In The Logic of Sense, Deleuze effectively argues that two types of relation between events govern their ‘evental’ or ‘ideal play’, and ultimately underlie determined substances, that is, worldly individuals and persons. Leibniz calls these relations ‘compossibility’ and ‘incompossibility’. Deleuze calls them ‘convergence’ and ‘divergence’. This paper explores how Deleuze appropriates and extends a number of Leibnizian concepts in order to ground the idea that events have ontological priority over substances ‘all the way down’.

The infinitesimal methods commonly used in the 17th and 18th centuries to solve analytical problems had a great deal of elegance and intuitive appeal. But the notion of infinitesimal itself was flawed by contradictions. These arose as a result of attempting to representchange in terms ofstatic conceptions. Now, one may regard infinitesimals as the residual traces of change after the process of change has been terminated. The difficulty was that these residual traces could not logically coexist with the static quantities (...) traditionally employed by mathematics. The solution to this difficulty, as it turns out, is to regard these quantities asalso being subject to (a form of) change, for then they will have the same nature as the infinitesimals representing the residual traces of change, and will become,ipso facto, compatible with these latter.In fact, the category-theoretic models which realize the Principle of Infinitesimal Linearity may themselves be regarded as representations of a general concept of variation (cf. Bell (1986)). While the static set-theoretical models represent change or motion by making a detour through the actual (but static) infinite, the varying category-theoretic models enable such change to be representeddirectly, thus permitting the introduction of geometric infinitesimals and, as we have attempted to demonstrate in this paper, the virtually complete incorporation of the methods of the early calculus.It is surely a remarkable — even an ironic — fact that the contradiction between the flux of the objective world and the stasis of mathematical entities has found its resolution in category theory, a branch of mathematics commonly, and, as one now sees, mistakenly, regarded as the summit of gratuitous abstraction. (shrink)

La filosofía de Wolff y Baumgarten ha sido tradicionalmente evaluada como nada más que una sistematización, carente de toda originalidad, de las doctrinas de Leibniz. El presente trabajo revisa esta opinión generaliza, concentrándose en el problema específico de la interacción de las sustancias naturales. Se muestra que Wolff y Baumgarten no siguen a Leibniz con el mismo grado de cercanía en relación a algunos de los principios centrales de la teoría armonía preestablecida y, con ello, se problematiza el uso de (...) la etiqueta “leibnizianismo” como referida a un cuerpo homogéneo e indiferenciado de doctrinas. (shrink)

InLeibniz: Perception, Apperception, and Thought, Robert McRae alleges a flat “contradiction” at the heart of Leibniz's doctrine of three grades of monads: bare entelechies characterized by perception; animal souls capable both of perception and of sensation; and rational souls, minds or spirits endowed not only with capacities for perception and sensation but also with consciousness of self or what Leibniz calls “apperception.” Apperception is a necessary condition of those distinctively human mental processes associated with understanding and with reason. Insofar as (...) it is also a sufficient condition of rationality, it is not ascribable to animals. But apperception is a necessary condition of sensation or feeling as well; and animals are capable of sensation, according to Leibniz, who decisively rejected the Cartesian doctrine that beasts are nothing but material automata. “On the one hand,” writes McRae, “what distinguishes animals from lower forms of life is sensation or feeling, but on the other hand apperception is a necessary condition of sensation, and apperception distinguishes human beings from animals”. “We are thus left with an unresolved inconsistency in Leibniz's account of sensation, so far as sensation is attributable both to men and animals”. (shrink)

While post-modernist assaults on modernity correctly expose the pretensions of modernity – including its constructs of meaning in history, its abnegation of mystery, and its lapses into scientism, historicism, and relativism – the philosopher and theologian Bernard Lonergan discerned progress as well as decline in recent intellectual history. In part this is because under contemporary conditions we can avoid the pretensions of modernity, since – in the wake of modern science and modern historical scholarship – we witness the differentiation of (...) interiority, which, properly understood as the discovery of the self, may be seen as leading to a new integration of the spiritual, the intellectual, the moral, and the historical. (shrink)

Intuitively, an object is something that coheres internally and is largely independent of its environment. But what is the environment? Viewed at one scale, it surrounds and separates objects and differentiates them. Viewed at another scale, it is itself a collection of objects surrounded by environment. At all scales, we describe the world in terms of objects in an environment. I examine the nature of the environment and its role in mediating the object-subject relation. This dedicated analysis of the environment (...) provides a new perspective on the notion of objectivity. (shrink)

Leibniz, it seems, wishes to reduce statements involving relations or extrinsic denominations to ones solely in terms of individual accidents or, respectively, intrinsic denominations. His reasons for this appear to be that relations are merely mental things (since they cannot be individual accidents) and that extrinsic denominations do not represent substances as they are on their own. Three interpretations of Leibniz''s reductionism may be distinguished: First, he allowed only monadic predicates in reducing statements (hard reductionism); second, he allowed also `implicitly (...) relational predicates'' such as `loves somebody'' (soft reductionism); third, he allowed also `explicitly relational predicates'' such as `loves Helen'' (nonreductionism). Hard reductionism is problematic with respect to Leibniz''s doctrines of universal expression and incompossibility (among other things). Nonreductionism, in turn, faces insurmountable problems with Leibniz''s doctrine of self-sufficiency and internal identification of substances, as well as with that of individual accidents. The remaining option, soft reductionism, standing between the other two interpretations, arguably avoids at least some of their problems. (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)

Despite his commitment to freedom, Leibniz’ philosophy is also founded on pre-established harmony. Understanding the life of the individual as a spiritual automaton led Leibniz to refer to the puzzle of the way out of determinism as the Labyrinth of Freedom. Leibniz claimed that infinite complexity is the reason why it is impossible to prove a contingent truth. But by means of Leibniz’ calculus, it actually can be shown in a finite number of steps how to calculate a summation of (...) infinite parts. It appears that the analogy Leibniz drew between the mathematics of infinite series and the logic of contingent truths did more harm than good. A solution consistent with Leibniz’ perception of infinity is proposed. Alongside the existence of the aforementioned analogy, it is based on a disanalogy between the mathematics of infinite series and the logic of infinitely complex truths. This is a disanalogy that Leibniz had already used to solve the Labyrinth of Continuum which he declared more than once could, like the Labyrinth of Freedom, be solved by means of the nature of infinity. The solution of both labyrinths is based on the fictitiousness of the infinitesimal. (shrink)

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

La finalidad de este artículo es elucidar el sentido de la doctrina leibniziana de la exigencia de existencia y el combate de los posibles, situándola dentro del conjunto de la metafísica de Leibniz y mostrando su absoluta compatibilidad con la afirmación de la creación libre y voluntaria por parte de Dios. Se intentará explicar qué elementos de la afirmación de la ‘exigencia de existencia’ y el ‘combate de los posibles’ reflejan tesis estric- tamente metafísicas, y cuáles pueden considerarse recursos metafóricos. (...) En este contexto, se explicará qué papel que juega la voluntad divina antecedente en la fundamentación de la tendencia de los posibles a la existencia, y se intentará focalizar el papel específico de la ‘sabiduría’, como atributo divino, en la determinación y elección del mejor mundo posible. Finalmente, se extraerán algunas consecuencias del análisis anterior, en relación con la libertad divina en el acto creador. (shrink)

In attempts to come to grips with Kant’s thought, the influence of the philosophy of Christian Wolff (1679-1754) is often neglected. In this paper, I consider three topics in Kant’s philosophy of mind, broadly construed, where Wolff’s influence is particularly visible: consciousness, self-consciousness, and psychology. I argue that we can better understand Kant’s particular arguments and positions within this context, but also gain a more accurate sense of which aspects of Kant’s accounts derive from the antecedent traditions and which constitute (...) genuine philosophical innovations. (shrink)

A typical view of Leibniz’ extraordinary metaphysical and methodological views is to regard them as having appeared by certain “applications” of his mathematical and physical discoveries. If we believe Couturat and Russell the monadology is largely only the expression of certain logically formal relationships: it is the logic of Leibniz that is basic to his mature metaphysics. Even more typical is the view that Leibniz’ work in mathematics, especially his work on the calculus, is the source of the key ideas (...) in his metaphysics. J. M. Child, the translator of the early mathematical manuscripts, says it straight out: “ … the main ideas of [Leibniz’] philosophy are to be attributed to his mathematical work, and not vice versa.” In a philosophically much more interesting way Paul Schrecker argues that what he calls Leibniz’ “infinitesimal method,” a method obviously derived from his mathematical work, pervades all of the important basic contributions of both his metaphysics and methodology. (shrink)

Si Dios es la razón suficiente del mundo, entonces parece seguirse que todos los eventos son consecuencia necesaria de un ser necesario. Para evadir esta conclusión, Leibniz formula en la década de 1670 una concepción modal que funda la contingencia en un rasgo lógico e intrínseco de las ideas de las cosas: la posibilidad de concebir la idea contraria sin contradicción. Hacia 1686, Leibniz complementa esta primera concepción con lo que considera su solución definitiva al problema de la contingencia: la (...) teoría del análisis infinito. Sin embargo, en otros escritos de ese año, propone dos vías alternativas de fundamentación de la contingencia. Este trabajo sugiere que esa pluralidad de modelos explicativos converge en una concepción integral de las modalidades que subyace como trasfondo de la reflexión modal leibniziana. If God is the sufficient reason for this world, then it seems to follow that every event is a necessary consequence of a necessary being. in order to avoid this conclusion, Leibniz states, during the 1670's, a modal conception that grounds contingency on a logical feature which is intrinsic to the ideas of things: the possibility of conceiving the opposite idea without contradiction. Towards 1686, Leibniz complements this first conception with what he considered to be his definitive solution to the problem of contingency: the theory of infinite analysis. However, in other writings from the same year, he proposes two different ways to explain contingency. This paper suggests that this plurality of models converges in a global conception of modalities, which lies at the background of Leibniz's modal thought. (shrink)