Can We “Show” the Correctness of Reasoning? On the Role of Diagrammatic Spatialization in Logical Justification

Our aim is to show that the “analytical diagrams” in the sense of Venn play a role that goes far beyond the simple pedagogical interest. In the first section, we will show that the possibility of using logic diagrams effectively as teaching aids comes from certain cognitive advantages of diagrams. These advantages are worthy of interest in themselves and explain why cognitive sciences and visual communication technicians currently rehabilitate the studies on these diagrams. In the next two sections,our aim will be to show that, beyond the cognitive advantages they bring, diagrams can acquire a truly fundamental function in logic. Two types of question must then be asked in turn. First of all: Can diagrams alone be used to validate all correct forms of reasoning? Or are diagrams destined to be nothing more than illustrations of a valid linguistic demonstration. To answer these first questions, our second section will draw on the results obtained over the last twenty years or so by exporting the methods of demonstration theory to the field of diagrammatic thinking. This section is based on a long appendix which we are publishing in parallel with this article. Then, in the third section, we will test the thesis inspired by Euler’s texts: Can (should?) diagrams be given the task of making the form of propositions and the sequence of correct reasoning intelligible? It is no longer simply a question of using diagrams as a support for demonstrative practice, but of using them as a means, dispensable or not (this is what our analysis will attempt to see), of acquiring the logical intuition that legitimizes inferences. Is the possibility of acquiring these logical intuitions from spatial intuitions a sign of an intimate connivance between the domain of space and that of demonstration, or is the rapprochement superficial and contingent? Finally, in a final section, we will return to the origins of logic, recalling the place that perhaps diagrammatic representation already played in Aristotelian logic, and we will articulate our analyses with those of the historians of ancient logic on this point.