The Interpretation of Meaning and Natural Deduction Systems

Abstract

This article analyzes the semantic foundations of an alternative proposal for the introductory teaching of logic in philosophy, focused exclusively on natural deduction systems. The need for this revision stems from a pedagogical gap in standard courses where, although deductive systems are used, their intrinsic meaning is not developed autonomously but is instead addressed through equivalences with model-theoretic concepts. This approach leaves students without a genuine understanding of meaning within the purely inferential framework in which they practice.

In contrast to the hegemony of model-theoretic semantics with its representationalist approach, this work proposes a semantic foundation for natural deduction based on a philosophy of language as use. Drawing on the reflections of the later Wittgenstein and Robert Brandom's normative inferentialism, the presented perspective shifts the focus from an ontological conception of truth towards justificatory practices and the inferential commitments that constitute logical meaning. It is argued that understanding inference rules as norms governing discursive practices provides an autonomous and pedagogically viable semantic basis. This approach, consistent with Dag Prawitz's framework of normalization of derivations, not only enriches the understanding of deduction but also reinstates the central role of pragmatics in the determination of meaning.