This chapter examines the historical roots of deduction in Ancient Greek philosophy and mathematics. It relies extensively on the work of G.E.R. Lloyd and Reviel Netz to argue that dialogical debating practices in a democratic city-state like Athens were causally instrumental for the emergence of the axiomatic-deductive method in mathematics. The same sociocultural political background was decisive for the emergence of practices of dialectic, the kinds of dialogical interactions famously portrayed in Plato’s dialogues. In turn, dialectic provided the background for the emergence of the first fully-fledged theory of deduction in history, namely Aristotle’s syllogistic.

This chapter focuses on the ‘phylogeny’ of deduction, i.e. how deductive reasoning may have emerged given the genetically endowed cognitive apparatus of humans. It discusses reasoning in non-human animals, Mercier and Sperber’s account of the evolution of reasoning, Heyes’ concept of cognitive gadgets, and neurological studies of deductive reasoning. It is argued that the emergence of deduction should not be viewed as genetically encoded in humans but rather as a product of cultural processes, roughly as described by the cognitive gadgets model.

This chapter argues that Aristotle’s syllogistic emerged from a dialectical matrix as well as from considerations pertaining to scientific demonstration and demonstration in mathematics. This means that, even early on, non-dialogical components motivated and were integrated into theories and practices of deduction. The chapter also briefly discusses two other formidable ancient intellectual traditions and their reflections on logic and reasoning, namely the Indian tradition and the Chinese tradition. It is argued that, while these were indeed highly sophisticated, fully-fledged theories of deduction are not to be found in classical Indian or classical Chinese thought.

This chapter defines and introduces the explanandum of the book, i.e. the phenomenon (or phenomena) that it is about: deductive reasoning and argumentation. It presents deduction as having three main characteristics: necessary truth-preservation – which is perhaps the most central one, distinguishing deduction from other forms of inference and argument such as induction and abduction – perspicuity, and belief-bracketing. It also discusses a number of puzzling features of deduction, i.e. philosophical issues pertaining to deduction that remain open questions, as they have not yet been adequately ‘solved.’ These are: the range and scope of deductive reasoning and argumentation, the nature of deductive necessity, and the function(s) of deduction.

This chapter critically discusses the prominent dialogical accounts of logic and deduction proposed by Lorenzen, Hintikka, and Lakatos. It is argued that, while they contain valuable insights, Lorenzen’s dialogical logic and Hintikka’s game-theoretical semantics ultimately both fail to provide a satisfactory philosophical account of logic and deduction in dialogical terms. This critical evaluation then leads to a precise formulation of the dialogical model defended in the book, the Prover–Skeptic model, which is by and large inspired by Lakatos’ ‘proofs and refutations’ model, but with some important modifications.