Locatedness is one of the fundamental notions in constructive mathematics. The existence of a positivity predicate on a locale, i.e. the locale being overt, or open, has proved to be fundamental in constructive locale theory. We show that the two notions are intimately connected.Bishop defines a metric space to be compact if it is complete and totally bounded. A subset of a totally bounded set is again totally bounded iff it is located. So a closed subset of a Bishop (...) compact set is Bishop compact iff it is located. We translate this result to formal topology. ‘Bishop compact’ is translated as compact and overt. We propose a definition of locatedness on subspaces of a formal topology, and prove that a closed subspace of a compact regular formal space is located iff it is overt. Moreover, a Bishop-closed subset of a complete metric space is Bishop compact — that is, totally bounded and complete — iff its localic completion is compact overt.Finally, we show by elementary methods that the points of the Vietoris locale of a compact regular locale are precisely its compact overt sublocales.We work constructively, predicatively and avoid the use of the axiom of countable choice. (shrink)

I take it that A. W. Moore is right when he said that ‘Wittgenstein was right: some things cannot be put into words. Moreover, some things that cannot be put into words are of the utmost philosophical importance’. There is, however, a constant threat of self-stultification whenever an attempt is made to put the ineffable into words. As Pamela Sue Anderson notes in Re-visioning gender in philosophy of religion: reason, love, and epistemic locatedness, certain recent approaches to ineffability—including Moore’s (...) approach—attempt to find a ‘third way’ of engaging with it, which displaces the traditional dichotomy between the effable and the ineffable, that is, between what can be said and what cannot be said. In this way, they seek to overcome the threat of self-stultification mentioned above. Still, one important challenge to this kind of approach, which Moore addresses, is, as he puts it, ‘to show how it is possible’ to talk about the ineffable ‘without belying its very ineffability’. His solution to the problem of the ineffable takes the notion of ‘knowing how’ to play a central role, and is formulated in accordance with his commitments to truth and objectivity. A further important challenge to the kind of approach to the ineffable Moore proposes concerns the issue of objectivity. In Re-visioning gender in philosophy of religion, Anderson draws attention to our epistemic locatedness, which brings in questions concerning, for example, gender and culture. Pursuing this view, the challenge is to show ineffable insight without ignoring our epistemic locatedness and, in particular, the role of gender in the conceptualisation and imagery through which we seek to come to terms with the ineffable. My paper deals with these challenges. By engaging with Moore’s and Anderson’s discussions of the ineffable, I examine how it is possible to talk philosophically about the ineffable, without breaking a commitment to enlarged or objective thinking, and without ignoring the epistemic locatedness of thinking. (shrink)

This text presents a new critical awareness of gender in philosophy and religion, suggesting new core concepts at the interface of philosophy and religion, and ethics and epistemology.

This essay offers a response to Pamela Sue Anderson’s book, Re-visioning Gender in Philosophy of Religion. It focuses on three key aspects of Anderson’s work: first, her concern with the often imperceptible reality of gender exclusions; secondly, her discussion of ineffability in dialogue with Adrian Moore’s work and thirdly, her defence of realism in response to Grace Jantzen. These themes constitute a welcome articulation of rationality within a feminist framework, whilst opening up rationality to the validity of non-propositional truths. The (...) essay ends by suggesting that Anderson does more to work out new conceptualizations of the divine, arguing that her work and that of Jantzen are not so far apart on this point as might first appear. (shrink)

We study operators with located graph in Bishop-style constructive mathematics. It is shown that a bounded operator has an adjoint if and only if its graph is located. Locatedness of the graph is a necessary and sufficient condition for an unbounded normal operator to have a spectral decomposition. These results suggest that located operators are the right generalization of bounded operators with an adjoint.

This paper proposes an original ubuntu-inspired account of human-animal moral status for engaging the problem of belongingness—the ethico-ecological community view. This account embodies two integrated features: locatedness and relationality. While locatedness prompts us to attend to the embeddedness of beings in the built and natural environment, relationality allows the discussion to focus on human-nonhuman interdependencies. I argue that a deep sense of both features prompts us to move the moral status conversation away from capacities to a non-capacity-based approach, (...) thereby helping to disrupt unjustified human moral superiority over animals in a way that commits us to environmental flourishing. (shrink)

Neopragmatism has been accused of having ‘an experience problem’. This paper begins by outlining Hume's understanding of perception according to which ideas are copies of impressions thought to constitute a direct confrontation with reality. This understanding is contrasted with Peirce's theory of perception according to which percepts give rise to perceptual judgments which do not copy but index the percept (just as a weather-cock indicates the direction of the wind). Percept and perceptual judgment thereby mutually inform and correct one another, (...) as the perceiver develops mental habits of interpreting their surroundings, so that, in this theory of perception, as Peirce puts it: “[n]othing at all…is absolutely confrontitional”. Paul Redding has argued that Hegel’s “idealist understanding of logical form” ran deeper than Kant’s in recognising that Mind is essentially embodied and located, and therefore perspectival. Peirce’s understanding arguably dives deeper still in distributing across the space of reasons (and thus Being) not just Mind’s characteristic features of embodiedness and locatedness, but also its infinite corrigibility. (shrink)

In this paper I want to suggest that causal and interpretive approaches to epistemology are in tension with one another. Drawing on the work of hermeneutic writers I suggest that epistemological justification is an interpretive process. The possibility of rational justification requires attention to our locatedness within the domain of reasons, into which we have been culturally initiated. The recognition that there is no transcendent processes of rational justification has to be addressed from within this framework and cannot be (...) resolved in a naturalizing way. The turn to hermeneutics in the context of epistemology allows us to reassign a central role to experience within epistemological justification. Here the very features of experience which render problematic its role in empiricist accounts form the basis of its position in hermeneutic ones. This presents us with an immanent conception of rationality, in place of the transcendent conception which so many writers have problematized. (shrink)

This article addresses the question as to whether it is logically possible to fashion a discourse exclusively for the natural environment. Could such a discourse emerge without colonization by other social spheres acting as proxy? The prospects appear to be rather bleak, for even in the case of two apparently non-human-directed or non-committal discourses, that of extensionist ethics and new sophisticated management (of environmental crises), the latent social-constructionism built into both renders them monistic discourses hegemonically mapping the territories of what (...) they refer to. It becomes increasingly difficult to escape the human epistemic locatedness anti-anthropocentric critics demand. Despite this, such an exercise offers us the benefit of being mindful of what the crisis of social-scientific discourses amounts to as well as what to expect of discourse analysis as such. Furthermore, the prospects of the two discourses examined are being mapped onto two modified models drawing on Foucault and Deleuze thus helping us understand the pattern of our diverse environmental responses. Ecological thinking is perhaps the first subject-matter that transcends or shatters discourse boundaries and strains both imagination and human powers when selecting between conceptual frameworks, making us aware of the ineluctable feature of social-constructionism present in our social thought. (shrink)

In archival footage uploaded online of a concert at the University of the Western Cape in 1988 musician Robbie Jansen declared that the next composition to be performed was named 'Freedom Where Have You Been'.1 Before counting the band in, Jansen offered a short discourse on the meaning of the phrase hoya chibongo. Hearing the Afrikaans hoorie (meaning listen here) in the expression hoya, Jansen proceeded to split up the word chibongo to accentuate chi- as aurally reminiscent of the suffix (...) -tjie that is used in Afrikaans to mark the diminutive. bongo, in this context as Jansen remarked, is the drum, leading Jansen to exclaim that the phrase hoya chibongo means to 'listen to the (small) drum', the drum that is, according to Jansen, 'the truth'. In Jansen's exact words, 'the drum speaks the truth and the drum has always been our language before these funny words that we are speaking now'. Jansen's translation was markedly oral, not only in its expression of speech and languaging but also in its invocation of a historicity through the oral; an oral tradition, for all intents and purposes. In its locatedness in a musically expressive and performative moment, Jansen expressed a duality of sound that exceeds the oral itself: calling attention to how language might be a conduit for the instrument, and how in some sense the drum might speak across time and space. It usefully deepens the often cliché proclamation rehearsed in and out of music studies in particular that music is universal, or that sound might be thought of as a kind of connective tissue that allows a specific sense-making of the social.2 In Jansens invocation of 'before' in his statement about the drum as language, and in debates around the meaning of sound to the social, it is history - or, a representation of pastness - that is called upon to bring about a set of futures where sound mediates the experience of a temporal matrix where truth, or freedom, might be found. What Jansen does/did was not necessarily an act of translation into a local vernacular as it is the blurring of the oral and the aural in a moment that might express the relation between sound, its interpretation, and its social life, obliquely. The truth for Jansen was what the drum expressed; but it was also the drum itself. The oral is aural, as the aural is oral. (shrink)

I wish to expose the possibility of a Kantian feminism made actual by Pamela Sue Anderson’s recent book Re-visioning Gender in Philosophy of Religion: Reason, Love and Epistemic Locatedness. In this paper I show how Kantian philosophy structures Anderson’s project, and I argue that in embodying the spirit of Kantian critique, this project may be used to turn that spirit against the letter of its expression in an act that would claim Kant for feminism.

Phenomenological analysis of the bodiliness of human existence establishes a sense in which human consciousness is prereflectively spatial and located at a particular place, and at the same time a sense in which consciousness detaches itself from its location by reflecting on it and itself. This paper probes a parallel aspect of that self which the reader becomes upon reading and entering the world of three selected fictive narratives: this “reading self,” as it will be called, replicates the structure of (...) real-world consciousness, for the reading self is both located at a specifiable place within each of the three fictive worlds and at the same time floats free of that location without leaving the narrative's world. Although the paper does not claim that the reading consciousness always or necessarily replicates real-world consciousness, it suggests that such replication, when it happens, is significantly related to the reading self's encounter with the fictive characters as both selves and others. To say that the latter are self-transcending selves is to say that the reading self may identify itself with them and move into the story's world; such identification does in fact take place. To say that at the same time the characters remain other selves is to say that the reading self, floating free within the story's world, also experiences a distance between itself and them. Yet this otherness does not turn the fictive characters into objects; that is, their otherness does not imply that they are merely objects to be explained in terms of social or biological forces nor that they are the products of an author's manipulations. Much of the paper is occupied with working out the interaction between the reading self's locatedness and non-locatedness, on the one hand, and the fictive characters' selftranscendence and otherness on the other. (shrink)

Walter Benjamin’s 1936 essay, ‘The Work of Art in the Age of Mechanical Reproduction’, constitutes one of the earliest reflections on the way in which the cultural experience and interpretation is transformed by the advent of what were then the ‘new’ media technologies of photography and film. Benjamin directs attention to the way in which these technologies release cultural objects from their unique presence in a place and make them uniformly available irrespective of spatial location. The way in which old (...) media technologies apparently obliterate the place of cultural objects is also a feature of new media. However, the apparent obliteration of place that occurs in this way is itself problematic, in giving rise to a loss of the sense of spatial and temporal distance, and so of the relative locatedness of both experiencing subject and interpreted object. The loss of a sense of the place of the object threatens a loss of the sense of place of the subject, and with it, a loss of a proper sense of heritage as such. (shrink)

What is the relation between our beliefs, or thoughts in general, and the perceptual experience of the world that gives rise to those beliefs? Donald Davidson is usually taken to have a well-known answer to this question that runs as follows: while our beliefs are, at least in part, caused by our experience, such experience does not thereby count as providing a rational ground for those beliefs; our beliefs are thus evidentially grounded in other beliefs, but not in the experience (...) that gives rise to them. John McDowell, among others, has challenged this Davidsonian picture on the grounds that it actually severs the connection between beliefs and their proper evidential grounds. Against such a view, this paper argues the Davidsonian position grounds belief in the specificity of our own locatedness in the world, and in the more general and prior embeddedness of belief in the world that is a part of the very concept of belief. (shrink)

: In this essay, I trace a rhetorical affinity between feminist postmodern theory and an Enlightenment narrative of development. This affinity consists in the valorization of mobility and the repudiation of locatedness. Although feminists deploy this rhetoric in order to accommodate differences and to accustom readers to the instability that results from such accommodation, I show how this rhetoric works to justify Western colonial development and to efface women's very different experiences of mobility in the early twenty-first century.

At the phenomenal level, consciousness can be described as a singular, unified field of recursive self-awareness, consistently coherent in a particualr way; that of a subject located both spatially and temporally in an egocentrically-extended domain, such that conscious self-awareness is explicitly characterized by I-ness, now-ness and here-ness. The psychological mechanism underwriting this spatiotemporal self-locatedness and its recursive processing style involves an evolutionary elaboration of the basic orientative reference frame which consistently structures ongoing spatiotemporal self-location computations as i-here-now. Cognition computes (...) action-output in the midst of ongoing movement, and consequently requires a constant self-locating spatiotemporal reference frame as basis for these computations. Over time, constant evolutionary pressures for energy efficiency have encouraged both the proliferation of anticipative feedforward processing mechansims, and the elaboration, at the apex of the sensorimotor processing hierarchy, of self-activating, highly attenuated recursively-feedforward circuitry processing the basic orientational schema independent of external action output. As the primary reference frame of active waking cognition, this recursive i-here-now processing generates a zone of subjective self-awareness in terms of which it feels like something to be oneself here and now. This is consciousness. (shrink)

Abstract: It is often claimed that realists about universals must be either “platonists,” holding that universals lack spatio-temporal location, or “aristotelians,” asserting that universals are located where their instances are. What’s more, both camps agree that locatedness or unlocatedness is part of the essential nature of universals; consequently, aristotelians say that universals cannot exist un located, and platonists allege that universals cannot be located. Here I argue that the dispute may be resolved by synthesizing the most attractive features of (...) each position. I claim that universals are located at their instances when instantiated by particulars which themselves possess a spatio-temporal location; however, un instantiated universals exist without location. This has the consequence that it will often be a contingent matter whether a given universal has a location, if the universal is only contingently instantiated. Nevertheless, I claim, objections to this position may be overcome. (shrink)

This paper provides a Bishop-style constructive analysis of the contrapositive of the statement that a continuous homomorphism of R onto a compact abelian group is periodic. It is shown that, subject to a weak locatedness hypothesis, if G is a complete (metric) abelian group that is the range of a continuous isomorphism from R, then G is noncompact. A special case occurs when G satisfies a certain local path-connectedness condition at 0. A number of results about one-one and injective (...) mappings are proved en route to the main theorem. A Brouwerian example shows that some of our results are the best possible in a constructive framework. (shrink)

In the present note, we study a generalization of Dedekind cuts in the context of constructive Zermelo–Fraenkel set theory CZF. For this purpose, we single out an equivalent of CZF's axiom of fullness and show that it is sufficient to derive that the Dedekind cuts in this generalized sense form a set. We also discuss the instance of this equivalent of fullness that is tantamount to the assertion that the class of Dedekind cuts in the rational numbers, in the customary (...) constructive sense including locatedness, is a set. This is to be compared with the situation for the partial reals, a generalization in a different direction: if one drops locatedness from the notion of a Dedekind real, then it becomes inherently impredicative. We make this precise, and further present the curiosity that the irrational Dedekind reals form a set already with exponentiation. (shrink)

It has been claimed that Val Plumwood’s work is vulnerable to the same charge of “assimi­lationism” that she has leveled against moral extensionist viewpoints. It is argued that while one might regard Plumwood’s position as suspect because of its emphasis on human-nature continuity, associating claims of continuity with assimilationism could lead one to seek a mode of relating to nature as absolutely other, a move which is claimed to be problematic for several reasons. Because the extensionist error is not simply (...) that of acknowledging human-nature continuity, Plumwood’s position is not extensionist in any objectionable sense. This issue is connected up with the ongoing debate about “perspectival anthropocentrism” in environmental ethics; however, allowing for human epistemic locatedness does not force the conclusion that all environmental ethics is ultimately assimilationist. (shrink)

It has been claimed that Val Plumwood’s work is vulnerable to the same charge of “assimi­lationism” that she has leveled against moral extensionist viewpoints. It is argued that while one might regard Plumwood’s position as suspect because of its emphasis on human-nature continuity, associating claims of continuity with assimilationism could lead one to seek a mode of relating to nature as absolutely other, a move which is claimed to be problematic for several reasons. Because the extensionist error is not simply (...) that of acknowledging human-nature continuity, Plumwood’s position is not extensionist in any objectionable sense. This issue is connected up with the ongoing debate about “perspectival anthropocentrism” in environmental ethics; however, allowing for human epistemic locatedness does not force the conclusion that all environmental ethics is ultimately assimilationist. (shrink)

Back in October 2015 I had the opportunity to chair the book launch for all three works discussed in this review essay. At the event, Shirley Anne Tate said, “Black feminist theory is the theory”. The comment referred to how it is not ‘just’ that Black feminist theory is typically marginalised within institutional contexts and academic scholarship, ‘even’ within critical, feminist and poststructural work, but also to highlight the capacity of Black feminist scholarship to unpick and destabilise the known and (...) knowable in ways that are profoundly ontological, and which offer potential routes to meaningful social change through the hard task of working across difference. The three books reviewed here by Shirley Anne Tate, Suryia Nayak and Shona Hunter are theoretically rich and complex in breadth, scope and range, drawing on extensive Black feminist scholarship, as well as critical race, critical feminist, psychosocial, psychoanalytic, postcolonial, decolonial and poststructural approaches. Each book is embedded in everyday practices and social processes, offering multi-layered movement across different spatial-social and affective scales in ways that allow ‘big’ insights to emerge from the locatedness and particularity of human experience. They are reviewed in turn and some concluding comments identify important commonalities across the texts. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Masao Abe and the Dialogue BreakthroughStephen RoweI am profoundly grateful to Masao Abe for many reasons, including his articulation of Zen and his responsiveness to my own work, but most especially for his breakthrough work on dialogue. For he, along with his Christian partner in dialogue, John B. Cobb Jr., has taken us to a new paradigm, one in which dialogue, in complementary relationship with our more particular practices (...) and traditions, can be valued as a religious practice.1 Together these two towering figures of our time have broken through the koan of abstracted universality versus incommensurable particularity, and hence opened up a possibility for the human future the significance of which cannot be overestimated.In October 1986, I had the good fortune to find myself at the Third North American Buddhist-Christian Theological Encounter, the stated theme of which was “Notions of Ultimate Reality in Buddhism and Christianity.” A critical tension was evident early on in this event. Masao Abe spoke very persuasively of the “perspec-tiveless perspective” of Zen, arising from the experience of sunyata as the negation of negation or the radicalizing of Nothingness, of Zen as the affirmation of radical return. John Cobb spoke with equal persuasiveness of our inescapable particularity as historical beings, our ineluctable locatedness, and the irreducible wisdom of Israel and Greece. Both of these opposing views seemed right. How could this be so?To heighten the juxtaposition, it was equally evident that there were three large propositions on which Abe and Cobb very much agreed: first, our need of transformation; second, that this must be mutual transformation; and, third, that transformation must be in the direction of a new universality of humankind, which Cobb describes as “a global memory.” 2 How is it possible for these powerful elements of agreement to be juxtaposed with the critical tension mentioned above? Cobb and Abe, not surprisingly, have their own responses to this question,3 and we can learn from what Abe says about universality and transformation, and how his understanding of both leads him to a specifically religious valuing of the dialogical encounter with the difference that is presented by Cobb.In the paper Masao Abe presented at the 1986 event, he proposed two crucial aspects of dialogue between world religions: (1) seeking clarification of the views peculiar to one’s own tradition through allowing the different views between traditions [End Page 123] to confront one another, and (2) being “free from the peculiarity of our own traditions in order to scrutinize the notion of ultimate reality itself most fitting to our contemporary human predicament and the future of humanity.” 4 The second aspect needs to involve “a very creative and penetrating discussion in which we must be radically critical of our own tradition so that we can re-examine and regrasp the essence of our religion from the more universal and more fundamental position,” and hence “find out the truly ultimate reality for the future of humanity.” 5There is a paradox here: Abe indicates both a more universal orientation and a reappropriation of the essence of our particular traditions. The key to movement beyond paradox as frustrating antinomy to paradox as gateway to vitality is the dialogical practice, and specifically dialogue in its association with mutual transformation and the emergence of a new universality of humankind. For Abe, this turns on the understanding of “universal”:To become a “universal” world religion does not imply a monolithic religion common to East and West, but rather calls for a dynamic structure capable of freely assuming any form, oriental or occidental, according to the area in which it develops and yet without being confined to any limitation of that area. Such a dynamic realization of the “universal” world religion may become possible for Christianity and Buddhism should they genuinely regrasp their respective notions of universal salvation for all mankind.6Dialogue as locus of “dynamic realization” makes possible a new universality, which, for Abe, is based on the self-negation that leads to the awakening of the “true Self,” and “enter[ing] the third historical age of mankind, namely the age of Self-awakened cosmology.” Because “true investigation of the self is always... (shrink)

Chapter 3 The locations of sounds 3.1 Where are sounds? 3.2 Locational hearing 3.3 Located sounds 3.4 ‘Coming from’ 3.5 Sounds without locations? 3.6 Locatedness and the metaphysics of sounds 3.7 The durations of sounds.

In this essay, I trace a rhetorical affinity between feminist postmodern theory and an Enlightenment narrative of development. This affinity consists in the valorization of mobility and the repudiation of locatedness. Although feminists deploy this rhetoric in order to accommodate differences and to accustom readers to the instability that results from such accommodation, I show how this rhetoric works to justify Western colonial development and to efface women's very different experiences of mobility in the early twenty-first century.