Leibniz and the rationality of the infinite

Part 1 Historically the term 'infinite' has had two apparently contrary meanings. On the one hand, it was taken by metaphysicians like Plotinus to mean that which " ... has never known measure and stands outside number, and so is under no limit either in regard to anything external or internal ... " (Branford 1949, V.5.11). 'Infinite' in this sense means 'irrevocably complete'. On the other hand, Aristotle defined it in this way: "A quantity is infinite if it is such that we can always take a part outside what has already been taken." (Hardie and Gaye 1941, 207a, 5-10) 'Infinite', in this second sense means, 'irrevocably incomplete'. Leibniz is someone who uses both these meanings. In particular, he identifies the irrevocably complete with God and the irrevocably incomplete with the world (as we know it). Given, firstly, that what is irrevocably complete includes everything and, secondly, that it excludes anything incomplete, the following conclusion can be drawn: Leibniz's philosophy of the infinite makes of the-world-as-we-know-it something that is logically dependent on God, but also something that exists in contradiction to 'him'. Leibniz cannot escape a kind of contradiction in what he says about God and the world but this is not a straightforward case of self-refutation. The reason turns on the consideration that to divorce the concept of the irrevocably complete from its object is to deprive this concept of its sense, specifically of its sense of completeness. For if the two are distinct, then there is something beyond the irrevocably complete, namely, how this is independently of its concept. It follows that to deny the irrevocably complete is, in the same breath, to affirm that very thing. Yet if we cannot quite deny the irrevocable complete, neither can we as human beings quite affirm it either-for the human mind is, we do not doubt, a limited one. Thus the irrevocably complete can neither be affirmed nor denied without contradiction. There is a strong resemblance between this paradox and the paradox of the liar: in both cases there is a thesis that says of itself that it is untrue and, in both cases, thesis and antithesis tum out to be equivalent. Part 2 Kant offers some powerful reasons to think that the paradox discussed in Part 1 involves no real contradiction. The critical philosophy suggests that the apparent contradiction is real, only if, per impossibile, we have some way to positively employ the concept of the world as it is independently of our conceptions of it. Kant's view of the infinite shares with Leibniz's the vice (if it is one) that it is paradoxical: both philosophers make use of a concept that cannot, strictly speaking, be possessed by the human mind. However each view has the significant virtue that it shows the difference between the irrevocably complete and the irrevocably incomplete to be not simply a logical difference. My overall conclusion is based on a synthesis of the Leibnizian and the Kantian philosophies of the infinite. According to Leibniz, neither the irrevocably complete, nor the irrevocably incomplete, can be eliminated from philosophy. According to Kant, infinity is-from a human perspective at least-something prior to conception; putting Leibniz and Kant together, I conclude that these modes of infinity combine to produce finitude, that they are the joint conditions under which difference, and therefore finitude, is possible. In particular, I argue that the irrevocably complete is the infinity of fullness, and that the irrevocably incomplete is the infinity of emptiness, and that logic is blind to any difference there might be between these, since both are, by definition, undifferentiated. Given that ethics, as well as logic, is dependent on finitude, I conclude, finally, that the perennial ambition to eliminate either the irrevocably complete or the irrevocably incomplete from philosophy is, not merely unrealisable, but potentially dangerous

One and the same reason

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, September 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 147-155).My dissertation is about the relationship between theoretical and practical reason. I argue that these two kinds of reason are unified in important respects. In Chapter One I argue that there is a single, fundamental kind of reasoning (roughly, unrestrained self-reflection) and that theoretical and practical reason ought to be understood as instances of this more fundamental kind of reasoning, distinguished only by their subject matter. I then argue that two formulations of Kant's Categorical Imperative jointly codify the activity of this basic reasoning. Therefore, the Categorical Imperative is, in this sense, the supreme principle of reason. In Chapter Two I show how the very abstract norms formulated in Chapter One can be sharpened if we connect them to the conditions of human agency. I argue that the demands of being an agent require us to submit to a procedure of negotiation and legislation with other agents that is similar to the contractualism of Hobbes and Rawls. The difference between my view and theirs is that my contractualism, because it is tied to our agency, issues in categorical requirements. In Chapter Three I develop a theory of normative concepts that satisfies two demands that have appeared incompatible: the demand that our normative concepts be intimately connected to human nature and the demand that normative items be things we aspire to, and thus things that are relevantly beyond us and our activities. I show how we can satisfy both of these desiderata through an open-ended constructivism that understands normative items as transcendent ideals. In Chapter Four I argue that a robust, philosophically serviceable distinction between theoretical judgments about the world and practical judgments about what one ought to do cannot be sustained because these two kinds of judgments are inextricably entangled. They are entangled because we must employ both kinds of judgment to fully explain actions. This fact entails that practical and theoretical judgments occupy a single holistic theory.by Kenneth Edward Dale Walden.Ph.D

Error, apariencia ilusoria y juicio. La doctrina de la imposibilidad del error total como pauta de lectura de la lógica trascendental de Kant

La doctrina de la imposibilidad del error total (DIET) sostiene que todo error en el que pueda incurrir el entendimiento es solo parcial, toda vez que la razón y el entendimiento no pueden contradecir los principios gracias a los cuales es posible el mismo juicio. El horizonte interpretativo que surge de la DIET ofrece una posible pauta de lectura de la división de la lógica trascendental en una lógica de la verdad (analítica trascendental) y en una crítica de la lógica de la ilusión (dialéctica trascendental). La concepción de la verdad trascendental en virtud de la cual es posible toda ulterior verdad empírica, así como toda predicación de verdad o falsedad en un juicio, muestra la plena compatibilidad de la analítica trascendental con la DIET. Sin embargo, no ocurre lo mismo con la dialéctica trascendental, no solo porque en ella se pone de manifiesto una connatural e inevitable apariencia ilusoria trascendental de la razón, sino porque en su forma más extrema dicha apariencia ilusoria adopta la forma de un conflicto de la razón consigo misma: la antinomia de la razón. La propuesta para evidenciar la estrecha compatibilidad entre la DIET y la idea de mundo a partir de la cual se genera dicha antinomia, es mostrar que se trata de un conflicto sólo aparente y que el vínculo con el principio regulativo del uso empírico del entendimiento de todas las ideas cosmológicas apela al principio de la concordancia de la razón consigo misma, el cual cimienta la exigencia normativa de no contradicción de sus principios al explicitarse como un principio doctrinal que deroga el principio dialéctico. En la medida en que la DIET es la expresión de una profunda confianza en las posibilidades de la razón humana, su estudio a partir del caso específico del conflicto de la antinomia de la razón permite acceder a una comprensión de la KrV como un ejercicio autorreflexivo, dialógico y crítico de la razón, mediante el cual esta se reconoce como fuente de verdad, pero también de error. Bajo el enfoque que proporciona la DIET problemas como el error y la apariencia ilusoria que Kant sitúa en el juicio, adquieren un significado más hondo y permiten comprender los aspectos comunes y diferenciales que su explicación ofrece respecto al conocimiento empírico y a la metafísica, descubriendo un importante nexo entre un ámbito y otro a partir del estudio de temas como la apparentia, la subrepción, el criterio externo de la verdad, los juicios provisionales, los prejuicios y la relación de estos con la reflexión y la investigación trascendentales

Kant in English: An Index

Kant in English: An Index / By Daniel Fidel Ferrer. ©Daniel Fidel Ferrer, 2017. Pages 1 to 2675. Includes bibliographical references. Index. 1. Ontology. 2. Metaphysics. 3. Philosophy, German. 4. Thought and thinking. 5. Kant, Immanuel, 1724-1804. 6. Practice (Philosophy). 7. Philosophy and civilization. 8). Kant, Immanuel, 1724-1804 -- Wörterbuch. 9. Kant, Immanuel, 1724-1804 -- Concordances. 10. Kant, Immanuel, 1724-1804 -- 1889-1976 – Indexes. I. Ferrer, Daniel Fidel, 1952-. MOTTO As a famous motto calls us back to Kant, Otto Liebmann’s writes (Kant and His Epigones of 1865): “Also muss auf Kant zurückgegangen werden.” “Therefore, must return to Kant.” Table of Contents 1). Preface and Introduction. 2. Background on Kant’s Philosophy (hermeneutical historical situation). 3). Main Index (pages, 25 to 2676). Preface and Introduction Total words indexed: 58,928; for the 12 volumes that are in the MAIN INDEX are indexed: pages 1 to 7321. This monograph by Daniel Fidel Ferrer is 2676 pages in total. The following is a machine index of 12 volumes written by Immanuel Kant and translated from German into English. Everything is indexed including the text, title pages, preface, notes, editorials, glossary, indexes, biographical notes, and even some typos. No stop words or words removed from this index. There are some German words in the text, bibliographies, and in the glossaries (also included in Main Index). Titles in English of Kant’s writings for this index (pages 1 to 7321). Anthropology, History, and Education [Starts on page 1 Correspondence [Starts on page 313 Critique of Pure Reason [Starts page 971 Critique of the Power of Judgment [Starts on page 1771 Lectures on Logic [Starts on page 2247 Lectures on Metaphysics [Starts on page 2991 Notes and Fragments [Starts on page 3670 Opus Postumum [Starts on page 4374 Practical Philosophy [Starts on page 4741 Religion and Rational Theology [Starts on page 5446 Theoretical Philosophy after 1781 [Starts on page 5990 Theoretical Philosophy, 1755-1770 [Starts on page 6541 Universal Natural History and Theory of the Heavens or An Essay on the Constitution and the Mechanical Origin of the Entire Structure of the Universe Based on Newtonian Principles [Starts on page 7162 The whole single file which includes all of these books ends on page 7321. 12 volumes are pages 1 to 7321. These actual texts of these books by Kant are not include here because of copyright. This is only an index of these 7321 pages by Immanuel Kant. There are some German words in the text and in the glossaries, etc. Searching this Main Index. Please note the German words that start with umlauts are at the end of the index because of machine sorting of the words. Starting with the German word “ße” on page 2674 page of this book (see in Main Index). Use the FIND FUNCTION for all examples of the words or names you are searching. Examples from the Main Index mendacium, 5171, 5329, 5389 mendation, 220 mendax, 2702, 2800 mended, 360 Mendel, 416, 925, 965 Mendelian, 2212 Mendels, 345, 363, 417, 458, 560, 572, 588, 926, 928, 929 MENDELSSOHN, 925 Mendelssohn, 8, 9, 19, 98, 99, 100, 101

Kant in English: An Index

Kant in English: An Index / By Daniel Fidel Ferrer. ©Daniel Fidel Ferrer, 2017. Pages 1 to 2675. Includes bibliographical references. Index. 1. Ontology. 2. Metaphysics. 3. Philosophy, German. 4. Thought and thinking. 5. Kant, Immanuel, 1724-1804. 6. Practice (Philosophy). 7. Philosophy and civilization. 8). Kant, Immanuel, 1724-1804 -- Wörterbuch. 9. Kant, Immanuel, 1724-1804 -- Concordances. 10. Kant, Immanuel, 1724-1804 -- 1889-1976 – Indexes. I. Ferrer, Daniel Fidel, 1952-. MOTTO As a famous motto calls us back to Kant, Otto Liebmann’s writes (Kant and His Epigones of 1865): “Also muss auf Kant zurückgegangen werden.” “Therefore, must return to Kant.” Table of Contents 1). Preface and Introduction. 2. Background on Kant’s Philosophy (hermeneutical historical situation). 3). Main Index (pages, 25 to 2676). Preface and Introduction Total words indexed: 58,928; for the 12 volumes that are in the MAIN INDEX are indexed: pages 1 to 7321. This monograph by Daniel Fidel Ferrer is 2676 pages in total. The following is a machine index of 12 volumes written by Immanuel Kant and translated from German into English. Everything is indexed including the text, title pages, preface, notes, editorials, glossary, indexes, biographical notes, and even some typos. No stop words or words removed from this index. There are some German words in the text, bibliographies, and in the glossaries (also included in Main Index). Titles in English of Kant’s writings for this index (pages 1 to 7321). Anthropology, History, and Education [Starts on page 1 Correspondence [Starts on page 313 Critique of Pure Reason [Starts page 971 Critique of the Power of Judgment [Starts on page 1771 Lectures on Logic [Starts on page 2247 Lectures on Metaphysics [Starts on page 2991 Notes and Fragments [Starts on page 3670 Opus Postumum [Starts on page 4374 Practical Philosophy [Starts on page 4741 Religion and Rational Theology [Starts on page 5446 Theoretical Philosophy after 1781 [Starts on page 5990 Theoretical Philosophy, 1755-1770 [Starts on page 6541 Universal Natural History and Theory of the Heavens or An Essay on the Constitution and the Mechanical Origin of the Entire Structure of the Universe Based on Newtonian Principles [Starts on page 7162 The whole single file which includes all of these books ends on page 7321. 12 volumes are pages 1 to 7321. These actual texts of these books by Kant are not include here because of copyright. This is only an index of these 7321 pages by Immanuel Kant. There are some German words in the text and in the glossaries, etc. Searching this Main Index. Please note the German words that start with umlauts are at the end of the index because of machine sorting of the words. Starting with the German word “ße” on page 2674 page of this book (see in Main Index). Use the FIND FUNCTION for all examples of the words or names you are searching. Examples from the Main Index mendacium, 5171, 5329, 5389 mendation, 220 mendax, 2702, 2800 mended, 360 Mendel, 416, 925, 965 Mendelian, 2212 Mendels, 345, 363, 417, 458, 560, 572, 588, 926, 928, 929 MENDELSSOHN, 925 Mendelssohn, 8, 9, 19, 98, 99, 100, 101