We propose in this paper to construct modal logics based on mathematical morphology. The contribution of this paper is twofold. First we show that mathematical morphology can be used to define modal operators in the context of normal modal logics. We propose definitions of modal operators as algebraic dilations and erosions, based on the notion of adjunction. We detail the particular case of morphological dilations and erosions, and of there compositions, as opening and closing. An extension (...) to the fuzzy case is also proposed. Then we show how this can be interpreted for spatial reasoning by using qualitative symbolic representations of spatial relationships (topological and metric ones) derived from mathematical morphology. This allows to establish some links between numerical and symbolic representations of spatial knowledge. (shrink)

Several logical operators are defined as dual pairs, in different types of logics. Such dual pairs of operators also occur in other algebraic theories, such as mathematical morphology. Based on this observation, this paper proposes to define, at the abstract level of institutions, a pair of abstract dual and logical operators as morphological erosion and dilation. Standard quantifiers and modalities are then derived from these two abstract logical operators. These operators are studied both on sets of states and (...) sets of models. To cope with the lack of explicit set of states in institutions, the proposed abstract logical dual operators are defined in an extension of institutions, the stratified institutions, which take into account the notion of open sentences, whose satisfaction is parametrised by sets of states. A hint on the potential interest of the proposed framework for spatial reasoning is also provided. (shrink)

Several tasks in artificial intelligence require the ability to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper, we exploit the algebraic framework of mathematical morphology in the context of propositional logic and define operations such as dilation or erosion of a set of formulas. We derive concrete operators, based on a semantic approach, that have an intuitive interpretation and that are formally well behaved, to perform revision, fusion and (...) abduction. Computation and tractability are addressed, and simple examples illustrate the main results. (shrink)

On étudie dans cet article l'apparence morphologique des plantes à travers des modèles géométriques et statiques puis on examine quelques caractères-clés des processus de croissance à la lumière des propriétés de certains systèmes différentiels.

Morphological engineering is an emerging research area in synthetic biology. In 2008 “synthetic morphology” was proposed as a prospective approach to engineering self-constructing anatomies by Jamie A. Davies of the University of Edinburgh. Synthetic morphology can establish a new paradigm, according to Davies, insofar as “cells can be programmed to organize themselves into specific, designed arrangements, structures and tissues.” It is obvious that this new approach will extrapolate morphology into a new realm beyond the traditional logic of (...) morphological research. However, synthetic morphology is a highly idealized vision of morphology which derives its visionary ideas from morphological engineering and mathematical idealizations in order to understand the principles of molecular morphology. Thus, the question is, if this approach will help to understand morphogenesis better or if it will just enable biologists to engineer morphogenesis. The paper investigates the development of synthetic morphology and its relation to synthetic biology as well as its epistemic gains. (shrink)

In 1952, Alan Turing published his last work on the concept of embryonic morphogenesis, propounding a computational framework for pattern formation within the developing embryo. This concept of morphogenesis and the concept of embryo pattern formation based on chemical diffusion patterns were corroborated with the discovery of the Homeobox or Hox genes. In the following decades, Hox gene research has expanded and is now shown to underlie the variety of morphological novelties that we experience in nature, the patterning of structural (...) aspects of different organs including the brain and also mutant animals that may in the future give rise to novel speciation. Turing had the foresight and vision and with his work created the field of computational biology and mathematical modeling in biological systems. In this paper, we will discuss the concept of Hox genes, their role in patterning the embryo, how it relates to Turing’s concept of morphogenesis and what further insights they may provide. (shrink)

The title of this volume—published in the series “Lisbon Philosophical Studies” devoted to “uses of language in interdisciplinary fields”—is potentially misleading, because its subject is, rather than linguistic morphology, the Morphologie associated with the German poet, playwright, and thinker, Johann Wolfgang Goethe. For Goethe, morphology is a science dedicated to the observation and description of everything that “is handled by chance and occasionally in other [sciences]”, and hence, it is intended to serve as a complement to any number (...) of disciplines: philosophy, art history, mathematics, cognitive science, linguistics, history, demography, computer science, and architecture . All these disciplines are, in one way or another, represented in this collection of papers, which arises from a project carried out at the IFL at the New University of Lisbon, the EHESS (School for Advanc .. (shrink)

Following a previous article published in Biological Theory, in this study we present a mathematical theory for a science of qualities as directly perceived by living organisms, and based on morphological patterns. We address a range of qualitative phenomena as observables of a psychological system seen as an impredicative system. The starting point of our study is the notion that perceptual phenomena are projections of underlying invariants, objects that remain unchanged when transformations of a certain class under consideration are (...) applied. The study develops with the observables, the entailed total order and metric, whence the algebra and the geometry of such a science, presenting a formal phenomenological model for phenomena that are not rigidly Euclidean. We show how non-Euclidean perception can have many useful Euclidean formalizations, as well as locally-homeomorphic-to-Euclidean-space models. The mathematical models we provide are tested on the basis of results from experimental psychology, in particular from the field of color, time, and space perception. (shrink)

Morphological EvoDevo is a field of biological inquiry in which explicit relations between evolutionary patterns and growth or morphogenetic processes are made. Historically, morphological EvoDevo results from the coming together of several traditions, notably Naturphilosophie, embryology, the study of heterochrony, and developmental constraints. A special feature binding different approaches to morphological EvoDevo is the use of formalisms and mathematical models. Here we will introduce anatomical network analysis, a new approach centered on connectivity patterns formed by anatomical parts, with its (...) own concepts and tools specifically designed for the study of morphological EvoDevo questions. Riedl’s concept of burden is tightly related to the use of anatomical networks, providing a nexus between the evolutionary patterns and the structural constraints that shape them. (shrink)

In this paper I argue that category theory ought to be seen as providing the language for mathematical discourse. Against foundational approaches, I argue that there is no need to reduce either the content or structure of mathematical concepts and theories to the constituents of either the universe of sets or the category of categories. I assign category theory the role of organizing what we say about the content and structure of both mathematical concepts and theories. Insofar, (...) then, as the structuralist sees mathematics as talking about structures and their morphology, I contend that category theory furnishes a framework for mathematical structuralism. (shrink)

Mathematical models of tumour invasion appear as interesting tools for connecting the information extracted from medical imaging techniques and the large amount of data collected at the cellular and molecular levels. Most of the recent studies have used stochastic models of cell translocation for the comparison of computer simulations with histological solid tumour sections in order to discriminate and characterise expansive growth and active cell movements during host tissue invasion. This paper describes how a deterministic approach based on reaction-diffusion (...) models and their generalisation in the mechano-chemical framework developed in the study of biological morphogenesis can be an alternative for analysing tumour morphological patterns. We support these considerations by reviewing two studies. In the first example, successful comparison of simulated brain tumour growth with a time sequence of computerised tomography (CT) scans leads to a quantification of the clinical parameters describing the invasion process and the therapy. The second example considers minimal hypotheses relating cell motility and cell traction forces. Using this model, we can simulate the bifurcation from an homogeneous distribution of cells at the tumour surface toward a nonhomogeneous density pattern which could characterise a pre-invasive stage at the tumour-host tissue interface. (shrink)

Formal spaces have become commonplace conceptual and computational tools in a large array of scientific disciplines, including both the natural and the social sciences. Morphological spaces are spaces describing and relating organismal phenotypes. They play a central role in morphometrics, the statistical description of biological forms, but also underlie the notion of adaptive landscapes that drives many theoretical considerations in evolutionary biology. We briefly review the topological and geometrical properties of the most common morphospaces in the biological literature. In contemporary (...) geometric morphometrics, the notion of a morphospace is based on the Euclidean tangent space to Kendall’s shape space, which is a Riemannian manifold. Many more classical morphospaces, such as Raup’s space of coiled shells, lack these metric properties, e.g., due to incommensurably scaled variables, so that these morphospaces typically are affine vector spaces. Other notions of a morphospace, like Thomas and Reif’s skeleton space, may not give rise to a quantitative measure of similarity at all. Such spaces can often be characterized in terms of topological or pretopological spaces. (shrink)

Darwin described biological species as groups of morphologically similar individuals. These groups of individuals can split into several subgroups due to natural selection, resulting in the emergence of new species. Some species can stay stable without the appearance of a new species, some others can disappear or evolve. Some of these evolutionary patterns were described in our previous works independently of each other. In this work we have developed a single model which allows us to reproduce the principal patterns in (...) Darwin’s diagram. Some more complex evolutionary patterns are also observed. The relation between Darwin’s definition of species, stated above, and Mayr’s definition of species is also discussed. (shrink)

For the purposes of this monograph, "by a degree" is meant a degree of recursive unsolvability. A degree [script bold]m is said to be minimal if 0 is the unique degree less than [script bold]m. Each of the six chapters of this self-contained monograph is devoted to the proof of an existence theorem for minimal degrees.

Kurt Gdel was the most outstanding logician of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Gdel's writings. The first three volumes, already published, consist of the papers and essays of Gdel. The final two volumes of the set deal with Gdel's correspondence with his contemporary mathematicians, this fourth volume consists of material from correspondents from A-G.

This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and (...) updated by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

Since the early days of physics, space has called for means to represent, experiment, and reason about it. Apart from physicists, the concept of space has intrigued also philosophers, mathematicians and, more recently, computer scientists. This longstanding interest has left us with a plethora of mathematical tools developed to represent and work with space. Here we take a special look at this evolution by considering the perspective of Logic. From the initial axiomatic efforts of Euclid, we revisit the major (...) milestones in the logical representation of space and investigate current trends. In doing so, we do not only consider classical logic, but we indulge ourselves with modal logics. These present themselves naturally by providing simple axiomatizations of different geometries, topologies, space-time causality, and vector spaces. (shrink)

In the research of motion video, the existing target detection methods are susceptible to changes in the motion video scene and cannot accurately detect the motion state of the target. Moving target detection technology is an important branch of computer vision technology. Its function is to implement real-time monitoring, real-time video capture, and detection of objects in the target area and store information that users are interested in as an important basis for exercise. This article focuses on how to efficiently (...) perform motion detection on real-time video. By introducing the mathematical model of image processing, the traditional motion detection algorithm is improved and the improved motion detection algorithm is implemented in the system. This article combines the advantages of the widely used frame difference method, target detection algorithm, and background difference method and introduces the moving object detection method combining these two algorithms. When using Gaussian mixture model for modeling, improve the parts with differences, and keep the unmatched Gaussian distribution so that the modeling effect is similar to the actual background; the binary image is obtained through the difference between frames and the threshold, and the motion change domain is extracted through mathematical morphological filtering, and finally, the moving target is detected. The experiment proved the following: when there are more motion states, the recall rate is slightly better than that of the VIBE algorithm. It decreased about 0.05 or so, but the relative accuracy rate increased by about 0.12, and the increase ratio is significantly higher than the decrease ratio. Departments need to adopt effective target extraction methods. In order to improve the accuracy of moving target detection, this paper studies the method of background model establishment and target extraction and proposes its own improvement. (shrink)

Isolated habitats, the consequence of the fragmentation process, are the object of external disturbance. This divides the patch area into two zones: interior and edge. The interior-to-edge ratio quantifies the potential disturbance impact. A method is presented to calculate a reference value for the interior-to-edge ratio, based upon the minimum edge for a given interior. The method is based on pixel geometry features and mathematical morphology. A corrected interior-to-edge ratio is defined using the reference value. The method is (...) illustrated for woodlot fragments in the Belgian Kempen region. (shrink)

Fractal art graphics are the product of the fusion of mathematics and art, relying on the computing power of a computer to iteratively calculate mathematical formulas and present the results in a graphical rendering. The selection of the initial value of the first iteration has a greater impact on the final calculation result. If the initial value of the iteration is not selected properly, the iteration will not converge or will converge to the wrong result, which will affect the (...) accuracy of the fractal art graphic design. Aiming at this problem, this paper proposes an improved optimization method for selecting the initial value of the Gauss-Newton iteration method. Through the area division method of the system composed of the sensor array, the effective initial value of iterative calculation is selected in the corresponding area for subsequent iterative calculation. Using the special skeleton structure of Newton’s iterative graphics, such as infinitely finely inlaid chain-like, scattered-point-like composition, combined with the use of graphic secondary design methods, we conduct fractal art graphics design research with special texture effects. On this basis, the Newton iterative graphics are processed by dithering and MATLAB-based mathematical morphology to obtain graphics and then processed with the help of weaving CAD to directly form fractal art graphics with special texture effects. Design experiments with the help of electronic Jacquard machines proved that it is feasible to transform special texture effects based on Newton's iterative graphic design into Jacquard fractal art graphics. (shrink)

. Textline segmentation in handwritten documents is of real challenge and interesting in the field of document image processing. In this paper, we propose a handwritten textline segmentation scheme based on the concept of linked list. The proposed method consists of three stages, namely, preprocessing, linked list and mathematical morphology. The concept of the linked list approach is used to build a textline sequence and mathematical morphology is used to obtain the line separator. We experimentally evaluated (...) our proposed method on a document containing handwritten Kannada script. The results are compared with recent methods and show encouraging results. (shrink)

Alan Turing’s pioneering work on computability, and his ideas on morphological computing support Andrew Hodges’ view of Turing as a natural philosopher. Turing’s natural philosophy differs importantly from Galileo’s view that the book of nature is written in the language of mathematics (The Assayer, 1623). Computing is more than a language used to describe nature as computation produces real time physical behaviors. This article presents the framework of Natural info-computationalism as a contemporary natural philosophy that builds on the legacy of (...) Turing’s computationalism. The use of info-computational conceptualizations, models and tools makes possible for the first time in history modeling of complex self-organizing adaptive systems, including basic characteristics and functions of living systems, intelligence, and cognition. (shrink)

The debate over how best to characterize inflectional morphology has been couched largely in terms of the “dual-mechanism” approach described in Pinker (Words and rules: the ingredients of language, Basic Books, 1999) versus “single-mechanism” connectionist approaches derived from Rumelhart and McClelland (On learning past tenses of English verbs, MIT, 1986). There are, however, other single-mechanism approaches. The exemplar-based or analogical models of Daelemans et al. (TimBL: Tilburg Memory-Based Learner, version 4.3 reference guide, ILK, 2002) and Skousen (Analogical modeling of (...) language, Kluwer Academic, 1989) also model inflectional usage accurately within a single-mechanism. The most striking theoretical claim peculiar to these purely analogical models is that they do not posit any resident linguistic generalizations for processing language. Instead they process new instances of usage by comparing them systematically to remembered instances of previous usage. Based on a comparison of their Minimal Generalization Model with an adaptation of Nosofsky's (Journal of Mathematical Psychology 34: 393–418, 1990) Generalized Context Model, Albright and Hayes (Cognition 90: 119–161, 2003) argue that such purely analogical models are intrinsically inadequate for modeling the English past tense. This paper shows, however, that Skousen's (Analogical modeling of language, Kluwer Academic, 1989) Analogical Model performs as well as the Minimal Generalization Model. The implications of these results for cognitive linguistics are discussed. (shrink)

Mitochondria can change their shape from discrete isolated organelles to a large continuous reticulum. The cellular advantages underlying these fused networks are still incompletely understood. In this paper, we describe and compare hypotheses regarding the function of mitochondrial networks. We use mathematical and physical tools both to investigate existing hypotheses and to generate new ones, and we suggest experimental and modelling strategies. Among the novel insights we underline from this work are the possibilities that (i) selective mitophagy is not (...) required for quality control because selective fusion is sufficient; (ii) increased connectivity may have non‐linear effects on the diffusion rate of proteins; and (iii) fused networks can act to dampen biochemical fluctuations. We hope to convey to the reader that quantitative approaches can drive advances in the understanding of the physiological advantage of these morphological changes. (shrink)

The purpose of this paper is to provide a unitary typology for the incompatibilities of meanings at stake on different levels of Husserlian pure logic—namely, between systems of axioms and pure morphology of meanings; I show that they perfectly match by converging on the notion of Widersinn.

The volume starts with the paper of Lynn Maurice Ferguson Arnold, former Premier of South Australia and former Minister of Education of Australia, concerning the Exposition Internationale des Arts et Techniques dans la Vie Moderne (International Exposition of Art and Technology in Modern Life) that was held from 25 May to 25 November 1937 in Paris, France. The organization of the world exhibition had placed the Nazi German and the Soviet pavilions directly across from each other. Many papers are devoted (...) to the interpretation of this opposition. Arnold’s paper considers the differences in the two totalitarian states’ architectural and design discourse styles. Although each of them communicated a totalitarian language of purposes, permissions, and boundaries, they essentially differed in the styles of discourse represented by the architecture and design of their respective pavilions. They were opposites of each other and the liberal ideals they contested. The internationalist viewpoint reflecting the multi-ethnic mix of the USSR is contrasted to the ein Volk homogeneity represented in the German pavilion. The Soviet pavilion opted for a utopian future to be arrived at by “benign” leadership, whereas the German pavilion anchored itself in the myth of Teutonic history with the nostalgic pride protected by the swastika-bearing eagle. Jean-Yves Béziau is best known as a logician and founder of Universal Logic. However, in this paper, he poses a new philosophical question: why philosophical discourse does not use images? The paper begins with a general analysis of different types of philosophical discourses. Then, he focuses on why images have been and are still rejected in philosophical discourse. He explains various ways to use images in a fruitful way to develop philosophical thinking and discourse and illustrates his view by providing several examples. He concludes with a promising programmatic declaration about founding a new journal entitled World Journal of Pictorial Philosophy to stimulate the usage of images for developing philosophical thinking. Although complaints about the obscurity of many philosophers’ discourse are widespread, Tatiana Denisova, ex-professor of the Surgut University and a research associate of the University of the Aegean undertakes a positive attitude to this problem. She explains that the reasons for the obscurity of philosophical texts, the subsequent complexity in communicating philosophers’ meanings and their eventual incomplete understanding is not a sign of their inferiority. On the contrary, it is a sign of the fruitfulness of philosophical discourse, which can generate new meanings. Thus, the darkness of philosophical discourse is like the life-giving chaos, and the obscurity that it inevitably contains can be the keeper of implicit meanings and even their generator. Katarzyna Gan-Krzywoszyńska and Piotr Leśniewski, authors of a monograph on Polish philosopher Kazimierz Ajdukiewicz (1890 – 1963), make a comparative analysis of his educational style with that of Paulo Reglus Neves Freire (1921 – 1997). The authors highlight that these scholars have distinctly different backgrounds. The former was an educator, philosopher and a leading advocate of critical pedagogy connected with the dialogical Latin-American tradition. The latter was a philosopher and logician, a notable representative of the Lwów–Warsaw school of logic with significant contributions to semantics, model theory and the philosophy of science. Despite their apparent difference, the authors identify some striking similarities regarding their attitudes towards education; notably, their approaches are essentially dialogical. Gilah Yelin Hirsch is a multidisciplinary artist who works as a painter, writer, curator, educator, and filmmaker. In her experiential paper, he explains how and why she uses four channels of communication in her creative expression: writing, painting, filmmaking, and teaching, as dialogic inquiry. She considers that these channels compose a continuum of discourse styles, each reaching a different facet of kaleidoscopic consciousness. She claims that her choice of medium is prompted by a need to communicate her insights profoundly. Thus, for instance, she created painted allegories to express narratives based on dreams and visions emerging from her subconscious. Art and healing is another Tibetan-rooted type of discourse practised by the author. Creating and observing a healing image produces a positive psychophysiological change in both the artist and the viewer. The discourse here is tripartite between creator, image, and viewer. Filmmaking is another type of discourse she practices between the filmmaker/artist as shaman or healer and the viewer as respondent or participant. These films are meant to be experienced frame by frame, physically and emotionally in both the body and mind. Jocelyn Ireson-Paine is a cartoonist and programmer. His paper offers an original attempt to use category theory in cartooning. Category theory is a branch of mathematics that provides concepts and methods to describe general abstract structures in terms of a labelled directed graph called category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms or transformations or mappings). The author explores different ways to define “style” in art using category theory and a relational view of art. Moreover, he examines how “translation” (transformation) between styles could be defined and reveals the difficulties of how it could be implemented in a computer using special software. Jens Lemanski is a philosopher who has revived research in Arthur Schopenhauer’s legacy by exploring his work on mathematical evidence, logic diagrams, and problems of semantics. In this paper, he advances a new approach to eristic as an art of protecting oneself from the one who deliberately violates norms of discourse ethics to win an argument. The author attributes the origins of this view to Schopenhauer, suggesting a new reading of his work. According to the author, eristic is a prohibitive technique that takes effect when the norms of discourse ethics are transgressed and violated. Thus, eristic is viewed as a discipline of Enlightenment philosophy and a correlate of discourse ethics. Roshdi Rashed is an authority on the history of Arabic mathematical sciences. Proceeding from Gilles-Gaston Granger’s definition of mathematical style, he studies the question of whether a mathematical work can be characterized by a single style or by a multitude of styles. This question is explored within the style of a single work, namely Menelaus’s Sphaerica, and through the study of the development of a single problem over time, namely the isoperimetric problem. He indicates Menelaus’s divergence from the Euclidean style of (plane and stereometric) geometry caused by the drop of the Parallel Postulate, which associated it with hyperbolic geometry. Hence, the author concludes that Menelaus’s Sphaerica incorporates the well-known Euclidean style with a variation of the non-Euclidean one. On the other hand, examining the isoperimetric problem reveals another interesting historical picture. A succession of different styles (cosmological, geometric, infinitesimalistic, style of the calculus of variations, of synthetic geometry) can be observed due to the transformation of the research object over time. Boris Shalyutin, a Russian social philosopher, and Ombudsman for Human Rights in the Kurgan Region, explores the origins of discourse in combination with the birth of society and law. He claims that legal discourse marks the historical emergence of discourse in general. Homo Juridicus generated Homo Sapiens, which have created new spheres of discourse, notably moral discourse and further philosophical, political, and scientific discourse. Petros Stefaneas, a logician, computer scientist and novelist, suggests an alternative to the traditional narratology approach for studying (interactive) social media discourse. He claims that style describes how the parts of a narrative are blended into a whole. The author relies upon Goguen’s and Harrel’s concept of style as a choice of blending principles and transfers to the study of the social media narratives elements from the methodology of studying Web-based collaborative search for mathematical proofs like those implemented within the Polymath project. The last paper belongs to Ghil‘ad Zuckermann, a linguist, language revivalist, and proponent of a model of the emergence of Israeli Hebrew, according to which Hebrew and Yiddish were the primary sources of Modern Hebrew. This paper explores the fascinating and multifaceted Yiddish language and its survival in Israeli. Yiddish is characterized by a unique style that embeds psycho-ostensive expressions throughout its discourse. The author highlights the cross-fertilization between Hebrew and Yiddish as it manifests itself in any aspect of the Israeli language. He claims that Yiddish survives beneath Israeli phonetics, phonology, discourse, syntax, semantics, lexis, and even morphology, although traditional and institutional linguists have been most reluctant to admit it. (shrink)

The living forms represented in this paper are sets of parts that spontaneously increase in organization. Their organizations are measured by an information-theoretic function derived from the work of Boltzmann and Shannon. We briefly review its derivation in the context of the troubled role of mathematics in biology, and then define the function. We illustrate its nature by measuring the 22 different organizations of a set of eight things; and we facilitate its use by defining the parameters that determine an (...) amount of organization. The measure is then applied to show that the organization of limb pairs on free-living arthropods, based on data given by Cisne, confirms a pattern of increasing organization in their evolution from the Cambrian era to the present. Further applications measure the changes in organizations of ideal (theoretical) life forms, and contrasting changes in inanimate systems. Our main results represent the reproduction of unicellular organisms, and the formation of hierarchies, as processes of increasing organization. (shrink)

Evolutionary developmental biology (evo-devo) is considered a ‘mechanistic science,’ in that it causally explains morphological evolution in terms of changes in developmental mechanisms. Evo-devo is also an interdisciplinary and integrative approach, as its explanations use contributions from many fields and pertain to different levels of organismal organization. Philosophical accounts of mechanistic explanation are currently highly prominent, and have been particularly able to capture the integrative nature of multifield and multilevel explanations. However, I argue that evo-devo demonstrates the need for a (...) broadened philosophical conception of mechanisms and mechanistic explanation. Mechanistic explanation (in terms of the qualitative interactions of the structural parts of a whole) has been developed as an alternative to the traditional idea of explanation as derivation from laws or quantitative principles. Against the picture promoted by Carl Craver, that mathematical models describe but usually do not explain, my discussion of cases from the strand of evo-devo which is concerned with developmental processes points to qualitative phenomena where quantitative mathematical models are an indispensable part of the explanation. While philosophical accounts have focused on the actual organization and operation of mechanisms, properties of developmental mechanisms that are about how a mechanism reacts to modifications are of major evolutionary significance, including robustness, phenotypic plasticity, and modularity. A philosophical conception of mechanisms is needed that takes into account quantitative changes, transient entities and the generation of novel types of entities, feedback loops and complex interaction networks, emergent properties, and, in particular, functional-dynamical aspects of mechanisms, including functional (as opposed to structural) organization and distributed, system-wide phenomena. I conclude with general remarks on philosophical accounts of explanation. (shrink)

This paper examines Karl Alfred von Zittel’s practice in order to uncover the roots of so-called idiographic paleontology. The great American paleontologist Stephen Jay Gould (1941–2002) defined the discipline of idiographic paleontology as illustration and description of the morphological features of extinct species. However, this approach does not investigate macroevolutionary patterns and processes. On the contrary, the paleobiological revolution of the 1970s implemented an epistemic methodology that illustrates macrovelutionary patterns and laws by combining idiographic data with a nomothetic form of (...) explanation. This article elucidates the features of the idiographic data as well as the acquired knowledge coupled with this approach. First of all, Heinrich G. Bronn’s (1800–1862) statistical method is analyzed. Zittel’s practice arose as a reaction against the approximate conclusions reached by Bronn’s quantitative approach. Second, the details of Zittel’s methodology are described in order to bring out its peculiarities. The microscope played a pivotal role in creating and forming Zittel’s morphological data. This analysis sheds new light on the reasons behind the so-called ideographic paleontology, thus revising Gould’s historical reconstruction, as well as on the notion of paleontological data. However, even though Zittel aimed at reaching precise and stable conclusions, his data cannot be used for elucidating evolutionary mechanisms: they are scientific in a purely descriptive sense, but completely useless for biological investigations. Finally, this paper examines how Zittel’s methodology affects the contemporary paleobiological enterprise and thereby reflects upon the notion of natural history. (shrink)

Few metaphors in biology are more enduring than the idea of Adaptive Landscapes, originally proposed by Sewall Wright (1932) as a way to visually present to an audience of typically non- mathematically savvy biologists his ideas about the relative role of natural selection and genetic drift in the course of evolution. The metaphor, how- ever, was born troubled, not the least reason for which is the fact that Wright presented different diagrams in his original paper that simply can- not refer (...) to the same concept and are therefore hard to reconcile with each other (Pigliucci 2008). For instance, in some usages, the landscape’s non- fitness axes represent combinations of individual genotypes (which cannot sensibly be aligned on a linear axis, and accordingly were drawn by Wright as polyhedrons of increasing dimensionality). In other usages, however, the points on the diagram represent allele or genotypic frequencies, and so are actually populations, not individuals (and these can indeed be coherently represented along continuous axes). (shrink)

Defending Robert Rosen’s claim that in every confrontation between physics and biology it is physics that has always had to give ground, it is shown that many of the most important advances in mathematics and physics over the last two centuries have followed from Schelling’s demand for a new physics that could make the emergence of life intelligible. Consequently, while reductionism prevails in biology, many biophysicists are resolutely anti-reductionist. This history is used to identify and defend a fragmented but progressive (...) tradition of anti-reductionist biomathematics. It is shown that the mathematicoephysico echemical morphology research program, the biosemiotics movement, and the relational biology of Rosen, although they have developed independently of each other, are built on and advance this antireductionist tradition of thought. It is suggested that understanding this history and its relationship to the broader history of post-Newtonian science could provide guidance for and justify both the integration of these strands and radically new work in post-reductionist biomathematics. (shrink)

There are many ways of understanding the nature of philosophical questions. One may consider their morphology, semantics, relevance, or scope. This article introduces a different approach, based on the kind of informational resources required to answer them. The result is a definition of philosophical questions as questions whose answers are in principle open to informed, rational, and honest disagreement, ultimate but not absolute, closed under further questioning, possibly constrained by empirical and logico-mathematical resources, but requiring noetic resources to (...) be answered. The article concludes with a discussion of some of the consequences of this definition for a conception of philosophy as the study (or “science”) of open questions, which uses conceptual design to analyse and answer them. (shrink)

Scientific papers written as dialogues evoke Platonist philosophical discourses and are foreseen as elementary forms of expression in neoclassical scientific renaissance. Here we report on a study of the Brazil nut effect in a series of macroscopic and microscopic systems in the form of a play in three acts. The nut effect predicting the segregation of smaller grains at the bottom of the mixture and larger ones at the top was observed in a polydisperse mix of manually shaken playground pebbles, (...) albeit following different kinetics than in an agitated pile of chess pieces. Common sense predicts that vertical, gravity-driven segregation in colloidal dispersions with heterogeneous particle size distributions is such that larger particles would settle toward the bottom and the lighter ones cream at the top. Here we refute this expectation and demonstrate that segregation of colloidal particles in the vertical direction conforms to the Brazil nut effect when the agitation is delivered in the forms of vortex mixing or audio vibration, but not when the colloids are manually shaken. The effect is demonstrated on aqueous dispersions of hydroxyapatite and iron oxide nanoparticles. Kinetic experiments showed that segregation increases with the agitation time in mixtures of pebbles and with the post-agitation aging time in fine particle colloids. The particle size gradient established due to agitation-induced segregation led to a corresponding gradient in optoelectronic properties—band gap, conductivity, lattice acoustics—in the vertical direction of the colloidal column for both types of nanoparticles. Such morphological gradients induced by the Brazil nut effect can be harnessed as affordable and facile templates for the synthesis of functionally gradient materials. Discussion of the mechanism and the application potential of the observed effect in colloidal and coarse systems is enriched with a literature review of this curious effect and entwined with the literary elements of the dramaturgical narrative involving a family of scientist in exile from mainstream scientific institutions: the mother, the father, an elementary school boy and a kindergarten girl. The narrative conforms in its structure to the shape of a Brazil nut and presents the first research study whose findings are enacted through a dream. The play questions the humaneness and creative prospects of modern science and celebrates children’s science projects performed with meager resources and a plentiful of imagination, showing that they could be gateways to important scientific discoveries. (shrink)

This thesis focuses on models of conceptual change in science and philosophy. In particular, I developed a new bootstrapping methodology for studying conceptual change, centered around the formalization of several popular models of conceptual change and the collective assessment of their improved formal versions via nine evaluative dimensions. Among the models of conceptual change treated in the thesis are Carnap’s explication, Lakatos’ concept-stretching, Toulmin’s conceptual populations, Waismann’s open texture, Mark Wilson’s patches and facades, Sneed’s structuralism, and Paul Thagard’s conceptual revolutions. (...) -/- In order to analyze and compare the conception of conceptual change provided by these different models, I rely on several historical reconstructions of episodes of scientific conceptual change. The historical episodes of scientific change that figure in this work include the emergence of the morphological concept of fish in biological taxonomies, the development of scientific conceptions of temperature, the Church-Turing thesis and related axiomatizations of effective calculability, the history of the concept of polyhedron in 17th and 18th century mathematics, Hamilton’s invention of the quaternions, the history of the pre-abstract group concepts in 18th and 19th century mathematics, the expansion of Newtonian mechanics to viscous fluids forces phenomena, and the chemical revolution. I will also present five different formal and informal improvements of four specific models of conceptual change. I will first present two different improvements of Carnapian explication, a formal and an informal one. My informal improvement of Carnapian explication will consist of a more fine-grained version of the procedure that adds an intermediate, third step to the two steps of Carnapian explication. I will show how this novel three-step version of explication is more suitable than its traditional two-step relative to handle complex cases of explications. My second, formal improvement of Carnapian explication will be a full explication of the concept of explication itself within the theory of conceptual spaces. By virtue of this formal improvement, the whole procedure of explication together with its application procedures and its pragmatic desiderata will be reconceptualized as a precise procedure involving topological and geometrical constraints inside the theory of conceptual spaces. My third improved model of conceptual change will consist of a formal explication of Darwinian models of conceptual change that will make vast use of Godfrey-Smith’s population-based Darwinism for targeting explicitly mathematical conceptual change. My fourth improvement will be dedicated instead to Wilson’s indeterminate model of conceptual change. I will show how Wilson’s very informal framework can be explicated within a modified version of the structuralist model-theoretic reconstructions of scientific theories. Finally, the fifth improved model of conceptual change will be a belief-revision-like logical framework that reconstructs Thagard’s model of conceptual revolution as specific revision and contraction operations that work on conceptual structures. -/- At the end of this work, a general conception of conceptual change in science and philosophy emerges, thanks to the combined action of the three layers of my methodology. This conception takes conceptual change to be a multi-faceted phenomenon centered around the dynamics of groups of concepts. According to this conception, concepts are best reconstructed as plastic and inter-subjective entities equipped with a non-trivial internal structure and subject to a certain degree of localized holism. Furthermore, conceptual dynamics can be judged from a weakly normative perspective, bound to be dependent on shared values and goals. Conceptual change is then best understood, according to this conception, as a ubiquitous phenomenon underlying all of our intellectual activities, from science to ordinary linguistic practices. As such, conceptual change does not pose any particular problem to value-laden notions of scientific progress, objectivity, and realism. At the same time, this conception prompts all our concept-driven intellectual activities, including philosophical and metaphilosophical reflections, to take into serious consideration the phenomenon of conceptual change. An important consequence of this conception, and of the analysis that generated it, is in fact that an adequate understanding of the dynamics of philosophical concepts is a prerequisite for analytic philosophy to develop a realistic and non-idealized depiction of itself and its activities. (shrink)

Heat sensitive pit organs in different species of snakes show various shapes. The relation between form characters and functions were analysed by means of two different research programs. This paper presents the methodological steps involved in these research programs. The first approach is called a qualitative explanation because it connects experimental data by means of qualitative statements in order to give a functional morphological explanation for the construction of the pits in respect to the behaviour of the snake. The second (...) approach is called a quantitative explanation because the core of the explanation is a mathematical model which in its consequences explaines the construction of the pits in respect to image formation. (shrink)

Most philosophical accounts on scientific theories are affected by three dogmas or ingrained attitudes. These dogmas have led philosophers to choose between analyzing the internal structure of theories or their historical evolution. In this paper, I turn these three dogmas upside down. I argue (i) that mathematical practices are not epistemically neutral, (ii) that the morphology of theories can be very complex, and (iii) that one should view theoretical knowledge as the combination of internal factors and their intrinsic (...) historicity. (shrink)

According to the computational theory of mind , to think is to compute. But what is meant by the word 'compute'? The generally given answer is this: Every case of computing is a case of manipulating symbols, but not vice versa - a manipulation of symbols must be driven exclusively by the formal properties of those symbols if it is qualify as a computation. In this paper, I will present the following argument. Words like 'form' and 'formal' are ambiguous, as (...) they can refer to form in either the syntactic or the morphological sense. CTM fails on each disambiguation, and the arguments for CTM immediately cease to be compelling once we register that ambiguity. The terms 'mechanical' and 'automatic' are comparably ambiguous. Once these ambiguities are exposed, it turns out that there is no possibility of mechanizing thought, even if we confine ourselves to domains where all problems can be settled through decision-procedures. The impossibility of mechanizing thought thus has nothing to do with recherché mathematical theorems, such as those proven by Gödel and Rosser. A related point is that CTM involves, and is guilty of reinforcing, a misunderstanding of the concept of an algorithm. (shrink)

On the basis of previous studies in relational biology and the phenomenological calculus, in my contribution I outline the mathematical foundations of biological perception generally, and visual perception specifically. In this approach, the premise is that objects in nature are not directly accessible, and that real manifestations are projections of these invariant objects. The morphology of observables is mathematically entailed by the duality of projections and projectors in a bilinear algebra that is the phenomenological calculus. The relationships between (...) what is not directly accessible (which can be defined as noumena) and phenomena may be explicated in terms of metabolism and repair, whence a geometric theory of the perceived, the visible in particular, may be formulated in the category-theoretic language of relational biology. (shrink)

The living mycelium networks are capable of efficient sensorial fusion over very large areas and distributed decision making. The information processing in the mycelium networks is implemented via propagation of electrical and chemical signals en pair with morphological changes in the mycelium structure. These information processing mechanisms are manifested in experimental laboratory findings that show that the mycelium networks exhibit rich dynamics of neuron-like spiking behaviour and a wide range of non-linear electrical properties. On an example of a single real (...) colony of _Aspergillus niger_, we demonstrate that the non-linear transformation of electrical signals and trains of extracellular voltage spikes can be used to implement logical gates and circuits. The approaches adopted include numerical modelling of excitation propagation on the mycelium network, representation of the mycelium network as a resistive and capacitive network and an experimental laboratory study on mining logical circuits in mycelium bound composites. (shrink)

In this paper, a formal theory is presented that describes syntactic and semantic mechanisms of philosophical discourses. They are treated as peculiar language systems possessing deep derivational structures called architectonic forms of philosophical systems, encoded in philosophical mind. Architectonic forms are constituents of more complex structures called architectonic spaces of philosophy. They are understood as formal and algorithmic representations of various philosophical traditions. The formal derivational machinery of a given space determines its class of all possible architectonic forms. Some of (...) them stand under factual historical philosophical systems and they organize processes of doing philosophy within these systems. Many architectonic forms have never been realized in the history of philosophy. The presented theory may be interpreted as falling under Hegel’s paradigm of comprehending cultural texts. This paradigm is enriched and inspired with Propp’s formal, morphological view on texts. The peculiarity of this modification of the Hegel-Propp paradigm consists of the use of algebraic and algorithmic tools of modeling processes of cultural development. To speak metaphorically, the theory is an attempt at the mathematical and logical history of philosophy inspired by the Internet metaphor. And that is why it belongs to the tradition of doing metaphilosophy in The Lvov-Warsaw School, which is continued today mainly by Woleński, Pelc, Perzanowski, and Jadacki. (shrink)

Arguments of stability, intended in a wide sense, including the discussion of the conditions of the onset of instability and of stability changes, play a central role in the main theorizations of morphogenesis in 20th century theoretical biology. The aim of this essay is to shed light on concepts and images mobilized in the construction of arguments of stability in theorizing morphogenesis, since they are pivotal in establishing meaningful relationships between mathematical models and empirical morphologies.

This paper examines Karl Alfred von Zittel’s practice in order to uncover the roots of so-called idiographic paleontology. The great American paleontologist Stephen Jay Gould (1941–2002) defined the discipline of idiographic paleontology as illustration and description of the morphological features of extinct species. However, this approach does not investigate macroevolutionary patterns and processes. On the contrary, the paleobiological revolution of the 1970s implemented an epistemic methodology that illustrates macrovelutionary patterns and laws by combining idiographic data with a nomothetic form of (...) explanation. This article elucidates the features of the idiographic data as well as the acquired knowledge coupled with this approach. First of all, Heinrich G. Bronn’s (1800–1862) statistical method is analyzed. Zittel’s practice arose as a reaction against the approximate conclusions reached by Bronn’s quantitative approach. Second, the details of Zittel’s methodology are described in order to bring out its peculiarities. The microscope played a pivotal role in creating and forming Zittel’s morphological data. This analysis sheds new light on the reasons behind the so-called ideographic paleontology, thus revising Gould’s historical reconstruction, as well as on the notion of paleontological data. However, even though Zittel aimed at reaching precise and stable conclusions, his data cannot be used for elucidating evolutionary mechanisms: they are scientific in a purely descriptive sense, but completely useless for biological investigations. Finally, this paper examines how Zittel’s methodology affects the contemporary paleobiological enterprise and thereby reflects upon the notion of natural history. (shrink)