The question of how to arrive at scientifically secured knowledge has accompanied research from the very beginning. Depending on the scientific context and the historical epoch, answers have been given, essentially depending on the demanded degree of truth and the scientific methodology. Recently, a new scientific methodology has emerged, which is best characterized as "probabilistic rationalism". This methodology is the subject of this book: Over the past decades, the fields of computer

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... and physics have collaborated to create AI-machine learning-based methods for analyzing massive amounts of data collected in modern experiments in view of their probabilistic properties. Artificial intelligence or machine learning is the methodology of the day. The considerations presented here are based on understanding the probabilistic character of scientific statements. In Dortmund, we have investigated not only isolated aspects of these analyses but the entire evolutionary process of knowledge expansion. In this first chapter, we combine interdisciplinary aspects of epistemology from the perspectives of physics, artificial intelligence, and philosophy to form an up-to-date and consistent model of knowledge acquisition. With this model, some known problems of existing epistemological approaches, e.g., the problem of inconsistent experimental results, can be overcome. The refutability of theories is based on testing, as in Popper's paradigm. The conclusion, however, is no longer a binary decision but a probability. Basics, Questions, and Motivation This book describes and discusses new data science methods developed as part of the Collaborative Research Center (CRC) "Data Analysis under Resource Constraints" to solve problems in the field of astro/particle physics. These methods contribute to the solution of the fundamental epistemological question of how conclusions to explanatory theories can be drawn from observations of nature or from measurements in experiments. Although methodologically a multitude of very different sub-problems had to be solved here, the methodological meshing of the algorithms, i.e., the entire analysis cycle, is at the center of our interest. In this first chapter, we sketch the sequence of the solution we have worked out and embed it in its epistemological context before we later turn to specific problems and exemplary approaches. Classically, the problem to be solved first appears in the form of Plato's Allegory of the Cave, in which the researchers are fixed on a bench behind a wall so that they Open Access.