The work of this dissertation, in a broad sense, seeks to rescue what may be in the original project or nucleus of philosophy, from its Socratic arising: the idea of elucidative rationality. This rationality is aimed at expressing our practices in a way that can be confronted with objections and alternatives. The notion of expression is central to this rationality. This centrality is elucidated by the contemporary philosopher Brandom (1994, 2000, 2008a, 2013), from his view of the semantic inferentialism. With (...) this view, this dissertation, in a strict sense, investigates evidences that leads to the distinction of the inferentially expressivist tradition of syllogistic. In this semantic inferentialism, logic is the “organ of semantic self-consciousness”. In this sense, logic does not define the rational, in the most basic sense, but allows us to be aware, through inferential articulation, of the conceptual contents, which govern all our thoughts. Evidences presented in the work of this dissertation seek to show that the syllogism is marked by the logical-elucidative character of this semantic self-consciousness, because of its expressive role as inseparable from the notion of inference. In the first part of this dissertation, then, the tradition of syllogistics is examined, in which the expression is the main notion. This study is based on the tradition of syllogistics, composed of the Aristotelian school of Campinas, organized by Angioni (2014a), the logical economist Keynes (1906), and the “formalist” schools, represented mainly by the logician Łukasiewicz (1957, 1929/1963) and by Corcoran (1972, 1974, 2009, 2015). The main claims of the Campinas school are analyzed: the non-epistemological, but explanatory, exposition of (scientific) knowledge, in the syllogism, the secondary role of the notion of truth, the priority of the predicative structure, and the suggestion of approaching of the syllogistic to the relevant system of logic. In this analysis, we add the discussion about the reasoning of the epagogic type, important to the practical understanding of the “first principles”. The key points of Keynes are also discussed: the semantic priority of propositional judgment and the explanatory role of deductive inference. The second part of this dissertation discusses the relation between expression, inference and the expressive role of logic, based on the semantic inferentialism of Brandom. In order to discuss this relationship, propaedeutic questions are raised, related to the semantic role of sentences and subsentences (terms and predicates) in language, to different conceptions of logical validity, beyond the truth-functional aspect, to the logical demarcation of symbolic rules, to demarcation of logic, the idea of “formal logic”, and the removal of formal semantics from natural language concern. Next, the theoretical framework of Brandom's semantic inferentialism is presented. In this framework, the idea of philosophical semantics, pragmatisms of the semantic and conceptual type, expressivisms of the rationalist, logical and propositional conceptual type, and the semantically primitive notion of incompatibility come into play. Thus, to those who are interested in the correspondence between ancient logic and modern logic, the work of this dissertation offers a useful contribution, especially to projects of formalization of the syllogistics, which need not appeal against or in favor of a strictly formal approach to logic. (shrink)