This essay is part of larger project in which I attempt to show that Western formal logic, from its inception in Aristotle onward, has both been partially constituted by, and partially constitutive of, what has become known as racism. More specifically, (a) racist/quasi-racist/proto-racist political forces were part of the impetus for logic’s attempt to classify the world into mutually exclusive, hierarchically-valued categories in the first place; and (b) these classifications, in turn, have been deployed throughout history to justify (...) and empower racism/quasi-racism/proto-racism. In other words, (a) an important part of the chaos and messiness that so troubles logic has been the natural bio-cultural diversity of human beings as described by concepts such as race and ethnicity; and (b) once these concepts were historically in place, taken for granted, buttressed with pseudo-science, and had their origins forgotten, they became tools for the oppression of diverse human groups. The central thesis of this essay is that close readings of a variety of Leibniz’s writings (including several essays and one letter) will reveal a pattern of mutual dependency and creation in regard to logic and racism in Leibniz. My conclusion will be that there is a meaningful connection between logic and racism (or at least between logic and politics in general) in Leibniz such that one should be skeptical of his logic’s claim to offer transparent and neutral descriptions of the world as well as imperatives for action. Put differently, I want to ask the following specific question: how do Leibniz’s own racially-informed political goals, along with the emergence of race-centric European colonialism, both invest and disguise themselves within Leibniz’s mathematizing of logic? (shrink)

Through the reconstruction of Leibniz's theory of the degrees of knowledge, this e-book investigates and explores the intrinsic relationship of imagination with space and time. The inquiry into this relationship defines the logic of imagination that characterizes both human and non-human animals, albeit differently, making them two different species of imaginative animals. -/- Lucia Oliveri explains how the emergence of language in human animals goes hand in hand with the emergence of thought and a different form of rationality (...) constituted by logical inferences based on identity and contradiction, principles that are out of reach of the imagination. The e-book concludes that the presence of innate principles in human animals transforms the way in which they sense-perceive the world, thereby constantly increasing the distinction between human and non-human animals. -/- Keywords: human and non-human animals, Leibniz and Locke on ideas, Leibniz on bodies, Leibniz on conceivability, Leibniz on degrees of knowledge, Leibniz on degrees of perception, Leibniz on innate ideas, Leibniz on modality, Leibniz on similarity and congruence, Leibniz on space and time, Leibniz’s philosophy of language, theory of types. (shrink)

Leibniz was born near the conclusion of the chaotic period of the Thirty Years War. He studied law and then spent much of his life in the service of nobility and royalty, particularly the House of Hanover that assumed the British Crown a few years before his death. Best known for his works on metaphysics, mathematics, and logic, Leibniz's extensive political correspondence and writings concerned the foundations of law, local and international political affairs and social problems, and moral (...) and political philosophy. (shrink)

Leibniz argues that there must be a fundamental level of simple substances because composites borrow their reality from their constituents and not all reality can be borrowed. I contend that the underlying logic of this ‘borrowed reality argument’ has been misunderstood, particularly the rationale for the key premise that not all reality can be borrowed. Contrary to what has been suggested, the rationale turns neither on the alleged viciousness of an unending regress of reality borrowers nor on the Principle (...) of Sufficient Reason, but on the idea that composites are phenomena and thus can be real only insofar as they have a foundation in substances, from which they directly ‘borrow’ their reality. The claim that composites are phenomena rests in turn on Leibniz's conceptualism about relations. So understood, what initially looked like a disappointingly simple argument for simples turns out to be a rather rich and sophisticated one. (shrink)

Our computational metaphysics group describes its use of automated reasoning tools to study Leibniz’s theory of concepts. We start with a reconstruction of Leibniz’s theory within the theory of abstract objects (henceforth ‘object theory’). Leibniz’s theory of concepts, under this reconstruction, has a non-modal algebra of concepts, a concept-containment theory of truth, and a modal metaphysics of complete individual concepts. We show how the object-theoretic reconstruction of these components of Leibniz’s theory can be represented for investigation by means of automated (...) theorem provers and finite model builders. The fundamental theorem of Leibniz’s theory is derived using these tools. (shrink)

Leibniz thinks that every created substance is causally active, and yet causally independent of every other: none can cause changes in any but itself. This is not controversial. But Leibniz also thinks that every created substance is existentially independent of every other: it is metaphysically possible for any to exist with or without any other. This is controversial. I argue that, given a mainstream reading of Leibniz’s essentialism, if one accepts the former, uncontroversial interpretation concerning causal independence, then one ought (...) also to accept the latter, controversial one concerning existential independence. This is a new way to defend the ‘existential independence’ interpretation. Moreover, this defense provides a new approach for defending the broadly ‘non-logical’ interpretive camp in the longstanding debate over Leibniz’s views on incompossibility, against perhaps the strongest objection leveled by advocates of the opposing broadly ‘logical’ interpretation. (shrink)

Llull and Leibniz both subscribed to conceptual atomism: the belief that the majority of concepts are compounds constructed from a relatively small number of primitive concepts. Llull worked out techniques for finding the logically possible combinations of his primitives, but Leibniz criticized Llull’s execution of these techniques. This article argues that Leibniz was right about things being more complicated than Llull thought but that he was wrong about the details. The paper attempts to correct these details.

The rigor and precision of Leibniz's "possible world" evolved into the concept of Turing machine, and with the birth of the first computer and the physical realization of Turing machine, human cognitive and intelligent activities were optimistically considered by cognitive scientists to be convertible into computational programs for simulation by machines. Cognitive science then formed the research agenda of "cognitive computationalism", and our Chinese scholars have responded to this general view that "the essence of cognition is computation" and that (...) the human brain and computers are merely formal systems for manipulating and processing symbols in their respective fields. Professor Hong Dingguo used the concepts of "manifest order" and "hidden order", Professor Jin Gulun used the philosophical categories of "constitutive theory" and "generative theory", and Liu Yuesheng used the concept of "cognition". Professor Hong Dingguo reinterpreted the relationship between the "real world" and the "possible world" by using the concepts of "manifest sequence" and "hidden sequence", Professor Jin Wulun used the philosophical categories of "composition theory" and "generation theory", and Professor Liu Yuesheng used the generalized information paradigm of "structural information" and "exchange information". "This provides a profound elucidation of the nature of cognitive logic and the process of human cognitive activities becoming symbols through coding and puts forward theoretical limits. The current theoretical dilemma and practical difficulty of cognitive science lies in the fact that it has developed algorithmic concepts in the Turing sense that can only model the explicitly sequential part of cognitive and intellectual activity, forming a constitutive atomic abstraction, or in our terms, classical "structural information", which cannot fully explain the inner mechanisms of human mental activity and its embodied flexibility, selectivity and self-emergence. Wu Xuemou's pan-system theory does not simply rely on logic and Turing machine algorithms, but models human intelligence by treating structural information as a complex large system composed of a collection of elements and a collection of relations (exchange information: five mutual eight chips), in order to break through the narrow path of seeking only the local consistency of the system as currently done; while Wang Dekui's exploration of the three-spin biological and physical path and Huang Zhanji's abandonment of the artificial means of logic to seek the large logical natural mechanisms and Mr. Zhou Liquan's proposal of a schema for successful communication using natural language on the basis of concepts such as context and implicit connotation ("Logic — A Theory of Correct Thinking and Successful Communication"), all reflect the milestones of Chinese scholars who seek to address the deeper issues of cognitive science. We believe that along this series of explorations, combined with new results in recent years in the fields of artificial life and evolutionary computation, a new research agenda in cognitive science will emerge. (shrink)

This paper argues for an interpretation of Leibniz’s claim that physics requires both mechanical and teleological principles as a view regarding the interpretation of physical theories. Granting that Leibniz’s fundamental ontology remains non-physical, or mentalistic, it argues that teleological principles nevertheless ground a realist commitment about mechanical descriptions of phenomena. The empirical results of the new sciences, according to Leibniz, have genuine truth conditions: there is a fact of the matter about the regularities observed in experience. Taking this stance, however, (...) requires bringing non-empirical reasons to bear upon mechanical causal claims. This paper first evaluates extant interpretations of Leibniz’s thesis that there are two realms in physics as describing parallel, self-sufficient sets of laws. It then examines Leibniz’s use of teleological principles to interpret scientific results in the context of his interventions in debates in seventeenth-century kinematic theory, and in the teaching of Copernicanism. Leibniz’s use of the principle of continuity and the principle of simplicity, for instance, reveal an underlying commitment to the truth-aptness, or approximate truth-aptness, of the new natural sciences. The paper concludes with a brief remark on the relation between metaphysics, theology, and physics in Leibniz. (shrink)

An objective of thisthesis is to investigate whether philosophical tradition can justify or support some of the arguments that are at the basis of Leibniz’s system (for example, monads have no window to the exterior world, a phrase that summarises the structure of Monadology). I shall demonstrate how Leibniz reflects the concerns and the positions of his key predecessors. Thus, the aim of the thesis is to explore key antecedents to Leibniz’s central doctrines. The thesis argues that Leibniz carried out (...) a logical development of some principles in the eclectic system of Plotinus, which resulted in the structure of Monadology. Whether Leibniz’s project was successful or not will depend on how we view those principles. (shrink)

This paper focuses on Leibniz’s conception of modality and its application to the issue of natural laws. The core of Leibniz’s investigation of the modality of natural laws lays in the distinction between necessary, geometrical laws on the one hand, and contingent, physical laws of nature on the other. For Leibniz, the contingency of physical laws entailed the assumption of the existence of an additional form of causality beyond mechanical or efficient ones. While geometrical truths, being necessary, do not require (...) the use of the principle of sufficient reason, physical laws are not strictly determined by geometry and therefore are logically distinct from geometrical laws. As a consequence, the set of laws that regulate the physical laws could have been created otherwise by God. However, in addition to this, the contingency of natural laws does not consist only in the fact that God has chosen them over other possible ones. On the contrary, Leibniz understood the status of natural laws as arising from the action internal to physical substances. Hence the actuality of physical laws results from a causal power that is inherent to substances rather than being the mere consequence of the way God arranged the relations between physical objects. Focusing on three instances of Leibniz’s treatment of contingency in physics, this paper argues that, in order to account for the contingency of physical laws, Leibniz maintained that final causes, in addition to efficient and mechanical ones, must operate in physical processes and operations. (shrink)

Contigency is a definition for which is noted for not having the principle of contradiction in itself, for which gives a different truths from what we are used to derive from geometry as an essential field for knowledge of creating strong logics. Leibniz clearly states one of his ideas for God, and why there must be contigent truths and necessary truths.

Maimonides’ Latin translation of Moreh Nevukhim | Guide for the Perplexed, was the most influential Jewish work in the last millennia (Di Segni, 2019; Rubio, 2006; Wohlman, 1988, 1995; Kohler, 2017). It marked the beginning of scholasticism, a daughter of Judaism raised by Jewish thinkers, according to historian Heinrich Graetz (Geschichte der Juden, L. 6, Leipzig 1861, p. xii). Printed by Gutenberg's first mechanical press, its influence in the West went as far as the Fifth Lateran Council (1512 — 1517) (...) "where scholars were encouraged to remove the difficulties which seemed to divide the whole of theology and philosophy (Leibniz, Théodicée, 11)." For centuries, the Guide revolutionized the curriculum of school instruction by reintegrating the natural laws of thought in the sphere of faith (the fourth of which became Leibniz’ Principle of sufficient reason). This complete collection of notes expounds the ideas of the Guide and features all the passages selected and rewritten by Leibniz. This first complete annotated bilingual translation of the original manuscripts in Latin serves as an entry point to the faith in conformity with Reason. This complete collection of notes expounds the ideas of the Guide as selected and rewritten by Leibniz, the famous mathematician inventor of computer arithmetic, considered the last universal genius. The first complete bilingual translation in three centuries features on the front cover Rembrandt's Philosopher in meditation, and a recommendation from Leibniz's himself on the back: "Rabbi Maimonides' excellent book, A Guide for the Perplexed, is more philosophical than I imagined and worthy of careful reading." According to Malbim’s translator, Noah Rosenbloom, the book’s epigraph indicates that nineteenth-century Rabbi Leibush ben Yehiel Michel Wisser, also known as Malbim, was familiar with Leibniz’ Theodicy. In Leibniz’ anthology of the Guide, the reader can get a detailed glimpse of Leibniz' impressions of Maimonides. The Foreword by Leibniz' translator Lloyd Strickland suggests that there were sympathies and perhaps even overlaps between the thoughts of both universal luminaries. -/- . (shrink)

Abstract -/- The indistinction between repose and uniform movement exposed in the principle of inertia marks one of the most famous dissertations: the discussion between Newton and Leibniz. Through their respective conceptions of space, both seek to solve the problem of indistinction. The relational space of Leibniz, supported by the principle of sufficient reason and the identity of indiscernibles leads to the kinematic solution of the problem of inertia. The objective of this paper is to show the contribution of Leibniz, (...) in terms of relations of order, by distinguishing between equality by identity and equality by equivalence. Under a philosophical approach we link identity, equivalence and equality as relations of order with the indiscernibility between different states of movement. We expose first the principle of sufficient reason and the identity of indiscernibles. Under Bernoulli's principle of indifference, we argue that we distinguish between equality in abstract and equality in concrete. As a third part, we present the relationship between the identity of the indiscernibles and the predicate of equality under logical analysis. Finally we present the conclusions. -/- . (shrink)

In this unpublished Latin fragment (which dates from May 1702) G. W. Leibniz criticizes the Cartesian conception of body and force and develops his own notion of matter, extension and his theory of forces. He argues against Descartes and Cartesians that 1) the essence of corporal bodies cannot be reduced to extension alone but the latter arise from the primitive force itself, 2) consequently Cartesian quantity of motion falls short to account the motive force of a moving body since the (...) true nature of physical bodies which can only be understood through a careful analysis of dynamical forces. -/- Mayıs 1702’de kaleme aldığı ve ölümünden sonra yayımlanan bu Latince fragmanda G. W. Leibniz, Kartezyen felsefenin cisim ve kuvvet anlayışını eleştirir ve kendi madde, uzam ve kuvvetler teorisini geliştirir. Leibniz, Descartes ve Kartezyenlere karşı 1) cisimlerin özünün yalnızca uzama indirgenemeyeceğini, bunun ilksel kuvvetin kendisinden kaynaklandığını, 2) sonuç olarak da Kartezyen hareket miktarının hareket eden bir cismin kuvvetini açıklamakta yetersiz kaldığını, çünkü fiziksel cisimlerin gerçek doğasının ancak dinamik kuvvetlerin dikkatli bir analiziyle anlaşılabileceğini ileri sürer. (shrink)

An English translation of Leibniz's fragment "Horizon rerum humanarum... " in which he announces a plan to demonstrate "that the number of truths or falsehoods enunciable by humans as they are now is limited; and also that if the present condition of humanity persisted long enough, it would happen that the greatest part of what they would communicate in words, whether by talking or writing, would have to coincide with what others have already communicated in the past; and moreover (...) that new humans would lead an entire life that appears thoroughly the same to the senses as lives that others have already led." . (shrink)

La traduction latine du livre de Maïmonide Moreh Nevukhim | Guide des égarés, a été l'ouvrage juif le plus influent des derniers millénaires (Di Segni, 2019 ; Rubio, 2006 ; Wohlman, 1988, 1995 ; Kohler, 2017). Elle marqua le début de la scolastique, fille du judaïsme élevée par des penseurs juifs, selon l'historien Heinrich Graetz (Geschichte der Juden, L. 6, Leipzig 1861, p. xii). Imprimée par la première presse mécanique de Gutenberg, son influence en Occident s'étendit jusqu'au Vème concile du (...) Latran (1512-1517) « où les savants furent encouragés à lever les difficultés qui semblaient diviser l'ensemble de la théologie et de la philosophie — (Leibniz, Théodicée, 11 ) ». Pendant des siècles, le Guide a révolutionné le programme d'instruction scolaire en réintégrant dans le domaine de la foi les lois de la pensée (dont la quatrième est devenue le principe de la raison suffisante de Leibniz). Cette collection complète de notes qui expose les idées du Guide fournit tous les passages sélectionnés et réécrits par Leibniz. Cette première traduction complète bilingue annotée des manuscrits originaux en latin sert de porte d'entrée à la foi conforme à la Raison. -/- « L'excellent livre du Rabbin Moïse Maïmonide, le Guide des égarés, est plus philosophique que je ne l'avais imaginé et mérite une lecture attentive. L'auteur, distingué par son intelligence en philosophie, était versé dans les mathématiques, l'art médical, et aussi dans la connaissance de Saintes Écritures. » — G. W. LEIBNIZ, 1685, Anthologie de Leibniz du Guide de Maïmonide, Chapitre III. (shrink)

“Probably Peirce’s best-known works are the first two articles in a series of six that originally were collectively entitled Illustrations of the Logic of Science and published in Popular Science Monthly from November 1877 through August 1878. The first is entitled ‘The Fixation of Belief’ and the second is entitled ‘How to Make Our Ideas Clear.’ In the first of these papers Peirce defended, in a manner consistent with not accepting naive realism, the superiority of the scientific method over (...) other methods of overcoming doubt and ‘fixing belief.’” — Robert Burch, “Charles Sanders Peirce,” entry in the Stanford Encyclopedia of Philosophy (2021 revision) -/- “Pragmatist epistemologies often explore how we can carry out inquiries in a self-controlled and fruitful way. (Where much analytic epistemology centres around the concept of knowledge, considered as an idealised end-point of human thought, pragmatist epistemology centres around the concept of inquiry, considered as the process of knowledge-seeking and how we can improve it.) So pragmatists often provide rich accounts of the capacities or virtues that we must possess in order to inquire well, and the rules or guiding principles that we should adopt. A canonical account is Peirce’s classic early paper ‘The Fixation of Belief‘. Here Peirce states that inquiry is a struggle to replace doubt with “settled belief“, and that the only method of inquiry that can make sense of the fact that at least some of us are disturbed by inconsistent beliefs, and will subsequently reflect upon which methods of fixing belief are correct is the Method of Science, which draws on the Pragmatic Maxim described above. This contrasts with three other methods of fixing belief: i) refusing to consider evidence contrary to one’s favored beliefs (the Method of Tenacity), ii) accepting an institution’s dictates (the Method of Authority), iii) developing the most rationally coherent or elegant-seeming belief-set (the A Priori Method).“ — Catherine Legg, “Pragmatism,” entry in the Stanford Encyclopedia of Philosophy (2021 revision). (shrink)

John Venn has the “uneasy suspicion” that the stagnation in mathematical logic between J. H. Lambert and George Boole was due to Kant’s “disastrous effect on logical method,” namely the “strictest preservation [of logic] from mathematical encroachment.” Kant’s actual position is more nuanced, however. In this chapter, I tease out the nuances by examining his use of Leonhard Euler’s circles and comparing it with Euler’s own use. I do so in light of the developments in logical calculus from (...) G. W. Leibniz to Lambert and Gottfried Ploucquet. While Kant is evidently open to using mathematical tools in logic, his main concern is to clarify what mathematical tools can be used to achieve. For without such clarification, all efforts at introducing mathematical tools into logic would be blind if not complete waste of time. In the end, Kant would stress, the means provided by formal logic at best help us to express and order what we already know in some sense. No matter how much mathematical notations may enhance the precision of this function of formal logic, it does not change the fact that no truths can, strictly speaking, be revealed or established by means of those notations. (shrink)

We explore the view that Frege's puzzle is a source of straightforward counterexamples to Leibniz's law. Taking this seriously requires us to revise the classical logic of quantifiers and identity; we work out the options, in the context of higher-order logic. The logics we arrive at provide the resources for a straightforward semantics of attitude reports that is consistent with the Millian thesis that the meaning of a name is just the thing it stands for. We provide (...) models to show that some of these logics are non-degenerate. (shrink)

Review of "The Construction of Logical Space", by Augustin Rayo. Oxford: OxfordUniversity Press, 2013. Pp. xix+220. H/b$35.00.

This paper examines Du Châtelet’s and Kant’s responses to the famous vis viva controversy – Du Châtelet in her Institutions Physiques (1742) and Kant in his debut, the Thoughts on the True Estimation of Living Forces (1746–49). The Institutions was not only a highly influential contribution to the vis viva controversy, but also a pioneering attempt to integrate Leibnizian metaphysics and Newtonian physics. The young Kant’s evident knowledge of this work has led some to speculate about his indebtedness to her (...) philosophy. My study corrects such speculations as well as misunderstandings of the Living Forces. This corrective result has implications for how to investigate Kant’s relation to the ever-evolving landscape of Leibniz exegeses. (shrink)

I show that intuitive and logical considerations do not justify introducing Leibniz’s Law of the Indiscernibility of Identicals in more than a limited form, as applying to atomic formulas. Once this is accepted, it follows that Leibniz’s Law generalises to all formulas of the first-order Predicate Calculus but not to modal formulas. Among other things, identity turns out to be logically contingent.

This paper is intended to examine Leibniz's Principle of Continuity, as well as the conditions of its application in leibnizian infinitesimal calculus, in the light of some aspects of formal language developed by Leibniz. It aims at evaluating whether, and to what extent, that principle can be justified on the basis of the logic of Leibniz.

Marsilius of Inghen’s account of imaginable impossibilities became paradigmatic in logic, semantics, and metaphysics throughout the later Middle Ages and well into the early modern period. The present study focuses on imaginable impossibilities in 14th-century logic, underlining the relevance of Marsilius of Inghen’s innovative approach through a comparison with the semantic accounts proposed by other mid-14th-century Parisian nominalists, namely John Buridan and Albert of Saxony. In particular, this paper tracks the specific issue of the admissibility of absolute impossibilities (...) – such as the chimera – within Marsilius of Inghen’s semantic analysis, proving that there is a sense in which the chimera is indeed treatable. The present study does so by analysing the issues involved in impossibilities on the levels of signification, supposition, and extended reference. In doing so it provides a clearer picture of the problems involved, where they emerge and why, as well as of the significance and range of Marsilius of Inghen’s approach. (shrink)

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, (...) the single valued neutrosophic set theory has been extensively studied in books and monographs, the properties of neutrosophic sets and their applications, by many authors around the world. Also, an international journal - Neutrosophic Sets and Systems started its journey in 2013. Neutrosophic triplet was first defined in 2016 by Florentin Smarandache and Mumtaz Ali and they also introduced the neutrosophic triplet groups in the same year. For every element “x” in a neutrosophic triplet set A, there exist a neutral of “x” and an opposite of “x”. Also, neutral of “x” must be different from the classical neutral element. Therefore, the NT set is different from the classical set. Furthermore, a NT of “x” is showed by . This first volume collects original research and applications from different perspectives covering different areas of neutrosophic studies, such as decision making, Triplet, topology, and some theoretical papers. This volume contains three sections: NEUTROSOPHIC TRIPLET, DECISION MAKING, AND OTHER PAPERS. (shrink)

The famous Cartesian Nicolas Malebranche (1638-1715) espoused the occasionalist doctrine that ‘there is only one true cause because there is only one true God; that the nature or power of each thing is nothing but the will of God; that all natural causes are not true causes but only occasional causes’ (LO, 448, original italics). One of Malebranche’s well-known arguments for occasionalism, known as, the ‘no necessary connection’ argument (or, NNC ) stems from the principle that ‘a true cause… is (...) one such that the mind perceives a necessary connection between it and its effect’ (LO, 450). The outline of this paper is as follows. I explicitly layout NNC and articulate some of its prima facie strengths (§1). I then critically discuss, what I take to be, the two main arguments against NNC of the Lee-Pyle interpretation (§2). The main conclusion from (§2) is that Malebranche did not abandon NNC in his later works given textual evidence from the Dialogues, contrary to the Lee-Pyle interpretation. In (§3) I discuss in what ways Suárez, Leibniz, Régis and Spinoza all accepted the main premise of NNC. Then, I rebut Steven Nadler’s influential and unchallenged criticism that Malebranche conflated causal and logical necessity, and provide a more accurate interpretation of Malebranche that only commits him to a partial reduction of causal to logical necessity (§4). (shrink)

The Epicurean account of the origin of language appealed to eighteenth-century thinkers who tried to reconcile a natural history of language with

the biblical account of Adamic name-giving. As a third way between Aristotelian linguistic conventionality and what was perceived as a Platonic supernatural congruence between words and things, Epicurus’

theory allowed for a measure of contingency to emerge in the evolution of initially natural signs. This hypothesis was taken up by authors as different from one another as Leibniz, Vico, Condillac and (...) Mendelssohn. By integrating the Epicurean account of language into their own theories, however, these authors also revived the tensions inherent in the ancient thesis and had to confront the ensuing difficulties in innovative ways. (shrink)

As these opening quotes acknowledge, the Prisoner’s Dilemma (PD) represents a core puzzle within the formal mathematics of game theory.3 Its rise in conspicuity is evident figure 2.1 above demonstrating a relatively steady rise in incidences of the phrase’s usage between 1960 to 1995, with a stable presence persisting into the twenty first century. This famous two-person “game,” with a stock narrative cast in terms of two prisoners who each independently must choose whether to remain silent or speak, each advancing (...) self-interest at the expense of the other and thereby achieving a mutually suboptimal outcome, mires any social interaction it is applied to into perplexity. The logic of this game proves the inverse of Adam Smith’s invisible hand: individuals acting on self interest will achieve a mutually suboptimal outcome. However, as this chapter illuminates, the assumptions underlying game theory drive this conclusion. (shrink)

Recently, a number of philosophers have argued that we can and should “consequentialize” non-consequentialist moral theories, putting them into a consequentialist framework. I argue that these philosophers, usually treated as a group, in fact offer three separate arguments, two of which are incompatible. I show that none represent significant threats to a committed non-consequentialist, and that the literature has suffered due to a failure to distinguish these arguments. I conclude by showing that the failure of the consequentializers’ arguments has implications (...) for disciplines, such as economics, logic, decision theory, and linguistics, which sometimes use a consequentialist structure to represent non-consequentialist ethical theories. (shrink)

In this article, the attempts by David Lewis and Brian Loar to make perspicuous the logical form of sentences ascribing propositional attitudes to individuals are set out and criticized. Both work within the assumption of the truth of 'type' physicalism, and require that logically perspicuous attitude ascriptions be compatible with the demands of such a doctrine. It is argued that neither carry out this task successfully - Lewis's perspicuous ascriptions have counter-intuitive implications, while Loar's avoidance of these undermines type physicalism (...) itself. (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)

Faith has many aspects. One of them is whether absolute logical proof for God’s existence is a prerequisite for the proper establishment and individual acceptance of a religious system. The treatment of this question, examined here in the Jewish context of Rabbi Prof. Eliezer Berkovits, has been strongly influenced in the modern era by the radical foundationalism and radical skepticism of Descartes, who rooted in the Western mind the notion that religion and religious issues are “all or nothing” questions. Cartesianism, (...) which surprisingly became the basis of modern secularism, was criticized by the classical American pragmatists. Peirce, James and Dewey all rejected the attempt to achieve infallible absolute knowledge, as well as the presumptuousness of establishing such a knowledge by means of casting Cartesian hyperbolic doubt. They advocated an alternative approach which was more holistic and humane. This paper lays out Descartes’s approach and the pragmatists’ critique. Despite the place that pragmatic considerations hold in Jewish tradition, some thinkers reject the relevance of these ideas. Yet Berkovits’s thought suggest a different path. He rejected Descartes’ radical skepticism and his radical foundationalism, in favor of a moderate foundationalism, which allows for a belief in God alongside constructive doubts. Similar to Peirce’s conception of the fixation of belief, Berkovits views local doubts (distinct from the hyperbolic doubt) as necessary for thought. Berkovits’s understanding of the biblical human-divine encounter, following Rosenzweig, Buber, and Heschel, is conceptualized here as “encounter theology”. Berkovits criticizes the propositionalist attempts to prove God’s existence logically, as well as the presumptuousness of basing religious belief on the teleological world-order. However, Berkovits’s conception of the ‘caring God’ is not provable, and thus defined as a pragmatic ‘postulate’. The article concludes by considering Berkovits’s “encounter theology”. In contrast to the approach described by Haym Soloveitchik, of halakhic stringency and lack of subjective experience of God’s face, Berkovits’s approach is dialogic through and through. (shrink)

David Lewis presented Convention as an alternative to the conventionalism characteristic of early-twentieth-century analytic philosophy. Rudolf Carnap is well known for suggesting the arbitrariness of any particular linguistic convention for engaging in scientific inquiry. Analytic truths are self-consistent, and are not checked against empirical facts to ascertain their veracity. In keeping with the logical positivists before him, Lewis concludes that linguistic communication is conventional. However, despite his firm allegiance to conventions underlying not just languages but also social customs, he pioneered (...) the view that convening need not require any active agreement to participate. Lewis proposed that conventions arise from “an exchange of manifestations of a propensity to conform to a regularity” (87–8). In reasserting the conventional quality of languages and other practices resting on mutual expectations, Lewis comfortably works within the analytic tradition. Yet he also deviates from his predecessors because his conventionalist approach is comprehensively grounded in instrumentalism. Lewis adopts an extension of David Hume's desire-belief psychology articulated in rational choice theory. He develops his philosophy of convention relying on the highly formal mid-twentieth-century expected utility and game theories. This attempt to account for language and social customs wholly in terms of instrumental rationality has the implication of reducing normativity to preference satisfaction. Lewis’ approach continues in the trend of undermining normative political philosophy because institutions and practices arise spontaneously, without the deliberate involvement of agents. Perhaps Lewis’ Convention is best seen as a resurgent form of analytic philosophy, characterized by “a style of argument, hostility to [ambitious] metaphysics, focus on language, and the dominance of logic and formalization” that solves the dilemma of “combining the analytic inheritance…with normative concerns” by reducing normativity to individuals’ preference fulfillment consistent with the axioms of rational choice. (shrink)

After years of neglect, alienation has again reached the agenda of critical thought. In my case, I recognize alienation as a challenge for education in contemporary societies. To obtain conceptual resources to overcome this challenge, I have revisited the comprehensive 20 th century discussion of alienation. Today, alienation is naturally discussed as an existential condition of human being, but still in the 1980s, there was a strong Marxist current that claimed alienation to be implied by capitalism, in particular by the (...) institution of private property and the social division of labor, and that alienation therefore should be criticized as part of the critique of capitalism and political economy and possibly overcome. Today, under the hegemony of neo-liberal capitalism, this critical and processual concept of alienation is more relevant than ever. Hence, in the present work I argue that the basic logic of Marx's idea of alienation still has critical potential. The argument forms a long engagement with mainly 20 th century literature, departing from the very idea of capitalism, considering the ideas of history, education and democracy, discussing how to distinguish and translate key terms, considering why alienation became an object of controversy among Marxists, offering an interpretation of Marx's critique relevant for contemporary society, thus considering alienation a consequence of working under conditions of private property, i.e. being a human being in a capitalist society, and finally presenting Marx's idea of communism as relevant to the contemporary educational agenda. (shrink)

Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit counterparts to modal logics. The behavior and interaction of agents in distributed system is often modeled using logics of knowledge and time. In this paper, we sketch some preliminary ideas on how the modal knowledge part of such logics of knowledge and time could be replaced with an appropriate justification (...) class='Hi'>logic. (shrink)

In this chapter, I consider the largely overlooked influence of E. W. von Tschirnhaus' treatise on method, the Medicina mentis, on Wolff's early philosophical project (in both its conception and execution). As I argue, part of Tschirnhaus' importance for Wolff lies in the use he makes of principles gained from experience as a foundation for the scientific enterprise in the context of his broader philosophical rationalism. I will show that this lesson from Tschirnhaus runs through Wolff's earliest philosophical discussions, and (...) indeed continues to inform his major texts in logic and mathematics just before the publication of the German Metaphysics. In the end, my discussion has the effect of revealing Tschirnhaus to be an exceptionally important influence on Wolff's development, perhaps even as important (or so I suggest) as Leibniz. (shrink)

Tong Shijun holds a concept of dialectics which can also be found in Mao’s writings and in classical Chinese philosophy. Tong, however, is ambivalent in his attitude to dialectics in this sense, and for this reason he recommends Chinese philosophy to focus more on formal logic. My point will be that with another concept of dialectics Tong can have dialectics without giving up on logic and epistemology. This argument is given substance by an analysis of texts by Mao, (...) Tong and Hegel. (shrink)

There are three questions associated with Simpson’s Paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP?, and (iii) What should be done about SP? By developing a logic-based account of SP, it is argued that (i) and (ii) must be divorced from (iii). This account shows that (i) and (ii) have nothing to do with causality, which plays a role only in addressing (iii). A counterexample is also presented against the causal account. Finally, the causal and (...) logic-based approaches are compared by means of an experiment to show that SP is not basically causal. (shrink)

In this paper , the authors explore neutrosophic statistics, that was initiated by Florentin Smarandache in 1998 and developed in 2014, by presenting various examples of several statistical distributions, from the work [1]. The paper is presented with more case studies, by means of which this neutrosophic version of statistical distribution becomes more pronounced.

Uses erotetic logic to model the courtroom objection "Improper Cross!". -/- Readers downloading the article should also please download the erratum et corrigendum, which is locally available.

Note: The author holds the copyright, and there was no agreement, express or implied, not to use a facsimile PDF. -/- Using erotetic logic, the paper defines the "the whole truth" in a manner consistent with U.S. Supreme Court precedent. It cannot mean "the whole story," as witnesses in an adversary system are permitted /only/ to answer the questions put to them, nor are they permitted to speculate, add irrelevant material, etc. Nor can it mean not to add an (...) admixture of falsity, as that is already included in "nothing but the truth," and, strictly speaking, in "the truth," as any such as admixture renders the whole thing false (given bivalence is presupposed) by &-introduction. (shrink)

Jim Sterba’s Is a Good God Logically Possible? looks to resurrect J. L. Mackie’s logical argument from evil. Sterba accepts the general framework that theists seeking to give a theodicy have favored since Leibniz invented the term: the search for some greater good provided or greater evil averted that would justify God in permitting the type and variety of evil we actually observe. However, Sterba introduces a deontic twist, drawing on the Pauline Principle (let us not do evil that good (...) may come) to introduce three deontic side constraints on God’s choice of action. He then splits the possible goods into four categories: first- vs. second-order goods, goods to which we have a right, and goods to which we do not have a right. He argues that his deontic constraints rule out each combination, thereby showing that no God-justifying good is on offer. To defuse the argument, I draw on a pair of ideas from Marilyn McCord Adams: (i) God is outside the bounds of morality, and (ii) God can defeat evils by incorporating them into an incommensurately valuable friendship with each human. Properly appreciated, these show that the new logical argument relies on a false premise that is not easily repaired. (shrink)

This paper is a discussion of the treatment of Leibniz's conception of substance in Heidegger's The Metaphysical Foundations of Logic. I explain Heidegger's account, consider its relation to recent interpretations of Leibniz in the Anglophone secondary literature, and reflect on the ways in which Heidegger's methodology may illuminate what it is to read Leibniz and other figures in the history of philosophy.

As the journal is effectively defunct, I am uploading a full-text copy, but only of my abstract and article, and some journal front matter. -/- Note that the pagination in the PDF version differs from the official pagination because A4 and 8.5" x 11" differ. -/- Traditionally, imperatives have been handled with deontic logics, not the logic of propositions which bear truth values. Yet, an imperative is issued by the speaker to cause (stay) actions which change the state of (...) affairs, which is, in turn, described by propositions that bear truth values. Thus, ultimately, imperatives affect truth values. In this paper, we put forward an idea that allows us to reason with imperatives using classical logic by constructing a one-to-one correspondence between imperatives and a particular class of declaratives. (shrink)

Rita Widmaier and Malte-Ludolf Babin have done a valuable scholarly service for studies of the early modern European reception of China in collecting letters from Leibniz's extensive correspondence concerning China and translating them from the original Latin and French into German. This multi-lingual and chronologically organized edition gathers letters to and from Leibniz as well as supplementary texts composed between the years 1694 and 1716. It incorporates helpful clarificatory notes as well as an informative and lucid introduction.This edition focuses (...) on the exchanges between Leibniz and the Jesuit theologian and philosopher Barthélemy Des Bosses S.J. and other Jesuits in Europe who were in... (shrink)