Peirce, among his vast logical works, also invented a less known logical framework called by him Existential Graphs. It offers a diagrammatic method to represent logical expressions and logical deductions, so that logical deductions are formulated as transformations of diagrams. In this paper, after a short introduction to Existential Graphs (EGs hereafter), I will propose an interpretation of the framework of EGs in a way that it offers a method for meaning explanation of logical connectives. According to this interpretation, I will try to show, that the meaning explanation displayed by EG is different both from truth-functional and inferentialist approaches. I will focus on the philosophical merits of this framework, more precisely I am going to suggest that the features of EGs satisfy certain essential criteria of a theory of logic as put forward by transcendental investigations. Indeed EGs provide us with a powerful tool to carry out logical analyses not only in a formal way but also as belonging to what Husserl calls the "phenomenology of reason".