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  • Formalizing Medieval Logic: Suppositio, Consequentiae and Obligationes
  • Mary Sirridge
Catarina Dutilh-Novaes . Formalizing Medieval Logic: Suppositio, Consequentiae and Obligationes. Logic, Epistemology and the Unity of Science, 7. Dordrecht: Springer, 2007. Pp. xii + 316. Cloth, $169.00.

The overarching aim of this excellent book is to demonstrate the common ground between medieval logic and logical theories of the twentieth century by analyzing some important medieval approaches to three important topics in medieval logic (suppositio, consequentiae, and obligationes) and then showing that in each case, once we determine what is really going on in the medieval theory, it can be formalized in such a way as to show how it resembles one or more developments in twentieth-century logical theory. Analysis in terms of modern logical theory has a lot to offer the study of medieval logical theories, the author claims, and twentieth-century theory can learn some interesting lessons from examining its medieval counterparts. Much of the material in these specific discussions has been presented in earlier versions in the author's published articles. "The Philosophy of Formalization" (part 4), however, is new. English translations are used in the text, though the Latin is supplied in the footnotes.

Mature supposition theory (Ockham, Burley, and Buridan) is presented, not as a theory of reference or quantification, but as a unified theory of "algorithmic hermeneutics" (77); it allows us to calculate systematically the possible meanings of a proposition as a whole from the meanings of its component parts, with an eye to "distinguishing" the different contents that can be asserted (denotatur) by speaking, writing, or thinking the expression. Such multiple meanings may be due to allowing terms to be self-referential (material supposition) or to stand for species or the like (simple supposition), but also to the sorts of ambiguities of quantifier scope, modal operators, and the like that regularly turn up in discussions of fallacies and sophisms. Some results agree substantially with earlier analyses of Ockham's logic. Ockham's theory ultimately amounts to "an extensional theory of intensions" (31), and the distinction among personal, simple, and material supposition turns out to be more or less functionally independent of the modes of personal supposition. Still, it is a very interesting metatheoretical point that the two parts of the theory are co-ordinate strategies for achieving a single objective: the calculation of propositional meanings. Moreover, the understanding of the distinctive usage of denotatur is not only new and significant; it sounds right.

Part 2, "Buridan's notion of consequentia," energetically pursues a search for twentieth-century near-relatives to Buridan's theory of entailment, an "intriguing combination of semantics and pragmatics" (113). Buridan's "token-based semantics" resembles the "two-dimensional semantics of Kaplan and Stalnaker," on which evaluation of the truth of a proposition involves both its content (abstract meaning) and its particular context of [End Page 469] utterance. Buridan's theory of consequence resembles the "hybrid" view of Shapiro (121); there is a broader notion of consequence (material consequence) similar to Etchemendy's "representational" approach to logical consequence that extends to entailments due to specific intensional content and to the inferability of one proposition from another due to pragmatic factors (inferences involving self-referential propositions or indexicals); a subset of these are valid on the basis of their logical form (formal consequence). One interesting side benefit of comparing Buridan's theory to its twentieth-century relatives is that it becomes clear that his token-based ontology, useful as it is for dramatizing self-reference, needs to be abandoned in favor of linguistic types and schemata if sense is be made of his theory of logical consequence, even if we allow him to avail himself of the notion of "equiform propositions."

"Obligationes as Formal Games" (part 3) presents the theories of Burley, Swynshed, and Strode, in which the Respondent must accept or deny propositions put forward by the Opponent based on their relation to an initial supposition (positum), in modern game-theoretical terms as variants of a game of logical consistency, not as exercises for school boys, explorations of counterfactuals, or just a means of dealing with sophismata and Liar-like paradoxes. The game-theoretical analysis of Burley's theory...