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Logic and Reality in Leibniz's Metaphysics.

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... 52]. 18 Leibniz held, as one of the first, that all propositions are of the subject-predicate form: saying something (predicate) about something else (subject). In De Arte Combinatoria (1666), we read: 20 A proposition is composed of subject and predicate; all propositions, therefore, are com2nations. ...
... The '2' in 'com2nations' is not a typo: Leibniz signals thereby that a proposition is composed of two concepts.21 Parkinson[14, p. 39].22 Parkinson[18],[14, Introduction], Ishiguro [19, ch. II], Castañeda[20], cf. ...
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We present what Aristotle wrote on identity in a leisurely manner, which is much more than is generally known, save among the cognoscenti (Aristotle scholars), and mutatis mutandis about the introduction of the identity-symbol (=). We add two codas, one on the so-called Leibniz’ Law, which is different (but resembles) what passes for it in logic and philosophy, and one on the status of identity, as accepted by mathematicians and logicians, in physics. This article is part of the theme issue ‘Identity, individuality and indistinguishability in physics and mathematics’.
... Sobre o assunto cf., por exemplo,Mendonça (2012), p. 471-474. 13 Acerca do caráter autorreferencial do método leibniziano na explicação científica, cf.Parkinson (1965), p. 117-123, e Gale (1982, p. 8-16. 14 Como assinalado por Gerhardt, no manuscrito, Leibniz anotou o nome de Molyneux à margem da folha. ...
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Neste trabalho, nos propomos percorrer algumas etapas do debate sobre a relevância das causas finais nas investigações físicas, que levou Leibniz a confrontar sua filosofia, de modo particular, com o cartesianismo e, mais em geral, com uma concepção estritamente mecanicista da natureza. Serão seguidos aqueles indícios que se encontram na obra de Leibniz, ao procurar pelas referências a Molyneux, um dos primeiros a receber e divulgar a perspectiva leibniziana, e, além disso, um dos poucos interlocutores com os quais se instaurou um diálogo de tons cordiais. Tentaremos mostrar que, todavia, tal troca não polêmica é fruto de um desentendimento de fundo entre os dois intelectuais.
... GP II, 55 [=LA]; GP VI, 440 [=Th]; GP VII, 305 [=ROR]; 311. 71 As has been pointed out several times ( Russell (1937), 174; Kauppi (1960), 113f.; Parkinson (1965), 82ff.), identification of primitive concepts with divine attributes issues in a serious difficulty when combined with Leibniz's conceptual atomism. The point is that since primitive concepts are by definition unanalysable and since qua divine attributes they are purely positive and absolute, it follows that all the primitive concepts are mutually compatible. ...
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The study offers a new account of one of the central topics of Leibniz’s philosophy: substance. It brings to light the metaphysical foundations of Leibniz’s notion of substance and shows – in opposition to many leading commentators – that his treatment of it is governed by clear standards of significance rooted in his broader metaphysical position. Starting from Leibniz’s general theory of definition – founded on his views concerning the science of metaphysics – the author identifies the set of basic defining features of substance for Leibniz and then provides a detailed analysis and interpretation of these features. A foundational role is given to a group of texts from the 1680’s in which Leibniz provides conceptual analyses of the most general items of reality.
... Estos métodos aún están en la base de la comprensión, modelado, simulado, diseño y desarrollo de sistemas físicos. En otro orden de cosas, Leibniz fue el primero en afirmar la posible existencia de algo equivalente a una lógica formal completa para describir el razonamiento [42] . No estaba satisfecho con la lógica aristotélica y desarrolló sus propias ideas para mejorarla. ...
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Resumen Presentamos una breve perspectiva histórica del desarrollo en pa-ralelo y, a veces, entrelazado, de la Lógica y las Matemáticas, con el objetivo final de presentar la Lógica Computacional y, en particular, la Deducción Automática, como u area de investigación matemática de extraordinario potencial práctico, no en balde distintos autores de conocido prestigio afirman que la Lógica es a la Computación como el Cálculo Infinitesimal es a la Física.
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This paper offers a fresh interpretation of Leibniz’s theory of relations. I argue that we should take seriously Leibniz’s idea of non-ideal relations inhering in one subject. Such single-inhering relations should not be understood in terms of non-relational, absolute properties, but in terms of perspectival relations. Through the notion of perspective, we can understand how a relation between two relata inheres in only one of those relata. For example, my perception of you involves my point of view. Therefore, it is individual to me. My perception of you is not equal to your perception of me. However, it does relate me to you. Perspective can thus explain how relations only inhere in one subject while nevertheless really relating one thing to another. This leads to a novel understanding of the rejection of purely extrinsic denominations and the supposed isolation of substances.
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The Principle of Sufficient Reason (PSR)—the principle that everything has a reason—plays a central role in Leibniz’s philosophical system. It is rather difficult, however, to determine what Leibniz’s attitude towards the modal status of the PSR is. The prevailing view is that Leibniz takes the PSR to be true necessarily. This paper develops a novel interpretation and argues that Leibniz’s PSR is a contingent principle. It also discusses whether a merely contingent PSR can do the metaphysical heavy lifting that Leibniz aims for. The paper shows that, despite appearance to the contrary, this is possible. In a nutshell, the argument is that the only possible PSR violation Leibniz allows for is God’s creation of a suboptimal world; there is no Leibnizian possible world, though, which intrinsically violates the PSR. Despite its contingency, then, Leibniz’s PSR is modally robust enough to serve as a foundational principle of his metaphysics.
Article
Leibniz's principle of sufficient reason (PSR) is the claim that everything has a sufficient reason. But is Leibniz committed to the necessity or to the contingency of his great principle? I argue that Leibniz is committed to its contingency, given that he allows for the absolute possibility of entities that he claims violate the PSR. These are all cases of qualitatively indiscernible entities, such as indiscernible atoms, vacua, and bodies. However, Leibniz's commitment to the contingency of the PSR seems to stand in tension with his inference of the PSR from his theory of truth. I argue that this apparent tension can be resolved satisfactorily. When it comes to his modal views on the PSR, Leibniz's position is entirely consistent.
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En el presente ensayo se aborda descriptiva y analíticamente la doctrina de la contingencia, expuesta y profesada por Leibniz, a la luz de su concepción de los mundos posibles, la que tenía por objeto refutar el determinismo metafísico estricto que derivó directamente del monismo panteísta de Spinoza y que afectaba, por definición, la afirmación de la libertad y la voluntad humanas.
Article
This article discusses Leibniz’s claim that every substance is endowed with the property of perception in connection with Platonism, rationalism and the problem of substance monism. It is argued that Leibniz’s ascription of perception to every substance relies on his Platonic conception of finite things as imitations of God, in whom there is ‘infinite perception’. Leibniz’s Platonism, however, goes beyond the notion of imitation, including also the emanative causal relation and the logical (i.e. definitional) priority of the absolute over the limited. It is proposed that Leibniz’s endorsement of Platonism, in conjunction with some rationalist elements of his philosophy, implies a monistic conception of particulars as modifications of a single substance. Following some scholars and opposing others, the article offers evidence that Leibniz accepted this implication during the last years of his Paris period. However, it is further argued that it was precisely the idea of perception as a property of every substance that allowed Leibniz to find a way out of monism after that period. More specifically, the article defends the view that what made room for ontological pluralism within Leibniz’s rationalist and Platonic outlook was the idea that perception is the property which constitutes the very being of substances: substances are their perceptions.
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Warum gibt es überhaupt irgendetwas und nicht vielmehr nichts? Ein Blickwinkel, unter den sich Leibniz' Denken insgesamt stellen läßt, ist definitiv die Seinsfrage. Leibniz ist der erste Philosoph, der diese Grundfrage der Philosophie begrifflich explizit formuliert und ins Zentrum seiner Reflexionen stellt. Gleichwohl kommt die Seinsfrage, als die radikal zu Ende geführte Frage nach dem zureichenden Grund von allem, weder denkerisch aus dem Nichts noch schwebt sie systematisch bindungslos im luftleeren Raum. Vielmehr ist von einem sachlich konsequenten Zusammenhang zwischen der Seinsfrage und Leibniz' konkreter Metaphysik auszugehen. Die Antwort auf die Frage beruht auch auf dem Was, Wie und Wozu des weltlichen Seins, die Rückschlüsse auf den Grund und die Motivation der Schöpfung erlauben. So stellt sich die Seinsfrage bei Leibniz ein vor dem Hintergrund seiner Logik, seiner Substanzlehre, seines Gottes- und Weltbegriffs, seiner Theorie des Verhältnisses von Möglichkeit und Wirklichkeit oder seiner Auffassung von der Aufgabe des Vorstellens, kann also ohne all dies in seiner speziellen Gestalt und Reichweite nicht verstanden werden. Die vorliegende Monographie versucht, die wesentlichen Elemente seines Systems auf die Seinsfrage hin zusammenzuführen, um dadurch den Grundcharakter seines Denkens aus der Perspektive dieser Frage sichtbar werden zu lassen.
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Las dos ramas principales de la lógica son la lógica formal (o lógica menor) y la lógica material (o lógica mayor). La lógica material se ocupa del contenido semántico de la argumentación. La lógica formal se interesa por la forma o estructura de los razonamientos, es la lógica clásica propiamente dicha. El libro tercero de Luigi Ferrajoli Principia iuris. Teoría del derecho y la democracia. 3. La sintaxis del derecho, es un esfuerzo congruente de xiomatización de su teoría conforme a la lógica simbólica o matemática.
Chapter
Gottfried Wilhelm Freiherr von Leibniz (1646–1716) is without a doubt one of the most important figures in the history of philosophical theism. His entire philosophical system might be termed a theodicy; in fact, the only book he ever wrote and published bears that title.1 All of Leibniz’s philosophical powers are brought to bear in support of the existence of the traditional theistic God, so much so that some have thought it incredible that such an innovative thinker as Leibniz should culminate and even centre his system in such a conservative, orthodox theology.2 But this he did, and he was eager to prove God’s existence by all means available, utilising the ontological argument, the cosmological argument, a special form of the teleological argument dependent upon his monadology, and the argument from eternal truths.3 He remarked, ‘I believe also that nearly all the means which have been employed to prove the existence of God are good and might be of service, if we perfect them...4 Leibniz’s attempt to perfect the ontological argument by supplying a missing premiss is well-known; however, the centre of our attention shall be directed toward the contributions he made in formulating the cosmological a gument. These are substantial; it is his version of the argument that Was employed by Christian Wolff and subsequently attacked by Immanuel Kant and that is the basic form of the argument discussed today. Fortunately, in terms of presuppositions, Leibniz’s version of the proof is largely independent of his monadological system, and we can therefore forgo a discussion of his general metaphysical Weltanschauung. But there are some underlying principles, an understanding of which is critical if we are to fully appreciate the thrust of his proof.
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The aim of the paper is to illuminate some core aspects of Leibniz’s conception of judgement and its place in his conception of the mind. In particular, the paper argues for three claims: First, the act of judgement is at the centre of Leibniz’s conception of the mind in that minds strive at actualising innate knowledge concerning derivative truths, where the actualising involves an act of judgement. Second, Leibniz does not hold a judgement account of predication, but a two-component account that distinguishes between predication and alethic evaluation. Third, Leibniz understands the act of affirmative judgement in terms of establishing active dispositions, i.e. strivings, to make reasons available for future reasoning that aims at answering whether-questions (whether a proposition p is true or not). Correspondingly, he understands the act of negative judgement in terms of establishing dispositions to ban propositions from future reasoning that aims at answering whether-questions. In the final analysis, the acts of affirmative as well as of negative judgement turn out to be acts of changing memory dispositions.
Chapter
We owe Russell’s book on Leibniz to a very improbable series of events, of which surely the most improbable of all was that McTaggart was getting married. It was McTaggart who was scheduled to give the lectures on Leibniz that Russell ended up giving at Trinity College, Cambridge during Lent Term of 1899 and it was McTaggart’s marriage that prevented him from giving them. Now getting married (even for McTaggart) would not normally be so traumatic an event as to prevent one from lecturing, butMcTaggart’s brideto- be was a New Zealander.
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La finalidad de este articulo es elucidar el sentido de la doctrina leibniziana de la exigencia de existencia y el combate de los posibles, situandola dentro del conjunto de la metafisica de Leibniz y mostrando su absoluta compatibilidad con la afirmacion de la creacion libre y voluntaria por parte de Dios. Se intentara explicar que elementos de la afirmacion de la ‘exigencia de existencia’ y el ‘combate de los posibles’ reflejan tesis estric- tamente metafisicas, y cuales pueden considerarse recursos metaforicos. En este contexto, se explicara que papel que juega la voluntad divina antecedente en la fundamentacion de la tendencia de los posibles a la existencia, y se intentara focalizar el papel especifico de la ‘sabiduria’, como atributo divino, en la determinacion y eleccion del mejor mundo posible. Finalmente, se extraeran algunas consecuencias del analisis anterior, en relacion con la libertad divina en el acto creador.
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Em diversas ocasioes, Leibniz recorre a autoridade de Aristoteles a fim de roborar sua tese da verdade como inerencia do predicado ao sujeito da proposicao. Nao e, contudo, evidente em que medida a filosofia aristotelica poderia oferecer amparo a essa reivindica- cao. Afinal, a Aristoteles tradicionalmente se atribui uma concepcao de verdade diferente, consistente em uma relacao de correspondencia entre a proposicao e a realidade que ela se destina a descrever. Sem discutir a conhecida tese da verdade como correspondencia , este trabalho e dedicado a investigar em que medida os escritos de Aristoteles permitem que Leibniz respalde neles as suas afirmacoes. Para tanto, a presente investigacao estara focada nos Primeiros e os Segundos Analiticos , obras em que Aristoteles expoe sua teoria do racio- cinio e da demonstracao. Visa-se averiguar se, e sob que condicoes, a nocao de inerencia ali mobilizada pode ser assimilada a nocao leibniziana de inerencia.
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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.
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The relationships humans express when describing images have powerful, but poorly understood, effects on how visual information is represented, structured, and processed in information systems. This study evaluates the benefits and difficulties of using content analysis and ontological analysis as predictors of relationship instances and types occurring in image descriptions. A random sample of 36 documented reference transactions from the administrative files of the Pittsburgh Photographic Library is analyzed in light of three describing contexts: image searcher, curator, and cataloger. Through the qualitative and quantitative assessment of image descriptions, the research leads to several key findings and contributions. The most important findings vindicate the claim that recognition, capture, and classification of relationship instances can be empirically grounded utilizing content analysis and ontological tools and methods. Evidence comes in successfully ascertaining and capturing in a Corpus the existence of 1,655 relationship instances. Further, the analysis finds evidence of relationship types and subtypes of relationships whose members share certain recognizable properties in common. The study also brings useful, new insights to the capture of background information surrounding events using situation-templates, introduces methods for formulating case relations and image attributes as binary predicates, and it offers a new, finer-grained definition of relationship. Contributions of this study include a corpus of relationship instances, an ontology of relationship types, and a methodological framework that provides significantly better results than earlier studies in the prediction of relationships (the architecture of which is depicted in Figure 22 on page 102). There are a number of ways this research could be extended and corroborated. First, event analysis ought to be tied to a system of semantic frame analysis. Second, test the content analysis form against other texts, which will result in elaboration of the core ontology of relationship types. Third, expand image description analysis beyond the current domain to include image description in visual ethnography, art history and criticism, and photography practices. Fourth, test how inference engines reason over relationships in knowledge-based environments. Finally, to aid in the analysis of the meanings of relationships, more work is needed in formalizing the ontological concepts used in image descriptions.
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http://dx.doi.org/10.5007/2177-7055.2013v34n67p53Las dos ramas principales de la lógica son la lógica formal (o lógica menor) y la lógica material (o lógica mayor). La lógica material se ocupa del contenido semántico de la argumentación. La lógica formal se interesa por la forma o estructura de los razonamientos, es la lógica clásica propiamente dicha. Establecer cuáles son las formas correctas y válidas de los raciocinios, la verdad de las premisas y de las conclusiones es una preocupación derivada para esta rama.
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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.
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The principle of the identity of indiscernibles says that two things that are indiscernible - that share all their properties - are one and the same thing. The principle was clearly formulated, and gained immense philosophical importance in Leibniz's thought. Turned round to read that identity is sufficient for indiscernibility, it seems compelling, and in this version it is connected with the principle of the substitutivity of identicals - that two terms which denote the same thing are substitutable for one another in any context salva veritate. We shall not concern ourselves here with this latter principle, but confine our attention to the original formulation -that indiscernibility is sufficient for identity. The exact interpretation of the principle in Leibniz's philosophy is not entirely clear. It sometimes appears as a sort of empirical generalization. But this surely does not exhaust its meaning, for it is obviously connected with same of Leibniz's central metaphysical doctrines such as the notion of a (complete) individual concept, or the principle of sufficient reason. In fact, most commentators regard the principle as 'analytic', or 'logically necessary'. 1 In this paper I shall not try to re-interpret the principle and its exact meaning in Leibniz; I shall completely ignore its metaphysical background, and its systematic status in his theory. I shall rather present a partial explication of the principle in more modern logical terminology, by which I shall contend that the principle is not analytic, that it is not "true by definition" or anything of the kind (sections II-IV), and yet that it is a necessary and a priori truth (sections V-VI). Under this particular interpretation the argument that the principle is not analytic is based on the difference between the notions of identity and indiscernibility, and the fact that identifying them in a particular language, is a step of great conceptual
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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.
Article
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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. Cet article discute de la théorie des dénominations, expression et notions individuelles de Leibniz. Son point central est que la clé pour élucider plusieurs thèses fondamentales de Leibniz est de se pencher sur son argumentation, en commençant par sa théorie de la vérité (voulant qu'un énoncé vrai soit un énoncé dont la notion du prédicat est comprise dans celle du sujet), laquelle s'oppose à l'idée de dénominations purement extrinsèques. Cet argument montre pourquoi il y a un fondement interne à toutes les dénominations, pourquoi tout dans le monde est interrelié, pourquoi chaque substance exprime toutes les autres et pourquoi chaque changement dans le monde se reflète par un changement véritable, interne, en chaque substance.
Article
Resumen: Partiendo de la definición de la identidad en Principia Mathematica, aquí se discute el estatus lógico del principio de la identidad de los indiscernibles con los criterios y argumentos de Leibniz y Clarke. En la defensa que hace Leibniz de este principio se establece la distinción entre una necesidad lógica y una necesidad moral, relacionada con la existencia y el buen juicio de Dios, que se resume en el principio de razón suficiente; esta posición se puede relacionar con el Tractatus, donde se critica a Russell en términos similares a los que Clarke usó en contra de Leibniz. Wittgenstein, sin embargo, habla de la experiencia necesaria para entender la lógica: la experiencia fundamental de que algo es; así, se puede sugerir un paralelo entre su posición y la distinción de Leibniz, el cual también nos llevaría a replantear y repensar en términos leibnizianos la independencia radical de la lógica. Abstract: The logical status of the identity of indiscernibles is considered in the context of Principia Mathematica's definition of identity and in reference to the Leibniz-Clarke polemics. In his defence Leibniz distinguishes between logical and moral necessity and relates the latter to existence, jure divino, and the principle of sufficient reason. In Wittgenstein's Tractatus Russell is criticised in the same terms that Clarke used against Leibniz, but Wittgenstein also talks about the 'experience' that something is, necessary to understand logic, and points out that logic could be prior to the question 'How?', but not to the question 'What?' From this a parallel is suggested between Wittgenstein's position and Leibniz's distinction which could be used to rethink in Leibnizian terms logic's radical independence.
Chapter
Undoubtedly the most puzzling of Kant’s Critical views is his thesis that virtually all aspects of our experience of objects are contributed by the perceiving subject rather than by the things experienced, and are not features of these things as they exist independently of sensible perceivers. This position, which Kant calls transcendental idealism, is striking because nothing could be less commonsensical than the belief that things as they appear to us have nothing in common with things as they are independently of being perceived. From a more technical point of view the doctrine is perplexing because Kant apparently does not support it very well. Beginning with Kant’s contemporaries, critics have pointed out that among all the arguments in the Critique of Pure Reason, none apparently entails the conclusion that things in themselves cannot be like objects of sense experience in any way. So, for example, although Kant’s theory of synthetic a priori knowledge provides some support for transcendental idealism, there is nothing in the analysis of the synthetic a priori ruling out the possibility that features contributed to experience by the perceiving subject may correspond to characteristics of things in themselves, although we might never know this to be so. And even though Kant views transcendental idealism as the solution to the Antinomies, this is at best indirect support for the position. Moreover, Kant asserts the merely subjective character of sensible representations in 1770, long before he developed the theory of the Antinomies. Because transcendental idealism is so radical, it seems that Kant should provide especially strong reasons in its support.
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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.
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