This chapter retraces the genealogical development of deduction in the Latin and Arabic medieval traditions and in the early modern period, and finally the emergence of mathematical logic in the nineteenth century. It is shown that dialogical conceptions of logic remained pervasive in the Latin medieval tradition, but that they coexisted with other, non-dialogical conceptualizations, in part because of the influence of Arabic logic. In the modern period, however, mentalistic conceptions of logic and deduction became increasingly prominent. The chapter thus explains why we (i.e. twenty-first-century philosophers) have by and large forgotten the dialogical roots of deduction.

This chapter returns to the three main features of deduction defined in Chapter 1 from a cognitive, empirically informed perspective: necessary truth-preservation, perspicuity, and belief-bracketing. It discusses experimental findings that lend support to the dialogical conceptualization of these three features presented in Chapter 4. It also discusses the notion of internalization as formulated by Lev Vygotsky, which allows for an explanation of how deductive practices can also take place in purely mono-agent situations: as an intrapersonal enactment of interpersonal dialogues. The upshot is that framing deductive practices dialogically provides cognitive scaffolding that facilitates the ontogenetic development of deductive reasoning in an individual.

In this chapter, it is argued that what is needed to make progress on the issues described in Chapter 1 is a ‘roots’ approach, i.e. going back to the roots of deduction. The distinction between phylogenetic, ontogenetic, and historical roots is introduced, and it is argued that all three perspectives must be taken into account. The chapter further briefly presents the four main senses in which deduction has dialogical roots treated in this book: philosophical roots, historical roots, cognitive roots, and with respect to mathematical practices.

This chapter presents an overview of experimental work on deductive reasoning, which has shown that human reasoners do not seem to reason spontaneously according to the deduction canons. However, there are also experimental results suggesting that, when tackling deductive tasks in groups, performance comes much closer to the canons. These findings offer a partial vindication of the dialogical conception of deduction insofar as they show that, when given the opportunity to engage in dialogues with others, humans become better deductive reasoners.

This chapter presents a dialogical rationale based on the Prover–Skeptic model for the three main features of deduction identified in Chapter 1: necessary truth-preservation, perspicuity, and belief-bracketing. Moreover, it addresses four important ongoing debates in the philosophy of logic: the normativity of logic, logical pluralism, logical paradoxes, and logical consequence. It is shown that the Prover–Skeptic model provides a promising vantage point to address the questions raised in these debates.