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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 late fourteenth-century English Carmelite Richard Lavenham was a prolific author of Latin and vernacular treatises on logic, physics, philosophy, and theology. Among other works pertaining to natural philosophy, he authored the short Tractatus terminorum naturalium , preserved in three complete or almost complete late fourteenth- or early fifteenth-century copies, with the opening passage preserved in three other manuscripts. The text is fundamentally a redaction of the Heytesburian Termini naturales , a brief glossary of technical vocabulary of the natural philosophy and physics of the Oxford Calculators, supplemented by additional textual and pictorial material. As such, Lavenham's treatise is a specific branch of an influential tradition of school texts that took the form of elementary treatises, additional glosses, quaestio -commentaries, and excerpts. [ABSTRACT FROM AUTHOR]

Since the late thirteenth century, the counterfactual Filioque debate, i.e., the question whether the Son and the Holy Spirit were distinct persons in the Trinity if the Holy Spirit only proceeded from the Father and not also from the Son, was an interesting context for developing the methodology of extreme thought experiments and the logic of conditionals with impossible antecedents and paradoxes of implication. In the mid-1620s, Puente Hurtado de Mendoza (1578–1641) introduced a strongly critical approach towards the scientific merits of positing certain types of impossible scenarios while joining this traditional debate in his Tractatus de Trinitate. He argued that the counterfactual Filioque problem is (at best) a needless detour and (at worst) either shifts to unreliable discussions of properties of fictional entities or is outright trivial for logical reasons. The present article offers a modern edition of the ninth disputation of Hurtado's Tractatus de Trinitate and analyses logical and methodological aspects of Hurtado's position in the counterfactual Filioque debate. [ABSTRACT FROM AUTHOR]

Scholastic logic provided us with a variety of accounts of validity. With some degree of simplification, validity translated into truth-preservation evaluated against a set of worlds (casus) and was tested against a set of counter-models (instantia). Which inferences are valid depends on replacing 'a set' by 'the set' in such definitions, in other words by specifying the underlying concept of modality. Four levels of modality can be identified in scholastic logic: what can be imagined (casus imaginabilis), what can be the case (casus possibilis), what is the case in situations similar to the actual world (ut nunc), and what is mostly the case (ut in pluribus). The result of these analyses are general accounts of both deductive and inductive validity. The paper aims at various uses of 'casus' (or equivalent concepts) pertaining to the analysis of validity between the fourteenth-century Calculatores and the eighteenth-century post-Bernoullian or post-Wolffian use of 'casus' (in the sense of an outcome in the mathematical treatment of probability and probabilistic logic). The way such concepts were appearing or disappearing in scholastic texts written between late medieval and early modern period will be outlined. [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]

There is a well-documented paradigm-shift in eighteenth century Jesuit philosophy and science, at the very least in Central Europe: traditional scholastic version(s) of Aristotelianism were replaced by early modern rationalism (Wolff's systematisation of Leibnizian philosophy) and early modern science and mathematics. In the field of probability, this meant that the traditional Jesuit engagement with probability, uncertainty, and truthlikeness (in particular, as applied to moral theology) could translate into mathematical language, and can be analysed against the background of the accounts of probability, pre-mathematical Jesuit logic, Wolff's conceptual analysis, and Bernoullian mathematisation. The works of two Jesuit philosophers, Berthold Hauser and Sigismund Storchenau, can be related to this context. The core of their logic of (epistemic) probability is the account of negation (or 'contradiction') and implication (or 'argument'), in particular, the algorithms for computing the reliability of one piece of evidence when compared to the respective counter-evidence and for computing the probability of a conclusion given the probability of its premises. [ABSTRACT FROM AUTHOR]

In the 1330s Roger Swyneshed formulated a solution to semantic paradoxes based on the distinction between correspondence with reality and self-falsification as truth-making factors. Since Swyneshed states that some valid inferences are not truth-preserving, his view implies the question of the general definition of validity which he does not address explicitly. Logical works attributed to Paul of Venice (1369–1429) contain developments of Swyneshed's contextualist semantics substantially modified by the assumption that sentential meanings are objective propositional entities. The main goals of this paper are to show the correlations between the ontological and logical developments of Swyneshed's semantics in the works of Paul of Venice and to outline a context-sensitive formal semantics that could serve as a model of this family of semantic theories. [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]

Expanding on the recent research of Stephen Read and Catarina Dutilh Novaes concerning Thomas Bradwardine's theory of truth, the present paper makes an effort to analyse the Currian conditional in terms of the so-called ‘Bradwardine principle’, i.e. the principle that meaning is closed under entailment. Based upon two possible applications of this approach, alternative solutions to the issues of semantic pathology and trivialisation of deductive systems are presented. [ABSTRACT FROM PUBLISHER]