17th/18th Century Logic

Leibniz developed several arithmetical interpretations of the assertoric syllogistic in a series of drafts from April 1679. In this article, I present what I take to be one of his most mature articulations of the arithmetical semantics from that series. I show that the assertoric syllogistic can be characterized exactly not only in the full divisibility lattice, as Leibniz implicitly suggests, but in a certain four-element sublattice thereof. This refinement is also shown to be optimal in the sense that the (...) assertoric syllogistic is not complete with respect to any smaller sublattice using Leibniz’s truth conditions. (shrink)

This is the first chapter of Mark Julyan's 'History of the Heavens' which, as a whole, focuses on the many different interpretational problems that emerge within the controversial and previously unavailable appendix to Kant's 'Universal Natural History and Theory of the Heavens'. The first chapter makes the contention that we should interpret J.L. Austin's curious and otherwise eccentric capitalization of the font in the word KANT (twice on pp.2-3) of his 'How to do Things with Words' (1962), through pp.13-14 of (...) the 'Elementum: eine Vorarbeit zum Griechischen und Lateinischen Thesaurus' of Hermann Diels (1899), where Diels describes the Thesaurus of the font based on Aristotle's description of ancient atomism (twice in the Metaphysics and Gen et Corr). This, alongside a play on the words of the name Bernard de Fontenelle and the provocative nature of Austin's obviously false statements regarding Kant, suggest he had seen Kant's astonishingly scandalous opening statement to the appendix; and that he was making a cryptic, but nonetheless fairly tangible reference to it, by means of showing us How To Do Things With Words by embodying a witticism ass encryption, an instance of his theory into his text. (shrink)

Amid the many figures who number among the Thomists writing during the early 20th century period of revival in scholastic thought in the Roman Catholic Church in the wake of the encyclical letter Aeterni Patris (1879) of Leo XIII, there is numbered the French convert, Jacques Maritain (1882–1973). Over the course of his long lifetime, Maritain authored works covering a host of philosophical and theological topics: epistemology, the philosophy of the sciences and natural philosophy, aesthetics, moral philosophy, political philosophy, metaphysics, (...) the philosophy of history, etc. The details concerning Maritain’s youth and conversion have been ably told by others and can be consulted by the interested reader. Detailed bibliographies of his works are available for those interested in engaging the full breadth of his writing. In this article, I will focus on the particular shape of Maritain’s Thomism and his place in the overall hermeneutics of the Thomistic tradition, in particular the debt that he owes to John Poinsot (1589–1644), to whom he refers as “John of St. Thomas,” in accord with the standard appellations within the Thomistic tradition in which he wrote. Following a general account of Maritain’s “style” of Thomism, I will provide a specific catalogue of some central themes in his thought that bear the clear impress of his engagement with the thought of John of St. Thomas. Without claiming to be exhaustive, this article intends to provide the reader with a sufficient appraisal of the main lines of influence exercised upon Maritain’s thought by the Baroque Commentator, without whose philosophical and theological works Maritain’s own labors would be unthinkable. (shrink)

I propose that Leibniz did not state Leibniz’s Law, the logically and metaphysically robust principle that is typically understood as the following biconditional: ∀x ∀y [(x = y) ↔ ∀P (Px ↔ Py)]. To arrive at this conclusion, I examine the three principles that have become associated with Leibniz’s Law: the Substitutivity Principle (salva veritate), the Indiscernibility of Identicals, and the Identity of Indiscernibles. I show that Leibniz intended salva veritate as a semantic principle, never explicitly stated the Indiscernibility of (...) Identicals, and understood the Identity of Indiscernibles as a metaphysical principle. In the debate about Leibniz’s Law, I focus on four commentators: (1) W. V. O. Quine’s construal of salva veritate as the Indiscernibility of Identicals, (2) Nicholas Rescher’s contention that both the Identity of Indiscernibles and salva veritate may be construed as Leibniz’s Law, (3) Fred Feldman’s argument that Leibniz did not state a law or definition of identity, but only a criterion of identity for concepts, and (4) Edwin Curley’s response to Feldman, that Feldman’s assumptions, along with passages in Leibniz, show Leibniz did state Leibniz’s Law. I argue that Feldman’s position is not completely correct but can be amended with insights from Quine, Rescher, and Curley and by reference to Leibniz’s Complete Concept Theory. (shrink)

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 (Eliot 1672) 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, Cambridge, MA: Marmaduke Johnson]. 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)

Im Folgenden stellen wir drei aktuelle Forschungsbereiche zur formalen Logik bei Kant allgemeinverständlich dar und greifen dabei auf die trans zendentale Logik nur dann zurück, wenn sie ein besseres Verständnis der formalen Logik ermöglicht: Zunächst wird Kants Beitrag zur Rezeption und Weiterentwicklung von Euler-artigen Diagrammen dargestellt. Diese Diagramme wurden in den 1990er Jahren wiederentdeckt, als formales System interpretiert und werden heute insbes. in der Didaktik, in den Kognitionswissenschaften, in der Linguistik, in KI-Bereichen wie der (Logik-basierten) Wissensrepräsentation eingesetzt, und auch in (...) der Philosophie verwendet (Kapitel 2). Mehrere Studien haben in den letzten Jahren gezeigt, dass Kant in weiten Teilen seines Systems Oppositionsverhältnisse verwendet, die der Struktur des logischen Quadrats entsprechen. Das logische Quadrat ist heute Gegenstand intensiver Forschung, da es neben der klassischen, auch die paravollständige und parakonsistente Negation abbildet (Kap. 3). Jüngst wurde zudem die Implementierbarkeit der kantischen Logik in ein formalisiertes deduktives System bewiesen. Die Bedeutung dieses Ergebnisses wird insbesondere im Hinblick auf die formalisierte Umsetzung der Sätze vom Widerspruch, vom zureichenden Grund und der Ausschließung des Mittleren erläutert (Kap. 4). Abschließend möchten wir ein paar Perspektiven für die Forschung zur formalen Logik bei Kant nennen (Kap. 5). -- -/- Note: No financial support acknowledged by the second autor (S. Kovač). (shrink)

This paper takes a fresh look at Johannes Clauberg’s Logica vetus et nova, in order to try to clarify its nature and character. Differently from prior readings of Clauberg that analyze his philosophy from the point of view of the construction of ‘ontology’, the approach of the present paper sees in Clauberg’s philosophy a late-Humanist work, accentuating his pedagogic and hermeneutical interests. Indeed, in Clauberg’s philosophy, hermeneutics and pedagogy are intrinsically bound together. This, the paper suggests, is supported not only (...) by the concrete subject-matters of his logic, but also by the examination of Clauberg’s milieu and of his sources. Analysis, in this framework, has a strictly hermeneutical usage. (shrink)

The present study defines the function of the foundation of science in early modern Dutch philosophy, from the first introduction of Cartesian philosophy in Utrecht University by Henricus Regius to the acceptance of Newtonian physics by Willem Jacob ‘s Gravesande. My main claim is that a foundation of science was required because the conceptual premises of new ways in thinking had to be justified not only as alternatives to the established philosophical paradigms or as an answer to the “sceptical crisis” (...) signalled by Richard Popkin, but also in order to be introduced in the academia. This being my general thesis, different kinds of foundation of scientific knowledge are analysed in the light of the specific problems philosophers had to face. To this end, foundational theories are analysed in the light of 1) the overall aim of their philosophy, 2) the relations of disciplines they thought out, 3) what they regarded as scientific knowledge. Through this analysis, I assess that the foundation of science was carried out by metaphysical, logical and theological arguments, which fitted the needs of answering the didactical and introductory requirements of new paradigms, assessed the reliability of new methodology in leading us to grasp the truth, and provided philosophy with its conceptual apparatus. Finally, I demonstrate that a philosophy of science as a reflection on the principles, methods, concepts and application of modern science emerged in the Dutch Republic. (shrink)

Logic diagrams have been increasingly studied and applied for a few decades, not only in logic, but also in many other fields of science. The history of logic diagrams is an important subject, as many current systems and applications of logic diagrams are based on historical predecessors. While traditional histories of logic diagrams cite pioneers such as Leibniz, Euler, Venn, and Peirce, it is not widely known that Kant and the early Kantians in Germany and England played a crucial role (...) in popularising Euler(-type) diagrams. In this paper, the role of the Kantians in the late eighteenth and early nineteenth centuries will be analysed in more detail. It shows that diagrams (or intuition in general) were a highly contentious topic that depend on the philosophical attitude and went beyond logic to touch on issues of physics, metaphysics, linguistics and, above all, mathematics. (shrink)

In this article I engage with a recent debate vis-à-vis Kant’s conception of logic, which deals with whether Kant saw logical laws as normative for, or rather as constitutive of, the faculty of understanding. On the former view, logical laws provide norms for the correct exercise of the understanding; on the latter, they define the necessary structure of the faculty of understanding per se. I claim that these two positions are not mutually exclusive, as Kant held both a normative and (...) a constitutive conception of logic. I also sketch a parallelism between Kant’s conceptions of logic and of ethics: Kant’s twofold conception of logic parallels his view of moral laws as normative (for the human will) but constitutive (of a holy will). (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)

Euler famously used diagrams to illustrate syllogisms in his Lettres à une princesse d’Allemagne [1]. His diagrams are usually seen as suffering from a fatal “ambiguity problem” [11]: as soon as they involve intersecting circles, which are required for the representation of existential statements, it becomes unclear what exactly may be read off from them, and as Hammer & Shin conclusively showed, any set of reading conventions can lead to erroneous conclusions. I claim that Euler diagrams can, however, be used (...) rigorously, if they are read in conjunction with the premises they are supposed to illustrate. More precisely, I give rigorous “heterogeneous” inference rules (in the sense of Barwise and Etchemendy) – rules whose premises are a sentence and a diagram and whose conclusion is a sentence – which allow to use them safely. I conclude that one should abandon the preconception that diagrams can only be used rigorously if they can be given a context-independent semantics. Finally, I suggest that context-dependence is a widespread feature of diagrams: for instance, Mumma [12] noticed that what may be read off from a Euclidean diagram depends not only on the diagram’s appearance, but also on the way it was constructed. (shrink)

Johannes Steuchius was a prominent Swedish Lutheran theologian and academic, a descendant of celebrated Lutheran bishops and academics. Born in 1676 in Härnösand in northern Sweden, Steuchius moved with his family to Lund in 1694 when his father, Matthias Steuchius, the renowned academic and theologian, was appointed Bishop of Lund. After completing his studies in logic and metaphysics at Uppsala University, Steuchius was given the opportunity to attend some of Europe’s foremost Protestant academic institutions, a luxury afforded to few. 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. He 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)

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)

Bolzano's theodicy is a very good example of Platonism in the philosophy of religion. Above all, Bolzano believes that there obtains an ideal realm of truths in themselves and mathematical objects, which are independent of God. Therefore, we are allowed to conclude that God is only a contractor; true, more powerful than Plato's demiurge because He created substances and sustains them in existence, but God must follow a project which is independent of Him. Since the world is determined, by the (...) program and God follows the program, then in fact the program is a god, or better, there is no God. Bolzano's project is not related to God's essence, since it is external to God, and is not made by God. Thus, Bolzano's theodicy is also the absolute opposite of the Cartesian theodicy. God in the Cartesian theodicy can change all rules, all scientific laws and, in consequence, He can create any world He wants. Bolzano's God cannot change anything and cannot create a different world than the world determined by the project, a world different than the one He has created. The responsibility of Bolzano's God for the evil in the world is limited by the project of the world. (shrink)

1. Something strange commenced to happen in the field of logic from the beginning of the seventeenth century. Oral disputation, rather than falling into oblivion as a relic of medieval darkness wit...

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)

A short reconstruction of the Medieval and early modern idea of the analytic-syntetic method.

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 ofsuppositio, 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.

First published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.