To See the Proof

Abstract

The paper continues studying the visual component's role in logic, starting in the article Logical Visualization of Meaning (2022). The research focuses on the cognitive substantiation of visual representations and the identification of the role of visualization in reasoning and proof. The starting point of the current analysis of the cognitive foundations of the reasoning procedure was to consider the results of neuro-cognitive studies of natural reasoning, which testify in favor of using both a rule-based, symbolic-linguistic mechanism and a representational one based on visual models in the process of natural reasoning. In so doing, I assert that a genuine understanding of the meaning of visual representations in logic involves an appeal to the very nature of logicality. In this regard, there are various approaches to logic as a science. The first one treat logic as an a priori science, purified from any psychological impurities, while according to the second, logic is a cognitively based science. Visualization, in this case, is considered not just as a backup or an illustrative technique but as the essential side of the proof procedure. One of the key questions for the cognitive examination of reasoning is proposed of how the visual component can manifest itself in reasoning. The two sides of this question are revealed: firstly, whether an image can serve as a premise in reasoning, and secondly, whether an illustration can replace/represent the process of reasoning per se as a transition from premises to conclusion. The research presented in the paper testifies to recognizing the visual component not only directly in the process of reasoning but also the corresponding logical formalisms, including proof and conclusion.