Contemporary architecture is increasingly grounded in science and mathematics. Architectural discourse has shifted radically from the sometimes disorienting Derridean deconstruction, to engaging scientific terms such as fractals, chaos, complexity, nonlinearity, and evolving systems. That's where the architectural action is -- at least for cutting-edge architects and thinkers -- and every practicing architect and student needs to become conversant with these terms and know what they mean. Unfortunately, the vast majority of architecture faculty are unprepared to explain them to students, not (...) having had a scientific education themselves. Here is an architecture book by an architect/scientist, just in time to help architects in the new millennium. Alexander discusses many of the scientific terms arising in cutting-edge architecture, and explains them to those who don't have scientific training or advanced mathematical knowledge. We find discussions of the evolution of forms; the importance of process in design; iteration; genetic algorithms; sequences of transformations; different levels of scale (i.e. fractals); etc. They are explained here by an architect who is also a scientist, because he wants to change the way architects think and build. Alexander is not merely popularizing other scientists' results and making them accessible to architects: he is in fact presenting new and original scientific work that ties many of these concepts together in a way that will be useful to architects. (shrink)

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

A topological inevitability of early developmental events through the use of classical topological concepts is discussed. Topological dynamics of forms and maps in embryo development are presented. Forms of a developing organism such as cell sets and closed surfaces are topological objects. Maps (or mathematical functions) are additional topological constructions in these objects and include polarization, singularities and curvature. Topological visualization allows us to analyze relationships that link local morphogenetic processes and integral developmental structures and also to find stable spatio-temporal (...) topological characteristics that are invariant for a taxonomic group. The application of topological principles reveals a topological imperative: certain topological rules define and direct embryogenesis. A topological stability of embryonic morphogenesis is proposed and a topological scenario of developmental and evolutionary transformations is presented. (shrink)

In diffusion creep, the contribution of grain-boundary sliding to the overall strain o s can be evaluated in arbitrary polycrystals, if the angular distribution of grain boundaries is known. A o s value of 0.5 is obtained for two-dimensional equiaxed microstructures consisting of regular hexagonal grains, equiaxed grains grown from a Voronoi structure or grains having a circular distribution of grain-boundary angles. The o s value is also evaluated for uniaxially deformed 2D microstructures, both diffusionally and uniformly deformed. (...) For the former, the deformed microstructure is obtained by the simulation of microstructural evolution in polycrystals with straight grain boundaries. The o s value increases gradually with increasing or decreasing strain and is larger in the diffusionally deformed microstructures than in the uniformly deformed microstructures for a given grain aspect ratio. The o s value for three-dimensional polycrystalline microstructures is also obtained from an ellipsoidal distribution of grain-boundary angles. The resultant o s value is 0.60 for 3D equiaxed polycrystals and increases gradually with increasing strain. (shrink)

Abstract. The aim of this paper is to present a topological method for constructing discretizations (tessellations) of conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. Alexandroff spaces, as they are called today, have many interesting properties that distinguish them from other topological spaces. In particular, they exhibit a 1-1 correspondence between their specialization orders and their topological structures. Recently, a special type of Alexandroff spaces was (...) used by Ian Rumfitt to elucidate the logic of vague concepts in a new way. According to his approach, conceptual spaces such as the color spectrum give rise to classical systems of concepts that have the structure of atomic Boolean algebras. More precisely, concepts are represented as regular open regions of an underlying conceptual space endowed with a topological structure. Something is subsumed under a concept iff it is represented by an element of the conceptual space that is maximally close to the prototypical element p that defines that concept. This topological representation of concepts comes along with a representation of the familiar logical connectives of Aristotelian syllogistics in terms of natural settheoretical operations that characterize regular open interpretations of classical Boolean propositional logic. In the last 20 years, conceptual spaces have become a popular tool of dealing with a variety of problems in the fields of cognitive psychology, artificial intelligence, linguistics and philosophy, mainly due to the work of Peter Gärdenfors and his collaborators. By using prototypes and metrics of similarity spaces, one obtains geometrical discretizations of conceptual spaces by so-called Voronoi tessellations. These tessellations are extensionally equivalent to topological tessellations that can be constructed for Alexandroff spaces. Thereby, Rumfitt’s and Gärdenfors’s constructions turn out to be special cases of an approach that works for a more general class of spaces, namely, for weakly scattered Alexandroff spaces. This class of spaces provides a convenient framework for conceptual spaces as used in epistemology and related disciplines in general. Alexandroff spaces are useful for elucidating problems related to the logic of vague concepts, in particular they offer a solution of the Sorites paradox (Rumfitt). Further, they provide a semantics for the logic of clearness (Bobzien) that overcomes certain problems of the concept of higher2 order vagueness. Moreover, these spaces help find a natural place for classical syllogistics in the framework of conceptual spaces. The crucial role of order theory for Alexandroff spaces can be used to refine the all-or-nothing distinction between prototypical and nonprototypical stimuli in favor of a more fine-grained gradual distinction between more-orless prototypical elements of conceptual spaces. The greater conceptual flexibility of the topological approach helps avoid some inherent inadequacies of the geometrical approach, for instance, the so-called “thickness problem” (Douven et al.) and problems of selecting a unique metric for similarity spaces. Finally, it is shown that only the Alexandroff account can deal with an issue that is gaining more and more importance for the theory of conceptual spaces, namely, the role that digital conceptual spaces play in the area of artificial intelligence, computer science and related disciplines. Keywords: Conceptual Spaces, Polar Spaces, Alexandroff Spaces, Prototypes, Topological Tessellations, Voronoi Tessellations, Digital Topology. (shrink)

This work intends to apprehend and emphasize the contribution of image-processing techniques and computer vision in the treatment of clay-based material known in Meknes region. One of the various characteristics used to describe clay in a qualitative manner is porosity, as it is considered one of the properties that with “kill or cure” effectiveness. For this purpose, we use scanning electron microscopy images, as they are considered the most powerful tool for characterising the quality of the microscopic pore structure (...) of porous materials. We present various existing methods of segmentation, as we are interested only in pore regions. The results show good matching between physical estimation and Voronoi diagram-based porosity estimation. (shrink)

Whether or not quantum physics can account for molecular structure is a matter of considerable controversy. Three of the problems raised in this regard are the problems of molecular structure. We argue that these problems are just special cases of the measurement problem of quantum mechanics: insofar as the measurement problem is solved, the problems of molecular structure are resolved as well. In addition, we explore one consequence of our argument: that claims about the reduction or emergence (...) of molecular structure cannot be settled independently of the choice of a particular resolution to the measurement problem. Specifically, we consider how three standard putative solutions to the measurement problem inform our under- standing of a molecule in isolation, as well as of chemistry’s relation to quantum physics. (shrink)

The central problem of social theory is 'structure and agency'. How do the objective features of society influence human agents? Determinism is not the answer, nor is conditioning as currently conceptualised. It accentuates the way structure and culture shape the social context in which individuals operate, but it neglects our personal capacity to define what we care about most and to establish a modus vivendi expressive of our concerns. Through inner dialogue, 'the internal conversation', individuals reflect upon their (...) social situation in the light of current concerns and projects. On the basis of a series of unique, in-depth interviews, Archer identifies three distinctive forms of internal conversation. These govern agents' responses to social conditioning, their individual patterns of social mobility and whether or not they contribute to social stability or change. Thus the internal conversation is seen as being the missing link between society and the individual, structure and agency. (shrink)

What is structural rationality? Specifically, what is the distinctive feature of structural requirements of rationality? Some philosophers have argued, roughly, that the distinctive feature of structural requirements is coherence. But what does coherence mean, exactly? Or, at least, what do structuralists about rationality have in mind when they claim that structural rationality is coherence? This issue matters for making progress in various active debates concerning rationality. In this paper, I analyze three strategies for figuring out what coherence means in the (...) debates on structural rationality. I argue that these strategies face problems. (shrink)

Structural realism is considered by many realists and antirealists alike as the most defensible form of scientific realism. There are now many forms of structural realism and an extensive literature about them. There are interesting connections with debates in metaphysics, philosophy of physics and philosophy of mathematics. This entry is intended to be a comprehensive survey of the field.

There is good reason to believe that scientific realism requires a commitment to the objective modal structure of the physical world. Causality, equilibrium, laws of nature, and probability all feature prominently in scientific theory and explanation, and each one is a modal notion. If we are committed to the content of our best scientific theories, we must accept the modal nature of the physical world. But what does the scientific realist’s commitment to physical modality require? We consider whether scientific (...) realism is compatible with Humeanism about the laws of nature, and we conclude that it is not. We specifically identify three major problems for the best-systems account of lawhood: its central concept of strength cannot be formulated non-circularly, it cannot offer a satisfactory account of the laws of the special sciences, and it can offer no explanation of the success of inductive inference. In addition, Humeanism fails to be naturalistically motivated. For these reasons, we conclude that the scientific realist must embrace natural necessity. (shrink)

Ontic Structural Realism is a version of realism about science according to which by positing the existence of structures, understood as basic components of reality, one can resolve central difficulties faced by standard versions of scientific realism. Structures are invoked to respond to two important challenges: one posed by the pessimist meta-induction and the other by the underdetermination of metaphysics by physics, which arises in non-relativistic quantum mechanics. We argue that difficulties in the proper understanding of what a structure (...) is undermines the realist component of the view. Given the difficulties, either realism should be dropped or additional metaphysical components not fully endorsed by science should be incorporated. (shrink)

Structural injustice broadly refers to objectionable outcomes produced by generally accepted social structures for members of particular social groups. But theorists of structural injustice have said relatively little about why certain outcomes are objectionable, and many theorists suggestively connect structural injustice to a worry about oppression without explaining their precise normative concerns. I provide a normative analysis of structural injustice that addresses this gap and clarifies its connection to oppression. On this view, there are two kinds of structural injustice, each (...) grounded in a distinct moral concern. One is a freedom-based concern for how social structures harmfully constrain members of a social group, depriving them of the means to develop and exercise their capacities. The other is an equality-based concern for how social structures subordinate a social group to others in hierarchies of power, standing, and esteem. By disentangling these concerns, this account shows that our social structures contain multiple kinds of injustice that do not necessarily travel together; some social groups experience unfreedom without being subordinated to others, and indeed their unfreedom is intertwined with their dominant position over subordinated groups. Furthermore, against prevailing philosophical accounts, this analysis shows that there are good reasons to understand oppression primarily as an issue of inequality rather than an issue of unfreedom. (shrink)

In contrast to individualistic explanations of social injustice that appeal to implicit attitudes, structural explanations are unintuitive: they appeal to entities that lack clear ontological status, and the explanatory mechanism is similarly unclear. This makes structural explanations unappealing. The present work proposes a structural explanation of one type of injustice that happens in conversations, discursive injustice. This proposal meets two goals. First, it satisfactorily accounts for the specific features of this particular kind of injustice; and second, it articulates a structural (...) explanation that overcomes their unattractiveness. The main idea is that discursive injustice is not the result of biased interlocutors, but of problematic discursive norms. (shrink)

In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally (...) a non-deterministic matrix. The aim of this paper is to obtain a swap structures semantics for some Ivlev-like modal systems proposed in 2015 by M. Coniglio, L. Fariñas del Cerro and N. Peron. Completeness results will be stated by means of the notion of Lindenbaum–Tarski swap structures, which constitute a natural generalization to multialgebras of the concept of Lindenbaum–Tarski algebras. (shrink)

The no-miracles argument for realism and the pessimistic meta-induction for anti-realism pull in opposite directions. Structural Realism---the position that the mathematical structure of mature science reflects reality---relieves this tension.

In recent years, there has been a wide-ranging debate about the neo-republican principle of non-domination. Neo-republicans argue that domination is a capacity for one to intentionally use arbitrary power to interfere in someone’s life. Critics of neo-republicanism argue that this definition of freedom as non-domination precludes a structural analysis of domination, which would explain and critique the ways in which societies produce structural domination unintentionally. The article focuses on capitalism’s labor process and its labor markets. It argues that critics are (...) correct to think that the neo-republican principle of non-domination has an insufficient scope, but that an alternative account of structural domination should still support the neo-republican idea that agency must be involved. Otherwise, we might simply fail to explain the social processes that reproduce structural domination. What is needed is to explain how the labor process creates incentives for agents to intentionally produce structures that have unintended, yet dominating effects, and in turn, how the intentions of agents are conditioned by their social positions. Domination is thus agential and structural. (shrink)

1 Knowledge and Justification This book is an investigation of one central problem which arises in the attempt to give a philosophical account of empirical ...

An increasing amount of twenty-first century metaphysics is couched in explicitly hyperintensional terms. A prerequisite of hyperintensional metaphysics is that reality itself be hyperintensional: at the metaphysical level, propositions, properties, operators, and other elements of the type hierarchy, must be more fine-grained than functions from possible worlds to extensions. In this paper I develop, in the setting of type theory, a general framework for reasoning about the granularity of propositions and properties. The theory takes as primitive the notion of a (...) substitution on a proposition (property, etc.) and, among other things, uses this idea to elucidate a number of theoretically important distinctions. A class of structures are identified which can be used to model a wide range of positions about the granularity of reality; certain of these structures are seen to receive a natural treatment in the category of M-sets. (shrink)

On scientific and moral revolutions -- Using the dead for the living: the benthamite moral revolution -- Immoralizing and criminalizing abortion: the doctors revolution -- Irredentism and counter-revolutions in geology and abortion -- The american bioethics revolution -- The structure of moral revolutions.

I argue that the ability to compute phrase structure grammars is indicative of a particular kind of thought. This type of thought that is only available to cognitive systems that have access to the computations that allow the generation and interpretation of the structural descriptions of phrase structure grammars. The study of phrase structure grammars, and formal language theory in general, is thus indispensable to studies of human cognition, for it makes explicit both the unique type of (...) human thought and the underlying mechanisms in virtue of which this thought is made possible. (shrink)

Semantic Structures is a large-scale study of conceptual structure and its lexical and syntactic expression in English that builds on the theory of Conceptual...

An approach to argument macrostructure -- The dialectical nature of argument -- Toulmin's problematic notion of warrant -- The linked-convergent distinction, a first approximation -- Argument structure and disciplinary perspective : the linked-convergent versus multiple-co-ordinatively compound distinctions -- The linked-convergent distinction, refining the criterion -- Argument structure and enthymemes -- From analysis to evaluation.

Noam Chomsky's book on syntactic structures is a serious attempts on the part of a linguist to construct within the tradition of scientific theory-construction ...

This is a collection of published and unpublished essays by distinguished philosopher Michael E. Bratman of Stanford University. They revolve around his influential theory, know as the "planning theory of intention and agency." Bratman's primary concern is with what he calls "strong" forms of human agency--including forms of human agency that are the target of our talk about self-determination, self-government, and autonomy. These essays are unified and cohesive in theme, and will be of interest to philosophers in ethics and metaphysics.

Expressions in a language, whether words, phrases, or sentences, have meanings. So it seems reasonable to suppose that there are meanings that expressions have. Of course, it is fashionable in some philosophical circles to deny this.

This collection of papers (including three completely new ones) by one of the foremost philosophers in epistemology transcends two of the most widely misunderstood positions in philosophy--foundationalism and coherentism. Audi proposes a distinctively moderate, internalist foundationalism that incorporates some of the virtues of both coherentism and reliabilism. He develops important distinctions between positive and negative epistemic dependence, substantively and conceptually naturalistic theories, dispositional beliefs and dispositions to believe, episodically and structurally inferential beliefs, first and second order internalism, and rebutting as (...) opposed to refuting skepticism. These contrasts are applied not only to rational belief, but to rational action and the rationality of desires and intentions. The overall position is a pluralist, moderately rationalistic, internalist theory of justification and a partly externalist conception of knowledge. However, by virtue of offering a theory of rationality as well as an account of knowledge and justified belief, it will interest philosophers of ethics, science, and the social sciences and teachers and students of epistemology. (shrink)

This paper explores structuralism as a way to model theories from scientific practice. As a case study I analyzed a theory about the dynamics of the basal ganglia, a part of the brain that is involved in Parkinson's disease. After introducing the case study I explore how to structurally represent qualitative assumptions about disease, intervention and dynamical systems in general. I further explicate the structure of the basal ganglia theory in detail, how it explains Parkinson's disease and how it (...) implies treatments. I close with a consideration of how a structuralist representation could be useful in practice to explore and develop theories with the aid of a computer. (shrink)

What is attention? How does attention shape consciousness? In an approach that engages with foundational topics in the philosophy of mind, the theory of action, psychology, and the neurosciences this book provides a unified and comprehensive answer to both questions. Sebastian Watzl shows that attention is a central structural feature of the mind. The first half of the book provides an account of the nature of attention. Attention is prioritizing, it consists in regulating priority structures. Attention is not another element (...) of the mind, but constituted by structures that organize, integrate, and coordinate the parts of our mind. Attention thus integrates the perceptual and intellectual, the cognitive and motivational, and the epistemic and practical. The second half of the book concerns the relationship between attention and consciousness. Watzl argues that attentional structure shapes consciousness into what is central and what is peripheral. The center-periphery structure of consciousness cannot be reduced to the structure of how the world appears to the subject. What it is like for us thus goes beyond the way the world appears to us. On this basis, a new view of consciousness is offered. In each conscious experience we actively take a stance on the world we appear to encounter. It is in this sense that our conscious experience is our subjective perspective. (shrink)

Theorising the interplay of structure and agency is the quintessential focus of sociological endeavour. This paper aims to be part of that continuing endeavour, arguing for a stratified social ontology, where structure and agency are held to be irreducible to each other and causally efficacious, yet necessarily interdependent. It thus aims not to be part of that on-going journey in search of the 'ontological holy grail'. Instead, it offers a way of linking structure and agency which enables (...) the practical education researcher concretely to examine their relative interplay over time. The methodological key to teasing out their relative interplay is held to be analytical dualism. It will be argued that such a methodological device is precluded by Giddens' structuration theory. (shrink)

This paper deals with causal analysis in the social sciences. We first present a conceptual framework according to which causal analysis is based on a rationale of variation and invariance, and not only on regularity. We then develop a formal framework for causal analysis by means of structural modelling. Within this framework we approach causality in terms of exogeneity in a structural conditional model based which is based on (i) congruence with background knowledge, (ii) invariance under a large variety of (...) environmental changes, and (iii) model fit. We also tackle the issue of confounding and show how latent confounders can play havoc with exogeneity. This framework avoids making untestable metaphysical claims about causal relations and yet remains useful for cognitive and action-oriented goals. (shrink)

I taxonomize a half-century of examples of intransitive preferences into four structures: (i) Cycles of Negligible-Value-Differences and Missing-Values; (ii) Condorcet-Voting-Paradox Style Cycles (iii) Sen’s-Libertarian-Paradox Style Cycles; and (iv) Sorites Cycles.

This paper develops a theory of analog representation. We first argue that the mark of the analog is to be found in the nature of a representational system’s interpretation function, rather than in its vehicles or contents alone. We then develop the rulebound structure theory of analog representation, according to which analog systems are those that use interpretive rules to map syntactic structural features onto semantic structural features. The theory involves three degree-theoretic measures that capture three independent ways in (...) which a system can be more or less analog. We explain how our theory improves upon prior accounts of analog representation, provides plausible diagnoses for novel challenge cases, extends to hybrid systems that are partially analog and partially symbolic, and accounts for some of the advantages and disadvantages of representing analogically versus symbolically. (shrink)

This paper makes an observation about the ``amount of structure'' that different classical and relativistic spacetimes posit. The observation substantiates a suggestion made by Earman and yields a cautionary remark concerning the scope and applicability of structural parsimony principles.

The theory of mind debate has reached a “hybrid consensus” concerning the status of theory-theory and simulation-theory. Extant hybrid models either specify co-dependency and implementation relations, or distribute mentalizing tasks according to folk-psychological categories. By relying on a non-developmental framework these models fail to capture the central connection between simulation and theory. I propose a “dynamic” hybrid that is informed by recent work on the nature of similarity cognition. I claim that Gentner’s model of structure-mapping allows us to understand (...) simulation as a process in which psychological representations are aligned, causing the spontaneous abstraction of theoretical generalizations about the psychological domain. (shrink)

Much has been written about epistemological skepticism in the last ten or so years, but there remain some unanswered questions concerning the structure of what has become the canonical Cartesian skeptical argument. In this paper, I would like to take a closer look at this structure in order to determine just which epistemic principles are required by the argument.