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.     

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.     

On Gene’s Action and Reciprocal Causation

Advancing the reductionist conviction that biology must be in agreement with the assumptions of reductive physicalism (the upward hierarchy of causal powers, the upward fixing of facts concerning biological levels) A. Rosenberg argues that downward causation is ontologically incoherent and that it comes into play only when we are ignorant of the details of biological phenomena. Moreover, in his view, a careful look at relevant details of biological explanations will reveal the basic molecular level that characterizes biological systems, defined by wholly physical properties, e.g., geometrical structures of molecular aggregates (cells). In response, we argue that contrary to his expectations one cannot infer reductionist assumptions even from detailed biological explanations that invoke the molecular level, as interlevel causal reciprocity is essential to these explanations. Recent very detailed explanations that concern the structure and function of chromatin—the intricacies of supposedly basic molecular level—demonstrate this. They show that what seem to be basic physical parameters extend into a more general biological context, thus rendering elusive the concepts of the basic level and causal hierarchy postulated by the reductionists. In fact, relevant phenomena are defined across levels by entangled, extended parameters. Nor can the biological context be explained away by basic physical parameters defining molecular level shaped by evolution as a physical process. Reductionists claim otherwise only because they overlook the evolutionary significance of initial conditions best defined in terms of extended biological parameters. Perhaps the reductionist assumptions (as well as assumptions that postulate any particular levels as causally fundamental) cannot be inferred from biological explanations because biology aims at manipulating organisms rather than producing explanations that meet the coherence requirements of general ontological models. Or possibly the assumptions of an ontology not based on the concept of causal powers stratified across levels can be inferred from biological explanations. The incoherence of downward causation is inevitable, given reductionist assumptions, but an ontological alternative might avoid this. We outline desiderata for the treatment of levels and properties that realize interlevel causation in such an ontology.     

The Classification Society’s Bibliography Over Four Decades: History and Content Analysis

The Classification Literature Automated Search Service, an annual bibliography based on citation of one or more of a set of around 80 book or journal publications, ran from 1972 to 2012. We analyze here the years 1994 to 2012. The Classification Society’s Service, as it was termed, was produced by the Classification Society. In earlier decades it was distributed as a diskette or CD with the Journal of Classification. Among our findings are the following: an enormous increase in scholarly production in this area post approximately 2000; and another big increase in quantity of publications from approximately 2004. The over 93,000 bibliographic records used is the basis for determining the research disciplines that we analyze. We make all this data available for download, formatted in text and in XML, with an accompanying Apache Lucene/Solr search interface.     

Minkowski Generalizations of Ward’s Method in Hierarchical Clustering

In this paper, we consider several generalizations of the popular Ward’s method for agglomerative hierarchical clustering. Our work was motivated by clustering software, such as the R function hclust, which accepts a distance matrix as input and applies Ward’s definition of inter-cluster distance to produce a clustering. The standard version of Ward’s method uses squared Euclidean distance to form the distance matrix. We explore the effect on the clustering of using other definitions of distance, such as the Minkowski distance.     

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.     

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.     

Cauchy’s Infinitesimals,His Sum Theorem,and Foundational Paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy’s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy’s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy’s proof closely and show that it finds closer proxies in a different modern framework.     

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.     

Meaningfulness: Civic or Political? A Response to Erik Claes’s ‘Civic Meaningfulness’

This reply examines to what extent Claes’s qualitative research on volunteers, meaningfulness and citizenship mirrors dimensions of republican citizenship. Republican citizenship brings together the idea of freedom as membership of a self-governing community and the ideal of commitment of those members to the common good of the community. According to the author, the idea of republican citizenship that emerges from the interviews is connected with (1) An experience of meaningfulness that is self-fulfilling, but at the same time places life in a larger context, (2) A deeper inner side of civic engagement, (3) A notion of civic virtue that is not too demanding due to its inner link with self-discovery through active citizenship, (4) A strong awareness of the plurality of ways of living a human life, and not a passive identification with an abstract, homogeneous social whole.     

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.     

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.     

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.’     

Civic Meaningfulness ‘Revisited’: A Final Reply to Honohan and Dekker

This final reply responds to Honohan’s invitation to articulate the Arendtian tone of the key-note paper. It spells out the philosophical intuition that the political life of citizens, at least potentially, is capable of making visible what makes human life worthwhile and fully meaningful, and the philosophical curiosity to see whether traces of this deep political awareness can be retrieved in dialogues with volunteers. In response to Dekker’s critical doubts, this final reply clarifies the central stakes of Claes’s paper. The core argument was not to show that the biographical model of meaningfulness is the prevailing approach of meaning in/of volunteering, but to assess the potentials and limits of the model’s interpretive power. Moreover, the paper argues for an alternative, existential model of meaningfulness. This approach refers to deep experiences of meaning that emerge from the practice of volunteering and that shift into powerful political experiences of hope, and a lived sense of equality.     

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.     

Mathesis Perennis: Mathematics in Ancient, Renaissance, and Modern Times

ApproachingAntiquity:ArchimedesandtheFieldsMedal Since1936theso calledFieldsMedal“isawardedeveryfouryearsontheoccasionofthe InternationalCongressofMathematicianstorecognizeoutstandingachievementforexistingwork andforthepromiseoffutureachievement”(http:/…     

‘The Economic’ According to Aristotle: Ethical, Political and Epistemological Implications

A renewed concern with Aristotle’s thought about the economic aspects of human life and society can be observed. Aristotle dealt with the economic issues in his practical philosophy. He thus considered ‘the economic’ within an ethical and political frame. This vision is coherent with a specific ontology of ‘the economic’ according to Aristotle. In a recent paper, I analysed this ontology and left its consequences, especially for Ethics and Politics, for another paper. In this article, I firstly summarise the reasoning and conclusions of the aforementioned paper. Then, I extract the ethical and political “lessons” of the Aristotelian conception. I finally add a section with epistemological “lessons”, and consequences for the teaching of Economics.     

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.