Showing papers in "Axiomathes in 2005"

Ontologies and construals in lexical semantics

Abstract: The purpose of this paper is to propose a framework of lexical meaning, broadly along the lines of Cognitive Semantics (Langacker 1987a). Within the proposed model, all aspects of meaning are to be explained in terms of properties of ontologies in conceptual space, i.e. properties of content ontologies and schematic ontologies and construals which are imposed on the conceptual structures on the occasion of use. It is through the operations of construals on ontological structures that different readings of lexical expressions arise. Lexical meanings are dynamic and sensitive to contextual demands, rather than fixed and stable. In a dynamic, usage-based model like this, polysemy and multiple readings emerge as a natural consequence of the human ability to think flexibly. Another more specific purpose of this paper is to draw attention to the usefulness of ontologies in linguistic research in general and semantic modelling in particular.

A biosemiotic and ecological approach to music cognition: Event perception between auditory listening and cognitive economy

Abstract: This paper addresses the question whether we can conceive of music cognition in ecosemiotic terms. It claims that music knowledge must be generated as a tool for adaptation to the sonic world and calls forth a shift from a structural description of music as an artifact to a process-like approach to dealing with music. As listeners, we are observers who construct and organize our knowledge and bring with us our observational tools. What matters is not merely the sonic world in its objective qualities, but the world as perceived. In order to make these claims operational we can rely on the ecological concept of coping with the sonic world and the cybernetic concepts of artificial and adaptive devices. Listeners, on this view, are able to change their semantic relations with the sonic world through functional adaptations at the level of sensing, acting and coordinating between action and perception. This allows us to understand music in functional terms of what it affords to us and not merely in terms of its acoustic qualities. There are, however, degrees of freedom and constraints which shape the semiotization of the sonic world. As such we must consider the role of event perception and cognitive economy: listeners do not perceive the acoustical environment in terms of phenomenological descriptions but as ecological events.

Defining Pictorial Style: Lessons from Linguistics and Computer Graphics

Abstract: A definition of pictorial style in terms of distinctive combinations of pictorial devices characteristic of a particular culture or period or the work of an individual artist is proposed. Four kinds of pictorial structure are described: the drawing (spatial) systems, the denotation systems, the mark systems and the attributes systems. Three pictures by Poussin, Rembrandt and the Achilles painter are then analyzed in terms of these four systems. It is suggested that descriptions of style of this kind can be thought of as hypotheses about the nature of the implicit rules that generated the pictures to which they were applied. Examples of ways of testing this suggestion by embodying such stylistic rules in computer graphics programs are given.

Visual Perception in Japanese Rock Garden Design

Abstract: We present an investigation into the relation between design principles in Japanese gardens, and their associated perceptual effects. This leads to the realization that a set of design principles described in a Japanese gardening text by Shingen (1466), shows many parallels to the visual effects of perceptual grouping, studied by the Gestalt school of psychology. Guidelines for composition of rock clusters closely relate to perception of visual figure. Garden design elements are arranged into patterns that simplify figure-ground segmentation, while seemingly balancing the visual salience of subparts and the global arrangement. Visual ‘ground’ is analyzed via medial axis transformation (MAT), often associated with shape perception in humans. MAT analysis reveals implicit structure in the visual ground of a quintessential rock garden design. The MAT structure enables formal comparison of structure of figure and ground. They share some aesthetic qualities, with interesting differences. Both contain naturalistic asymmetric, self-similar, branching structures. While the branching pattern of the ground converges towards the viewer, that of the figure converges in the opposite direction.

Identity, Indiscernibility, and Philosophical Claims

Abstract: The concept of indiscernibility in a structure is analysed with the aim of emphasizing that in asserting that two objects are indiscernible, it is useful to consider these objects as members of (the domain of) a structure. A case for this usefulness is presented by examining the consequences of this view to the philosophical discussion on identity and indiscernibility in quantum theory.

The Epistemological Status of Vision and its Implications for Design

Abstract: Computational theories of vision typically rely on the analysis of two aspects of human visual function: (1) object and shape recognition (2) co-calibration of sensory measurements. Both these approaches are usually based on an inverse-optics model, where visual perception is viewed as a process of inference from a 2D retinal projection to a 3D percept within a Euclidean space schema. This paradigm has had great success in certain areas of vision science, but has been relatively less successful in understanding perceptual representation, namely, the nature of the perceptual encoding. One of the drawbacks of inverse-optics approaches has been the difficulty in defining the constraints needed to make the inference computationally tractable (e.g. regularity assumptions, Bayesian priors, etc.). These constraints, thought to be learned assumptions about the nature of the physical and optical structures of the external world, have to be incorporated into any workable computational model in the inverse-optics paradigm. But inference models that employ an inverse optics plus structural assumptions approach inevitably result in a naive realist theory of perceptual representation. Another drawback of inference models for theories of perceptual representation is their inability to explain central features of the visual experience. The one most evident in the process and visual understanding of design is the fact that some visual configurations appear, often spontaneously, as perceptually more coherent than others. The epistemological consequences of inferential approaches to vision indicate that they fail to capture enduring aspects of our visual experience. Therefore they may not be suited to a theory of perceptual representation, or useful for an understanding of the role of perception in the design process and product.

The Meaning of Meaning-Fallibilism

Abstract: Much discussion of meaning by philosophers over the last 300 years has been predicated on a Cartesian first-person authority (i.e. “infallibilism”) with respect to what one’s terms mean. However this has problems making sense of the way the meanings of scientific terms develop, an increase in scientific knowledge over and above scientists’ ability to quantify over new entities. Although a recent conspicuous embrace of rigid designation has broken up traditional meaning-infallibilism to some extent, this new dimension to the meaning of terms such as “water” is yet to receive a principled epistemological undergirding (beyond the deliverances of “intuition” with respect to certain somewhat unusual possible worlds). Charles Peirce’s distinctive, naturalistic philosophy of language is mined to provide a more thoroughly fallibilist, and thus more realist, approach to meaning, with the requisite epistemology. Both his pragmatism and his triadic account of representation, it is argued, produce an original approach to meaning, analysing it in processual rather than objectual terms, and opening a distinction between “meaning for us”, the meaning a term has at any given time for any given community and “meaning simpliciter”. the way use of a given term develops over time (often due to a posteriori input from the world which is unable to be anticipated in advance). This account provocatively undermines a certain distinction between “semantics” and “ontology” which is often taken for granted in discussions of realism.

Compositionality, Relevance, and Peirce’s Logic of Existential Graphs

Abstract: Charles S. Peirce’s pragmatist theory of logic teaches us to take the context of utterances as an indispensable logical notion without which there is no meaning. This is not a spat against compositionality per se , since it is possible to posit extra arguments to the meaning function that composes complex meaning. However, that method would be inappropriate for a realistic notion of the meaning of assertions. To accomplish a realistic notion of meaning (as opposed e.g. to algebraic meaning), Sperber and Wilson’s Relevance Theory (RT) may be applied in the spirit of Peirce’s Pragmatic Maxim (PM): the weighing of information depends on (i) the practical consequences of accommodating the chosen piece of information introduced in communication, and (ii) what will ensue in actually using that piece in further cycles of discourse. Peirce’s unpublished papers suggest a relevance-like approach to meaning. Contextual features influenced his logic of Existential Graphs (EG). Arguments are presented pro and con the view in which EGs endorse non-compositionality of meaning.

From Design to Self-organization, or: A Proper Structure for a Proper Function

Abstract: It is suggested that Charles Sanders Peirce's triadic semiotics provides a framework for a diagrammatic representation of a sign's proper structure. The action of signs is described at the logical and psychological levels. The role of (unconscious) abductive inference is analyzed, and a diagram of reasoning is offered. A series of interpretants transform brute facts into interpretable signs thereby providing human experience with value or meaning. The triadic structure helps in de-mystifying the relations between Penrose's three worlds when the latter are considered as constituting a semiotic triangle.

Divergent conceptions of the continuum in 19th and early 20th century mathematics and philosophy

Abstract: The opposition between continuity and discreteness has animated the development of mathematics since antiquity. Indeed, tradition defined mathematics as ‘‘the science of discrete and continuous magnitude’’. A striking example of this opposition – amounting, one might say, to a collision – is the Pythagorean discovery of incommensurable magnitudes. Here the realm of continuous geometric magnitudes resisted the Pythagorean attempt to reduce it to the discrete form of pure number. The theory of proportions later invented by Eudoxus to resolve the problem of incommensurability was in essence an extension of the idea of number – i.e., of the discrete – adequate to the task of expressing the relations between continuous magnitudes. The opposition resurfaced with renewed vigour in the seventeenth century with the emergence of the differential and integral calculus. Here the controversy centred on the concept of infinitesimal. According to one school of thought, the infinitesimal was to be regarded as an actual, infinitely small, indivisible element of a continuum, similar to the atoms of Democritus, except that now their number was considered to be infinite. Calculation of areas and volumes, i.e., integration, was thought of as summation of an infinite number of these infinitesimal elements. An area, for example, was taken to be the ‘‘sum of the lines of which it is formed’’. Thus the continuous was, in a way, again reduced to the discrete, but now, with the intrusion of the concept of the infinite, in a subtler and more complex way than before. The conception of infinitesimals as actual entities was gradually displaced by the idea – originally suggested by Newton – of the infinitesimal as a continuous variable which becomes arbitrarily small. By the start of the nineteenth century, when the rigorous theory of limits was in the process of being created, this new conception of infinitesimal had gained general acceptance. In general, a continuum such as a line was now understood not to consist of ‘‘points’’ or

Third culture: cybersemiotic’s inclusion of a biosemiotic theory of mind

Abstract: The necessity of a third culture to find new cultural synergy between the two incompatible cultures of science and technology on one hand and humanities and social sciences on the other hand is stronger than ever in the globalized world. Today, complexity science with cybernetic, cognitive information science informed by general systems theory on one hand and one the other biosemiotics, informed by Peirce’s pragmaticistic philosophy on the other seem to be the two most obvious candidates to make the new transdisciplinary framework. The informational paradigm cannot make its philosophical framework encompass signification and first person experience and many researchers are instead trying to eliminate these aspects as having no causal influence on reality. A way out seem to use the still more advanced interpretations of C. S. Peirce’s semiotic philosophy in the form of biosemiotics as a foundation and adding the theories of complexity, self-organization, systems evolution, emergence, down ward causation, information, closure, agency and autopoiesis on this new foundation. I call this new framework Cybersemiotics and explore the ontological aspects of it here suggesting five distinct levels of organization making a synergy of scientific, semiotic, evolutionary, system theoretical and cybernetic concepts.

Emergence, Drop-Back And Reductionism in Living Systems Theory

Abstract: Miller’s Living Systems Theory (LST) is known to be very comprehensive. It comprises eight nested hierarchical levels. It also includes twenty critical subsystems. While Miller’s approach has been analyzed and applied in great detail, some problematic features remain, requiring further explication. One of these is the relationship between reduction and emergence in LST. There are at least four relevant possibilities. One is that LST exhibits neither clear reductionism nor emergence, but is essentially “neutral” in this regard. Another is that the apparent comprehensiveness of LST is illusory, as the approach remains vulnerable to reduction that could ultimately reduce it to a shadow of its present self. The charge of reductionism has been made by critics leading Miller to defend this theory vehemently as nonreductionist in nature. A third possibility is that LST is not reductionist, but is in fact an emergent theory. Miller makes this claim quite strongly. A fourth possibility, and in some ways the most analytically problematic, is that LST exhibits evidence of both reductionism and emergence simultaneously. Some critics might see this fourth situation as evidence of a troubling paradox or anomaly that must be resolved before further progress can be made in the explication and application of LST. The purpose of the paper is to remove this apparent anomaly. The paper removes this anomaly by differentiating between new-variable emergence and transformational emergence. No concrete evidence is found to contradict Miler’s claim of emergence in LST, and thus no true anomaly exists.

Quality Instances and the Structure of the Concrete Particular

Abstract: In this paper, I examine a puzzle that emerges from what J. P. Moreland has called the traditional realist view of quality instances. Briefly put, the puzzle is to figure out how quality instances fit into the overall structure of a concrete particular, given that the traditional realist view of quality instances prima facie seems incompatible with what might be called the traditional realist view of concrete particulars. After having discussed the traditional realist views involved and the puzzle that emerges from their juxtaposition, I propose an alternative realist view of quality instances which resolves the puzzle. In short, the puzzle is solved by treating the distinction between a concrete particular and its quality instances as a distinction of reason, and by adopting the view that the individuating element of a concrete particular must also serve as its unifying element – a view which Moreland, one of traditional realism’s most stalwart contemporary defenders, rejects.

Complex systems from the perspective of category theory: II. Covering systems and sheaves

Abstract: Using the concept of adjunctive correspondence, for the comprehension of the structure of a complex system, developed in Part I, we introduce the notion of covering systems consisting of partially or locally defined adequately understood objects. This notion incorporates the necessary and sufficient conditions for a sheaf theoretical representation of the informational content included in the structure of a complex system in terms of localization systems. Furthermore, it accommodates a formulation of an invariance property of information communication concerning the analysis of a complex system

Complex Systems from the Perspective of Category Theory: I. Functioning of the Adjunction Concept

Abstract: We develop a category theoretical framework for the comprehension of the information structure associated with a complex system, in terms of families of partial or local information carriers. The framework is based on the existence of a categorical adjunction, that provides a theoretical platform for the descriptive analysis of the complex system as a process of functorial information communication.

The impossibility of relations between non-collocated spatial objects and non-identical topological spaces

Abstract: I argue that relations between non-collocated spatial entities, between non-identical topological spaces, and between non-identical basic building blocks of space, do not exist. If any spatially located entities are not at the same spatial location, or if any topological spaces or basic building blocks of space are non-identical, I will argue that there are no relations between or among them. The arguments I present are arguments that I have not seen in the literature.

Oppositions and Paradoxes in Mathematics and Philosophy

Abstract: In this paper a number of oppositions which have haunted mathematics and philosophy are described and analyzed. These include the Continuous and the Discrete, the One and the Many, the Finite and the Infinite, the Whole and the Part, and the Constant and the Variable.

In Search of a Reconciliation Between Semiotics, Thermodynamics and Metasystem Transition Theory

Abstract: The disciplines of cybernetics, semiotics and thermodynamics investigate evolutionary processes quite independently from each other. The aim of this paper is to draw the parallels and point out the possibility and necessity of a reconciliation between these disciplines. The concept of metasystem transition has been proposed by Turchin as a quantum of evolution from a cybernetic point of view. Semiotic processes are of prime importance for the realisation of metasystem transitions in the course of evolution. From a thermodynamic point of view, the emergence of more complex, self-producing agents depends on the emergence of more advanced forms of semiosis. As an evolutionary consequence, more symbolic forms of semiosis that allow higher competence for abstraction and anticipation emerge.

Internal, External and Intra-Individual Relations

Abstract: In this paper I argue that there are in fact external relations in Russell’s sense. The level at which we are forced to acknowledge them is, however, not the level of relations between concrete individual objects. All relations of this kind, which I will call “inter-individual” relations, can be construed as supervenient on the monadic properties of their terms. But if we pursue our ontological analysis a little bit deeper and consider the internal structure of a concrete individual, then we will inevitably find irreducible external relations. I mean for example the relation of instantiation (in the frame of a realist’s theory) or that of concurrence (in the frame of a trope theory). I will show that such “intra-individual” relations – the relations that make up the internal structure of a concrete individual out of more primitive metaphysical “building blocks” like universals or tropes – could not (even in principle) be construed as supervenient.

Causes, conditions and counterfactuals

Abstract: The article deals with one particular problem created by the counterfactual analysis of causality a la Lewis, namely the context-sensitivity problem or, as I prefer to call it, the background condition problem. It appears that Lewis’ counterfactual definition of causality cannot distinguish between proper causes and mere causal conditions – i.e. factors necessary for the effect to occur, but commonly not seen as causally efficacious. The proposal is put forward to amend the Lewis definition with a condition, based on the notion of cotenability, which would eliminate the problem. It is shown that the corrected definition of causality leads to the transitivity of the causal relation. Possible objections to the proposed solution, involving the assumption of indeterminism and the preemption cases, are given a thorough consideration.

Pictorial depth: intensity and aesthetic surface

Abstract: Philosophers seldom ask questions regarding how certain phenomena occur, because such questions tend to be the province of the sciences or of technology. However, the question how pictures have depth requires philosophical reflection because it takes place on the surface of pictorial objects and involves both physical and phenomenal, i.e. aesthetic, features of those surfaces. This essay examines how pictures have depth by first separating the aesthetic question from interpretive considerations, and thereby refining the question how pictures have depth. Next it explicates two sorts of conceptual tools required to understand the question: several complex concepts needed to understand surfaces, and the concept of intensity. These are then used to understand how pictures can have depth by showing how intensities produce both an aesthetic surface and depth within it.

Some aspects of product shape in mechanical engineering

Abstract: The paper examines some of the many factors that influence the shape of designed products in the mechanical engineering industries. It is shown that, once the detailed shape of a product has been determined, the analysis of that shape from the viewpoints of various engineering activities downstream of design leads to a range of inherently different perceptions of it.