17th/18th Century Logic

In 1672 John Eliot, English Puritan educator and missionary to New England, published _The Logick Primer: Some Logical Notions to initiate the INDIANS in the knowledge of the Rule of Reason; and to know how to make use thereof_. This roughly 80 page pamphlet introduces syllogistic vocabulary and reasoning so that syllogisms can be created from Biblical texts. The use of logic for proselytizing purposes is not distinctive: What is distinctive about Eliot's book is that it is bilingual, written in (...) both English and Massachusett (Wôpanâak), an Algonquian language spoken in eastern coastal and southeastern Massachusetts. It is one of the earliest bilingual logic textbooks and it is the first, and perhaps only, textbook in an indigenous American language. -/- In this paper, we (1) introduce John Eliot and the linguistic context he was working in; (2) introduce the contents of the _Logick Primer_---vocabulary, inference patterns, and applications; (3) discuss notions of 'Puritan' logic that inform this primer; and (4) address the importance of his work in documenting and expanding the Massachusett language and the problems that accompany his colonial approach to this work. (shrink)

Faust Vrančić's (Faustus Verantius, 1551-1617) logic is analyzed in comparison to Renaissance Aristotelianism in logic with regard to the problem of determining logic, the subject of logic, and understanding the method. Vrančić's logic is compared to Markantun de Dominis' understanding of logic and to the understanding of logic in Jacopo Zabarella and in the Jesuit Renaissance tradition (P. Fonseca, F. Toletus, F. Suárez). In addition, the concept of science is discussed. "Censura logicae" published at the end of Vrančić's "Logica nova" (...) (1616) is attributed to de Dominis. (shrink)

Faust Vrančić's (Faustus Verantius, 1551-1617) logic is analyzed in comparison to Renaissance Aristotelianism in logic with regard to the problem of determining logic, the subject of logic, and understanding the method. Vrančić's logic is compared to Markantun de Dominis' understanding of logic and to the understanding of logic in Jacopo Zabarella and in the Jesuit Renaissance tradition (P. Fonseca, F. Toletus, F. Suárez). In addition, the concept of science is discussed. "Censura logicae" published at the end of Vrančić's "Logica nova" (...) (1616) is attributed to de Dominis. -- German version: 'Faust Vrančić and der Aristotelismus in der Logik', Studia historiae philosophiae Croaticae 2 (1993), 229-252). (shrink)

Johannes Steuchius’ disputatio uses Arabic logic to present an historical account of the development of philosophical thought in Arabia before and after the emergence of Islam. Steuchius first proposes that philosophy drew its origins from the East. His evidence for this claim is that many of the Greek philosophers, considered the forefathers of European philosophy, began cultivating their philosophical thinking as a result of exposure to ancient Eastern philosophy. After the introduction of Greek philosophy, it is agreed that dialectic was (...) among the first of the arts the Arabs practiced. (shrink)

In this fascinating book, Mehmet Karabela reveals the many roles assigned to Islam, Islamic history, the Ottoman Empire, Turks and Arabs by northern European Protestant intellectuals, mostly German Lutherans, from 1650 to 1800. The texts cover many topics that famously captivated European thinkers during a period which Karabela elects to call post-Reformation rather than Enlightenment. There are comparative studies of religion, philosophy, and literature. Karabela’s introduction provides a robust review of the historiography and offers context for patterns that emerge from (...) the texts. (shrink)

Bacon’s philosophy had a wide dissemination in Dutch Seventeenth Century context. This can be explained by the coeval diffusion of Cartesianism. Bacon’s project of a reformation of science was deemed by Heereboord and De Raey as the manifesto of a new philosophy. Along with Geulincx, moreover, De Raey borrowed Bacon’s arguments on the causes of error and on the replacement of Aristotelian natural history, aimed at integrating Descartes’s physics. Also in logic Bacon’s influence was noticeable, as the development of a (...) new Organon had its accomplishment in the Cartesian logic of Clauberg and of De Raey himself. In theology, Heidanus relied on Bacon in order to confute Socinianism. The fortune of Dutch Baconianism had its end with the rise of Newtonianism: as a quantitative, experimental philosophy arose, Bacon’s works were no more regarded as a valuable source of arguments. (shrink)

This article offers an account of the philosophy of language expounded in the Cogitata de interpretatione (1692) of the Dutch philosopher Johannes De Raey (1620-1702). In this work, De Raey provided a theory of the formation and meaning language based on the metaphysics of René Descartes. De Raey distinguished between words signifying passions and sensations, ideas of the intellect, or external things. The aim of this article is to shift away the discussion of De Raey’s critique on the application of (...) the language of practical matters by Lodewijk Meijer and Spinoza, and to redirect modern interpretations to the originality of De Raey’s own reflections on the uses of language. In his linguistic thought, De Raey criticized philosophers such as Hobbes, who supposedly deprived Aristotelian terminology of any reference and meaningful use. The analysis of De Raey testifies to the emergence of the philosophy of language out of the double traditions of logic and metaphysics. It is to be interpreted as an effect of the emergence of an alternative worldview to Aristotelianism. This called for an update of the semantic catalogue of philosophy and practical disciplines. (shrink)

The main aim of the French logician and philosopher Petrus Ramus was to provide a method of teaching the liberal arts enabling the completion of the undergraduate program of studies in 7 years. This method was based on a new logic, in which the complex structure of Aristotle’s Organon and of the Summulae logicales of Peter of Spain is reduced to two main doctrines: the invention of arguments, by which it is possible to find the notions for reasoning and disputing (...) in any discipline, and the disposition of arguments in judgment, i.e., in propositions and syllogisms. Since this logic applies both to demonstrative and to probable reasoning, Ramus and Rudolph Agricola, who first introduced it, labeled it as dialectic. Ramus completed this twofold dialectic with a method, according to which disciplines have to be taught by providing general definitions, to be explained by subsequent dichotomous divisions. According to Ramus, this method ensures a well-ordered hierarchy and division of disciplines, and an efficient means to teach them in a shorter time than in the pedagogical programs of Juan Luis Vivès, Johann Sturm, and Philipp Melanchthon. This method had its main diffusion in the pre-university institutions such as the German gymnasia and gymnasia illustria (e.g., of Herborn), while in Reformed and Catholic universities the acceptance of Ramism was hindered by the predominance of the Aristotelian curriculum. (shrink)

Aristotle divided arguments that persuade into the rhetorical (which happen to persuade), the dialectical (which are strong so ought to persuade to some degree) and the demonstrative (which must persuade if rightly understood). Dialectical arguments were long neglected, partly because Aristotle did not write a book about them. But in the sixteenth and seventeenth century late scholastic authors such as Medina, Cano and Soto developed a sound theory of probable arguments, those that have logical and not merely psychological force but (...) fall short of demonstration. Informed by late medieval treatments of the law of evidence and problems in moral theology and aleatory contracts, they considered the reasons that could render legal, moral, theological, commercial and historical arguments strong though not demonstrative. At the same time, demonstrative arguments became better understood as Galileo and other figures of the Scientific Revolution used mathematical proof in arguments in physics. Galileo moved both dialectical and demonstrative arguments into mathematical territory. (shrink)

Salomon Maimon, a Lithuanian born philosophical autodidact who emigrated to Germany in the late eighteenth century, plays an increasingly important role in the research of classical German philosop...

This volume offers the first-ever complete English translation of Leibniz’s Dissertatio De Arte Combinatoria together with a critical edition of the original Latin text on fa...

This paper formulates a bilateral account of harmony that is an alternative to one proposed by Francez. It builds on an account of harmony for unilateral logic proposed by Kürbis and the observation that reading the rules for the connectives of bilateral logic bottom up gives the grounds and consequences of formulas with the opposite speech act. I formulate a process I call 'inversion' which allows the determination of assertive elimination rules from assertive introduction rules, and rejective elimination rules from (...) rejective introduction rules, and conversely. It corresponds to Francez's notion of vertical harmony. I also formulate a process I call 'conversion', which allows the determination of rejective introduction rules from assertive elimination rules and conversely, and the determination of assertive introduction rules from rejective elimination rules and conversely. It corresponds to Francez's notion of horizontal harmony. The account has a number of features that distinguish it from Francez's. (shrink)

The History of Philosophical and Formal Logic introduces ideas and thinkers central to the development of philosophical and formal logic. From its Aristotelian origins to the present-day arguments, logic is broken down into four main time periods: Antiquity and the Middle Ages The early modern period High modern period Early 20th century Each new time frame begins with an introductory overview highlighting themes and points of importance. Chapters discuss the significance and reception of influential works and look at historical arguments (...) in the context of contemporary debates. To support independent study, comprehensive lists of primary and secondary reading are included at the end of chapters, along with exercises and discussion questions. By clearly presenting and explaining the changes to logic across the history of philosophy, The History of Philosophical and Formal Logic constructs an easy-to-follow narrative. This is an ideal starting point for students looking to understand the historical development of logic. (shrink)

The article analyzes the method of oral disputation in Keckermann’s Gymnasium logicum (f. p. 1605), in his Systematis logici plenioris pars altera (this is a variant of the first treatise, f. p. 1609), in Logicae artis compendium (1615) by Robert Sanderson, and in Ars disserendi seu Logica (1667) by Jacques Chanevelle, S.J. It demonstrates that the disputation method described in Gymnasium logicum consists in the Objection-solving paradigmatic method and, with a qualification, in the Asking-answering paradigmatic method. Most importantly, it shows (...) that both Sanderson and Chanevelle utilize various Keckermann’s elements in the descriptions of disputation. Keckermann therefore seems to play part in the emergence of the Second-scholasticism disputation handbooks. (shrink)

This paper explores Locke’s thinking specifically about syllogisms and more generally about logic and proper logical method. Locke’s texts display a mixed attitude toward syllogisms. On the one hand, he was highly critical of syllogisms and their central role in Scholastic disputation. On the other hand, he sometimes allowed that syllogisms could effectively capture valid forms of inference and could be useful in certain contexts. This paper seeks to explain Locke’s mixed attitude by showing that he believed syllogisms were useful (...) in the context of explanation but not in the context of discovery. Syllogisms could help to formalize and evaluate arguments already constructed using informal psychologistic methods, but they would not help to generate new arguments or to make new discoveries. The second part of the paper examines substantial changes to the fourth edition of the Essay in which Locke expands his critical remarks on syllogisms and related topics. Evidence is presented that strongly suggests Locke made these changes to the Essay in response to works published by John Sergeant. This discovery is important because it indicates Locke’s willingness to consider the views of his adversaries and reformulate his own views accordingly. (shrink)

The seventeenth century can be viewed as an era of innovation in the formal and natural sciences and of paradigmatic diversity in philosophy. 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, or a set of observations regarding a particular theory. 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. (shrink)

A short reconstruction of the analytic-synthetic method, a key idea in Medieval and Early Modern Logic.

Based on an analysis of the category of “infinite judgments” in Kant, we will introduce the logical hexagon of predicate negation. This hexagon allows us to visualize in a single diagram the general structure of both Kant’s solution of the antinomies of pure reason and his argument in favor of Transcendental Idealism.