathematics and other sciences are crucial, not only from a theoretical perspective but also in terms of practical aspects, which are particularly significant in the context of teaching and the development of new com petences among teachers. The first aspect addressed here is the age of AI and its potential impact, not just on scientists but on society as a whole. The second aspect focus es on mental imagery, which can be influenced by various factors and, in turn, shape scientific thinking. The third aspect, briefly mentioned, is the issue of the social responsibility of science. Our research approach is grounded in actor-network theory as well as the extended mind thesis. The main problem analysed here is the relationship between the diver sity of mental representations and critical concept kinds in the context of solving mathematical problems (e.g., constructing new structures). Our key conclusion is that this diversity in mental representations can be linked to the presence of critical concept kinds, thereby aiding in the effective construction of new concepts and problem-solving. The need for this diversity in representations can – and should – be cultivated and introduced at the educational level.

This paper presents a new interpretation of Dedekind’s philosophy of mathematics, based on an analysis of a selected part of his mathematical practice. The article consists of three parts. In the first part, I describe selected interpretations of Dedekind’s philosophy of mathematics, such as fictionalism, creationism, or realism on the one hand, and the ontology of the intentional object or structuralism on the other. In the second part, I introduce the tools and methods that I use in the third part of the article, such as Giaquinto’s proposed use of visual thinking in mathematical practice, as well as the socio-historical perspective of the development of mathematical knowledge. I also explain why a perspective of the philosophy of mathematical practice is useful here. In the last part of the article, I analyze how Dedekind introduced two number systems and present a new and original suggestion for the interpretation of his philosophy. The main object of the research is Dedekind’s mathematical texts and the mathematical concepts and objects they describe, but I also try to reinterpret the non-mathematical statements contained in these texts. Finally, I argue that in addition to certain “technical” arguments that can be made against fictionalism, realism, and creationism in Dedekind’s case, the interpretation presented here can also be used as an argument from the perspective of cognitive psychology and the socio-historical perspective of mathematical practices.

We consider application of the structural approximation method to research information flow in social networks. The notations of potential, interparticle flux and energy are considered in terms of social networks. The basic notations of society functioning related to the communication and information transfer processes are modeled by means of multidimensional potentials and the corresponding interactions arisen in networks. A graph associated to the network is considered in the high dimensional space R^d when d is comparable with the number of vertices in graphs.

Książka Grzegorza Hołuba Understanding the Person. Essays on the Personalism of Karol Wojtyła zawiera próbę rekonstrukcji filozofii osoby w ujęciu Karola Wojtyły. Zawiera omówienie następujących zagadnień: geneza filozofii osoby u K. Wojtyły, jego epistemologia i metafizyka osoby, stanowisko w kwestiach świadomości, emocji, działania i godności osoby. Wieloaspektowość i wszechstronność opracowanych zagadnień pozwalają nie tylko zrekonstruować personalistyczną teorię K. Wojtyły, ale również wytyczyć kierunki jej dalszego rozwoju – metafizykę osoby, analizę fenomenologiczną, osoba w kontekście neuronauk. Do tych kierunków można dodać teorię sieci społecznych. Narzędzie to pozwoliłoby na poszerzenie teorii personalistycznej o społeczny, praktyczny wymiar relacji międzyludzkich i praktyczną analizę fenomenów takich, jak np. wolność, odpowiedzialność, solidarność, miłość czy sprawiedliwość. Wyniki tych badań mogłyby uzupełnić filozofię osoby o płaszczyznę społeczną. ------------------------- Zgłoszono: 19/09/2022. Zrecenzowano: 29/10/2022. Zaakceptowano do publikacji: 13/12/2022.