The explicit analysis of argument forms has a history that goes back to Aristotle. He was the first to explore the validity and invalidity of chains of propositions in abstraction from the question of the truth or falsity of individual premisses. He insisted, further, that the laws of non-contradiction and of excluded middle are axioms presupposed by all intelligible communication. If someone is inclined to deny the law of non-contradiction, that principle cannot be demonstrated (that is what it is to be an axiom—to be an indemonstrable self-evident truth), but he or she can be refuted ad hominem. If one indicates something, anything, that presupposes the very principle that the doubter wishes to challenge.
Aristotelian syllogistic focuses on relations of class inclusion and class exclusion between terms. It was the Stoics who proposed a new and more general analysis in terms of propositions as such, and since then the study of formal logic has undergone several major shifts, including, in recent years, the proposal of alternative logics, intuitionist logics (e.g. Dummett 2000 , Prawitz 1980), relevance logics (Read 1988 , 1994), so-called fuzzy logics (Zadeh 1987 , Haack 1996) and other systems that deny bivalence or the principle of non-contradiction or both (e.g. Priest and Routley 1989 , Putnam 1975a : ch. 9, 1983 : ch. 15). I shall have more to say about that later.
The first question that this chapter addresses is how far, or in what sense, the findings of formal logic can claim universal validity. The first, naive, response would have it that whatever logical system we adopt, it has to be universally applicable. On that view, one of the criteria by which such a system has to be judged is, precisely, whether it can be applied to all human communication. The denial of the universal applicability of logical rules implies a radical incommensurability between different conceptual frameworks. That has indeed been some people's reaction to the apparent diversity in systems of belief attested in