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The article is devoted to selected new trends in metaethics, ethics, political philosophy, and the practice of philosophy with the use of artificial intelligence. It consists of five parts. In the first part, I analyze the meaning of the question about new trends in analytical philosophy. In the second part, I present the latest trends in metaethics. In the third part, I briefly characterize the ethics of artificial intelligence. The fourth part, devoted to political philosophy, includes a presentation of the latest publications on meritocracy. The article concludes with considerations about practicing philosophy in the age of artificial intelligence. [ABSTRACT FROM AUTHOR]

The foundations of mathematics cover mathematical as well as philosophical problems. At the turn of the 20th century logicism, formalism and intuitionism, main foundational schools were developed. A natural problem arose, namely of how much the foundations of mathematics influence the real practice of mathematicians. Although mathematics was and still is declared to be independent of philosophy, various foundational controversies concerned some mathematical axioms, e.g. the axiom of choice, or methods of proof (particularly, non-constructive ones) and sometimes qualified them as admissible (or not) in mathematical practice, relatively to their philosophical (and foundational) content. Polish Mathematical School was established in the years 1915–1920. Its research program was outlined by Zygmunt Janiszewski (the Janiszewski program) and suggested that Polish mathematicians should concentrate on special branches of studies, including set theory, topology and mathematical logic. In this way, the foundations of mathematics became a legitimate part of mathematics. In particular, the foundational investigations should be conducted independently of philosophical assumptions and apply all mathematically accepted methods, finitary or not, and the same concerns other branches of mathematics. This scientific ideology contributed essentially to the remarkable development of logic, set theory and topology in Poland.

A recognizable topological model construction shows that any consistent principles of classical set theory, including the validity of the law of the excluded third, together with a standard class theory, do not suffice to demonstrate the general validity of the law of the excluded third. This result calls into question the classical mathematician's ability to offer solid justifications for the logical principles he or she favors.

An interview with Charles McCarty by Piotr Urbańczyk concerning mathematical explanation.

At the end of the 19th century in the fundamentals of mathematics appeared a crisis. It was caused by the paradoxes found in Cantor’s set theory. One of the ideas a resolving the crisis was intuitionism – one of the constructivist trends in the philosophy of mathematics. Its creator was Brouwer, the main representative was Heyting. In this paper described will be attempt to construct a suitable logic for philosophical intuitionism theses. In second paragraph Heyting system will be present – its axioms and matrices truth-. Later Gödel theorem about the inadequacy of finite dimensional matrices for this system will be explained. At the end this paper an infinite sequence of matrices adequate for Heyting axioms proposed by Jaśkowski will be described.

The aim of the article. The purpose of this article is to comprehensively reconstruct and present the theory of knowing of values according to Henryk Elzenberg. Epistemology of values is one of the parts of the of Elzenberg's formal axiology. The reconstruction method and conceptual analysis were used for realisation of the proposal. Discussed concepts. The reconstruction begins with the presentation of the main elements of Elzenber's philosophy of values. First, the concepts of utilitarian and perfectionist value are distinguished, and later perfectionist value is defined as the 'feature' of an object, which is as it should be. Then, Elzenberg's notion of intuition as individual non-sensual representation is explained. Elzenberg's deliberations on the nature of primary judgments are reconstructed. Reflection leads to the conclusion that the fundamental judgments in axiology are individual judgments about features which endow values. Later, Elzenberg's critique of the positions negating the cognitive meaning of the evaluations are presented. The main point of criticism was to demonstrate that the presence of the notion of perfectionist value shows the inability to reduce values to subjective states of consciousness, and that the influence of emotions in the recognition of values can be limited. This leads to the question of a methodology of knowing values, which recommends asceticism and limiting emotions that may side by side determine the value judgment. Cognitive value of the text. The text synthesizes various threads of Elzenberg's epistemology of values. The fundamental to Elzenberg's link between the theory of knowing values and the rest of general axiological considerations is visible. Using the materials contained in unpublished manuscripts, there is some important information on the Elzenberg's concept of intuition. The presented concept shows various arguments that can be used against positions that negate the autonomous and objective character of values, especially against positions that deny the possibility of a competent adjudication of presence of values. [ABSTRACT FROM AUTHOR]

The starting point of my paper is a critique of philosophy of life as it has been presented by Heinrich Rickert in his book Die Philosophie des Lebens (1920). Rickert's critique goes along the line of a dualistic opposition of a subjective and an objective sphere. Life is understood namely, on the one hand, as a subjective experience that by its very nature cannot be conceptualized and, on the other, as an objective natural phenomenon. In the second part of my presentation I focus on a critique that Helmuth Plessner formulated against Rickert's position as well as I analyze his own proposition of philosophy of life. The crucial question of this part is if the philosophy of life as presented in Die Stufen des Organischen actually avoids the critique posed by Rickert. In his philosophy Plessner follows Dilthey's hermeneutical method and combines it with a phenomenological approach by Husserl. In result we get a conception that treats life as an autonomous, "third" reality being located in between the subjective and an objective sphere. This solution makes it possible to overcome Rickert's dualism as well as to propose such a philosophy of life that, first, is able to meet conceptual requirements of philosophical thinking and, second, to address life directly in its variability and dynamism. [ABSTRACT FROM AUTHOR]