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 contents. 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.     

Leibniz’s Theory of Space

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.     

Newton’s Neo-Platonic Ontology of Space

This paper investigates Newton’s ontology of space in order to determine its commitment, if any, to both Cambridge neo-Platonism, which posits an incorporeal basis for space, and substantivalism, which regards space as a form of substance or entity. A non-substantivalist interpretation of Newton’s theory has been famously championed by Howard Stein and Robert DiSalle, among others, while both Stein and the early work of J. E. McGuire have downplayed the influence of Cambridge neo-Platonism on various aspects of Newton’s own spatial hypotheses. Both of these assertions will be shown to be problematic on various grounds, with special emphasis placed on Stein’s influential case for a non-substantivalist reading. Our analysis will strive, nonetheless, to reveal the unique or forward-looking aspects of Newton’s approach, most notably, his critical assessment of substance ontologies, that help to distinguish his theory of space from his neo-Platonic contemporaries and predecessors.     

A Critical Use of Foucault’s Art of Living

Foucault’s vocabulary of arts of existence might be helpful to problematize the entwinement of humans and technology and to search for new types of hybrid selves. However, to be a serious new ethical vocabulary for technology, this art of existence should be supplemented with an ongoing critical discourse of technologies, including a critical analysis of the subjectivities imposed by technologies, and should be supplemented with new medical and philosophical regimens for an appropriate use of technologies.     

On the Properties of <Emphasis Type="Italic">α</Emphasis>-Unchaining Single Linkage Hierarchical Clustering

In the election of a hierarchical clustering method, theoretic properties may give some insight to determine which method is the most suitable to treat a clustering problem. Herein, we study some basic properties of two hierarchical clustering methods: α-unchaining single linkage or SL(α) and a modified version of this one, SL?(α). We compare the results with the properties satisfied by the classical linkage-based hierarchical clustering methods.     

The Issue of “Closure” in Jagers op Akkerhuis’s Operator Theory

Attempts to define life should focus on the transition from molecules to cells and the “closure” aspects of this event. Rather than classifying existing objects into living and non-living entities I believe the challenge is to understand how the transition from non-life to life can take place, that is, the how the closure in Jagers op Akkerhuis’s hierarchical classification of operators, comes about.     

Understanding Scientific Inquiries of Galileo’s Formulation for the Law of Free Falling Motion

The purpose of this study is to gain a better understanding of the role of abstraction and idealization in Galileo’s scientific inquiries into the law of free falling motion, and their importance in the history of science. Because there is no consensus on the use of the terms “abstraction” and “idealization” in the literature, it is necessary to distinguish between them at the outset. This paper will argue (1) for the importance of abstraction and idealization in physics and the theories and laws of physics constructed with abduction from observations and (2) that these theoretical laws of physics should be tested with deduction and induction thorough quasi-idealized entities rather than empirical results in the everyday world. Galileo’s work is linked to thought experiments in natural science. Galileo, using thought experiments based on idealization, persuaded others that what had been proven true for a ball on an inclined plane would be equally true for a ball falling through a vacuum.     

A Formal Proof of a Paradox Associated with Cohen’s Kappa

Suppose two judges each classify a group of objects into one of several nominal categories. It has been observed in the literature that, for fixed observed agreement between the judges, Cohen’s kappa penalizes judges with similar marginals compared to judges who produce different marginals. This paper presents a formal proof of this phenomenon.     

Symbolic Languages and Natural Structures a Mathematician’s Account of Empiricism

The ancient dualism of a sensible and an intelligible world important in Neoplatonic and medieval philosophy, down to Descartes and Kant, would seem to be supplanted today by a scientific view of mind-in-nature. Here, we revive the old dualism in a modified form, and describe mind as a symbolic language, founded in linguistic recursive computation according to the Church-Turing thesis, constituting a world L that serves the human organism as a map of the Universe U. This methodological distinction of L vs. U helps to understand how and why structures of phenomena come to be opposed to their nature in human thought, a central topic in Heideggerian philosophy. U is uncountable according to Georg Cantor’s set theory but Language L, based on the recursive function system, is countable, and anchored in a Gray Area within U of observable phenomena, typically symbols (or tokens), prelinguistic structures, genetic-historical records of their origins. Symbols, the phenomena most familiar to mathematicians, are capable of being addressed in L-processing. The Gray Area is the human Environment E, where we can live comfortably, that we manipulate to create our niche within hostile U, with L offering overall competence of the species to survive. The human being is seen in the light of his or her linguistic recursively computational (finite) mind. Nature U, by contrast, is the unfathomable abyss of being, infinite labyrinth of darkness, impenetrable and hostile to man. The U-man, biological organism, is a stranger in L-man, the mind-controlled rational person, as expounded by Saint Paul. Noumena can now be seen to reside in L, and are not fully supported by phenomena. Kant’s noumenal cause is the mental L-image of only partly phenomenal causation. Mathematics occurs naturally in pre-linguistic phenomena, including natural laws, which give rise to pure mathematical structures in the world of L. Mathematical foundation within philosophy is reversed to where natural mathematics in the Gray Area of pre-linguistic phenomena can be seen to be a prerequisite for intellectual discourse. Lesser, nonverbal versions of L based on images are shared with animals.     

The Art of Living with Technology: Turning Over Philosophy of Technology’s Empirical Turn

In this article we seek to lay bare a couple of potential conceptual and methodological issues that, we believe, are implicitly present in contemporary philosophy of technology (PhilTech). At stake are (1) the sustained pertinence of and need for coping strategies as to ‘how to live with technology (in everyday life)’ notwithstanding PhilTech’s advancement in its non-essentialist analysis of ‘technology’ as such; (2) the issue of whether ‘living with technology’ is a technological affair or not (or both); and (3) the tightly related question concerning the status of the methodological bedrock of contemporary PhilTech, the ‘empirical turn.’ These matters are approached from the perspective of the philosophical notion of the ‘art of living,’ and our argumentation is developed both as a context for and on the basis of the contributions to the special issue ‘The Art of Living with Technology.’     

Blindness and Seeing in Systems Epistemology: Alfred Locker’s Trans-Classical Systems Theory

Appreciating the undeniable value of General Systems Theory (GST), Alfred Locker considers the question whether or not GST is able to go beyond a mere scientific point of view. Locker’s own systems theoretical approach, Trans-Classical Systems Theory, proposes not only to include usual observations into a systems view, but likewise their theoretical presuppositions. Locker hereby creates two levels of observation; an ortho- and a meta-level, where otherwise incommensurable viewpoints are united into whole. In this way, Locker is able to articulate a holistic systems theory of seeming opposites, like, for example, creation and evolution.     

The Constructive Realist Account of Science and Its Application to Ilya Prigogine’s Conception of Laws of Nature

Sciences are often regarded as providing the best, or, ideally, exact, knowledge of the world, especially in providing laws of nature. Ilya Prigogine, who was awarded the Nobel Prize for his theory of non-equilibrium chemical processes—this being also an important attempt to bridge the gap between exact and non-exact sciences [mentioned in the Presentation Speech by Professor Stig Claesson (nobelprize.org, The Nobel Prize in Chemistry 1977)]—has had this ideal in mind when trying to formulate a new kind of science. Philosophers of science distinguish theory and reality, examining relations between these two. Nancy Cartwright’s distinction of fundamental and phenomenological laws, Rein Vihalemm’s conception of the peculiarity of the exact sciences, and Ronald Giere’s account of models in science and science as a set of models are deployed in this article to criticise the common view of science and analyse Ilya Prigogine’s view in particular. We will conclude that on a more abstract, philosophical level, Prigogine’s understanding of science doesn’t differ from the common understanding.

Advertising Aristotle: A Preliminary Investigation into the Contemporary Relevance of Aristotle’s Art of Rhetoric

In this article, a preliminary investigation will be conducted in order to try to discover whether or not Aristotle’s the Art of Rhetoric can have any relevance as a handbook for the rhetoricians of the twenty-first century and in particular for advertising designers. First, the background against which this question is posed will be set out. Second, the chosen methodology will be explained. Thereafter, some qualitative data will be presented and discussed. Finally, some conclusions will be drawn suggesting that The Art of Rhetoric may be just as relevant and influential today for advertising professionals as it was for the lawyers and politicians of classical times.     

On the Equivalence of Cohen’s Kappa and the Hubert-Arabie Adjusted Rand Index

It is shown that one can calculate the Hubert-Arabie adjusted Rand index by first forming the fourfold contingency table counting the number of pairs of objects that were placed in the same cluster in both partitions, in the same cluster in one partition but in different clusters in the other partition, and in different clusters in both, and then computing Cohen’s κ on this fourfold table. The author thanks Willem Heiser, Mark de Rooij, Marian Hickendorff and three anonymous reviewers for their helpful comments and valuable suggestions on earlier versions of this article. Published online xx, xx, xxxx.     

On the Philosophical Nature of Einstein’s Mass-Energy Equivalence Formula E=mc^{2}

The historical development of the famous Einstein formula \(E=mc^{2}\) is briefly discussed. In this paper, on the basis of the Einstein viewpoint a new general approach is proposed for demonstrating the correctness of the formula \(E=mc^{2}\) . It is can be seen that the generalized approach leads to Einstein’s famous formula, too. During recent years, various papers have been published concerning the incompleteness of this famous formula. It is demonstrated that the presented claims in these articles are not mathematically legitimate. It is clear that there are still some important misunderstandings concerning the interpretation of Einstein’s mass-energy equivalence formula.     

The Construction of ‘Reality’ in the Robot: Constructivist Perspectives on Situated Artificial Intelligence and Adaptive Robotics

This paper discusses different approaches incognitive science and artificial intelligenceresearch from the perspective of radicalconstructivism, addressing especially theirrelation to the biologically based theories ofvon Uexküll, Piaget as well as Maturana andVarela. In particular recent work in ‘New AI’ and adaptive robotics on situated and embodiedintelligence is examined, and we discuss indetail the role of constructive processes asthe basis of situatedness in both robots andliving organisms.     

Revisiting <Emphasis Type="Italic">Tom Tom:</Emphasis> Performative Anamnesis and Autonomous Vision in Ken Jacobs’ Appropriations of <Emphasis Type="Italic">Tom Tom the Piper’s Son</Emphasis>

In 1969 the American avant-garde filmmaker Ken Jacobs gained wide recognition with a two-hour long interpretation of a 1905 silent short film. Ever since, the artist has kept on revisiting the same material, each time with a different technological approach. Originally hailed as a prime example of structural filmmaking, Jacobs’ more recent variations on the theme of Tom Tom the Piper’s Son beg for a broader understanding of his methods and the meanings implied. To gain a deeper insight in this on-going mise-en-abyme (and an obsession dominating a large part of his career), this essay expands comments by the artist himself with concepts taken from animation, media-archaeology and Warburg’s Mnemosyne atlas. Rereading a filmic text with minute attention, remediating it from an analogue to an electronic format, and reanimating the original action by adding a variety of intervals: all Jacobs’ strategies are aimed at demonstrating the afterlife of Tom Tom in a contemporary cultural context.     

The Documentary Surreal: Film and Painting in Luciano Emmer’s <Emphasis Type="Italic">La Leggenda di Sant’Orsola</Emphasis> (1948) and Henri Storck’s <Emphasis Type="Italic">Le Monde de Paul Delvaux</Emphasis> (1946)

This article deals with the aesthetics of the art documentary of the 1940s and 1950s, which can be considered as the Golden Age of the genre. Prior to the breakthrough of television in Europe, which would usurp and standardize the art documentary, cinematic reproductions of artworks resulted in experimental shorts that were highly self-reflexive. These films became visual laboratories to investigate the tensions between movement and stasis, the two- and three-dimensional, and the real and the artificial—a film on art was self-consciously presented as an art film. Focusing on La Leggenda di Sant’Orsola (1948) by Luciano Emmer and Le Monde de Paul Delvaux (1946) by Henri Storck, this article also investigates how the animation of the static image by the film medium relates to Surrealist practices.