In a recent paper Johan van Benthem reviews earlier work done by himself and colleagues on ‘natural logic’. His paper makes a number of challenging comments on the relationships between traditional logic, modern logic and natural logic. I respond to his challenge, by drawing what I think are the most significant lines dividing traditional logic from modern. The leading difference is in the way logic is expected to be used for checking arguments. For traditionals the checking is local, i.e. separately (...) for each inference step. Between inference steps, several kinds of paraphrasing are allowed. Today we formalise globally: we choose a symbolisation that works for the entire argument, and thus we eliminate intuitive steps and changes of viewpoint during the argument. Frege and Peano recast the logical rules so as to make this possible. I comment also on the traditional assumption that logical processing takes place at the top syntactic level, and I question Johan’s view that natural logic is ‘natural’. (shrink)

this book concerns the debates on the functions of "imagination" (phantasia, imaginatio) in the arousal of passions in the Aristotelian and post-Aristotelian traditions till the XVIIth Century. The simple fact that often a mental representation is followed by pleasure or sorrow and that these emotions can cause actions, became progressively part of a wider theory of animal and human behaviour. In the case of human behaviour, the "force of imagination" became a kind of general justification of all kind of anomic (...) and irregular behaviour and beliefs, including true paranormal conditions of the body. The book recapitulates the main evolution of this way of seeing passions - from Aristotle to Avicenna and his Latin followers - till the age of the authors who see the inner work of "imagination" as a constant danger for human reason, and imagination itself as faculty to control with care for its propension to be the "advocate" of the "inferior part of the soul", such as Gianfrancesco Pico, Juan Luis Vivés, Pierre Charron, Blaise Pascal and a large part of the French Augustinian Moral Philosophers. (shrink)

The article attempts to reconsider the relationship between Leibniz’s and Kant’s philosophy of geometry on the one hand and the nineteenth century debate on the foundation of geometry on the other. The author argues that the examples used by Leibniz and Kant to explain the peculiarity of the geometrical way of thinking are actually special cases of what the Jewish-German mathematician Felix Hausdorff called “transformation principle”, the very same principle that thinkers such as Helmholtz or Poincaré applied in a more (...) general form in their celebrated philosophical writings about geometry. The first two parts of the article try to show that Leibniz’s and Kant’s philosophies of geometry, despite their differences, appear to be preoccupied with the common problem of the impossibility to grasp conceptually the intuitive difference between two figures (such as a figure and its scaled, displaced or mirrored copy). In the third part, it is argued that from the perspective of Hausdorff’s philosophical-geometrical reflections, this very same problem seems to find a more radical application in Helmholtz’s or Poincaré’s thought experiments on the impossibility of distinguishing distorted copies of our universe from the original one. I draw the conclusion that in Hausdorff’s philosophical work, which has received scholarly attention only recently, one can find not only an original attempt to frame these classical arguments from a set-theoretical point of view, but also the possibility of considering the history of philosophy of geometry from an uncommon perspective, where especially the significance of Kant’s infamous appeal to “intuition” can be judged by more appropriate standards. (shrink)

Leibniz propôs que demonstrações fossem reformuladas como deduções a partir de identidades, e que proposições do tipo A = A fossem a fonte única de verdade. Neste artigo, procuro explicar essa teoria da prova (e do conhecimento), assim como seus conceitos elementares, ou seja, os conceitos de identidade, verdade (ou possibilidade) e proposição (inclusive a teoria leibniziana da redutibilidade a proposições sujeito-predicado). Leibniz proposed that demonstrations be reformulated as deductions from identities, and that propositions of the type A = A (...) be the only source of truth. In this article, I aim to explain this theory of proof (and knowledge), as well as its elementary concepts, such as identity, truth (or possibility) and proposition (including Leibniz's theory of reducibility of propositions to subject-predicate form). (shrink)

In this paper I offer a fresh interpretation of Leibniz’s theory of space, in which I explain the connection of his relational theory to both his mathematical theory of analysis situs and his theory of substance. I argue that the elements of his mature theory are not bare bodies (as on a standard relationalist view) nor bare points (as on an absolutist view), but situations. Regarded as an accident of an individual body, a situation is the complex of its angles (...) and distances to other co-existing bodies, founded in the representation or state of the substance or substances contained in the body. The complex of all such mutually compatible situations of co-existing bodies constitutes an order of situations, or instantaneous space. Because these relations of situation change from one instant to another, space is an accidental whole that is continuously changing and becoming something different, and therefore a phenomenon. As Leibniz explains to Clarke, it can be represented mathematically by supposing some set of existents hypothetically (and counterfactually) to remain in a fixed mutual relation of situation, and gauging all subsequent situations in terms of transformations with respect to this initial set. Space conceived in terms of such allowable transformations is the subject of Analysis Situs. Finally, insofar as space is conceived in abstraction from any bodies that might individuate the situations, it encompasses all possible relations of situation. This abstract space, the order of all possible situations, is an abstract entity, and therefore ideal. (shrink)

The paper discusses Leibniz's theory of denominations, expression, and individual notions, the central claim being that the key to many of Leibniz's fundamental theses is to consider his argument, starting from his predicate-in-subject account of truth (that in a true statement the notion of the predicate is contained in that of the subject), against purely extrinsic denominations: this argument shows why there is an internal foundation for all denominations, why everything in the world is interconnected, why each substance expresses all (...) the others, and why every change in the world is reflected as a real, internal change in every substance. (shrink)

According Leibniz's thesis of universal expression, each substance expresses the whole world, i.e. all other substances, or, as Leibniz frequently states, from any given complete individual notion (which includes, in internal terms, everything truly attributable to a substance) one can "deduce" or "infer" all truths about the whole world. On the other hand, in Leibniz's view each (created) substance is internally individuated, self-sufficient and independent of other (created) substances. What may be called Leibniz's expression problem is, how to reconcile these (...) views with each other, that is, how a substance that expresses the whole world, even in the sense that the whole world can be "inferred" from its complete individual notion, can be self-sufficient and internally individuated. The purpose of this paper is to give an exact account of this tricky problem of universal expression, an account that retains substances' self-sufficiency under the constraint that all truths about the whole world are to be obtained from complete individual notions. It will also be shown how the explication of universal expression to be given accounts for Leibniz's thesis of universal change, i.e. the view that any change in any substance is reflected as a real, internal change in each and every other substance. (shrink)

Gottfried Wilhelm Leibniz (1646–1716) was one of the great thinkers of the seventeenth and eighteenth centuries and is known as the last “universal genius”. He made deep and important contributions to the fields of metaphysics, epistemology, logic, philosophy of religion, as well as mathematics, physics, geology, jurisprudence, and history. Even the eighteenth century French atheist and materialist Denis Diderot, whose views could not have stood in greater opposition to those of Leibniz, could not help being awed by his achievement, writing (...) in his Encyclopedia, “Perhaps never has a man read as much, studied as much, meditated more, and written more than Leibniz… What he has composed on the world, God, nature, and the soul is of the most sublime eloquence. If his ideas had been expressed with the flair of Plato, the philosopher of Leipzig would cede nothing to the philosopher of Athens.” (Vol. 9, p. 379) Indeed, Diderot's mood was almost despairing in a remark from another piece, which also has a great deal of truth in it: “When one compares the talents one has with those of a Leibniz, one is tempted to throw away one's books and go die quietly in the dark of some forgotten corner.” More than a century later, Gottlob Frege, who fortunately did not cast his books away in despair, expressed similar admiration, declaring that “in his writings, Leibniz threw out such a profusion of seeds of ideas that in this respect he is virtually in a class of his own.” (“Boole's logical Calculus and the Concept script” in Posthumous Writings , p. 9) The aim of this entry is primarily to introduce Leibniz's life and summarize and explicate his views in the realms of metaphysics, epistemology, philosophical theology, and natural philosophy. (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)

There is a lively debate in contemporary Analytic Philosophy of Religion about the consistency of the Trinitarian doctrine. In this context, the notion of ‘mystery’ has become crucial. However, although it is currently considered the main challenge of Trinitarian theology, its definition remains rather partial and superficial. After a brief description of today’s Mysterianism, I analyse three ‘emblematic’ positions in light of the current debate: Aquinas, Leibniz and Hegel present three ways to believe in a mysterious Trinity. I will point (...) out a few possible weaknesses in the positions of the first two authors in order to better highlight the usefulness of the Hegelian position, often underestimated in the contemporary analytic debate. I will also analyse the connection between the three positions and their respective metaphysics, showing the epistemological premises (e.g., analogy and univocity) that need to be better investigated in the future. (shrink)

Incongruent counterparts are pairs of objects which cannot be enclosed in the same spatial limits despite an exact similarity in magnitude, proportion, and relative position of their parts. Kant discerns in such objects, whose most familiar example is left and right hands, a “paradox” demanding “demotion of space and time to mere forms of our sensory intuition.” This paper aims at an adequate understanding of Kant’s enigmatic idealist argument from handed objects, as well as an understanding of its relation to (...) the other key supports of his idealism. The paper’s central finding is that Kant’s idealist argument from incongruent counterparts rests essentially on his theory of freedom. The surprising result sheds new light on deep and overlooked links among the pillars of transcendental idealism, pointing the way to a comprehensive and unified reading of Kant’s system of idealist arguments. (shrink)

Imaguire-Guido_On-the-ontology-of-relations.

Is there an explanation of why the state of x's bearing the non-symmetric binary relation R to y is different from its differential opposite, the state of y's bearing R to x? One traditional view has it that the explanation is that non-symmetric relations hold of objects in an essentially directional way, ordering the relevant relata. We call this view ‘directionalism’. Kit Fine has suggested that this approach is subject to significant metaphysical difficulties, sufficient to motivate seeking an alternative analysis. (...) He considers two such alternative explanations, which he labels ‘positionalism’ and ‘anti-positionalism’. Of these he endorses the latter. We argue that anti-positionalism fails to provide a coherent explanation of the distinction between differential opposites, and that one should simply hold the minimalist position that there is no explanation for this metaphysical difference. (shrink)

Drawing on a Leibnizian panpsychist ontology of living beings that have a body and a soul, this paper outlines a theory of space based on the perceptual and appetitive relations among these creatures’ souls. In parallel with physical space founded on relations among bodies subject to efficient causation, teleological space results from relations among souls subject to final causation and is described qualitatively in terms of creatures’ pleasure and pain, wellbeing and happiness. Particular places within this space include the kingdom (...) of grace, where morally responsible, rational beings act as far as possible in accord with the ideal of justice as universal love and wise benevolence. However, while Leibniz considered love as properly directed only towards rational beings, it is argued here that the truly wise person will direct their love and benevolence towards all living things. Ausgehend von Leibniz’ panpsychistischer Ontologie von Lebewesen, die einen Körper und eine Seele haben, skizziert dieser Beitrag eine Theorie des Raumes, der auf den perzeptuellen und appetitiven Relationen zwischen den Seelen der Geschöpfe beruht. Parallel zum physikalischen Raum, der in Relationen zwischen den effizient kausal interagierenden Körper begründet liegt, ergibt sich aus den Relationen zwischen den Seelen, die finaler Verursachung unterliegen und in qualitativen Begriffen von Freude und Schmerz wie von Wohl und Zufriedenheit beschrieben werden, ein teleologischer Raum. Besondere Regionen dieses Raumes bilden das Königreich der Gnade, wo moralisch verantwortliche, rationale Wesen so weit wie möglich in Übereinstimmung mit dem Ideal der Gerechtigkeit als universale Liebe und weise Güte handeln. Während Leibniz jedoch meinte, dass sich echte Liebe nur auf rationale Wesen richte, wird hier argumentiert, dass eine wahrhaft weise Person ihre Liebe und Güte auf alle Lebewesen beziehen wird. (shrink)

Leibniz’s claim that it is possible for us to gain metaphysical knowledge through reflection on the self has intrigued many commentators, but it has also often been criticized as flawed or unintelligible. A similar fate has beset Leibniz’s arguments against materialism. In this paper, I explore one of Leibniz’s lesser-known arguments against materialism from his reply to Bayle’s new note L, and argue that it provides us with an instance of a Leibnizian “argument from reflection”. This argument, I further show, (...) does not constitute a flawed appeal to mere introspection, but is in fact securely grounded in an important corollary of the Principle of Sufficient Reason: Leibniz’s Principle of Intelligibility. (shrink)

Whitehead's system may be interpreted as a majestic attempt at recasting Leibniz's theory of monads in terms of sounder ontological categories. After a brief introductory section on the sources of Whitehead's knowledge of Leibniz's philosophy, the paper explains why Whitehead turned to Leibniz for metaphysical inspiration. Attention then shifts to Whitehead's understanding of the problems involved with Leibniz's theory of monads and his alternative explanation of monadic causation. Whitehead's endeavour to install windows in Leibniz's monads may not be entirely convincing, (...) but there are philosophical gems scattered here and there in his analyses – true moments of insight that repay close examination. (shrink)

This paper is concerned with De Morgan’s explanation of the validity of arguments that involve relational notions. It discusses De Morgan’s expansion of traditional logic aimed at accommodating those inferences, and makes the point that his endeavour is not successful in that the rules that made up his new logic are not sound. Nevertheless, the most important scholarly work on De Morgan’s logic, and contrary to that De Morgan’s mistake is not beyond repair. The rules that determine his new logic (...) are in fact monotonie replacement rules. And provided they are restricted in the correct way, these rules are demonstrably sound. (shrink)

I present a formal framework historically faithful to Leibniz's analysis of relational sentences, which: (i) engrafts thematic roles and the non-truth-functional connective insofar as (quatenus) into the monadic fragment of first-order logic; (ii) suggests a plausible ontological picture of thematic roles and relational facts; (iii) supports argument deletion and related inferential patterns that are not taken into account by standard first-order logic.