It is shown that in ZF set theory the axiom of choice holds iff every non empty topological space has a maximal closed filter.

During the Zimbabwean crisis, millions crossed through the apartheid-era border fence, searching for ways to make ends meet. Maxim Bolt explores the lives of Zimbabwean migrant labourers, of settled black farm workers and their dependants, and of white farmers and managers, as they intersect on the border between Zimbabwe and South Africa. Focusing on one farm, this book investigates the role of a hub of wage labour in a place of crisis. A close ethnographic study, it addresses the complex, shifting (...) labour and life conditions in northern South Africa's agricultural borderlands. Underlying these challenges are the Zimbabwean political and economic crisis of the 2000s and the intensified pressures on commercial agriculture in South Africa following market liberalization and post-apartheid land reform. But, amidst uncertainty, farmers and farm workers strive for stability. The farms on South Africa's margins are centers of gravity, islands of residential labour in a sea of informal arrangements. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Anthony Close THE EMPIRICAL AUTHOR: SALMAN RUSHDIE'S THE SATANIC VERSES HOBBES, comparing the author ofan action to the owner ofgoods, asserts, "And as the right of possession, is called dominion; so the right of doing any action, is called authority" (Leviathan, Book I, chap. 16). My purpose in this essay is to apply this Hobbesian maxim to the relation Author/Text, expanding somewhat Hobbes's notion of authority. I presuppose that (...) in our day-to-day dealings with our fellow men, we envisage each others' acts as exhibiting purpose and commitment, which make them ours in more than the platitudinous sense that we performed them. By virtue of that, they confer on us a privileged, though clearly not unchallengeable, authority in saying what they are and what they are for. Such, in effect, is the position reached by Austin in How to Do Things with Words, and it broadly corresponds to that of various philosophical writings on human action—by Anscombe, Davidson, and Melden.1 To be sure, we may legitimately consider human behavior from other viewpoints (e.g., structuralist, anthropological, psychoanalytical, Marxist) trained on its unconscious presuppositions. Yet, insofar as such theorizing fails to acknowledge the priority of the Hobbesian perspective, it will seem perverse for a reason that has been well put by Charles Taylor. Precisely because history is made up of purposeful activity, Taylor argues, we need to explain historical patterns in a way that is "intelligible in relation to conscious action" even though they may not "issue from conscious action."2 By this criterion much of our modern literary theory is defective. A vivid measure of the deficiency is provided by the furor over Salman Rushdie's TL· Satanic Verses, culminatingin thefatwa pronounced against Philosophy and Literature, © 1990, 14: 248-267 Anthony Close249 him by the Ayatollah Khomeini in February 1989. I take it that for anyone vocationally committed to the practice or study ofliterature and to the cause of freedom of expression, the defense of Rushdie cannot be a matter of indifference. Nor can one be indifferent to the chasm of misunderstanding that separates Rushdie and his apologists from the novel's Muslim opponents. I believe that these two causes—defending Rushdie and bridging the chasm—can be reconciled by offering better explanations ofhis novel in place ofcrude denunciations or, from some non-Muslim quarters, smug and knowing dismissals. Yet, as we shall see, the task of explanation could be considered hamstrung by our modern poetics. I was reminded ofHobbes's textby Rushdie's lucid and cogent defense of his novel in TL· Independent (London, February 4, 1990). Against the accusations that he had deliberately reviled the Islamic faith, he argued as follows. Though TL· Satanic Verses, like many novels that Rushdie esteems, is a work of radical dissent, questioning, and reimagining, it is motivated by a spirit of serious inquiry rather than debunking derision. More particularly, it reflects a determination that underlies all Rushdie's work: "to create a literary language and literary forms in which the experience offormerly-colonised, still-disadvantaged peoples might find full expression." He continues: "It is written from the very experience of uprooting, disjuncture and metamorphosis... that is the migrant condition, and from which, I believe, can be derived a metaphor for all humanity.... [It] celebrates hybridity, impurity, intermingling, the transformation that comes of new and unexpected combinations of human beings, cultures, ideas, politics, movies, songs. It rejoices in mongrelisation and fears the absolutism of the Pure." Note the insistence on how these themes flow direcdy from Rushdie's own experience. Two days after the publication of this article, Harold Pinter gave on Rushdie's behalf a lecture on the relationship of literature to religion and society at the Institute of Contemporary Arts in London. In this lecture, Rushdie articulated a Bakhtinian view of the novelist's function: to dramatize ironically and noncommittally the clash of voices, languages, and ideologies in a world without gods and without traditionsanctioned truth. Rushdie referred specifically, I think, to a species of postmodernist novel which we may dub "palimpsest history";3 the species includes Rushdie's works, García Márquez's One Hundred Years of Solitude, Carlos Fuentes's Terra Nostra... (shrink)

In many-valued logic the decision of functional completeness is a basic and important problem, and the thorough solution to this problem depends on determining all maximal closed sets in the set of many-valued logic functions. It includes three famous problems, i.e., to determine all maximal closed sets in the set of the total, of the partial and of the unary many-valued logic functions, respectively. The first two problems have been completely solved , and the solution to (...) the third problem boils down to determining all maximal subgroups in the k-degree symmetric group Sk, which is an open problem in the finite group theory. In this paper, all maximal closed sets in the set of unary p-valued logic functions are determined, where p is a prime. (shrink)

Let {: i ∈I } be a family of compact spaces and let X be their Tychonoff product. [MATHEMATICAL SCRIPT CAPITAL C] denotes the family of all basic non-trivial closed subsets of X and [MATHEMATICAL SCRIPT CAPITAL C]R denotes the family of all closed subsets H = V × Πmath imageXi of X, where V is a non-trivial closed subset of Πmath imageXi and QH is a finite non-empty subset of I. We show: Every filterbase ℋ ⊂ (...) [MATHEMATICAL SCRIPT CAPITAL C]R extends to a [MATHEMATICAL SCRIPT CAPITAL C]R-ultrafilter ℱ if and only if every family H ⊂ [MATHEMATICAL SCRIPT CAPITAL C] with the finite intersection property extends to a maximal [MATHEMATICAL SCRIPT CAPITAL C] family F with the fip. The proposition “if every filterbase ℋ ⊂ [MATHEMATICAL SCRIPT CAPITAL C]R extends to a [MATHEMATICAL SCRIPT CAPITAL C]R-ultrafilter ℱ, then X is compact” is not provable in ZF. The statement “for every family {: i ∈ I } of compact spaces, every filterbase ℋ ⊂ [MATHEMATICAL SCRIPT CAPITAL C]R, Y = Πi ∈IYi, extends to a [MATHEMATICAL SCRIPT CAPITAL C]R-ultrafilter ℱ” is equivalent to Tychonoff's compactness theorem. The statement “for every family {: i ∈ ω } of compact spaces, every countable filterbase ℋ ⊂ [MATHEMATICAL SCRIPT CAPITAL C]R, X = Πi ∈ωXi, extends to a [MATHEMATICAL SCRIPT CAPITAL C]R-ultrafilter ℱ” is equivalent to Tychonoff's compactness theorem restricted to countable families. The countable Axiom of Choice is equivalent to the proposition “for every family {: i ∈ ω } of compact topological spaces, every countable family ℋ ⊂ [MATHEMATICAL SCRIPT CAPITAL C] with the fip extends to a maximal [MATHEMATICAL SCRIPT CAPITAL C] family ℱ with the fip”. (shrink)

Given two structures${\cal M}$and${\cal N}$on the same domain, we say that${\cal N}$is a reduct of${\cal M}$if all$\emptyset$-definable relations of${\cal N}$are$\emptyset$-definable in${\cal M}$. In this article the reducts of the Henson digraphs are classified. Henson digraphs are homogeneous countable digraphs that omit some set of finite tournaments. As the Henson digraphs are${\aleph _0}$-categorical, determining their reducts is equivalent to determining the closed supergroupsG≤ Sym of their automorphism groups.A consequence of the classification is that there are${2^{{\aleph _0}}}$pairwise noninterdefinable Henson digraphs which (...) have no proper nontrivial reducts. Taking their automorphisms groups gives a positive answer to a question of Macpherson that asked if there are${2^{{\aleph _0}}}$pairwise nonconjugate maximal-closed subgroups of Sym. By the reconstruction results of Rubin, these groups are also nonisomorphic as abstract groups. (shrink)

We study the filter ℒ*(A) of computably enumerable supersets (modulo finite sets) of an r-maximal set A and show that, for some such set A, the property of being cofinite in ℒ*(A) is still Σ0 3-complete. This implies that for this A, there is no uniformly computably enumerable “tower” of sets exhausting exactly the coinfinite sets in ℒ*(A).

l investigate versions of the Maximality Principles for the classes of forcings which are <κ-closed. <κ-directed-closed, or of the form Col (κ. <Λ). These principles come in many variants, depending on the parameters which are allowed. I shall write MPΓ(A) for the maximality principle for forcings in Γ, with parameters from A. The main results of this paper are: • The principles have many consequences, such as <κ-closed-generic $\Sigma _{2}^{1}(H_{\kappa})$ absoluteness, and imply. e.g., that ◇κ holds. I (...) give an application to the automorphism tower problem, showing that there are Souslin trees which are able to realize any equivalence relation, and hence that there are groups whose automorphism tower is highly sensitive to forcing. • The principles can be separated into a hierarchy which is strict, for many κ. • Some of the principles can be combined, in the sense that they can hold at many different κ simultaneously. The possibilities of combining the principles are limited, though: While it is consistent that MP<κ-closed(HκT) holds at all regular κ below any fixed α. the "global" maximality principle, stating that MP<κ-closed(Hκ ∪ {κ}) holds at every regular κ. is inconsistent. In contrast to this, it is equiconsistent with ZFC that the maximality principle for directed-closed forcings without any parameters holds at every regular cardinal. It is also consistent that every local statement with parameters from HκT that's provably <κ-closed-forceably necessary is true, for all regular κ. (shrink)

Given an uncountable regular cardinal κ, we study the structural properties of the class of all sets of functions from κ to κ that are definable over the structure 〈H,∈〉 by a Σ1-formula with parameters. It is well known that many important statements about these classes are not decided by the axioms of ZFC together with large cardinal axioms. In this paper, we present other canonical extensions of ZFC that provide a strong structure theory for these classes. These axioms are (...) variations of the Maximality Principle introduced by Stavi and Väänänen and later rediscovered by Hamkins. (shrink)

An ordering (≤K) on maximal almost disjoint (MAD) families closely related to destructibility of MAD families by forcing is introduced and studied. It is shown that the order has antichains of size.

We propose a model of uncertain belief. This models coherent beliefs by a filter, ????, on the set of probabilities. That is, it is given by a collection of sets of probabilities which are closed under supersets and finite intersections. This can naturally capture your probabilistic judgements. When you think that it is more likely to be sunny than rainy, we have{????|????(????????????????????)>????(????????????????????)}∈????. When you think that a gamble ???? is desirable, we have {????|Exp????[????]>0}∈????. It naturally extends the model (...) of credal sets; and we will show it captures all the expressive power of the desirable gambles model. It also captures the expressive power of sets of desirable gamble sets (with a mixing axiom, but no Archimadean axiom). (shrink)

If $\mathcal{F}$ is a filter on $\omega$, we say that $\mathcal{F}$ is Canjar if the corresponding Mathias forcing does not add a dominating real. We prove that any Borel Canjar filter is $F_{\sigma}$, solving a problem of Hrušák and Minami. We give several examples of Canjar and non-Canjar filters; in particular, we construct a $\mathsf{MAD}$ family such that the corresponding Mathias forcing adds a dominating real. This answers a question of Brendle. Then we prove that in all the (...) “classical” models of $\mathsf{ZFC}$ there are $\mathsf{MAD}$ families whose Mathias forcing does not add a dominating real. We also study ideals generated by branches, and we uncover a close relation between Canjar ideals and the selection principle $S_{\mathrm{fin}}$ on subsets of the Cantor space. (shrink)

We introduce the property “F-linked” of subsets of posets for a given free filter F on the natural numbers, and define the properties “μ-F-linked” and “θ-F-Knaster” for posets in a natural way. We show that θ-F-Knaster posets preserve strong types of unbounded families and of maximal almost disjoint families. Concerning iterations of such posets, we develop a general technique to construct θ-Fr-Knaster posets (where Fr is the Frechet ideal) via matrix iterations of <θ-ultrafilter-linked posets (restricted to some level (...) of the matrix). This is applied to prove consistency results about Cichoń's diagram (without using large cardinals) and to prove the consistency of the fact that, for each Yorioka ideal, the four cardinal invariants associated with it are pairwise different. At the end, we show that three strongly compact cardinals are enough to force that Cichoń's diagram can be separated into 10 different values. (shrink)

We explore the problem of constructing maximal and unbounded filters on computable posets. We obtain both computability results and reverse mathematics results. A maximal filter is one that does not extend to a larger filter. We show that every computable poset has a \Delta^0_2 maximal filter, and there is a computable poset with no \Pi^0_1 or \Sigma^0_1 maximal filter. There is a computable poset on which every maximal filter is Turing (...) complete. We obtain the reverse mathematics result that the principle "every countable poset has a maximal filter" is equivalent to ACA₀ over RCA₀. An unbounded filter is a filter which achieves each of its lower bounds in the poset. We show that every computable poset has a \Sigma^0_1 unbounded filter, and there is a computable poset with no \Pi^0_1 unbounded filter. We show that there is a computable poset on which every unbounded filter is Turing complete, and the principle "every countable poset has an unbounded filter" is equivalent to ACA₀ over RCA₀. We obtain additional reverse mathematics results related to extending arbitrary filters to unbounded filters and forming the upward closures of subsets of computable posets. (shrink)

An adequate moral theory must – or so many philosophers have argued – be compatible with the attitudes and practical requirements of deep friendship. Bernard Williams suggested that the decision procedure required by both deontology and consequentialism inserts a fetishising filter between the natural moral motivation of any normal person to prioritise friends and the decision to act on it. But this injects ‘one thought too many’ into the moral reaction mechanism. It is standardly assumed that virtue ethics is (...) somehow immune to this objection. The present article explores this assumption and finds it wanting in various respects. Virtue ethics filters friendship throughphronesisand thus inserts an extra thought into the mechanism in question. To escape Williams's curse, the only way is to argue that the extra thought required by virtue ethics is not ‘one thought too many’. The article closes with an attempt to show that, contra deontology, the friendship motivation in virtue ethics is derived from the moral virtue, not the intellectual filter, and, contra consequentialism,phronesisdoes not require the maximisation of value. The presumed advantage of virtue ethics must lie in the content of its filter rather than the filter's non-existence. (shrink)

I argue that classical counterfactual semantics in the style of Stalnaker, Lewis, and Kratzer validates an inference pattern that is disconfirmed in natural language. The solution is to alter the algorithm we use to handle inconsistency in premise sets: rather than checking all maximally consistent fragments of a premise sets, as in Krazter’s semantics, we selectively remove some of the premises. The proposed implementation starts from standard premise semantics and involves a new ‘filtering’ operation that achieves just this removal. The (...) resulting semantics is interestingly related to the semantics for counterfactuals emerging from Judea Pearl’s causal models framework in computer science: in particular, filtering is a possible worlds semantics counterpart of Pearl’s interventions. (shrink)

Two countable filters on ω are incompatible if they have no common infinite pseudointersection. Letting α(P f ) denote the minimal size of a maximal uncountable family of pairwise incompatible countable filters on ω, we prove the consistency of t $.

Two countable filters on $\omega$ are incompatible if they have no common infinite pseudointersection. Letting $\alpha(P_f)$ denote the minimal size of a maximal uncountable family of pairwise incompatible countable filters on $\omega$, we prove the consistency of t $< \alpha(P_f)$.

Neutrosophic set is a new mathematical tool for handling problems involving imprecise, indetermi nacy and inconsistent data. Pseudo-BCI algebra is a kind of non-classical logic algebra in close connection with various non-commutative fuzzy logics. Recently, we applied neutrosophic set theory to pseudo-BCI al gebras. In this paper, we study neutrosophic filters in pseudo-BCI algebras. The concepts of neutrosophic regular filter, neutrosophic closed filter and fuzzy regular filter in pseudo-BCI algebras are introduced, and some basic properties are (...) discussed. Moreover, the relationships among neutrosophic regular filter, fuzzy filters and anti-grouped neutrosophic filters are prese nted, and the results are proved: a neutrosophic filter (fuzzy filter) is a neutrosophic regular filter (fuzzy regular filter), if and only if it is both a neutrosophic closed filter (fuzzy closed filter) and an anti-grouped neutrosophic filter (fuzzy anti-grouped filter). (shrink)

With the troubles of core losses and all-state confined to certain limitations which are the innate traits of permanent magnet synchronous motors, this article develops a command filtered adaptive backstepping approach to follow the track of PMSM’s desired rotor position. To begin with, the RBF neural network technique is utilized to get close to the uncharted nonlinear terms which existed in PMSM’s mathematical model. Meanwhile, an advanced adaptive command filter control methodology is constructed to avoid the computing explosion during (...) the process of backstepping design. Furthermore, to make sure that all the state variables are confined into certain ranges, we employed the barrier Lyapunov function at every step of the controllers construction. In addition, an error compensating mechanism is proposed to neutralize filtering errors and only one adaptive law is required. At last, simulation results bear out the superiority of the aforementioned control scheme. (shrink)

continent. 2.2 (2012): 155–158 Michel Serres. Biogea . Trans. Randolph Burks. Minneapolis: Univocal Publishing. 2012. 200 pp. | ISBN 9781937561086 | $22.95 Conveying to potential readers the significance of a book puts me at risk of glad handing. It’s not in my interest to laud the undeserving, especially on the pages of this journal. This is not a sales pitch, but rather an affirmation of a necessary work on very troubled terms: human, earth, nature, and the problematic world we made. (...) It is this world that aspirates the silence (so to speak), and therefore the subject which, along with the development of the “made world” exports the excess augmentation of the cosmically missing, this silence of the natural, et cetera. Had we learned from Locke that lesson of “labor,” to consume what we need… but perhaps we need more than what matters? Serres’ Biogea has several functions on this manner, if it is indeed a book to be consumed. First, readers searching for novelistic entertainment have a place to dwell. Biogea deserves a place in your back pocket; biographical generosity and poetic fluidity should satisfy most textual fetishes. For lay philosophers who want to refresh their acumen, Biogea deserves a place on the book shelf, one already reads a sorely needed postmodern tune-up here. Serres’ style is clearly French; he leaves few cheese crumbs on his words, rather preciseness and breathing in the work give way to a sweeping manner that breaks the narrative line of sight. A circular narrative and anachronistic fragmentation of terms allows an abyssal atmosphere to swell, if only to pump into the book the externality of its broader text. Biogea aspires to a higher standard and the book, at times, is thinking this negentropic problem too. Univocal, the publisher, has crafted a book appropriate for the hands to hold and the translations are an achievement of an otherwise difficult writer to translate. Terms are the conditions of a broader text. It is important to note that Serres’ content is as much a thinking of terminal ports. There is a regard for the transportation technology of the written word. For me, this is the mark of genius, a craftiness that tells of a book device that I may trust. Serres is an accomplished thinker and a necessary voice to check the putative trendiness of anti-postmodernist and market-driven theory of endless cultural liquidation. Offering interventions on subjectivity as an open system we are given a chance to affirm the human, not merely to discard it, but to engage its poetic image emotion, the calibratory silent sense of the analogic world; the terms on which we base our efforts. 1 The human is the center of its own negation, constantly mediating it. Something deeper at stake appears in the work then, and it is quite obvious from the onset. Certainly, a book is an intensification of possible text and those who brought this actual book into existence have captured a rarity in regards to the subject matter and artistic accomplishment. I mentioned terms as conditions, so let us understand Biogea as bio-yea, a yes to bios . An affirmation of living and accepting presence for all of its defiance of images, words, and things temporal. Therefore Serres’ existence and its existants plays parts; out of linearity and still like a porous bone pumping blood it manufactures into the fleshy life it becomes. Starting from a man named silence chaos emerges, or the man “Old Taciturn” takes up a journey anticipating a great flood. In other words, a development akin to the one in Genesis. In dealing with this ancestral occupation, fusing Genesis with contemporary philosophical terms, Serres initiates this anachronistic fragmentation under the forming subjectivity of his own autobiography. This mutation in the open system is precisely one of Serres’ terms. There an abyss is at work, stated, but also measured by heels on the ground—the abyss dispatching earthen tensions, that which plays our tunes, that which we abide by and recognize in volcanoes, rivers, oceans, earthquakes and weaponry in the battles of the world. Set in later stages of the book, such tensions are harnessed through scientific principles in an attempt to unify the terms of natural force if only to terminate the world. Thus the elevation of the earth into the world is clearly set forth. Here already, and few pages in, a resonance is set forth under appellations such as the river Garonne, a subjectivity as much as it is inhuman, the river is the inhuman that makes us human. I get the sense that Serres is taking up a challenge issued by Wallace Stevens; namely, that the great poems of heaven and hell have been written, but that only the poem of the earth has resisted composition. 2 On this level we cannot avoid the killing factor of silence, given that our cognition blocks its pure, radical obliteration. Thus a silence of attunement to the earth is in a novel dialectic of the rithmic and rhythm. A technological world, a triumph of termination is set forth. If a text imposes its will given the reader who authorizes it, it is made to convey or convect a presupposition to a reader or its inhabitant(s). Text is therefore both, in-content, contenting, contentedness, and in reading it, a way to navigate self-destruction (dis-content). Here then would one note that the “inhuman” reveals itself, “an aperiodic rhythm of lovers and beloved…the sea as our friend…but as our enemy…maternal vivifying sea.” The sea is an open book, or vaginal birth canal, where the engagement of text comes forth: “…woman sea, open vulva.” One sees like the sea, but only after it, when the uninhabitable truth of inhabiting it switches the polarity of the sailors soul: “I was seeing like the sea” (9-11). In other words, we are invited to embrace the nonsense of the visible. At this point I am taken to Jean-François Lyotard’s work The Inhuman , specifically the first entry on negentropy that would be congruent with Serres’ thematic. 3 The human being exports, deports, or transplants its relation through text, through the system— and this is its sense or relation to silence, to music. Unaware of Serres’ proximity to this work, the concept of gender interrelation as regards a solar catastrophe runs clear. It would be, on this basis, that Serres references his peers, the other texts that, as mentioned above, are discarded in philosophy today. For students of philosophy what we have here is perhaps a gift, a needed project. If silence and death are at work, there is a political valence to deal with, and here, much like the domain of the text and the dominion of the reader, we confront the world of natural, fluid violence. The anti-postmodernist critique is in part based on a weak idea that the loss of ideology, of a world vision, motivates the “correlationist” project. 4 Serres seems to offer another way to view this when he notes that whereas persons “sometimes kill,” it is clearly “the collective” that “always kills” (17). What is the collective today, if not an organizing function we never see yet acts in its favor in the name of truth? One feels a sense of enigma here, if only to link to what Stevens remarked of communism as a “grubby faith,” providing this applies for capitalism as well, namely any ideology of progress overly interested in absolutes. Here we get the sense that the inhuman, silence, this type of killing, always killing, could not be matched by human-made, political dynamos. Or that if it comes to an equilibrium, a catastrophe is never too far from us to read with our heels. We are left to note that the forces of nature presuppose and permeate political systems, the more these systems obtain force, the more the system takes upon itself the proper name of nature that motivates its dissemination, albeit falsely. This note, that in an age of ecocide and technological captivity (sustainability and transparency) political regimes won’t grow our soul-learning ears any larger than our tongues, stands clear to us. The promise of technological desubjectification is here pushed aside. Regarding politics, Serres illustrates this fact: Where did this corpse come from? Who was it? Who killed it? I don’t know. I won’t try to find out. I refuse to get vengeance for it. And I only see Garonne. For our victims, today, are the rivers, too. Their waters have irrigated my life, enchanted my thought, invigorated my body; I’ve known them to be threatening, untamable, as dangerous as the sea when it rages. Yes, murderous. They decided to control their courses; dams, sometimes senseless, destroying sites and valleys, reduced entire populations to servile displacements; programs for the irrigation of thirsty farmland, often beneficial of course, completed their drying up.(22) Serres enters into his idea concerning the captivity of language from the natural into a world system: For thousands of years, we have been licking things with our tongues, covering and daubing them so as to appropriate things for ourselves. If language boils down to a convention, this convention took place between the speakers without consulting the thing named, become as a result the property of those who covered it in this way with their drawn or voiced productions. Malfeasance analyzes these acts of appropriation. Thus every inert object, every living thing as well, sleeps under the covers of signs, a little in the way that, today, a thousand posters shouting messages and ugly riots of color drown, with their filthy flood, the landscapes, or better, exclude them from perception because the meaning, almost nil, of this false language and these base images forms an irresistible source of attraction to our neurons and eyes. This appropriation covers the world’s beauty with ugliness. (38-39) Technological concealment coming to bear, we begin to get a sense of another commentary on the condition of sensing, driving home the necessity of a text dealing with such subject matter to be what its terms insist. Thus toward new openings: The new opening. As low beneath our feet as you like, the Biogea opens us to another space, high enough for us to be able to acquire a wisdom there, that of redeveloping this same place differently from our fathers, this place that’s still politically cut up by old hatreds, beneath the flood of tears and blood that we call history. Without this soft place, spiritually very old, but newly conceived in this way, without the juridical construction of a common good, opposed to our filthy ownership, I don’t see how our planet, hard, will survive. Hardness that depends on a softness, material belonging that depends on this temporary rented location (51). Serres enters into a summit on the content and the structure of his work. Archimedes is brought in with the concept of three volcanoes. Meaning fire, but as well earth, water, air. For it was Archimedes’ war machines that sought to lift the earth, thus bringing in the question of principles of science: “can a principle be invented while controlling its consequences?” (66-7). May the earth be put in a sentence, terminated by terminology, appellations, gone wild? By means of these element-dominating laws, this old physicist began to tear nature away from the ancient myths; by a strange return, today we’re plunging our successes back into the anxieties and terrors from which that ancient physics was born. Yes, our new history of science and technology is plunging, today, as though in a loop, into the fundamental human myths from which Empedocles’ first laws came. A major progression and a regression on the nether side of the origins. Consequently, the contemporary time requires that we try to return to that unity in which the principles of hate and love are at the same time human, living, inert and global. We will never attain a deontology of our knowledge and actions without thinking the subjective, the objective, the collective, and the cognitive all together simultaneously. Here, hate and love are the result of these four components.(71) Working then on the concept of fire-starting mirrors to the atomic annihilation of the Second War, Serres works into the subjectivity in question on the matter of rhythm—say rithmic— precisely at that point: Knowledge is changing today. The all-political is dying; the monarchy of the sciences said to be hard is coming to a close. The science of the things of the world will have to communicate just as much as the things of the world do, which do it much better than humans do, who don’t always want to do it. Let’s celebrate two changes this morning. The first one strikes a new blow to our narcissism. No, knowledge and the world don’t resemble our analytical enjoyments of refined cutting up, of endless debates and of exclusions full of hate. They, on the contrary, form a bloc and a sum, alliance and alloys. Uniting the fields of knowledge among themselves the way the things are connected among themselves, the second newness puts into place sets united by interlacing, webs and simplexes that combine with the things of the world, themselves combined, the combined knowledge that understands them.(130-1) Biogea closes on its opening flood thematic, approaching the initial telos of Genesis. Here the trees are brought into a position with atmosphere, the opaque abyssal reservoir, the tomb of the sun, sea in the polarity of the earthen heaven and hell. The poem of the earth then is silent but deadly, indeed, as funny as that phrase is, mainly a tomb gas. The meaning of the living and the non-meaning of things converge in the muteness of the world; this meaning and non-meaning plunge there and come out, the ultimate eddy. Mundus patet: through a fissure, through an opening, a fault, a cleft come noises, calls as small as these apertures. I’m listening, attentive, I’m translating, I’m advancing in the scaled-down meaning and science. Mundus patet: should the world open greatly, it will launch me into its silence. The totality remains silent. Knowledge expanded in elation. White origin of meaning, fountain of joy. (198) Final Remarks One test of a review is the long term trajectory the referee thinks the book will have. I see Serres’ text lending greatly into the vision of Biogea . In fact, in the vision of the novel inquiries of Stephen Jay Gould’s work there is something to be thought on the level of the individual and the species; namely, that humanity and its uniqueness is in its deferral, its thinking and naming, a thinking surrounded by silence that filters into everything, that pulls us through the world, the kinetic pulse we recognize, and all of that we cleave away in the base philosophical maxim of difference itself. Unique individuals are spatial creatures: we dwell, and we ought to get good at it. Yet this is an imaginative space that, if you are crazy enough to believe it, de-term-ine the conditions of its own terms. That is why we are not merely creating spaces on the acceleration of time, or so this ignoramus thinks, to accidentally transcend. Imagination already has this insatiable silence that we drink up and fail to manifest. Space is timeless. The imagination itself, shared by humans for themselves, their objects, and the species as a whole, is a non-defined space of relation; a whole human trajectory as part of nature, and part of worlds that are the other side of thinking nature, the consequence of it, at least our attempt to do so. Our survival is based on our deliberation, our caution, our natural deconstructive sense toward this silence that is already part of the song, sung, singing of this century without end. Good books will let us inhabit this space and recognize a form of life. Serres’ text moves toward dwelling, as noted, in masterful and accessible ways. The pitched battles are the falling replays of anemic and dead politics. As soon as we realize there is humanity, we may be able to enjoy the end of it, our inhuman capability of listening to silence. NOTES 1. See Michel Serres. The Parasite . Minneapolis: University of Minnesota Press. 2007. 2. Wallace Stevens, “Imagination as Value” [ca. 1945], in Collected Poetry and Prose . New York: The Library of America. 1997. 724-39. 3. Jean-François Lyotard. The Inhuman: Reflections on Time . Trans. Geoffrey Bennington & Rachel Bowlby. Stanford, CA: Stanford University Press. 1992. 4. See the introduction: Quentin Melliassoux. After Finitude: An Essay on the Necessity of Contingency . Trans. Ray Brassier. New York: Continuum. 2008. EDITOR'S NOTE: This review was updated on August 8, 2012. Substantial edits include block quotes from the book under review as well as the inclusion of comments from the author. (shrink)

Ethical considerations, especially those religiously driven, play a significant role in shaping business conduct and priorities. Profit levels and earnings constitute an integral part of business considerations and are relevant and closely linked to prevailing ethics. In this paper, Islamic prescriptions on profit maximization are introduced. Islamic business ethics are outlined as well. It is suggested that while Islamic teaching treats profits as reward for engaging in vital activities necessary for serving societal interests, profit maximization is not sanctioned and therefore (...) should not be the goal of ethically guided business ventures. (shrink)

Generalizations of partial meet contraction are introduced that start out from the observation that only some of the logically closed subsets of the original belief set are at all viable as contraction outcomes. Belief contraction should proceed by selection among these viable options. Several contraction operators that are based on such selection mechanisms are introduced and then axiomatically characterized. These constructions are more general than the belief base approach. It is shown that partial meet contraction is exactly characterized by (...) adding to one of these constructions the condition that all logically closed subsets of the belief set can be obtained as the outcome of a single (multiple) contraction. Examples are provided showing the counter-intuitive consequences of that condition, thus confirming the credibility of the proposed generalization of the AGM framework. (shrink)

In this paper, the notion of the radical of a filter in BL-algebras is defined and several characterizations of the radical of a filter are given. Also we prove that A/F is an MV-algebra if and only if Ds ⊆ F. After that we define the notion of semi maximal filter in BL-algebras and we state and prove some theorems which determine the relationship between this notion and the other types of filters of a BL-algebra. Moreover, (...) we prove that A/F is a semi simple BL-algebra if and only if F is a semi maximal filter of A. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (shrink)

This report brings out a simple observation on the close connection of lters with algebraic closure systems. In [1], Orrin Frink gave a general denition of ideals in ordered sets. Here, we use the dual notion of lter and apply it to preordered sets. When referring to nite sets fc1; : : : ; ckg we often omit the brackets. The symbol ; denotes the empty set and, X f Y means that X is a nite subset of Y.

For each integer n ≥ 2, MVn denotes the variety of MV-algebras generated by the MV-chain with n elements. Algebras in MVn are represented as continuous functions from a Boolean space into a n-element chain equipped with the discrete topology. Using these representations, maximal subalgebras of algebras in MVn are characterized, and it is shown that proper subalgebras are intersection of maximal subalgebras. When A ∈ MV3, the mentioned characterization of maximal subalgebras of A can be given (...) in terms of prime filters of the underlying lattice of A, in the form that was conjectured by A. Monteiro. (shrink)

For each integer n ≥ 2, MVn denotes the variety of MV-algebras generated by the MV-chain with n elements. Algebras in MVn are represented as continuous functions from a Boolean space into a n-element chain equipped with the discrete topology. Using these representations, maximal subalgebras of algebras in MVn are characterized, and it is shown that proper subalgebras are intersection of maximal subalgebras. When A ∈ MV3, the mentioned characterization of maximal subalgebras of A can be given (...) in terms of prime filters of the underlying lattice of A, in the form that was conjectured by A. Monteiro. (shrink)

The motivation for this paper is the following: In [4] I showed that it is inconsistent with ZFC that the Maximality Principle for directed closed forcings holds at unboundedly many regular cardinals κ (even only allowing κ itself as a parameter in the Maximality Principle for < κ -closed forcings each time). So the question is whether it is consistent to have this principle at unboundedly many regular cardinals or at every regular cardinal below some large cardinal κ (...) (instead of ∞), and if so. how strong it is. It turns out that it is consistent in many cases, but the consistency strength is quite high. (shrink)

There is a systemic condition inherent in contemporary markets that compel managers not to pursue more morally preferable initiatives if those initiatives will require actions that conflict with profit maximization. Normative arguments for implementing morally preferable practices within the existing system fail because they are insufficient to counter-act the systemic conditions affecting decision-making that is focused on maximizing profit as the primary operational value. To overcome this constraint we must elevate a more normatively preferable value, ‚ideal environmental sustainability,’ to the (...) level of being the primary filtering value through which other competing values are evaluated, prioritized, and implemented. In order for this to occur in practice, a change must be made relative to the laws, rules, and regulations that define and guide the market. This can be done by suitably defining the epistemic constraint of impartiality utilizing Rawls’ notion of a ‚veil of ignorance’ as a heuristic device. (shrink)

It is shown that by realizing the isomorphism features of the frequency and geometric interpretations of probability, Reichenbach comes very close to the idea of identifying mathematical probability theory with measure theory in his 1949 work on foundations of probability. Some general features of Reichenbach’s axiomatization of probability theory are pointed out as likely obstacles that prevented him making this conceptual move. The role of isomorphisms of Kolmogorovian probability measure spaces is specified in what we call the “Maxim of Probabilism”, (...) which states that a necessary condition for a concept to be probabilistic is its invariance with respect to measure-theoretic isomorphisms. The functioning of the Maxim of Probabilism is illustrated by the example of conditioning via conditional expectations. (shrink)

This paper gives a formalization of general topology in second-order arithmetic using countably based MF spaces. This formalization is used to study the reverse mathematics of general topology. For each poset P we let MF denote the set of maximal filters on P endowed with the topology generated by {Np | p ∈ P}, where Np = {F ∈ MF | p ∈ F}. We define a countably based MF space to be a space of the form MF for (...) some countable poset P. The class of countably based MF spaces includes all complete separable metric spaces as well as many nonmetrizable spaces. The following reverse mathematics results are obtained. The proposition that every nonempty Gδ subset of a countably based MF space is homeomorphic to a countably based MF space is equivalent to [Formula: see text] over ACA0. The proposition that every uncountable closed subset of a countably based MF space contains a perfect set is equivalent over [Formula: see text] to the proposition that [Formula: see text] is countable for all A ⊆ ℕ. The proposition that every regular countably based MF space is homeomorphic to a complete separable metric space is equivalent to [Formula: see text] over [Formula: see text]. (shrink)

ABSTRACT:Many scholars and managers endorse the idea that the primary purpose of the firm is to make money for its owners. This shareholder wealth maximization objective is justified on the grounds that it maximizes social welfare. In this article, the first of a two-part set, we argue that, although this shareholder primacy model may have been appropriate in an earlier era, it no longer is, given our current state of economic and social affairs. To make our case, we employ a (...) utilitarian moral standard and examine the apparent logical sequence behind the link between shareholder wealth maximization and social welfare. Upon close empirical and conceptual scrutiny, we find that utilitarian criteria do not support the shareholder model; that is, shareholder wealth maximization is only weakly linked to social welfare maximization. In view of the dubious validity of this sequential argument, we outline some of the features of a superior corporate objective—a variant of normative stakeholder theory. In the second article, we will advance and defend our preferred alternative and then discuss some institutional arrangements under which it could be implemented. (shrink)

For each integer $n\geq 2,{\Bbb MV}_{n}$ denotes the variety of MV-algebras generated by the MV-chain with n elements. Algebras in ${\Bbb MV}_{n}$ are represented as continuous functions from a Boolean space into a n-element chain equipped with the discrete topology. Using these representations, maximal subalgebras of algebras in ${\Bbb MV}_{n}$ are characterized, and it is shown that proper subalgebras are intersection of maximal subalgebras. When $A\in {\Bbb MV}_{3}$, the mentioned characterization of maximal subalgebras of A can be (...) given in terms of prime filters of the underlying lattice of A, in the form that was conjectured by A. Monteiro. (shrink)

Epistemic closure refers to the assumption that humans are able to recognize what entails or contradicts what they believe and know, or more accurately, that humans’ epistemic states are closed under logical inferences. Epistemic closure is part of a larger theory of mind ability, which is arguably crucial for downstream NLU tasks, such as inference, QA and conversation. In this project, we introduce a new automatically constructed natural language inference dataset that tests inferences related to epistemic closure. We test (...) and further fine tune the model RoBERTa-large-mnli on the new dataset, with limited positive results. (shrink)

In response to the growing criticisms to shareholder primacy, Oliver Hart, a Nobel Economics Prize recipient, and Luigi Zingales, a very well-known finance professor, have offered a revision to Milton Friedman’s dominant account. Seeking to incorporate social and moral concerns into the objective function of the firm, they have proposed that managers should maximize shareholder welfare instead of shareholder value. Their account has been highly influential and reflects many of the substantive and methodological assumptions of corporate governance scholars within the (...) law and economics literature. In this paper, we engage closely with their account from a normative perspective, unearthing and criticizing the implications of many of these assumptions. In doing so, we also formulate a set of principles necessary to ensure the ethical legitimacy of any proposal that puts shareholders at the center of the firm’s objective function. (shrink)

This paper is one of several contributions in a series, illustrating the application of a specific deductive methodology to explain diversity of form. The methodology facilitates the explanation of feeding morphologies in various ducks as a transformation of the mallard's feeding design maximized for specific proportions of performance that are contributed by pecking and filter feeding mechanisms.The earlier described anatomy and formal analyses of the three mechanisms in the mallard served as the initial conditions used in simulation models. Four (...) elements of the feeding system were chosen that play a major role in all three mechanisms. For each element, the main parameter was selected: storage capacity of the rostral mouth cavity, transport capacity of the rostral mouth tube, storage capacity of the caudal mouth cavity and transport capacity of the caudal mouth tube. The boundary conditions for the simulation were determined from internal organismic constraints. The total food uptake of the mallard was regarded as the function to be maximized. This object function is the summation of the food uptake by one second of pecking and one second of filter feeding. The drinking mechanism was shown not to interfere, since that mechanism operates sufficiently whenever the pumping mechanism works properly. (shrink)

This paper has two parts. The first is concerned with a variant of a family of games introduced by Holy and Schlicht, that we call Welch games. Player II having a winning strategy in the Welch game of length [Formula: see text] on [Formula: see text] is equivalent to weak compactness. Winning the game of length [Formula: see text] is equivalent to [Formula: see text] being measurable. We show that for games of intermediate length [Formula: see text], II winning implies (...) the existence of precipitous ideals with [Formula: see text]-closed, [Formula: see text]-dense trees. The second part shows the first is not vacuous. For each [Formula: see text] between [Formula: see text] and [Formula: see text], it gives a model where II wins the games of length [Formula: see text], but not [Formula: see text]. The technique also gives models where for all [Formula: see text] there are [Formula: see text]-complete, normal, [Formula: see text]-distributive ideals having dense sets that are [Formula: see text]-closed, but not [Formula: see text]-closed. (shrink)

In this article, we describe and attempt to solve a puzzle arising from the interpretation of modified numerals like less than five and between two and five. The puzzle is this: such modified numerals seem to mean different things depending on whether they combine with distributive or non-distributive predicates. When they combine with distributive predicates, they intuitively impose a kind of upper bound, whereas when they combine with non-distributive predicates, they do not. We propose and explore in detail four solutions (...) to this puzzle, each involving some notion of maximality, but differing in the type of maximality involved and in the source of maximality. While the full range of data we consider do not conclusively favor one theory over the other three, we do argue that overall the evidence goes against the view that modified numerals lexically encode a ‘standard’ maximality operator, and suggests the need for a pragmatic blocking mechanism that filters out readings of sentences that are generated by the grammar but intuitively unavailable. (shrink)

Two intuitions lie at the heart of our conception of free will. One intuition locates free will in our ability to deliberate effectively and control our actions accordingly: the ‘Deliberation and Control’ (DC) condition. The other intuition is that free will requires the existence of alternative possibilities for choice: the AP condition. These intuitions seem to conflict when, for instance, we deliberate well to decide what to do, and we do not want it to be possible to act in some (...) other way. I suggest that intuitions about the AP condition arise when we face ‘close calls,’ situations in which, after deliberating, we still do not know what we really want to do. Indeed, several incompatibilists suggest such close calls are necessary for free will. I challenge this suggestion by describing a ‘confident agent’ who, after deliberating, always feels confident about what to do (and can then control her actions accordingly). Because she maximally satisfies the DC condition, she does not face close calls, and the intuition that the AP condition is essential for free will does not seem to apply to her. I conclude that intuitions about the importance of the AP condition rest on our experiences of close calls and arise precisely to the extent that our deliberations fail to arrive at a clear decision. I then raise and respond to several objections to this thought experiment and its relevance to the free will debate. (shrink)

In this paper I argue that there would be no obligatory maxims if the only standards for assessing maxims were Kant’s universalizability tests. The paper is divided into five sections. In the first, I clarify my thesis: I define my terms and disambiguate my thesis from other related theses for which one might argue. In the second, I confront the view that says that if a maxim passes the universalizability tests, then there is a positive duty to adopt that maxim; (...) I also confront a close relative of this view. In the third, I confront the view that says that if a maxim does not pass the universalizability tests, then there is a positive duty to adopt the contradictory of that maxim. In the fourth, I confront two variations of the view that says that if a maxim does not pass the universalizability tests and an agent is deliberating about the action in the maxim, then the agent has a positive duty to adopt the contrary of that maxim. In the fifth, I confront the view that says that if an agent has adopted a maxim of ends, then the agent has a positive duty to universalize that end. I then wrap up the paper with some concluding remarks. (shrink)

Structured argumentation formalisms, such as ASPIC +, offer a formal model of defeasible reasoning. Usually such formalisms are highly parametrized and modular in order to provide a unifying framework in which different forms of reasoning can be expressed. This generality comes at the price that, in their most general form, formalisms such as ASPIC + do not satisfy important rationality postulates, such as non-interference. Similarly, links to other forms of knowledge representation, such as reasoning with maximal consistent sets of (...) rules, are insufficiently studied for ASPIC + although such links have been established for other, less complex forms of structured argumentation where defeasible rules are absent. Clearly, for a formal model of defeasible reasoning it is important to understand for which range of parameters the formalism displays a behavior that adheres to common standards of consistency, logical closure and logical relevance and can be adequately described in terms of other well-known forms of knowledge representation. In this paper we answer this question positively for a fragment of ASPIC + without the attack form undercut by showing that it satisfies all standard rationality postulates of structured argumentation under stable and preferred semantics and is adequate for reasoning with maximal consistent sets of defeasible rules. The study is general in that we do not impose any other requirements on the strict rules than to be contrapositable and propositional and in that we also consider priorities among defeasible rules, as long as they are ordered by a total preorder and lifted by weakest link. In this way we generalize previous similar results for other structured argumentation frameworks and so shed further light on the close relations between assumption-based argumentation and ASPIC +. (shrink)

Inspired by locale theory, we propose “pointfree convex geometry”. We introduce the notion of convexity algebra as a pointfree convexity space. There are two notions of a point for convexity algebra: one is a chain-prime meet-complete filter and the other is a maximal meet-complete filter. In this paper we show the following: the former notion of a point induces a dual equivalence between the category of “spatial” convexity algebras and the category of “sober” convexity spaces as well (...) as a dual adjunction between the category of convexity algebras and the category of convexity spaces; the latter notion of point induces a dual equivalence between the category of “m-spatial” convexity algebras and the category of “m-sober” convexity spaces. We finally argue that the former notion of a point is more useful than the latter one from a category theoretic point of view and that the former notion of a point actually represents a polytope and the latter notion of a point properly represents a point. We also remark on the close relationships between pointfree convex geometry and domain theory. (shrink)

This research was partially supported by Grant-in-Aid for Scientific Research (No. 06640178 and No. 06640336), Ministry of Education, Science and Culture of Japan Mathematics Subject Classification: 03E05 --> Abstract. Following Carr's study on diagonal operations and normal filters on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\cal P}_{\kappa}\lambda$\end{document} in [2], several weakenings of normality have been investigated. One of them is to consider normal filters without \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\kappa$\end{document}-completeness, for (...) example, see DiPrisco-Uzcategui [3]. The other is weakening normality itself while keeping \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\kappa$\end{document}-completeness such as in Mignone [10] and Shioya [11]. We take the second one so that all filters are assumed to be \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\kappa$\end{document}-complete. In Sect. 1 a hierarchy of filters on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\cal P}_{\kappa}\lambda$\end{document} is presented which corresponds to the length of diagonal intersections under which the filters are closed. It turns out that many ranks exist between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $FSF_{\kappa\lambda}$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $CF_{\kappa\lambda}$\end{document}. We consider seminormal ideals in Sect. 2 and determine the minimal seminormal ideal extending Johnson's result in [6]. Its precise descripti on changes according to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $cf(\lambda )$\end{document} although we can write it in a single form as well. We also prove that a nonnormal seminormal ideal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $I\supset NS_{\kappa\lambda}$\end{document} exists if and only if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\lambda$\end{document} is regular. (shrink)