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This paper discusses the notion of the “sphere of action” (sphaera activitatis) as developed by a group of seventeenth-century Jesuit intellectuals: Hurtado, Arriaga, Oviedo, and Compton. The problem inherited from fourteenth-century natural philosophers was to describe natural action which is spatially limited and decreases with distance at a regular rate. To capture natural patterns, scholastic philosophers introduced various forms of regularity or “uniformity,” the relevant type for the present context being “uniform difformity.” While the scholastic tradition also defined more sophisticated forms of regularity, these were not part of the discussion in the analyzed corpus. [ABSTRACT FROM AUTHOR]

The seventeenth century can be viewed as an era of (closely related) innovation in the formal and natural sciences and of paradigmatic diversity in philosophy (due to the coexistence of at least the humanist, the late scholastic, and the early modern tradition). Within this environment, the present study focuses on scholastic logic and, in particular, syllogistic. In seventeenth-century scholastic logic two different approaches to logic can be identified, one represented by the Dominicans Báñez, Poinsot, and Comas del Brugar, the other represented by the Jesuits Hurtado, Arriaga, Oviedo, and Compton. These two groups of authors can be contrasted in three prominent features. First, in the role of the theory of validity, which is either a common basis for all particular theories (in this case, sentential logic and syllogistic), or a set of observations regarding a particular theory (in this case, syllogistic). Second, in the view of syllogistic, which is either an implication of a general theory of validity and a semantics of terms, or an algebra of structured objects. Third, in the role of the scholastic analysis of language in terms of suppositio, which either is a semantic underpinning of syllogistic, or it is replaced by a semantics of propositions. [ABSTRACT FROM AUTHOR]

From a general semantic point of view, Thomas Bricot (d. 1516) and John Mair (1467–1550) are proponents of the solution to semantic paradoxes based on appreciation of the contextuality of truth, who differ in their approach to the relations of logical consequence and contradiction. The core of the study is the analysis of Mair's criticism of Bricot presented in the sixth quaestio of his Tractatus insolubilium where the consequences of non-compositional semantics for the concepts of synonymy and logical form are addressed. The polemic between John Mair and Thomas Bricot is construed as having immediate consequences for research in the area of non-compositional semantics. [ABSTRACT FROM AUTHOR]

The paper focuses on the concepts of truth, truth-making and truth- preservation and their role in defining deductive validity as analysed by the late-medieval nominalist scholar Martin Le Maistre (1432-1481) in his Tractatu consequentiarum. This treatise, examined from the point of view of fourteenth- century British and Parisian influences, can be characterised as a critical adoption of the previous logical tradition and as the analysis of validity in term of truth-preservation. Part of this analysis is a study of self-referential phenomena, in particular, of self-referential inferences which are addressed in terms of a Bradwardinian implicit-meaning analysis of self-reference by Le Maistre. Also, his analysis of "consequentia farmalis" summarises the fourteenth-century development of the discussion and compares alternative approaches towards formality. [ABSTRACT FROM AUTHOR]

John Poinsot's concept of logic from his compendium Cursus philosophicus thomisticus will be reconstructed in terms of his concept of logical analysis (resolutio). The fundamental perspective of the research will assume that logical analysis is the central issue of Poinsot's logic which thereby offers a technique of contriving a perfectly transparent language. Three basic concepts of logical analysis are endorsed in Cursus philosophicus: 1. the syntactic concept of analysis: resolutio as explication of compound expressions; 2. the semantic concept of analysis: resolutio as reduction of general statements to singular statements or as making their truth and assertability conditions explicit; 3. the epistemological concept of analysis: resolutio as axiomatisation through deducing all provable sentences from fundamental principles of the respective scientific theory. Theories of definition, "exponibilia", "suppositio", deductive validity, and demonstrative knowledge will be construed as techniques of logical analysis, contributing to syntactic, semantic, logical, and epistemic transparency of perfect languages. [ABSTRACT FROM AUTHOR]