We investigate computability theoretic and topological properties of spaces of orders on computable orderable groups. A left order on a group G is a linear order of the domain of G, which is left-invariant under the group operation. Right orders and bi-orders are defined similarly. In particular, we study groups for which the spaces of left orders are homeomorphic to the Cantor set, and their Turing degree spectra contain certain upper cones of degrees. Our approach unifies and extends (...) Sikora’s [28] investigation of orders on groups in topology and Solomon’s [31] investigation of these orders in computable algebra. Furthermore, we establish that a computable free group Fn of rank n>1 has a bi-order in every Turing degree. (shrink)

Abstract.We use a model theoretic approach to investigate properties of local-global principles for positive primitive formulas in spaces of orderings, such as the existence of bounds and the axiomatizability of local-global principles. As a consequence we obtain various classes of special groups satisfying local-global principles for all positive primitive formulas, and we show that local-global principles are preserved by some natural constructions in special groups.

The paper deals with pp formulas in the language of reduced special groups, and the question of when the validity of a pp formula on each finite subspace of a space of orderings implies its global validity [18]. A large new class of pp formulas is introduced for which this is always the case, assuming the space of orderings in question has finite stability index. The paper also considers pp formulas of the special type $b\in \Pi _{i=1}^{n}\,D\langle 1,a_{i}\rangle (...) $. Formulas of this type with n = 3 are the simplest sort of pp formula not covered by the result, and are also the source of the recent counterexamples in [9] and [19]. (shrink)

Is there a space of the sensory modalities? Such a space would be one in which we can represent all the actual, and at least some of the possible, sensory modalities. The relative position of the senses in this space would indicate how similar and how different the senses were from each other. The construction of such a space might reveal unconsidered features of the actual and possible senses, help us to define what a sense is, and provide grounds that (...) we might use to decide what is one token sense rather than multiple token senses. -/- In this paper, I explore, refine, and defend the idea that we can construct such a space—an idea that I briefly proposed in earlier work (Macpherson 2011a and 2011b). In doing so, I defend the idea from an objection that Richard Gray (2012) has voiced. Gray claims that the dimensions of the space of sensory modalities must generate a non-­‐arbitrary ordering of the senses. He argues that we cannot find dimensions that do so. I disagree. I identify different ways in which a space could be arbitrary but I argue that we can define a space of the sensory modalities in a non-arbitrary manner. I give examples of what the dimensions might be. (shrink)

How we define the space of possibilities of dispositional essentialism —that is, the set of possible worlds that are genuinely possible from the point of view of DE—has important consequences for central modal debates such as how to understand the concept of essence or the relation between DE and the necessity of laws of nature. In order to define DE’s space of possibilities we need to explore DE’s consequences regarding both necessity and possibility. Unfortunately, the notion of possibility has not (...) received much attention within the DE literature. In this paper, I attempt to fill this gap. I argue that the standard way of understanding possibility found in the literature—a proposition is possible iff it expresses the manifestation of some actual disposition—needlessly restricts the space of possibilities by not accepting global and absolute possibilities, including some alien properties, as genuinely possible. I propose instead to accept a more permissive understanding of possibility: a proposition is possible iff it does not contradict any of the necessities that follow from the core commitments of DE. This allows dispositionalists to expand their modal space and to account for modal intuitions that may otherwise undermine the tenability of DE. (shrink)

The emergence of macroscopic variables can be effected through coarse graining. Despite practical and fundamental benefits conveyed by this partitioning of state space, the apparently subjective nature of the selection of coarse grains has been considered problematic. We provide objective selection methods, deriving from the existence of relatively slow dynamical time scales. Using a framework for nonequilibrium statistical mechanics developed by us, we show the emergence of both spatial variables and order parameters. Although significant objective criteria are introduced in the (...) coarse graining, we do not provide a unique prescription. Most significantly, the grains, and by implication entropy, are only defined modulo a characteristic time scale of observation. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 35.4 (2002) 328-344 [Access article in PDF] Spaces of Invention:Dissension, Freedom, and Thought in Foucault Kendall R. Phillips Over the past two decades, invention has become an increasingly difficult concept to discuss. In an age when the free, rational actor has become not only de-centered but viewed as both impossible and undesirable by some social theorists, the traditional conception of invention, especially rhetorical invention, becomes (...) more tenuous. While some continue to promote a rational deliberative model of the human subject—Habermas is a prime example of this school of thought—the harsh and unrelenting critiques of poststructural and postmodern thinkers have cast these recovery efforts in a nostalgic and often negative light. Chief among these critics of the modern, humanist conception of human action is Michel Foucault. Within Foucault's perspective our utterances are governed by underlying rules of discourse formations, our actions are proscribed and authorized by relations of power, and our very conception of our self is circumscribed by technologies of subjectivity. Contained within these intertwined relations of knowledge, power, and subjectivity, the human subject takes on a very different meaning and even the concept of "human subject" is itself a product of these intertwined relations; a product that may, in time, disappear under new relations of discourse and governance.Despite the apparent centrality of a creative human subject to the study of rhetoric, Foucault has taken his place within the study of rhetoric. Of course, neither this incorporation of Foucault nor the observation of its peculiarity is particularly new. The incorporation of Foucault into rhetoric took its most dramatic turn in 1989 with Raymie McKerrow's "Critical Rhetoric" essay and the implications of this union of Foucault and rhetoric were forcefully raised by Barbara Biesecker in "Michel Foucault and the Question of Rhetoric" (1992). These two important essays made the relationship between Foucault and rhetoric most pressing: McKerrow by offering [End Page 328] a practical agenda for a Foucaultian rhetorical perspective and Biesecker by opening a space for reflection on this type of agenda. In the intervening decade, however, the incorporation of Foucault into rhetoric has outstripped the reflection on this incorporation and Foucault now sits as comfortably in the bibliographies of rhetorical scholars as Burke or McKeon or Perelman.The purpose of the present essay is to revisit this relationship between Foucault and rhetoric. I pursue this end not in order to critique McKerrow's project or to outstrip Biesecker's reflections, but in order to press the importance of their earlier arguments. The project of a Foucaultian rhetoric should be taken seriously, seriously enough to keep the peculiarity of this union in the forefront of our minds as we pursue it. My present effort furthers this end by seeking within Foucault a space for invention and, in so doing, asks the question: how might invention be rendered within a Foucaultian framework?My contention is that a space for invention exists within Foucault's studies of knowledge, power, and subjectivity and that this space can be demonstrated by considering the counterpoints to his tripartite understanding of the human condition. The limiting/enabling relations of knowledge/power/subjectivity are counterpointed by three terms that describe the conditions for invention: dissension, freedom, and thought. Before turning to the conditions for these spaces of invention and the unique shape of invention that emerges from them, I will briefly consider previous discussions of Foucault. Power, resistance, and invention Rhetoricians, to be clear, are not the first to be concerned with the apparent foreclosing of the possibility of invention within Foucault. Focusing mainly on dominating relations of power/knowledge/subjectivity, Foucault seems to leave little ground for the creation of new ways of acting, speaking, or being. However, what I call a concern for invention has generally not been expressed as such; rather, in rhetoric and in other fields, criticism of Foucault has been largely couched in terms of resistance. Edward Said (1986), for instance, contends that Foucault's work is "not finally as contestatory, or as oppositional as on the surface it seems to be" (152... (shrink)

We introduce a notion of the space of types in positive model theory based on Stone duality for distributive lattices. We show that this space closely mirrors the Stone space of types in the full first-order model theory with negation (Tarskian model theory). We use this to generalise some classical results on countable models from the Tarskian setting to positive model theory.

The ArgumentEmergency medicine, a new medical specialty in the United States, is an ethical practice that has developed through its interaction with the spaces in which it is situated. We discuss this claim in two steps followed by a demonstration. First we examine the historical evolution of the hospital, to provide the background for a lengthier account of the historical transformation of the emergency room. We then introduce Foucault's approach to ethics, to explain the sense in which emergency medicine (...) is an ethical practice constituted, in part, by its space of operation. The preliminaries of the application of our historico-ethical framework to emergency medicine, are presented, focusing on cardiopulmonary resuscitation. Our intention is to provide a framework for the newest clinical specialty as an ethical practice in order to understand how to individuate its emerging ethical problems. The emphasis on space throughout enables us to integrate the historical development of emergency medicine with its present concrete setting, and to establish a basis for analyzing emergency medicine that does not rely uncritically on either a preferred ethical perspective or the perspective of its practitioners. (shrink)

An extensive analysis of all social psychology textbooks included a history chapter published in French between 1947 and 2001, provides a rich corpus for the study of the history of social psychology. Drawing upon this corpus, in this article we study the historical spaces of social psychology in order to show how the discipline was located in geographical, urban, institutional and collective spaces. We argue that spaces are essentially related to some solitary and consensual scholars' names without (...) any informative reference to their institutions, nor to any trace of collective work. Moreover, we try to highlight several styles, ways and norms of collective writing the history of this discipline. (shrink)

A simple recurrent artificial neural network is used to classify situations as permissible or impermissible. The trained ANN can be understood as having set up a similarity space of cases at the level of its internal or hidden units. An analysis of the network’s internal representations is undertaken using a new visualization technique for state space approaches to understanding similarity. Insights from the literature on moral philosophy pertaining to contributory standards will be used to interpret the state space set up (...) by the ANN as being structured by implicit reasons. The ANN, on its own, is not capable of explicitly representing or offering reasons to itself or others. That said, the low level similarity space set up by the network could be made available to higher order processes that exploit it for case-based reasoning. It is argued that for normative purposes, similarity could be seen as a contributor to procedural coherence in case-based reasoning and local forms of substantive coherence, but not to global forms of coherence given the computational complexity of managing those more ambitious forms of coherence. (shrink)

Philosophers and scientists have across the ages been amazed about the fact that development and learning often lead to not just a merely incremental and gradual change in the learner but sometimes to a result that is strikingly different from the learner’s original situation: amazed, but at times also worried. Both philosophical and cognitive neuroscientific insights suggest that experts appear to perform ‘different’ tasks compared to beginners who behave in a similar way. These philosophical and empirical perspectives give some insight (...) into what happens when a novice is transitioning to a stage of expertise. Generally, this implies that increased skill and expertise support better results and a more flexible performance, in part because these allow an agent to withdraw part of her attention and other cognitive resources from the tasks involved, enabling her to devote those resources to supporting, or completely different, tasks. As positive as these developments appear, these changes have also raised concerns. The main concern is whether gaining expertise is like raising a ‘cognitive monster’ which escapes the individual’s conscious control and influences her actions with undesirable automatisms. If so, we should ask ourselves whether experts are capable of taming this monster. The answer appears initially not to be positive. Indeed, it has been noted that since it is difficult for experts to withhold automatic responses this can lead to inflexibility or performance that is only optimal under certain conditions, because it is limited to a specific domain, often context-dependent, biased and inflexible. In what follows, I will consider this challenge of protecting expertise and harnessing this brittleness from philosophical and cognitive neuroscientific perspectives. Taking into account that action is in general determined by a multitude of factors, with learning and development affecting how these factors exert their influence, a philosophical question is how this complex and dynamic process can be explained and subsequently, how controlling it might be understood. First, though, I will present the issue at hand more closely: should we appreciate expertise if it is similar to growing a ‘cognitive monster’? Second, I will introduce the framework of a “Sculpted Space of Actions” (Keestra, 2014), which I developed in order to explain how the challenge of selecting an adequate option for action is facilitated by expertise as it helps to constrain the space of potential action options. Subsequently, the question is raised of how such a Sculpted Space of Actions influences an expert’s engagement with specific situations, like teaching students in a classroom setting. It will be argued that a well prepared expert—teacher or otherwise— is not only able to rely upon her routines but will at the same time be more perceptive and attentive to unforeseen events and actions, according to the recent cognitive neuroscientific theory of Predictive Processing. Integrating the theory of Predictive Processing with the Sculpted Space of Actions framework, I conclude that expertise contributes to adaptive and flexible responses to specific contexts, yet only if it is associated with explicit planning and articulation of situation specific intentions—the latter effectively putting the cognitive monster at rest for a while. (shrink)

_ Source: _Volume 48, Issue 1, pp 119 - 146 Masks are devices and symbols. In the first instance, they are artifacts that allow opposite poles to take each other’s place. They split the world into appearance and reality, manifest and repressed, sacred and profane. In this sense, they are dualistic. But by so doing they invert these terms. In this sense, they are dialectical. In the second instance, they exemplify doubt about people’s identities and the veracity of their words; (...) they denote duplicity, inauthenticity, and hypocrisy. The conjunction of these two senses resides in the fact that masks are at the threshold between reality and fiction. Such a threshold makes possible the emergence of a space of play which asserts that the world does not express a determinate and final order but is infinitely open to the emergence of new, yet transient, forms of self-organization and open new spatiotemporal worlds. (shrink)

This chapter argues that gaining expertise can be understood in part as the development of a continuously updated space of adequate knowledge structures or representations that can be defined along different dimensions. It considers the challenge of protecting expertise and harnessing this brittleness from philosophical and cognitive neuroscientific perspectives. The chapter introduces the framework of a Sculpted Space of Actions, in order to explain how the challenge of selecting an adequate option for action is facilitated by expertise as it helps (...) to constrain the space of potential action options. The emphasis of action‐perception cycles as the main source of the generative models that are being exploited in predictive processing may suggest that it allows no role for the explicit articulated intentions that were found to be an important dimension of the Sculpted Space. The chapter explores whether the integrative cognitive neuroscientific account concurs with what we know about expertise in education. (shrink)

We prove that the category of Nachbin’s compact ordered spaces and order-preserving continuous maps between them is dually equivalent to a variety of algebras, with operations of at most countable arity. Furthermore, we observe that the countable bound on the arity is the best possible: the category of compact ordered spaces is not dually equivalent to any variety of finitary algebras. Indeed, the following stronger results hold: the category of compact ordered spaces is not dually equivalent to (...) any finitely accessible category, any first-order definable class of structures, and any class of finitary algebras closed under products and subalgebras. An explicit equational axiomatisation of the dual of the category of compact ordered spaces is obtained; in fact, we provide a finite one, meaning that our description uses only finitely many function symbols and finitely many equational axioms. In preparation for the latter result, we establish a generalisation of a celebrated theorem by Mundici: our result—whose proof is independent of Mundici’s theorem—asserts that the category of unital commutative distributive lattice-ordered monoids is equivalent to the category of what we call MV-monoidal algebras.Abstract taken directly from the thesis.E-mail: [email protected]: https://air.unimi.it/retrieve/handle/2434/812809/1698986/phd_unimi_R11882.pdf. (shrink)

Abstract -/- The indistinction between repose and uniform movement exposed in the principle of inertia marks one of the most famous dissertations: the discussion between Newton and Leibniz. Through their respective conceptions of space, both seek to solve the problem of indistinction. The relational space of Leibniz, supported by the principle of sufficient reason and the identity of indiscernibles leads to the kinematic solution of the problem of inertia. The objective of this paper is to show the contribution of Leibniz, (...) in terms of relations of order, by distinguishing between equality by identity and equality by equivalence. Under a philosophical approach we link identity, equivalence and equality as relations of order with the indiscernibility between different states of movement. We expose first the principle of sufficient reason and the identity of indiscernibles. Under Bernoulli's principle of indifference, we argue that we distinguish between equality in abstract and equality in concrete. As a third part, we present the relationship between the identity of the indiscernibles and the predicate of equality under logical analysis. Finally we present the conclusions. -/- . (shrink)

Most, if not all, philosophers agree that computers cannot learn what words refers to from raw text alone. While many attacked Searle’s Chinese Room thought experiment, no one seemed to question this most basic assumption. For how can computers learn something that is not in the data? Emily Bender and Alexander Koller ( 2020 ) recently presented a related thought experiment—the so-called Octopus thought experiment, which replaces the rule-based interlocutor of Searle’s thought experiment with a neural language model. The Octopus (...) thought experiment was awarded a best paper prize and was widely debated in the AI community. Again, however, even its fiercest opponents accepted the premise that what a word refers to cannot be induced in the absence of direct supervision. I will argue that what a word refers to _is_ probably learnable from raw text alone. Here’s why: higher-order concept co-occurrence statistics are stable across languages and across modalities, because language use (universally) reflects the world we live in (which is relatively stable). Such statistics are sufficient to establish what words refer to. My conjecture is supported by a literature survey, a thought experiment, and an actual experiment. (shrink)

Let M = 〈M, +, <, 0, {λ}λ∈D〉 be an ordered vector space over an ordered division ring D, and G = 〈G, ⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to the t-topology, then it is definably isomorphic to a 'definable quotient group' U/L, for some convex V-definable subgroup U of 〈Mⁿ, +〉 and a lattice L of rank n. As two consequences, we derive Pillay's conjecture (...) for a saturated M as above and we show that the o-minimal fundamental group of G is isomorphic to L. (shrink)

Science and technology studies scholars have turned their attention to the materiality of objects and buildings in order to examine what they make users do in practice. Taking a close look at a therapeutic community in a psychiatric day care center for teenagers, this paper joins these discussions by exploring the materiality of “spaces of care” as part of the center’s everyday practice. The analysis incorporates the concepts of scripts and dispositifs to describe the conditions of possibility in which (...) caregivers and youths may position themselves in relation to others and to the space itself. This paper describes how spaces of care offer open, enticing, and variable conditions for fostering a dynamic of personal and relational responses as part of the care work. In this sense, the material environment entails potentialities in ways that are unpredictable but nonetheless consequential. Rather than arguing that material arrangements and things act, this paper draws attention to their impact via their potential within dispositifs of care that request participants’ attentiveness and responsiveness. Describing these potentialities brings out the subtler requirements of material environments in care practices that aim at circumventing the coercion of disciplinary spaces and their impersonal classifications. (shrink)

Post algebras of order + as a semantic foundation for +-valued predicate calculi were examined in [5]. In this paper Post spaces of order + being a modification of Post spaces of order n2 (cf. Traczyk [8], Dwinger [1], Rasiowa [6]) are introduced and Post fields of order + are defined. A representation theorem for Post algebras of order + as Post fields of sets is proved. Moreover necessary and sufficient conditions for the existence of representations preserving a (...) given set of infinite joins and infinite meets are established and applied to Lindenbaum-Tarski algebras of elementary theories based on +-valued predicate calculi in order to obtain a topological characterization of open theories. (shrink)

Let (L; f) be a finite simple Ockham algebra and let (X;g) be its dual space. We first prove that every connected component of X is either a singleton or a generalised crown (i.e. an ordered set that is connected, has length 1, and all vertices of which have the same degree). The representation of a generalised crown by a square (0,1)-matrix in which all line sums are equal is used throughout, and a complete description of X, including the number (...) of connected components and the degree of the vertices, is given. We then examine the converse problem of when a generalised crown can be made into a connected component of (X; g). We also determine the number of non-isomorphic finite simple Ockham algebras that belong properly to a given subvariety P 2n,0. Finally, we show that the number of fixed points of (L; f) is 0,1, or 2 according to the nature of X. (shrink)

In this article, I discuss how the space of the classroom is a contested object that is constituted by historical, cultural, political, social, psychological, and discursive practices (Lefebvre in The production of space, Blackwell, Oxford, UK, 1991). I then employ Deleuze and Guattari’s notion of “assemblage” to characterize the ways in which educational spaces cohere “content and affect” quoted in Puar (Terrorist assemblages: Homonationalism in queer times, Duke University Press, Durham, 2007, 193) into discursive figures of the heteronormative and (...) racialized national “family.” Finally, I argue that in order to advance contemporary theorizing on safe space we might consider shifting the metaphor of the classroom (and/or schooling) as a situation of home (in loco parentis) to that of a metaphor of camp. As a discursive practice, “camp” is like “home” in that it has multiple associations of past histories. However, the advantage of the metaphor of classroom as camp allows for a more capacious range of past histories of association, from recreation to temporary inhabitation to forced relocation, thus foregrounding the innate political implications of theorizing space. Moreover, the metaphor of camp implies transience (whether real or imaginary) while keeping in mind the partial and situated nature of particular places and spaces. Foregrounding the transient component/feature of safe space allows us to make visible and explore the possibilities and limitations of conceptualizing relations of power as circuitous, contested and performative through competing claims to particular places as objects of safety. (shrink)

We introduce two extreme methods to pairwisely compare ordered lists of the same length, viz. the comonotonic and the countermonotonic comparison method, and show that these methods are, respectively, related to the copula T M (the minimum operator) and the Ł ukasiewicz copula T L used to join marginal cumulative distribution functions into bivariate cumulative distribution functions. Given a collection of ordered lists of the same length, we generate by means of T M and T L two probabilistic relations Q (...) M and Q L and identify their type of transitivity. Finally, it is shown that any probabilistic relation with rational elements on a 3-dimensional space of alternatives which possesses one of these types of transitivity, can be generated by three ordered lists and at least one of the two extreme comparison methods. (shrink)

Summary I outline an approach to the phenomenology of improvised music which takes typification and the development of multi‐ordered phenomenological structures as central. My approach here is firmly in line with classical Husserlian phenomenology, taking the discussion of types in Experience and Judgment (Husserl, 1973) and Brudzińska (2015) as guide. I provide a phenomenological analysis of musical types as they are found in improvisational contexts, focusing on jazz in the 20th century. Styles are higher‐order musical types. Musical types are structures (...) that are temporally “thick,” relying on sedimented typification and knowledge, driving expectations as definitional. In most forms of music (including improvised music), musical styles involve maintaining a balance between confirming expectations and flouting expectations. I show that improvised music has a phenomenal structure which is enriched by the communicative and “ real‐time” nature of improvised music. Improvised music can be seen as an exploration of a possibility space rendered by the juxtaposition of the musical types afforded by a performance environment (instrumentation, harmonic and melodic traditions, etc.). I show that improvisation in music is a multi‐vectoral form of communication. The communication is founded in what Dieter Lohmar calls “non‐linguistic thinking.” The expression is constituted in the results of active and synthesis. The culmination of improvisational exploration of possibility spaces is the precisification and enrichment of styles‐as‐types, while in some cases developing new styles in the process. (shrink)

We introduce two extreme methods to pairwisely compare ordered lists of the same length, viz. the comonotonic and the countermonotonic comparison method, and show that these methods are, respectively, related to the copula TM (the minimum operator) and the Ł ukasiewicz copula TL used to join marginal cumulative distribution functions into bivariate cumulative distribution functions. Given a collection of ordered lists of the same length, we generate by means of TM and TL two probabilistic relations QM and QL and identify (...) their type of transitivity. Finally, it is shown that any probabilistic relation with rational elements on a 3-dimensional space of alternatives which possesses one of these types of transitivity, can be generated by three ordered lists and at least one of the two extreme comparison methods. (shrink)

Closure spaces are generalizations of topological spaces, in which the Intersection of two open sets need not be open. The considered logic is related to closure spaces just as the standard logic S4 to topological ones. After describing basic properties of the logic we consider problems of representation of Lindenbaum algebras with some uncountable sets of infinite joins and meets, a notion of equality and a meaning of quantifiers. Results are extended onto the standard logic S4 and (...) they are valid also for some other standard modal logics. (shrink)

The thought of Wilfrid Sellars has figured prominently in recent discussions of the relationship between naturalism and normativity . On the one hand, some have appealed to Sellars' philosophy in defence of the thesis that what he called the normative 'space of reasons' is in some sense sui generis and irreducible to the natural causal order described by the natural sciences. On the other hand, others have exploited equally central aspects of Sellars' philosophy in defence of the seemingly incompatible project (...) of attempting to give an exhaustive scientifically naturalist account of mind and meaning, and perhaps of the nature of normativity itself. I contend that what Sellars described as 'the Janus-faced character of languagings as belonging to both the causal order and the order of reasons' ( Naturalism and Ontology ) is the key to understanding his normative and pragmatist variety of naturalism. Sellars saw himself as having articulated a detailed philosophical perspective within which the normative aspects of meaning, knowledge, truth, and representation are themselves opened up, in principle, to naturalistic explanation. (shrink)

This thesis explores whether the three standard value relations, “better than”, “worse than” and “equally as good”, exhaust the possibilities in which things can relate with respect to their value. Or more precisely, whether there are examples in which one of these relations is not instantiated. There are cases in which it is not obvious that one of these relations does obtain; these are referred to as “hard cases of comparison”. These hard cases of comparison become interesting, since if it (...) not the case that the standard three value relations obtains in these cases then the three standard relations do not exhaust the possibility of instantiated value relations. It is argued that for some of the hard cases of comparison, the standard relations determinately obtain. For some it is indeterminate, due to vagueness, which of the three relations obtains, but it is determinate that one of them obtains. Thereafter it is argued that the influential Collapsing Argument fails in ruling out other accounts of the hard cases of comparison. Since one cannot depend on the Collapsing Argument in order to conclude that all items are related by the standard three relations, the investigation continues. It is argued that none of the hard cases of comparison are cases of incomparability. Furthermore, none of them are cases of a fourth basic positive value relation such as “parity”. Consequently, for all the hard cases of comparison one of the standard value relations holds, although sometimes we do not know which one and sometimes it is indeterminate which one holds. This means that there is no reason to assume that one of the standard three value relations does not hold between items we are comparing. This is followed by a brief discussion about the normative consequences of this result. The thesis ends with four different appendices in which related topics are discussed. (shrink)

While much has been written on the cultural and intellectual antecedents that gave rise to Carolus Linnaeus?s herbarium and his Systema Naturae, the tools that he used to transform his raw observations into nomenclatural terms and categories have been neglected. Focusing on the Philosophia Botanica, the popular classification handbook that he published in 1751, it can be shown that Linnaeus cleverly ordered and reordered the work by employing commonplacing techniques that had been part of print culture since the Renaissance. Indeed, (...) the functional adaptability of commonplace heads allowed him to split and combine the book?s chapters and tables and played a notable conceptual role in the way in which he spatialized words and, to a certain extent, specimens. (shrink)

Worldwide, healthcare has been touched by neoliberal policies to the extent that it has some of its characteristics, such as being asymmetrical, competitive, dehumanized, and profit driven. In Colombia, Law 100/93 was created as an ambitious reform aimed at integrating the social security and public sectors of healthcare in order to create universal access, and at the same time to generate market competence with the objective of improving effectiveness and responsiveness. Instead, however, Colombian health reform has served to generate competition (...) which has aggravated inequalities among people. Within this context, we practice nursing. As nurses, our responsibility is to advocate for our patients. We cannot ignore what is happening worldwide in hospitals and community health settings because our responsibility is to promote health, prevent disease, and care for human beings. So, today, when the world pushes for economical profit and competence on one hand, and, on the other, for moral compromises to care, respect, and advocacy for all human beings, being a nurse in the Colombian health system represents a challenge for us. This challenge is especially significant because harm and benefit, justice and injustice, respect and disrespect are separated by a fine line that is easy to transgress. (shrink)

We study the class of Sperner spaces, a generalized version of affine spaces, as defined in the language of pointline incidence and line parallelity. We show that, although the class of Sperner spaces is a pseudo-elementary class, it is not elementary nor even ℒ∞ω-axiomatizable. We also axiomatize the first-order theory of this class.

The dominant male discourse as expressed in the law of sexuality constructs the male subject. In each area — rape, incest and prostitution, it creates and extends the power which underpins the sexuality of the male subject to facilitate the non-consensual taking of women in rape and incest and the buying of them on the subject's own terms in prostitution.Further, the law constructs the female as Other not as freely consenting subject but as Other for the male subject in the (...) space of unreason, for the logic of desire.In these constructions, lie the paradox of the law of sexuality. It exists purportedly to defend and protect the “victims” of rape, incest and prostitution but even in so far as it does so, it reasserts, through its constructions, the power of the speaking male subject through and the exclusion of the woman as Other from, the dominant male discourse as it is expressed in and enshrined by that law. (shrink)

In this paper, I first examine the classification of mental derangements contained in Kant’s "Anthropology from a Pragmatic Point of View", in order to highlight the role played by imagination in their pathogenesis. Later, on the basis of this examination, I reflect on the origins of critical philosophy, which can be seen as an attempt to construct a control device for the imagination structured as a systematic, organic space.

I consider the first-order modal logic which counts as valid those sentences which are true on every interpretation of the non-logical constants. Based on the assumptions that it is necessary what individuals there are and that it is necessary which propositions are necessary, Timothy Williamson has tentatively suggested an argument for the claim that this logic is determined by a possible world structure consisting of an infinite set of individuals and an infinite set of worlds. He notes that only the (...) cardinalities of these sets matters, and that not all pairs of infinite sets determine the same logic. I use so-called two-cardinal theorems from model theory to investigate the space of logics and consequence relations determined by pairs of infinite sets, and show how to eliminate the assumption that worlds are individuals from Williamson’s argument. (shrink)

A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lüders-von Neumann quantum measurement as a probability conditionalization rule. A major result shows that the operator algebras must be replaced by order-unit spaces with some specific properties in the generalized approach, and it is analyzed under which conditions these order-unit spaces become Jordan algebras. An application of this result (...) provides a characterization of the projection lattices in operator algebras. (shrink)

SUMMARYThe essay argues that Jeremy Bentham played a major role in the transitional process between the eighteenth and the nineteenth centuries leading to the ‘discovery' or ‘invention of society' as an order, i.e., as an autonomous object of knowledge. By comparing Bentham's discourse with those developed by select protagonists of that transition, particularly Ferguson, Sieyès, and Mirabeau, it is shown how society emerges as the logical and historical space of a set of relationships that affects both the rationalisation and the (...) practice of government. In contrast with Michel Foucault's interpretation of Bentham's role in the genealogy of neoliberalism, recently developed by Pierre Dardot and Christian Laval, this paper suggests that ‘the new governmental reason’ rose from within the discourse of law. Consequently, the problem of ‘constitution’ was not left behind by the epistemological change of the eighteenth century, as they argue. Rather, the scientific and political understanding of society as a code became the base for an innovative conception of both law and politics. (shrink)

The aim of this paper is to elucidate the relationship between Aristotelian conceptual oppositions, commutative diagrams of relational structures, and Galois connections.This is done by investigating in detail some examples of Aristotelian conceptual oppositions arising from topological spaces and similarity structures. The main technical device for this endeavor is the notion of Galois connections of order structures.

‘Space does not exist fundamentally: it emerges from a more fundamental non-spatial structure.’ This intriguing claim appears in various research programs in contemporary physics. Philosophers of physics tend to believe that this claim entails either that spacetime does not exist, or that it is derivatively real. In this article, I introduce and defend a third metaphysical interpretation of the claim: reductionism about space. I argue that, as a result, there is no need to subscribe to fundamentality, layers of reality and (...) emergence in order to analyse the constitution of space by non-spatial entities. It follows that space constitution, if borne out, does not provide empirical evidence in favour of a stratified, Aristotelian in spirit, metaphysics. The view will be described in relation to two particular research programs in contemporary physics: wave function realism and loop quantum gravity. (shrink)

In “Knowledge and the Internal” John McDowell presents a deep and interesting argument. I think everything he says is true and important. Still, there are a number of points that bear expanding on in order to be properly understood. So I want to say something about his point of departure: the idea of standings in the space of reasons. And I want to fill in further the picture at which he finally arrives, by saying how I think we ought to (...) understand knowledge as a standing in the space of reasons, once we have freed ourselves from a prevalent deformed conception of that space. McDowell’s strategy is to show that that conception of the space of reasons is inadequate—that it deserves to be called a ‘deformation’—by showing that it leaves no room for anything recognizable as knowledge. I’ll try to reconstruct that argument by showing what it looks like in the context of a crucial dimension of the space of reasons that McDowell never mentions: its essentially social articulation. The effect of this supplementation, I think, is not to turn a bad argument into a good one, but to turn what is already a good argument into one that further illuminates the phenomena with which it deals. (shrink)