THE FORMAL AND THE FORMALIZED: THE CASES OF SYLLOGISTIC AND SUPPOSITION THEORY

As a discipline, logic is arguably constituted of two main sub-projects: formal theories of argument validity on the basis of a small number of patterns, and theories of how to reduce the multiplicity of arguments in non-logical, informal contexts to the small number of patterns whose validity is systematically studied (i.e. theories of formalization). Regrettably, we now tend to view logic 'proper' exclusively as what falls under the first sub-project, to the neglect of the second, equally important sub-project. In this paper, I discuss two historical theories of argument formalization: Aristotle's syllogistic theory as presented in the "Prior Analytics", and medieval theories of supposition. They both illustrate this two-fold nature of logic, containing in particular illuminating reflections on how to formalize arguments (i.e. the second sub-project). In both cases, the formal methods employed differ from the usual modern technique of translating an argument in ordinary language into a specially designed symbolism, a formal language. The upshot is thus a plea for a broader conceptualization of what it means to formalize.

The Hermeneutical Rehabilitation of Supposition Theory in Seventeenth-Century Protestant Logic

The paper focuses on some aspects of the early modern aftermath of supposition theory within the framework of the protestant logical tradition. Due to the growing influence of Humanism, supposition theory from the third decade of the sixteenth century was the object of general neglect and contempt. While in the late sixteenth-century a number of standard textbooks of post-Tridentine scholastic logic reintegrated this doctrine, although in a bowdlerized version, it remained for a century out of the scope of Protestant logic. The situation changed when the Strasburg Lutheran theologian J.C. Dannhauer, who in 1630 developed and propagated the program of a new discipline which he called ‘general hermeneutics’ (hermeneutica generalis), accentuating the importance of supposition theory as an indispensable device for the purpose of textual interpretation. Due to Dannhauer’s influence on later developments of hermeneutics, which in the seventeenth and early eighteenth centuries was regarded as a logical discipline, supposition theory is still present in several logical treatises of the eighteenth century. The explication of the underlying views on the notion of supposition and its logico-semantic function may give at least some clues as to how to answer the question of what supposition theory was all about.

A Quantified Temporal Logic for Ampliation and Restriction

Temporal logic as a modern discipline is separate from classical logic; it is seen as an addition or expansion of the more basic propositional and predicate logics. This approach is in contrast with logic in the Middle Ages, which was primarily intended as a tool for the analysis of natural language. Because all natural language sentences have tensed verbs, medieval logic is inherently a temporal logic. This fact is most clearly exemplified in medieval theories of supposition. As a case study, we look at the supposition theory of Lambert of Lagny (Auxerre), extracting from it a temporal logic and providing a formalization of that logic.

Semantics and OntologyAn Assessment of Medieval Terminism

This paper aims to assess medieval terminism, particularly supposition theory, in the development of Aristotelian thought in the Latin West. The focus is on what the present author considers the gist of Aristotle’s strategy of argument, to wit conceptual focalization and categorization. This argumentative strategy is more interesting as it can be compared to the modern tool known as ‘scope distinction’.

Supposition Theory and Porretan Theology: Summa Zwettlensis and Dialogus Ratii et Everardi

The article investigates how the problem of (linguistic) reference is treated in the theology of two pupils of Gilbert of Poitiers by means of suppo* terms (supponere; suppositus,-a,-um; suppositio). Supposition is for Gilbert an action performed by a speaker, not a property of terms, and he considers language as a system for communication between human beings: key notions are the ‘sense in the author’s mind’ and the ‘interpreter’s understanding’. In contrast, the two Porretans tend to objectify language as a formal system of terms. Suppositio becomes in the Summa Zwettlensis the name itself as subject term in a proposition, and is divided into many kinds; formal rules are described which govern the influence of the predicate on the subject term’s denotation. In Everard of Ypres’ Dialogus Ratii et Everardi, supponere is a function (officium) of the name, and ‘human is a species of individuals’ is, as in some logical treatises and differently from Gilbert, a case of rhetorical transfer.

The Role of ‘Denotatur’ in Ockham’s Theory of Supposition

In the scholarship on medieval logic and semantics of the last decades, Ockham’s theory of supposition is probably the most extensively studied version of such theories; yet, it seems that we still do not fully understand all its intricacies. In this paper, I focus on a phrase that occurs countless times throughout Ockham’s writings, but in particular in the sections dedicated to supposition in the Summa logicae: the phrase ‘denotatur’. I claim that an adequate understanding of the role of the concept of denotatur within Ockham’s supposition theory shall yield a deeper understanding of the theory as a whole. Here, I first examine a few uses of the term ‘denotatur’ and its variants by other authors. I then turn to Ockham: first I briefly mention some uses of the term in contexts other than his theory of supposition. Following that, I focus on his supposition theory, in particular on how ‘denotatur’ allows him to deal with two crucial puzzles, namely the supposition of empty terms and the supposition of terms in false affirmative propositions. The treatment of these two puzzles suggests that Ockham’s theory of supposition must be understood as a theory chiefly intended for the generation of the meanings of propositions.