Objectivity, as one of the key attributes of science, has become an indispensable part of its ethos and a central theme of the philosophy of science. As such, it has been a subject of philosophical reflection by a number of authors. In our project - in which both philosophers of science and scientists participate - we examine the concept of objectivity in the natural sciences with the tools of experimental philosophy. We aim to identify specific operational dimensions of objectivity, those with which current scientist actually work, thus making them accessible for further theoretical analysis and research. In this text, we present results from the first, qualitative phase of our research based on in-depth interviews and focus groups with scientists working in the Czech Republic. Further, we confront this empirical data with theoretical notions of objectivity (Hacking, Crombie, Solomon, Popper, Galison, Daston, Quine, Kuhn and others). We also present other findings from the research and formulate hypotheses for the research's subsequent phases. [ABSTRACT FROM AUTHOR]