Representing and abstracting. An Analysis of Leibniz’s Concept of Symbolic Knowledge (original) (raw)
Related papers
The Epistemological Functions of Symbolization in Leibniz's Universal Characteristic
Leibniz's universal characteristic is a fundamental aspect of his theory of cognition. Without symbols or characters it would be difficult for the human mind to define several concepts and to achieve many demonstrations. In most disciplines, and particularly in mathematics, the mind must then focus on symbols and their combinatorial rules rather than on mental concepts. For Leibniz, mental perception is most of the time too confused for attaining distinct notions and valid deductions. In this paper, I argue that the functions of symbolization differ depending upon the kind of concepts that are replaced with characters. In my view, most commentators did not sufficiently underline the distinction between two main functions of formal substitution in Leibniz's characteristic: either increasing our knowledge or simply structuring it. In the first case, we complete our knowledge because formal substitution makes sensible and imaginary concepts more distinct. In the second case, symbolization helps to organize contents that are already conceived of by reason. Thus the process of substitution is not always identically applicable, for symbols replace different types of concepts.
Visualization and Symbolic Knowledge in Leibniz and Lambert
published in: Breger, H., Herbst, J. y Ernder, S. (comp.), Actas del IX. Internationaler Leibniz-Kongress Natur und Subjekt, Hannover, 26. September bis 1. Oktober 2011, Hannover, Gottfried-Wilhelm-Leibniz-Gesellschaft, Bände 1-3, 2011ISBN 978-3-9808167-4-8, Vol. 1, pp. 312-323.
Ontological and Semiotic Grounds of LEibniz Characteristica Universalis
Ontological and Semiotic Grounds of LEibniz Characteristica Universalis, 2019
One of the most relevant systems that are precedent of modern Symbolic Logic was Leibniz’s Characteristica Universalis, this is a universal language that pretends to improve both reasoning and the practice of scientific inquiry. This universal language, however, supposes that every sign that we use in reasoning has something that is not arbitrary, i.e., certain proportion between the characters we use and the things that they express, this constitutes an ontological as well as logical and semiotic ground of signhood. Signs also permit a set of traceable relations, and Leibniz concerned about this particular aspect of signs as the inferential power of his Characteristica Universalis. In this work we explore the two aspects of signhood as ontological and semiotic in order to show the importance of such Leibnizian project and its relevance for syntactic and semiotic purposes.
Studia Leibnitiana (45/1), 2013, “Analysis as a mathematical method in Leibniz”, edited by Herbert Breger and Wenchao Li, pp. 109-130 , 2014
The meaning of the term “analysis” in Leibniz’s work is multifarious and it is doubtful that one could ever succeed in gathering this variety of meanings into a unified whole. However it has long been remarked that a landmass seems to detach itself from these moving waters – an island sometimes called by its inventor “The Most General Analytics of Human Thoughts”. Already sketched in the De Arte Combinatoria (1666) as a reform of the “analytical part” of Logic (pars logices analytica), it rested on a very simple intuition: the possibility of developing, in parallel, three analyses, namely an analysis of thoughts (analysis notionum et veritatum), an analysis of the structure of language by which we express these thoughts (analysis linguarum or analysis grammatica) and an analysis of the symbols by which we represent them (analysis characterum). This “General Analytics” achieved, any human thought could be related to a catalog of simple notions expressed by basic characters (the so called alphabetum cogitationum humanarum) and, as a direct consequence, any truth could be expressed as a combination of these primitive symbols. http://www.steiner-verlag.de/programm/zeitschriften/studia-leibnitiana/studia-4520131.html
Revue de métaphysique et de morale, 2011
Reviewed by Ohad Nachtomy, Bar-Ilan University and Fordam University T his volume consists of an introduction and seven articles (all in French, whose titles can be translated as follows): "Mathematics and Theology: the infinite in Nicholas Cusanus" by Jean Celeyrette; "The missing link" by Pierre Magnard, which seeks to restore the gap between Nicholas Cusanus and the moderns through the work of Charles de Bovelles (ignored by many historians of ideas); "Perfection, harmony, and divine choice in Leibniz: in what sense is the world best?" by Paul Rateau; "Mathematical and metaphysical infinity: on how to use Leibniz to read Cusanus (and others)" by David Rabouin; "Leibniz and the perception of the future" by Marc Parmentier; "The power of infinity and the paradoxes of singularity. Infinity and contraction in Nicholas Cusanus", by Frédéric Vengeon; and "The paradoxes of singularity: infinity and perception in G.W. Leibniz" by Anne-Lise Rey. As the editors of this very interesting collection state, its aim is to compare the philosophical systems of Nicholas Cusanus and that of Leibniz. The method of comparison they propose is very interesting as well: On the one hand, they are not seeking to merely establish causal links from Cusanus to Leibniz (although they provide decisive textual evidence that Leibniz read Cusanus). On the other hand, they also wish to avoid an examination of the systems in abstraction from their historical context. Instead, what the editors of this volume seek to highlight are the philosophical relations between the systems of Cusanus and Leibniz. An attempt to compare a premodern/medieval metaphysics with one that relates directly to the metaphysical systems of Descartes and Spinoza might raise some eyebrows. It goes without saying that the 15 th century's metaphysics of Cusanus and that of Leibniz respond to very different contexts. The editors are well aware of this gap and their methodological approach reflects the way they address this difficulty. Their comparative project is based on the conviction that Cusanus and Leibniz's systems present profound homologies. The homologies the editors have in mind are summed up as follows: Each thinker presents a metaphysics of the infinite (as pointed out by the articles of Celeyrette and Rateau); an expressive ontology within the framework of complicatio/explicatio (see Rey's article); a valuation of singularity in its relation to its source (Vengeon's article treats this point) (147).
The Leibnizian perspectivism The point of view became in Leibniz's thought one of the main concepts of his metaphysical and epistemological conceptions. We must remember his preference for perspectivistic metaphors when presenting a plastic image of the monadological world. However, Leibniz's perspectivism, due partly to Nietzsche, has been interpreted as a way of subjectivism, as a subjectivizing projection of the individual, as an expression of the will to power. This is, for example, the evaluation of the Leibnizian perspectivism in Heidegger and Gadamer. 1 It is not my intention to amend this interpretation, which runs in subtle ways from a criticism to all the occidental metaphysics. I neither pretend to save Leibniz from this criticism, if that were appropriate. In any case, my modest intention is to show that, beyond a certain understanding of the whole criticism to metaphysics, Leibnizian perspectivism, at least considered at its face value, is far away from constituting another expression of modern subjectivism. As I will try to show, the Leibnizian perspectivism is based on an ontological conception of structural character concerning the nature of things. The Leibnizian perspectivism, against its subjectivizing interpretations, implies the concept of projective exposition or displaying, in which fundamental elements of what is projected are conserved. As we will soon analyze, the concept of expression, which in essence can be understood as a transformation that conserves some invariants, is one of the main concepts of this way of understanding the Leibnizian perspectivism. The Leibnizian concept of expression is closely connected with the notion of representation, which in Leibniz assumes, from an epistemological point of view, a clearly contemporary nuance. 2 However, the expression has still deeper roots. On the one hand, it is a metaphysical concept whose exploration is still open. On the other hand, it reveals formal aspects, which have a mathematical and logical origin (if by 'logical' we understand issues about the structure or form of objects in general). The possibility of transformation under invariance between different objects is based on a community of structure: either they have an identical structure or a certain homology under certain respects can be established between them. Thus, a science of these formal possibilities would constitute, at the same time, a structural foundation of the expression.
The Logic of Leibniz’s Generales Inquisitiones De Analysi Notionum et Veritatum
The Review of Symbolic Logic, 2016
TheGenerales Inquisitiones de Analysi Notionum et Veritatumis Leibniz’s most substantive work in the area of logic. Leibniz’s central aim in this treatise is to develop a symbolic calculus of terms that is capable of underwriting all valid modes of syllogistic and propositional reasoning. The present paper provides a systematic reconstruction of the calculus developed by Leibniz in theGenerales Inquisitiones. We investigate the most significant logical features of this calculus and prove that it is both sound and complete with respect to a simple class of enriched Boolean algebras which we call auto-Boolean algebras. Moreover, we show that Leibniz’s calculus can reproduce all the laws of classical propositional logic, thus allowing Leibniz to achieve his goal of reducing propositional reasoning to algebraic reasoning about terms.
en Laura Herrera Castillo, Äusserungen des Inneren. Beiträge zur Problemgeschichte des Ausdrucks, Berlin/Boston, De Gruyter, 2019, 2019