Abstract

In this introductory chapter, I set out the background against which the theses and arguments of the rest of this book must be understood. I explain my (minimal) version of pragmatism, and how I use the central concepts that this book is about. My inspiration has been some claims defended or suggested by Frege, and some further developments of Fregean inferentialism promoted by Robert Brandom. I discuss my take on assertion as an activity for whose outcome the agent is accountable. I also offer a complete characterization of the kind of item that propositions are, giving their individuation and identification criteria. In this task, I follow some Fregean insights related to Hume’s Principle and the Julius Caesar problem for the definition of number. Frege is also the source of the approach to the existence of abstract objects that I endorse. Existence is instantiation: a second-level concept. It is legitimate to discuss what is meant by existential claims in science. Nevertheless, the claim that numbers exist, or that propositions exist, is not something that is up for discussion; we simply cannot doubt it, since they are presupposed in our mathematical and assertive practices, respectively. Our very nature as producers and consumers of reasons rests on the assumption that judgeable contents, i.e., propositions, are exchanged in those discursive practices that define human rationality. Finally, in the last section, I explain what I will understand by the notions of argument, argumentation, and inference in the chapters ahead, and discuss material inferences that I contend, following Danielle Macbeth, were accepted by Frege as genuine logical inferences.