We study concepts of decidability for subsets of Euclidean spaces ℝk within the framework of approximate computability . A new notion of approximate decidability is proposed and discussed in some detail. It is an effective variant of F. Hausdorff's concept of resolvable sets, and it modifies and generalizes notions of recursivity known from computable analysis, formerly used for open or closed sets only, to more general types of sets. Approximate decidability of sets can equivalently (...) be expressed by computability of the characteristic functions by means of appropriately working oracle Turing machines. The notion fulfills some natural requirements and is hereditary under canonical embeddings of sets into spaces of higher dimensions. However, it is not closed under binary union or intersection of sets. We also show how the framework of resolvability and approximate decidability can be applied to investigate concepts of reducibility for subsets of Euclidean spaces. (shrink)

It is shown that the classes of discrete parts, A ∩ ℕk, of approximately resp. weakly decidable subsets of Euclidean spaces, A ⊆ ℝk, coincide and are equal to the class of ω-r. e. sets which is well-known as the first transfinite level in Ershov's hierarchy exhausting Δ02.

This is an abstract of the paper accepted for publication in \Acta Uni- versitatis Wratislaviensis", series \Prace Filozoczne { Logika". The paper was presented at the 25th Conference for the History of Logic, Krakow, October 5-7, 1979.

In this paper we give an axiom system of a logic which we call an approximation logic (AL), whose Lindenbaum-Tarski algebra is a strong Bunge algebra (or simply s-Bunge algebra), and show thatFor every s-Bunge algebra , a quotient algebra by a maximal filter is isomorphic to the simplest nontrivial s-Bunge algebra ;The Lindenbaum algebra of AL is an s-Bunge algebra;AL is complete;AL is decidable.

The ability of ordinary differential equations (ODEs) to simulate discrete machines with a universal computing power indicates a new source of difficulties for event detection problems. Indeed, nearly any kind of event detection is algorithmi- cally undecidable for infinite or finite half-open time intervals, and explicitly given “well-behaved” ODEs (see [18]). Practical event detection, however, usually takes place on finite closed time intervals. In this paper the undecidability of general event detection is extended to such intervals. On the other hand, (...) on finite closed time in- tervals event detection in a certain approximate sense is quite generally decidable, which partly saves the case for practicable event detection. The capability of simulat- ing universal Turing machines is still there, and is used to give complexity lower bounds in terms of accuracy of event detection. The ODEs used here are of course quite complicated, but not artificial, in that even from the point of view of practical event detection it would appear difficult to find criteria to exclude them. (shrink)

This paper develops an explicit, pragmatic solution to the problem of deciding when an explanans which only approximately "covers" a desired event-explanandum E is acceptable as an adequate explanation. It shows in detail how comparisons made by the explanation's audience with the numerical value in E are what determine how closely E must be approximated for success. With the aid of several physics examples, it spells out the principles that govern these explanandum-comparisons, the conditions under which those principles hold, and (...) the audience traits that influence which comparisons they take seriously. (shrink)

The signature of the formal language of mereology contains only one binary predicate P which stands for the relation “being a part of”. Traditionally, P must be a partial ordering, that is, ${\forall{x}Pxx, \forall{x}\forall{y}((Pxy\land Pyx)\to x=y)}$ and ${\forall{x}\forall{y}\forall{z}((Pxy\land Pyz)\to Pxz))}$ are three basic mereological axioms. The best-known mereological theory is “general extensional mereology”, which is axiomatized by the three basic axioms plus the following axiom and axiom schema: (Strong Supplementation) ${\forall{x}\forall{y}(\neg Pyx\to \exists z(Pzy\land \neg Ozx))}$ , where Oxy means ${\exists (...) z(Pzx\land Pzy)}$ , and (Fusion) ${\exists x\alpha \to \exists z\forall y(Oyz\leftrightarrow \exists x(\alpha \land Oyx))}$ , for any formula α where z and y do not occur free. In this paper, I will show that general extensional mereology is decidable, and will also point out that the decidability of the first-order approximation of the theory of complete Boolean algebras can be shown in the same way. (shrink)

There is no uniquely standard concept of an effectively decidable set of real numbers or real n-tuples. Here we consider three notions: decidability up to measure zero [M.W. Parker, Undecidability in Rn: Riddled basins, the KAM tori, and the stability of the solar system, Phil. Sci. 70(2) (2003) 359–382], which we abbreviate d.m.z.; recursive approximability [or r.a.; K.-I. Ko, Complexity Theory of Real Functions, Birkhäuser, Boston, 1991]; and decidability ignoring boundaries [d.i.b.; W.C. Myrvold, The decision problem for entanglement, (...) in: R.S. Cohen et al. (Eds.), Potentiality, Entanglement, and Passion-at-a-Distance: Quantum Mechanical Studies fo Abner Shimony, Vol. 2, Kluwer Academic Publishers, Great Britain, 1997, pp. 177–190]. Unlike some others in the literature, these notions apply not only to certain nice sets, but to general sets in Rn and other appropriate spaces. We consider some motivations for these concepts and the logical relations between them. It has been argued that d.m.z. is especially appropriate for physical applications, and on Rn with the standard measure, it is strictly stronger than r.a. [M.W. Parker, Undecidability in Rn: Riddled basins, the KAM tori, and the stability of the solar system, Phil. Sci. 70(2) (2003) 359–382]. Here we show that this is the only implication that holds among our three decidabilities in that setting. Under arbitrary measures, even this implication fails. Yet for intervals of non-zero length, and more generally, convex sets of non-zero measure, the three concepts are equivalent. (shrink)

In this engaging and provocative book, Sher explores the normative moral and social problems that arise from living in a decidedly non-ideal world_a world that contains immorality, evil, and injustice, and in which resources are often inadequate. Sher confronts difficult issues surrounding preferential treatment and equal opportunity, compensatory justice and punishment, the allocation of goods, and moral compromise.

Propositional logics in general, considered as a set of sentences, can be undecidable even if they have “nice” representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already intuitionistic logic is PSPACE-complete). On the other hand, finite-valued logics are computationally relatively simple—at worst NP. Moreover, finite-valued semantics are simple, and general methods for theorem proving exist. This raises the question to what extent and under what circumstances propositional logics represented in various ways can (...) be approximated by finite-valued logics. It is shown that the minimal m-valued logic for which a given calculus is strongly sound can be calculated. It is also investigated under which conditions propositional logics can be characterized as the intersection of (effectively given) sequences of finite-valued logics. (shrink)

The theory of rough sets starts with the notion of an approximation space , which is a pair ( U , R ), U being the domain of discourse, and R an equivalence relation on U . R is taken to represent the knowledge base of an agent, and the induced partition reflects a granularity of U that is the result of a lack of complete information about the objects in U . The focus then is on approximations of concepts (...) on the domain, in the context of the granularity. The present article studies the theory in the situation where information is obtained from different sources. The notion of approximation space is extended to define a multiple-source approximation system with distributed knowledge base , which is a tuple , where N is a set of sources and P ranges over all finite subsets of N . Each R P is an equivalence relation on U satisfying some additional conditions, representing the knowledge base of the group P of sources. Thus each finite group of sources and hence individual source perceives the same domain differently (depending on what information the group/individual source has about the domain), and the same concept may then have approximations that differ with the groups. In order to express the notions and properties related with rough set theory in this multiple-source situation, a quantified modal logic LMSAS D is proposed. In LMSAS D , quantification ranges over modalities, making it different from modal predicate logic and modal logic with propositional quantifiers. Some fragments of LMSAS D are discussed and it is shown that the modal system KTB is embedded in LMSAS D . The epistemic logic is also embedded in LMSAS D , and cannot replace the latter to serve our purpose. The relationship of LMSAS D with first and second-order logics is presented. Issues of expressibility, axiomatization and decidability are addressed. (shrink)

I was invited to contribute this short piece to a book published in Russia, consisting of brief statements on the nature of morality written by approximately 90 scholars. Each essay is published in both English and Russian. My essay offers my considered answer to the question posed in the title, though in the end all contributions were published without titles.

The topological arithmetical hierarchy is the effective version of the Borel hierarchy. Its class Δta 2 is just large enough to include several types of pointsets in Euclidean spaces ℝ k which are fundamental in computable analysis. As a crossbreed of Hausdorff's difference hierarchy in the Borel class ΔB 2 and Ershov's hierarchy in the class Δ0 2 of the arithmetical hierarchy, the Hausdorff-Ershov hierarchy introduced in this paper gives a powerful classification within Δta 2. This is based on suitable (...) characterizations of the sets from Δta 2 which are obtained in a close analogy to those of the ΔB 2 sets as well as those of the Δ0 2 sets. A helpful tool in dealing with resolvable sets is contributed by the technique of depth analysis. On this basis, the hierarchy properties, in particular the strict inclusions between classes of different levels, can be shown by direct constructions of witness sets. The Hausdorff-Ershov hierarchy runs properly over all constructive ordinals, in contrast to Ershov's hierarchy whose denotation-independent version collapses at level ω 2. Also, some new characterizations of concepts of decidability for pointsets in Euclidean spaces are presented. (shrink)

In order to modelize the reasoning of an intelligent agent represented by a poset T, H. Rasiowa introduced logic systems called “Approximation Logics”. In these systems a set of constants constitutes a fundamental tool. In this papers, we consider logic systems called L′T without this kind of constants but limited to the case where T is a finite poset. We prove a weak deduction theorem. We introduce also an algebraic semantics using Hey ting algebra with operators. To prove the completeness (...) theorem of the L′T system with respect to the algebraic semantics, we use the method of H. Rasiowa and R. Sikorski for first order logic. In the propositional case, a corollary allows us to assert that it is decidable to know “if a propositional formula is valid”. We study also certain relations between the L′T logic and the intuitionistic and classical logics. (shrink)

We present some characterizations of the members of Δta2, that class of the topological arithmetical hierarchy which is just large enough to include several fundamental types of sets of points in Euclidean spaces ℝk. The limit characterization serves as a basic tool in further investigations. The characterization by effective difference chains of effectively exhaustible sets yields only a hierarchy within a subfield of Δta2. Effective difference chains of transfinite (but constructive) order types, consisting of complements of effectively exhaustible sets, as (...) well as another closely related concept, yield a rich hierarchy within the whole class Δta2. The presentation always first reports analogies between Hausdorff's difference hierarchy within the Borel class ΔB2 and Ershov's hierarchy within the class Δ02 of the arithmetical hierarchy; after that the counterparts for Δta2 are developed. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

In the common man reasoning the presence of vague predicates is pervasive and under the name “fuzzy logic in narrow sense” or “formal fuzzy logic” there are a series of attempts to formalize such a kind of phenomenon. This paper is devoted to discussing the limits of these attempts both from a technical point of view and with respect the original and principal task: to define a mathematical model of the vagueness. For example, one argues that, since vagueness is necessarily (...) connected with the intuition of the continuum, we have to look at the order-based topology of the interval [0,1] and not at the discrete topology of the set {0,1}. In accordance, in switching from classical logic to a logic for the vague predicates, we cannot avoid the use of the basic notions of real analysis as, for example, the ones of “approximation“, “convergence“, “continuity“. In accordance, instead of defining the compactness of the logical consequence operator and of the deduction operator in terms of finiteness, we have to define it in terms of continuity. Also, the effectiveness of the deduction apparatus has to be defined by using the tools of constructive real analysis and not the one of recursive arithmetic. This means that decidability and semi-decidability have to be defined by involving effective limit processes and not by finite steps stopping processes. (shrink)

Most recent studies of dual use research have focused on the life sciences, although some researchers have suggested that dual use research occurs across many disciplines. This research is an initial investigation into the prevalence of dual use research in other scientific disciplines by surveying senior editors of scientific journals, drawn from Journal Citation Reports. The survey was emailed to 7,500 journal editors with a response rate of 10.1 %. Approximately 4.8 % of life science editors reported they had to (...) consider whether to publish dual use research and 38.9 % said they decided to not publish the research in question. In disciplines other than the life sciences, 7.2 % of editors from other science disciplines reported that they had to consider whether to publish dual use research, and 48.4 % declined to publish it. The survey investigated relationships between dual use and the journal’s source of funding and place of publication, but no relationships were found. Further research is needed to better understand the occurrence of dual use research in other science disciplines. (shrink)

Delaware’s famous corporate law and its highly respected specialized Court of Chancery attract entrepreneurs from all over the world, who choose the small state as their locus of incorporation and litigation forum, and global investors who choose Delaware law as the law governing their corporate investments and mergers and acquisitions. Other jurisdictions vie with Delaware in regard to these choices. This interjurisdictional competition makes Delaware a significant global norm exporter in the field of corporate law because jurisdictions emulate some of (...) its corporate law. Israel leads the global pack. For two decades, it has been approximating its corporate law to Delaware’s and emulating its principal institutions, including by establishing a specialized Chancery-like court whose judges seek guidance in Delaware’s case law in deciding open corporate law questions. This Article employs qualitative methods—interviews with M&A practitioners from the United States, the United Kingdom, and Israel. We use the interviews to assess whether the project of approximating Delaware corporate law has succeeded in shifting incorporation decision preferences away from Delaware to Israel and watering down the natural reluctance of global investors to accepting an unfamiliar corporate law when engaging in cross-border corporate M&A transactions involving an Israeli party. Our findings indicate that the approximation project has countervailing effects, opinions about its success being polarized and nuanced; that approximation increases the familiarity of domestic practitioners with the foreign law being emulated, making the emulated law easier to implement; and that approximation creates more room for other aspects of interjurisdictional competition to influence private choices. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Kennedy Institute of Ethics Journal 14.3 (2004) vii-viii [Access article in PDF] John C. Fletcher 1931-2004 John Fletcher was one of the pioneers in the still-young field of bioethics. In this short tribute, I can only hope to highlight a few of the many contributions he made to the field.For many of us, our first introduction to John occurred in October 1971. At an international symposium sponsored by the (...) Kennedy Foundation, the film "Who Should Survive?" depicted the dramatic case of an infant with Down syndrome and an intestinal blockage. The parents of the infant refused surgery to relieve the obstruction, and the healthcare providers for the infant decided not to pursue a court order permitting the surgery. During a period of approximately two weeks the infant was allowed to die.In the second part of "Who Should Survive?" John was one of several panelists invited to discuss the decisions made in this case. After acknowledging how troubling the infant's death was to him, John nonetheless sought to be empathic with the parents. He pointed out that in the re-enactment of the case the faces of the parents were never seen, and he worried that the film did not permit the parents to discuss the reasons for the choice they had made. John realized that his position would not be shared by most other panelists. Yet he had the courage to take an unpopular stand and to challenge other panelists—and the audience—not to reach premature closure on complex ethical dilemmas.Already in 1967, John had begun contributing to the literature of bioethics. His essay "Human Experimentation: Ethics in the Consent Situation," appeared in Law and Contemporary Problems. At the time, John was deeply immersed in studying the ethical dimensions of research with human subjects at the NIH Clinical Center. Paul Ramsey cited John's work with appreciation in his 1970 book, The Patient as Person. By the time he completed his dissertation at Union Theological Seminary in 1969, John was arguably one of the best trained bioethicists in the world—before there was a field of bioethics.After serving as chaplain, teaching at Virginia Theological Seminary, and founding and leading a seminary without walls in Washington, DC, John became the chief of the ethics program at the NIH Clinical Center in 1977. There he had the unenviable task of providing a second review for all clinical protocols emerging from the intramural programs of the NIH institutes. John discovered that in some cases the institutional review boards of the institutes had overlooked important ethical questions. This role also [End Page vii] required courage. At times John found it necessary to challenge senior NIH researchers, even institute directors, and to request protocol revisions that in his view were required for the protection of human subjects.In 1980, after Martin Cline had performed an unauthorized gene transfer experiment involving thalassemia patients, John joined with physician W. French Anderson to write an essay entitled "Gene Therapy in Human Beings: When Is It Ethical to Begin?" [New England Journal of Medicine 303: 1293-97]. Not only did this essay help to defuse a potentially explosive problem for NIH, which had funded Cline's research. It also provided a set of guidelines for the conduct of human gene transfer research that is of continuing relevance today.At times John disagreed with federal policies on research, for example, conservative policies on human embryo research. He also chafed at the idea of subjecting his publications to prior NIH review, both for accuracy and for political correctness. Thus, he welcomed the opportunity to move to the University of Virginia in 1987. There his academic career flowered, and he enjoyed some of his most productive years of research and writing.Among his many contributions during these later years, John participated as Committee co-chair in an effort to "redress the wrongs of Tuskegee." The Tuskegee Syphilis Study Legacy Committee proposed in May 1996 that President Clinton apologize to the participants in the Tuskegee study on behalf of the federal government. In May 1997, the President did in... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Closing the Gaps in Pediatric HIV/AIDS Care, One Step at a TimeLisa V. Adams, Helga Naburi, Goodluck Lyatuu, Paul Palumbo, and C. Fordham von ReynFatuma's* doctors were completely perplexed. It was 2003 and she had returned to the DARDAR clinic in her hometown of Dar es Salaam, Tanzania three times that week with vague complaints of various pains and aches. Her doctors were considering whether these symptoms were due (...) to the initiation of her recent treatment with antiretroviral medications for her HIV infection or related to the last administration of the investigational tuberculosis (TB) vaccine that the DARDAR Health Study was evaluating. Fatuma's doctor, Dr. Lillian Mtei, consulted with Dartmouth's chief of Infectious Disease, Dr. Ford von Reyn, who happened to be in Dar that week on a site visit. Neither physician could determine the basis for her symptoms. Dr. Mtei returned to the exam room once more and this time emerged with the answer: Fatuma had just learned that her three year old daughter was HIV-infected, likely contracted from Fatuma during or shortly after she gave birth to her daughter. Fatuma believed that her HIV diagnosis was a death sentence for her daughter since antiretroviral therapy was not widely available for children.Dr. von Reyn, Dartmouth's lead clinical researcher in Africa and a father, knew too well the harsh reality of inequities in a resource-limited country. He turned to Dr. Mtei and said decidedly, "we need to do something about this."Thus the DARDAR Pediatric Program was born.Pediatric HIV: A Neglected DiseaseThe need for HIV treatment among children in Tanzania, as in most of sub-Saharan Africa, is compelling. At the end of 2009, approximately 160,000 children aged zero to fourteen in Tanzania were living with HIV (Joint United Nations Programme on HIV/AIDS [UNAIDS], 2011). Even with successful roll out of prevention of mother to child transmission programs in Tanzania, there were nearly 29,000 perinatal infections in 2009. As of December 2010, only 18% of these were enrolled in HIV treatment programs (UNAIDS, 2011; World Health Organization [WHO], 2011). Without antiretroviral therapy (ART), one-half of HIV-infected children will die before their second birthday. Since clinical research to determine efficacy and safety of new medical treatments is conducted almost exclusively in adults, provision of new medical treatments to [End Page 75] children always lags behind advances for adults. Furthermore, children are often underrepresented in programs for antiretroviral drugs for the following reasons: 1) they are not prioritized for care; 2) facilities lack infant diagnostic capabilities; 3) there is limited pediatric HIV training and consequently, a shortage of pediatric providers; and 4) pediatric antiretroviral formulations are frequently unavailable. The unacceptable delays in pediatric HIV drug development and treatment access led the international organization Drugs for Neglected Diseases initiative to publish an editorial in which they referred to pediatric HIV as a "neglected disease" (Lallemant, Chang, Cohen, & Pecoul, 2011).The Tip of the Iceberg: More than Just MedicinesWith a grant from the New York-based Foundation for the Treatment of Children with AIDS, the DARDAR Pediatric Program, a joint collaboration between Geisel School of Medicine at Dartmouth and Muhimbili University of Health and Allied Sciences, began seeing patients in May 2006. It was the first dedicated pediatric HIV Care and Treatment Center in Tanzania and operates in accordance with Tanzania's National AIDS Control Programme's guidance. Testing for both children and infants (the latter of which requires a more sophisticated assay) is available.The day the clinic opened we celebrated this collaborative effort that would provide HIV-infected children in Dar es Salaam access to antiretroviral treatment. One of our first patients was a six-year-old boy whose mother, like Fatuma, was a participant in our TB vaccine trial. She had been advised to bring her son to us for HIV screening. Her son looked healthy so she was surprised and understandably distraught when his test results indicated that not only was he HIV-infected, but his CD4 percentage was very low. His mother was reluctant to have him started on antiretrovirals given his general appearance and young age—and that he was... (shrink)

This research analyses to what extent the use of debates on literature and cross-cutting themes presented by means of journalistic texts encourages critical thinking in the compulsory secondary education (ESO), concretely within a sample of 128 participants from third year of the secondary school. Firstly, the study investigates the effectiveness of these debates for the correct establishment of literary knowledge from the chosen book, The Life of Lazarillo de Tormes; secondly, the progression (or regression) of critical thinking among the students. (...) To do so, it has been developed and validated a required tool to measure this critical capacity, taking as a starting point Watson Glaser Critical Thinking Test; even if the test was too complex and ambiguous for the level of the students, the test fulfilled most of the requirements to perform this measurement. That is why it was decided to adapt the structure of this test to a new one, Critical Competence Test (CCT), that allows a test to be carried out to assess the key aspects of critical thinking such as identifying assumptions, evaluating arguments, drawing conclusions, and problem solving. The development of the CCT is of great importance because a short test was obtained, with an approximate duration of ten minutes and an understandable language for any level as it has been formulated on purpose for Spanish speakers. All this to facilitate the study participants to carry out the test and the improvement of critical capacity that is intended to be obtained with this research. (shrink)

What lies at the heart of physical inquiry? What are the foundational ideas and working assumptions that inform the enterprise of natural science? What principles guide research? How do scientists decide whether they are building theories in the right direction? Is there a right direction? Do physical theories actually approximate an objective reality, or are they simply useful summaries, mnemonics for experimental results? This book is Nobel Prize winner Jim Peebles's contribution to such big, classic debates in the philosophy (...) of science, drawing on a lifetime of experience as a leading physicist and taking the development of physical cosmology as a "worked example." He begins with a consideration of the history of thought about the nature of the physical sciences since Einstein, culminating in a succinct statement of what he sees as the fundamental working assumptions of physics. Then, through a careful examination of the development of the general theory of relativity, Einstein's cosmological principle, the big bang theory, and our current model of the universe, he makes the argument that physical theories ultimately are useful approximations to an objective reality whose nature science is discovering. An essential reflection on and interrogation of the nature and practice of science by a giant in the field, The Whole Truth will be illuminating reading for cosmologists, physicists, and historians, philosophers, and sociologists of science alike. (shrink)

We consider a situation in which individuals search for accurate decisions without direct feedback on their accuracy, but with information about the decisions made by peers in their group. The “wisdom of crowds” hypothesis states that the average judgment of many individuals can give a good estimate of, for example, the outcomes of sporting events and the answers to trivia questions. Two conditions for the application of wisdom of crowds are that estimates should be independent and unbiased. Here, we study (...) how individuals integrate social information when answering trivia questions with answers that range between 0% and 100%. We find that, consistent with the wisdom of crowds hypothesis, average performance improves with group size. However, individuals show a consistent bias to produce estimates that are insufficiently extreme. We find that social information provides significant, albeit small, improvement to group performance. Outliers with answers far from the correct answer move toward the position of the group mean. Given that these outliers also tend to be nearer to 50% than do the answers of other group members, this move creates group polarization away from 50%. By looking at individual performance over different questions we find that some people are more likely to be affected by social influence than others. There is also evidence that people differ in their competence in answering questions, but lack of competence is not significantly correlated with willingness to change guesses. We develop a mathematical model based on these results that postulates a cognitive process in which people first decide whether to take into account peer guesses, and if so, to move in the direction of these guesses. The size of the move is proportional to the distance between their own guess and the average guess of the group. This model closely approximates the distribution of guess movements and shows how outlying incorrect opinions can be systematically removed from a group resulting, in some situations, in improved group performance. However, improvement is only predicted for cases in which the initial guesses of individuals in the group are biased. (shrink)

The Machiavellian model is often praised as a realistic description of modern corporate life. My analysis of Tne Prince follows Rousseau in arguing that the prince can survive and prosper most easily by creating an environment in which almost all the citizens prosper. Far from licensing unrestrained self-aggrandizement, in this model success only comes from providing real value to almost every citizen for the entire period of one's leadership.Translation from the early sixteenth to the late twentieth century is far from (...) simple; for example, the CEO is in many ways far less powerful than a Medici prince. The closest approximation is a far less bureaucratic organization with very small units possessing maximum autonomy. Also, deciding who is, and who is not, a citizen is not nearly as straightforward as it was for Machiavelli; it probably includes every stakeholder on whom the corporation has a major impact. (shrink)

continent. 2.2 (2012): 76–81 Comments on Eugene Thacker’s “Cosmic Pessimism” Nicola Masciandaro Anything you look forward to will destroy you, as it already has. —Vernon Howard In pessimism, the first axiom is a long, low, funereal sigh. The cosmicity of the sigh resides in its profound negative singularity. Moving via endless auto-releasement, it achieves the remote. “ Oltre la spera che piú larga gira / passa ’l sospiro ch’esce del mio core ” [Beyond the sphere that circles widest / penetrates (...) the sigh that issues from my heart]. 1 The axiomatic sigh of the pessimist is in a way the pure word of philosophy, a thought that thinks without you, speaks where you are not. The live pneumatic form of the soul’s eventual exit from the dead body’s mouth, the sigh restores consciousness to the funeral of being, to the passing away that is existence. Pessimism speaks in piercing aphorisms because first it sighs. “Beyond the sphere passeth the arrow of our sigh. Hafiz! Silence.” 2 … pessimism is guilty of that most inexcusable of Occidental crimes—the crime of not pretending it’s for real. To the pessimist, the ‘real’ world—the world on whose behalf we are expected to wake up in the morning—is a ceaseless index of its own unreality. The pessimist’s day is not an illumined space for the advancement of experience and action, but a permanently and inescapably reflective zone, the vast interior of a mirror where each thing is only insofar as it is, at best, a false image of itself. Within this speculative situation, inside the doubleness of the mirror, pessimism splits into two paths, false and true, one that tries to fix pessimism (establish a relation with the mirror) and decides in favor of the apparent real, and another that totally falls for pessimism (enters the mirror) and communes with the greater reality of the unreal. These two paths are distinguished by their relation to pessimism’s guilt vis-à-vis the world’s reality-project. The first form, that which remains pessimism for the world and puts on a smiling face, stays guilty to itself (i.e. unconscious) and thus turns hypocritical, becoming at once the pessimism of the commoner who really just wants things to be better for himself and the pessimism of the elite who wants to critically refashion reality in his own image. The general form of this worldly, hypocritical pessimism is the impulse to ‘make the world a better place’, which is the global mask under which the world is diurnally made worse. The second form, that which follows pessimism away from the world and ceases to put on a smiling face, refuses guiltiness as itself theessential Occidental mode of pretense and turns honest, becoming at once the intelligent pessimism required of all ordinary action and the radical pessimism necessary for self-knowledge: seeing that no one is capable of doing good. The general form of this universal, honest pessimism is the impulse not to worry, to give up and embrace dereliction, which is the only real way the world is actually improved. Where worldly pessimism is the engine productive of interminably warring secular and sacred religions (good-projects), universal pessimism strives hopelessly for the paradise of a supremely instantiated pessimus: things are getting so bad that there is no longer any time for them to get worse; things are so constantly-instantly worst that this is BEST. Cosmic pessimism is the mode of universal pessimism which can yet discourse with the world, which has not chosen silence and can spread the inconceivably BAD NEWS in an orderly form ( kosmos ) that the world can understand (if it wanted to). … the result of a confusion between the world and a statement about the world. That is what the world is (the result of a confusion between the world and a statement about the world). … a generalized misanthropy without the anthropos. Pessimism crystallizes around this futility—it is its amor fati , rendered as musical form. Pessimism’s love of fate is a blind love, a love of the blindness of being human in a cosmos conceived around the human’s eclipse, a heavy levitation in the contradictory space between the inescapability of its having been and the impossibility of its will-be. Pessimism’s song of futility is a sensible way of loving fate, with a minimum of eros, by means of a kind of matrimonial love of the fatal. As music, pessimism stays open to the irreparable and the inexorable without the binding of affirmation, in the apparent absence of the radical, infinitely surplus will that absolute amor fati seems to require. Crying, laughing, sleeping—what other responses are adequate to a life that is so indifferent? “Unless a man aspires to the impossible, the possible that he achieves will scarcely be worth the trouble of his achieving it. We should aspire to the impossible, to absolute and infinite perfection [….] The apocatastasis is more than a mystical dream: it is a norm of action, it is a beacon for high deeds [….] For true charity is a species of invasion [….] It is not charity to rock and lull our fellow men to sleep in the inertia and heaviness of matter, but rather to arouse them to anguish and torment of spirit.” 3 … the impossibility of ever adequately accounting for one’s relationship to thought. “The paroxysm of interior experience leads you to regions where danger is absolute, because life which self-consciously actualizes its roots in experience can only negate itself [….] There are no arguments [….] On the heights of despair, the passion for the absurd is the only thing that can still throw a demonic light on chaos [….] I live because the mountains do not laugh and the worms do not sing .” 4 It took three attempts before she was fully decapitated, all the while she continued, perhaps miraculously, to sing. According to the earliest account of Cecilia’s martyrdom, the beheading turns out worse. After not severing her head in three strokes, “the cruel executioner left her half dead” (seminecem eam cruentus carnifex dereliquit). 5 Cecilia’s effortlessly powerful endurance of the three strokes—a fitting icon for pessimism as an art of dereliction—demonstrates the “passivity and absence of effort [….] in which divine transcendence is dissolved.” 6 There’s a ghost that grows inside of me, damaged in the making, and there’s a hunt sprung from necessity, elliptical and drowned. Where the moving quiet of our insomnia offers up each thought, there’s a luminous field of grey inertia, and obsidian dreams burnt all the way down. Like words from a pre-waking dream. There is no reason to think that they are not. NOTES 1. Dante Alighieri. Vita Nuova . ed. and trans. Dino S. Cervigni and Edward Vasta. Notre Dame: University of Notre Dame Press. 1995. 41:10. 2. Hafiz of Shiraz. The Divan . trans. H. Wilberforce Clarke. London: Octagon Press. 1974. 10.9. 3. Miguel de Unamuno. The Tragic Sense of Life in Men and Nations . trans. Anthony Kerrigan. Princeton: Princeton University Press. 1972. 305-6. 4. E.M. Cioran. On the Heights of Despair . trans. Ilinca Zarifopol-Johnston. Chicago: University of Chicago Press. 1992. 9-10. 5. Giacomo Laderchi. S. Caeciliae Virg[inis] et Mart[yris] Acta. . . Rome. 1723. 38. 6. Georges Bataille. On Nietzsche . trans. Bruce Boone. London: Continuum. 2004. 135. See Nicola Masciandaro. “ Half Dead: Parsing Cecilia .” A Commentary on Eugene Thacker’s "Cosmic Pessimism" Gary J. Shipley Pessimism is the refusal to seek distraction, the refusal to remodel failure into a platform for further (doomed) possibilities, the refusal of comfort, the acceptance of the sickness of healthy bodies, the cup of life overflowing with cold vomit. If, as Ligotti suggests when discussing Invasion of the Body Snatchers , 1 humans prefer the anxieties of their familiar human lives to the contentment of an alien one, then the pessimist, we could argue, represents some perverted combination of the two, preferring (presuming he has a choice) the defamiliarization of human life to the contentment of its unquestioned mundanity. The quasi-religious state of mind that Wittgenstein would mention on occasion, that of “feeling absolutely safe,” 2 is a state the pessimist could only imagine being approximated by death, or perhaps some annihilative opiate-induced stupor. This Wittgensteinian commingling of certainty and faith looks every bit the futile gesture, a mere rephrasing of collapse or partial collapse. The only certainty open to the pessimist is that of the toxic formula of life itself—a formula known and lacuna-free. Certainty, far from being the gateway to deliverance, becomes the definitive impediment; and the possibility of salvation, as long as it remains, becomes crucially reliant on postulations of ignorance, epistemic gaps, a perennial incompleteness: “the perfect safety of wooed death […] the warm bath of physical dissolution, the universal unknown engulfing the miniscule unknown.” 3 The height of Leibniz’s Panglossian insanity nurtured the idea that our knowing everything—via the universal calculus—could be accurately described a triumph, as opposed to a nightmare in which our every futility is laid bare. Stagnancy and boredom are perhaps two of the greatest ills of Western civilisation, and the most potent pessimism tells you that you’re stuck with both. The most we can hope for, by way of salvation, is to throw open our despair to the unknown. The fact that Schopenhauer’s pessimism stopped short of morality and allowed him to play the flute, as Nietzsche complained, highlights the predicament of a man who despite having adorned nothingness with a smiling face still found himself alive. The demand here is that it be felt: a cross-contamination of intellect and emotion. The safety net of numerous parentheses makes for a failed philosophy, rather than a philosophy of failure. Depressives make bad pessimists, because, unless they choose to die, living will always infect them with necessities of hope, forcing them to find something, anything (all the various “as ifs”) to make existence tolerable. For as Cioran observed, while “[d]epressions pay attention to life, they are the eyes of the devil, poisoned arrows which wound mortally any zest and love of life. Without them we know little, but with them, we cannot live.” 4 And even when cured of our depressions we’ll find ourselves consumed, eaten alive by the hyper-clinical (borderline autistic) mania that replaces them: a predicament captured all too clearly in the microscriptual fictions of Robert Walser, where spectral men and women stifle their depressive madness with protective comas of detail, their failed assimilations buried beneath thick crusts of remote data. Like Beckett’s Malone their stories may have ended, but cruelly their lives have not. Pessimism is an extraneous burden (a purposeless weight) that makes everything else harder to carry, while at the same time scooping it out and making it lighter. If pessimism had a sound it would be the harsh non-noise of tinnitus—the way that every person would hear themselves if they refused their distractions long enough to listen: a lungless scream from the extrasolar nothing of the self. The music of pessimism—if indeed we can imagine such a thing—is the reverberating echo of the world’s last sound, conjectured but never heard, audible only in its being listened for. The one consolation of this hollow paradox of audibility being, that “he will be least afraid of becoming nothing in death who has recognized that he is already nothing now.” 5 The pessimist suffers a derangement of the real, a labyrinthitis at the nucleus of his being: he’s the stumbling ghost relentlessly surprised that others can see him. If Cioran’s refusal is manifested in sleep (when even saying ‘no’ is too much of a commitment), then Pessoa’s resides in the dreams inside that sleep. Pessoa chooses to exploit the fact that he’s being “lived by some murmuring non-entity both shadowy and muddied” 6 by growing more voids to live him. His is a Gnostic breed of sleep, “sleeping as if the universe were a mistake,” 7 a sleep that dreams through Thacker’s cosmic pessimism (“a pessimism of the world-without-us.”, “the unhuman orientation of deep space and deep time” 8 ), through the critical error of there being anything at all when there could be nothing. The metaphysical pessimist is someone who, however well life treats them, still desires to wake from it, as from the poisonous air of a bad dream. Pessimism is a paradox of age, being simultaneously young and old; its youth residing in a refusal to accept the authority of existence (its rich history, its inherent beneficence), a refusal to “get over” the horror of what it sees with its perpetually fresh eyes, and its maturity in the unceremonious disposal of the philosophical playthings (those futile architectures) of adolescence. As Thacker remarks: “Pessimism abjures all pretenses towards system—towards the purity of analysis and the dignity of critique.” 9 A sentiment shared with Pessoa, who duly categorizes those that choose to enact this futile struggle: “The creators of metaphysical systems and of psychological explanations are still in the primary stage of suffering.” 10 If the pessimist has shared a womb with anyone, it’s with the mystic and not the philosopher. As Schopenhauer tells us: “The mystic is opposed to the philosopher by the fact that he begins from within, whereas the philosopher begins from without. […] But nothing of this is communicable except the assertions that we have to accept on his word; consequently he is unable to convince.” 11 The crucial difference between the mystic and the pessimist is not the latter’s impassivity and defeatism, but his unwillingness/inability to contain in any way the spread of his voracious analyticity, his denial of incompleteness, his exhaustive devotion to failure. The truth of our predicament, though heard, is destined to remain unprocessed. Like the revelations of B.S. Johnson’s Haakon (“We rot and there’s nothing that can stop it / Can’t you feel the shaking horror of that?” 12 ) the pessimist’s truths are somehow too obvious to listen to, as if something inside us were saying, “Of course, but haven’t we gotten over that?” Pessimism is simple and ugly, and has no desire to make itself more complex or more attractive. The true moral pessimist knows that the Utilitarian’s accounts will always be in the red. He can see that for all his computational containments, his only honest path is a negative one, and that such a path has but one logical destination: that of wholesale human oblivion. Thacker notes how at the core of pessimism lies the notion of “the worst,” through which death is demoted by the all-pervasive suffering of a life that easily eclipses its threat. And so with doom made preferable to gloom, death begins to glint with promise, “like beauty passing through a nightmare.” 13 But even among pessimists suicide is, for the most part, thought to be an error. Schopenhauer, for instance, regarded suicide a mistake grounded in some fundamentally naïve disappointment or other. Pessoa too thought suicide an onerous escape tactic: “To die is to become completely other. That’s why suicide is a cowardice: it’s to surrender ourselves completely to life.” 14 There is a call here to be accepting of and creative with the puppetry of your being, an insistence that it’s somehow a blunder to attempt to hide in death from the horrors you find inlife. 15 Tied up with this perseverance is the slippery notion of the good death, for maybe, as Blanchot warns, suicide is rarely something we can hope to get right, for the simple reason that “you cannot make of death an object of the will.” 16 “Even in cases where the entire corpus of an author is pessimistic, the project always seems incomplete,” 17 and this is not simply because the project itself belies something yet to be disclosed, but because the project itself is a thing waiting. It waits on a cure it knows will not come, but for which it cannot do anything (as long as it continues to do anything) but wait. NOTES 1. See Thomas Ligotti. The Conspiracy Against the Human Race . New York: Hippocampus Press. 2010. 91. 2. Ludwig Wittgenstein. “A Lecture on Ethics.” Philosophical Review . (74) 1. 1965. 8. 3. Vladimir Nabokov. Pale Fire . New York: Vintage. 1989. 221. 4. E. M. Cioran. The Book of Delusions . trans. Camelia Elias. Hyperion. 5.1. (2010): 75. 5. Arthur Schopenhauer. The World as Will and Representation. vol. 2 . trans. E .F J. Payne. New York: Dover. 1966. 609. 6. Eugene Thacker. “Cosmic Pessimism.” continent. . 2.2 (2012): 67. 7. Fernando Pessoa. The Book of Disquiet . trans. Richard Zenith. London: Penguin. 2002. 35. 8. Eugene Thacker. “Cosmic Pessimism.” continent. . 2.2 (2012): 68. 9. Ibid. 73. 10. Fernando Pessoa. The Book of Disquiet . trans. Richard Zenith. London: Penguin. 2002. 341. 11. Arthur Schopenhauer. The World as Will and Representation. vol. 2 . trans. E .F J. Payne. New York: Dover. 1966. 610-11. 12. B.S Johnson. “You’re Human Like the Rest of Them.” in Jonathan Coe. Like a Fiery Elephant: The Story of B.S. Johnson . London: Picador. 2004. 177. 13. Fernando Pessoa. The Book of Disquiet . trans. Richard Zenith. London: Penguin. 2002. 415. 14. Ibid. 199. 15. “Suicide is, after all, the opposite of the poem.” Anne Sexton. No Evil Star: Selected Essays, Interviews and Prose . ed. Steven Gould Axelrod. Ann Arbor: University of Michigan Press. 1985. 92. 16. Maurice Blanchot. The Space of Literature . trans. Ann Smock. Lincoln: University of Nebraska Press. 1989. 105. 17. Eugene Thacker. “Cosmic Pessimism.” continent. . 2.2 (2012): 75. (shrink)

The following result is an approximation to the answer of the question of Kokorin about decidability of a quantifier-free theory of field of rational numbers. Let Q0 be a subset of the set of all rational numbers which contains integers 1 and −1. Let be a set containing Q0 and closed by the functions of addition, subtraction and multiplication. For example coincides with Q0 if Q0 is the set of all binary rational numbers or the set of all decimal (...) rational numbers. It is clear that , where Z is the set of all integers and Q is the set of all rational numbers. A negationless theory uses only conjunction and disjunction as logical connectives. Let T be a quantifier-free negationless elementary theory of signature , where Pol is the list of all polynomials with rational coefficients from Q0 in which exponent of the polynomials and rational coefficients are written in binary number system. Theorem 1. Theory T is NP-hard and if is everywhere dense then the theory T is decidable by an algorithm which belongs to EXPTIME. The set of all rational numbers or the set of all binary rational numbers may be taken instead of . The quantifier-free negationless theory of the field of rational numbers may be regarded as a base of constructive mathematics. (shrink)

The concept of truth is at the core of science, journalism, law, and many other pillars of modern society. Yet, given the imprecision of natural language, deciding what information should count as true is no easy task, even with access to the ground truth. How do people decide whether a given claim of fact qualifies as true or false? Across two studies (N = 1181; 16,248 observations), participants saw claims of fact alongside the ground truth about those claims. Participants classified (...) each claim as true or false. Although participants knew precisely how accurate the claims were, participants classified claims as false more often when they judged the information source to be intending to deceive (versus inform) their audience, and classified claims as true more often when they judged the information source to be intending to provide an approximate (versus precise) account. These results suggest that, even if people have access to the same set of facts, they might disagree about the truth of claims if they attribute discrepant intentions to information sources. Such findings may shed light on the robust and persistent disagreements over claims of fact that have arisen in the “post-truth era”. (shrink)

This nation’s obesity epidemic is hardly a laughing matter. Approximately 300,000 Americans die from obesity-related causes each year, and without corrective measures, obesity may soon be responsible for as many deaths as cigarette smoking. Sixty-one percent of adults are overweight or obese, and the cost of obesity for the year 2000 was estimated to be 117 billion dollars.In Pelman v. McDmalds, a case decided in September 2003, a federal judge dismissed an amended complaint that attempted to hold McDonalds liable for (...) its customers’ obesity-related illnesses. While many argue that such litigation is frivolous and that the plaintiffs did not deserve direct compensation for their injuries, the debate has largely overlooked the important question raised by these cases - who should pay for the enormous financial strain that obesity places on America’s health care system? Although the courtroom may not be the appropriate forum to deal with this issue, the litigation has undoubtedly brought a great deal of much-needed attention to a vexatious social problem. (shrink)

Given a rich environment, how do we decide on what information to use? A view of a single entity (e.g., a group of birds) affords many distinct interpretations, including their number, average size, and spatial extent. An enduring challenge for cognition, therefore, is to focus resources on the most relevant evidence for any particular decision. In the present study, subjects completed three tasks—number discrimination, surface area discrimination, and convex hull discrimination—with the same stimulus set, where these three features were orthogonalized. (...) Therefore, only the relevant feature provided consistent evidence for decisions in each task. This allowed us to determine how well humans discriminate each feature dimension and what evidence they relied on to do so. We introduce a novel computational approach that fits both feature precision and feature use. We found that the most relevant feature for each decision is extracted and relied on, with minor contributions from competing features. These results suggest that multiple feature dimensions are separately represented for each attended ensemble of many items and that cognition is efficient at selecting the appropriate evidence for a decision. (shrink)

A standing question in consciousness science is whether consciousness arises gradually or in a sudden way. This empirical question is connected to a metaphysical one, concerning the kind of property that consciousness is, i.e., graded or categorical. Recently, Lee (2022) suggested that settling this question requires deciding which theory of consciousness is true. Applying an insight from Wiese (2020), this chapter pursues a way of approximating answers by examining properties that are necessary for consciousness, which consciousness must have regardless of (...) which theory turns out true in the end. One such property is attention. This chapter suggests that attention is connected to consciousness in such a way that a graded view of the former brings support for a graded view of the latter. To this effect, evidence is discussed that degrees of attention are reflected in several acknowledged dimensions of consciousness. The upshot of this view is that the transition from unconscious information processing to conscious experience is gradual and is a function of degree of attention. (shrink)

Sometimes I dream that I am an astronaut. I land my spaceship on a distant planet. When I tell me children on that planet that on earth school is compulsory and that we have homework every evening, they split their sides laughing. And so I decide to stay with them for a long, long time… Well anyway… until the summer holidays. Each state of the mind is irreducible. The mere act of giving it a name, that is of classifying it, (...) implies a falsification of it. From all this, it would be possible to deduce that there is no science in Tlon, let alone rational thought. The paradox, however, is that sciences exist, in countless number… The metaphysicians of Tlon are not looking for truth, nor even for an approximation of it; they are after a kind of amazement. They consider metaphysics a branch of fantastic literature. They know that a system is nothing more than the subordination of all aspects of the universe to some one of them. Even the phrase ‘all the aspects’ can be rejected, since it presupposes the impossible inclusion of the present moment, and of past moments. (shrink)

Effective inseparability of pairs of sets is an important notion in logic and computer science. We study the effective inseparability of sets which appear as index sets of subsets of an effectively given topological T0-space and discuss its consequences. It is shown that for two disjoint subsets X and Y of the space one can effectively find a witness that the index set of X cannot be separated from the index set of Y by a recursively enumerable set, if X (...) intersects the topological closure of an effectively enumerable subset of Y. As a consequence of a more general parametric inseparability result a theorem of Rice-Shapiro type is obtained. Moreover, under some additional requirements it follows that nonopen subsets have productive index sets. This implies a generalized Rice theorem: Connected spaces have only trivial completely recursive subsets. As application some decision problems in computable analysis and domain theory are studied. It follows that the complement of the halting problem can be reduced to the problem to decide of a number whether it is a computable irrational. The same is true for the problems to decide whether two numbers are equal, whether one is not greater than the other, and whether a number is equal to a given number. In the case of an effectively given continuous complete partial order the complexity of the last problem depends on whether the given element is the smallest element, in which case the complement of the halting problem is reducible to it, whether it is a base element and maximal, then the decision problem is recursively isomorphic to the halting problem, or whether it is none of these. In this case, both the halting problem and its complement are reducible to the problem. The same is true in nontrivial cases for the problems whether an element belongs to the basis, whether two elements of the partial order are equal, or whether one approximates the other. In general, for any nonempty proper subset of the partial order either the halting problem or its complement can be reduced to the membership problem of the subset. (shrink)

It is folklore that if a continuous function on a complete metric space has approximate roots and in a uniform manner at most one root, then it actually has a root, which of course is uniquely determined. Also in Bishop's constructive mathematics with countable choice, the general setting of the present note, there is a simple method to validate this heuristic principle. The unique solution even becomes a continuous function in the parameters by a mild modification of the uniqueness (...) hypothesis. Moreover, Brouwer's fan theorem for decidable bars turns out to be equivalent to the statement that, for uniformly continuous functions on a compact metric space, the crucial uniform “at most one” condition follows from its non-uniform counterpart. This classification in the spirit of the constructive reverse mathematics, as propagated by Ishihara and others, sharpens an earlier result obtained jointly with Berger and Bridges. (shrink)

This paper describes the application of eight statistical and machine-learning methods to derive computer models for predicting mortality of hospital patients with pneumonia from their findings at initial presentation. The eight models were each constructed based on 9847 patient cases and they were each evaluated on 4352 additional cases. The primary evaluation metric was the error in predicted survival as a function of the fraction of patients predicted to survive. This metric is useful in assessing a model’s potential to assist (...) a clinician in deciding whether to treat a given patient in the hospital or at home. We examined the error rates of the models when predicting that a given fraction of patients will survive. We examined survival fractions between 0.1 and 0.6. Over this range, each model’s predictive error rate was within 1% of the error rate of every other model. When predicting that approximately 30°K of the patients will survive, all the models have an error rate of less than 1.5%. The models are distinguished more by the number of variables and parameters that they contain than by their error rates; these differences suggest which models may be the most amenable to future implementation as paper-based guidelines. (shrink)

Background: Recent research demonstrates that people sometimes make different medical decisions for others than they would make for themselves. This finding is particularly relevant to end-of-life decisions, which are often made by surrogates and require a trade-off between prolonging life and maintaining quality of life. We examine the impact of decision role, patient age, decision maker age and multiple individual differences on these treatment decisions. Methods: Participants read a scenario about a terminally ill cancer patient faced with a choice between (...) an aggressive chemotherapy regimen that will extend life by two years and palliative treatments to control discomfort for one remaining month. Participants were randomly assigned to one of three decision roles (patient, physician, or an abstract other) and the scenario randomly varied whether the patient was described as 25 or 65-years old. Results: When deciding for a 65-year old patient, approximately 60% of participants selected aggressive chemotherapy regardless of decision role. When deciding for a 25-year old patient, however, participants were more likely to select chemotherapy for a patient (physician role) or another person (abstract other) than for themselves (70%, 67%, and 59%, respectively). In addition, confidence that powerful others (eg, physicians) control one’s health, as well as respondents’ age and race, consistently predicted treatment choices. Conclusions: Patient age appears to influence medical decisions made for others but not those that we make for ourselves. These findings may help to explain the discord that often occurs when younger cancer patients refuse life-extending treatments. (shrink)

An important lesson that philosophy can learn from the Turing Test and computer science more generally concerns the careful use of the method of Levels of Abstraction (LoA). In this paper, the method is first briefly summarised. The constituents of the method are “observables”, collected together and moderated by predicates restraining their “behaviour”. The resulting collection of sets of observables is called a “gradient of abstractions” and it formalises the minimum consistency conditions that the chosen abstractions must satisfy. Two useful (...) kinds of gradient of abstraction – disjoint and nested – are identified. It is then argued that in any discrete (as distinct from analogue) domain of discourse, a complex phenomenon may be explicated in terms of simple approximations organised together in a gradient of abstractions. Thus, the method replaces, for discrete disciplines, the differential and integral calculus, which form the basis for understanding the complex analogue phenomena of science and engineering. The result formalises an approach that is rather common in computer science but has hitherto found little application in philosophy. So the philosophical value of the method is demonstrated by showing how making the LoA of discourse explicit can be fruitful for phenomenological and conceptual analysis. To this end, the method is applied to the Turing Test, the concept of agenthood, the definition of emergence, the notion of artificial life, quantum observation and decidable observation. It is hoped that this treatment will promote the use of the method in certain areas of the humanities and especially in philosophy. (shrink)

When quantum scattering theory is applied strictly from the point of view that the state of a system is completely described by the density matrix, whether pure or mixed, it is not possible to assume that colliding particles are at all times individually in pure states. Exact results are significantly different from conventionally accepted approximations. In particular, it turns out that the cross section as ordinarily defined in theS-matrix formalism is an adequate parameter for deciding the outcome of interactions only (...) when the particles are carefully prepared in matching pure states. In general the use of the cross section in studying pair collisions in a real gas is shown to be analogous to a repeated “collapse of the wave function” after each collision, and involves arbitrary removal of nondiagonal elements of the density matrix, thus violating the basic laws of quantum dynamical evolution. (shrink)

BackgroundProfessional guidelines have addressed ethical dilemmas posed by a few types of nontraditional procreative arrangements, but many questions arise regarding how providers view and make decisions about these and other such arrangements.MethodsThirty-seven ART providers and 10 patients were interviewed in-depth for approximately 1 h each. Interviews were systematically analyzed.ResultsProviders faced a range of challenges and ethical dilemmas concerning both the content and the process of decisions about requests for unconventional interfamilial and other reproductive combinations. Providers vary in how they respond (...) — what they decide, who exactly decides, and how — often undergoing complex decision-making processes. These combinations can involve creating or raising the child, and can shift over time — from initial ART treatment through to the child’s birth. Patients’ requests can vary from fully established to mere possibilities. Arrangements may also be unstable, fluid, or unexpected, posing challenges. Difficulties emerge concerning not only familial but social, combinations. These arrangements can involve blurry and confusing roles, questions about the welfare of the unborn child, and unanticipated and unfamiliar questions about how to weigh competing moral and scientific concerns — e.g., the autonomy of the individuals involved, and the potential risks and benefits. Clinicians may feel that these requests do not “smell right”; and at first respond with feelings of “yuck,” and only later, carefully and explicitly consider the ethical principles involved. Proposed arrangements may, for instance, initially be felt to involve consanguineous individuals, but not in fact do so. Obtaining and verifying full and appropriate informed consent can be difficult, given implicit familial and/or cultural expectations and senses of duty. Social attitudes are changing, yet patients’ views of these issues may also vary, based on their cultural backgrounds.ConclusionsThese data, the first to examine how clinicians make decisions about unconventional reproductive arrangements, highlight several critical ethical questions and ambiguities, and variations in clinicians’ responses. While several professional guidelines exist, the current data highlight additional challenges, and have vital implications for improving future guidelines, practice, education and research.Trial registrationNot applicable. (shrink)

Many economic theorists hold that social institutions can lead otherwise irrational agents to approximate the predictions of traditional rational choice theory. But there is little consensus on how institutions do so. I defend an economic internalist account of the institution-actor relationship by explaining economic rationality as a feature of individuals whose decision-making is aided by institutional structures. This approach, known as the subjective transaction costs theory, represents apparently irrational behavior as a rational response to high subjective transaction costs of (...) thinking and deciding. The theory has two attractive features. First, it reconciles rational choice theory with the increasing body of evidence cataloguing putative errors in economic decision-making. Second, it vindicates the explanatory power of individual choice against externalist challenges; the subjective transaction costs theory keeps economic rationality in the head. (shrink)

As in every religious issue, the two main resources of Islām which are the Qur’ān and the Sunnah/ḥadīths are the first reference sources for deciding the things that are forbidden by Islam. There is no evidence in the Qur’ān that suggests specific types of animals are forbidden to eat except pork. Other than pork, only the animals which are slaughtered without the name of Allah, their blood and their carcass are forbidden to consume. Except these restricted ill-gotten meats, in the (...) Qur’ānic verses there are no other limitations referring to different animals. However, in Ḥadīth sources there are some narratives referring to the Prophet Muḥammad, implying that He named some other forbidden animals beside the ones specified in the Qur’ān. Collecting the narratives and evaluating them as a whole will contribute for a better understanding of the rules and principles of prohibitions that the Prophet Muḥammad imposed on this issue. Moreover, it will help to identify whether those rulings on some animals are unconditional and world-wide or cause-related and thus changeable according to the conditions. Furthermore, in this matter, although some animals‘ meat are not mentioned as forbidden in the Qur’ān, they are banned by the Prophet Muḥammad. This brings the need to highlight the importance of the capacity of the Prophet Muḥammad on deciding what is permissible (ḥalāl) and forbidden (ḥarām) in the religion.SummaryWhile the authority for determining what is ḥalāl (lawful) and what is ḥarām(forbidden) belongs essentially to Allah, the Prophet Muḥammad is also authorized to appoint what is ḥalāl-ḥarām by Allah.Authority of the Prophet Muḥammadrelated to the issue is not absolute and stems from the Qur’ān. Ḥalāland ḥarāmin the Qur’ān prescribed by Allah can be included in the concepts of maʿrūf (right) - munkar (wrong) andṭayyibāt (clean) - hkabāis (filthy). It is understood that the Prophet Muḥammadgrounded his commands in the concept of hkabāis.Prohibitions related to animal meats in the Qur’ānare limited to four: carcass, blood, pork and animals, which are not slaughtered in the name of Allah. However, in the Ḥadīth resources there are some narratives about the Prophet’s prohibition on consuming some types of animals other than the forbidden animals specified in the verses. These narratives can be classified in three titles:1. Animals, which are prohibited to be eaten 2. Animals, which are prohibited because of the way they are fed and slaughtered3. The matter of prohibition of the animals, which are commanded or forbidden to be slaughtered by the Prophet Muḥammad.At the end of the studies conducted based upon ḥadīth resources, in particular Kutūb al-Sittah (the well-known six ḥadīth books), it has been discovered that the animals, which are mentioned as not being permissible in the narratives, they are limited to domesticated donkey and the species of “predatory animals, predatory birds”, namely wolf, fox and cat. Even though the narratives about hyena imply as eatable, hyena is included in this article as it’s a predatory animal.The narratives regarding the prohibition of meat of domesticated donkey were transferred by approximately twenty Companions in respect to the time of the Battle of Khyber. This prohibition is generally stated in the ḥadīthresources as: “We were having dire hunger at the nights of Khyber. When the day for Khyber came, we encountered domesticated donkeys. We immediately slaughtered them. When we put the meat in the pot and started to boil it, crier of the Prophet Muḥammadcalled “Knock over the pots and don’t eat any of the donkey meat”. Regarding the issue there are such statements of some Companions like “we were banned from eating domesticated donkey”, “The Prophet banned the meat of domesticated donkey” among the narratives about the ban. In addition to a large number of narratives about the prohibition of domesticated donkey meat, there are two narratives related to permission of the Prophet for eating domesticated donkey and a narrative that Ibn ‘Abbās did not accept the ban. One of the said narratives is not among the narratives in the Kutūb al-Sittah while the other one is stated solely in the Sunanof Abū Dāwūd and thought to be acceptable by the traditionists. Even though this narrative’s authenticity is accepted, it is understood that there is an implication for the permission based on a necessity. According to the narrative, Ibn ʿAbbās referred to 145thverse of the surah al-An’am as a proof to his view saying “What ḥalālis what Allah allowed, what ḥaramis what Allah forbidden and the things about which there is no judgement of Allah are mubāḥ (permissible)”. As for us, the fact that Ibn ʿAbbās did not accepted the prohibition implies that he did not recognize the Prophet’s command related to the prohibition as an absolute prohibition. The conveyances of many Companions, which are consistent with each other, about the Prophet’s prohibition on eating domesticated donkey during the Battle of Khyber, proved that the prohibition was applied. Even though there is no dispute about prohibiting domesticated donkey, it is controversial whether the prohibition is absolute, constant or provisional based on certain reasons. It is more reasonable to accept that this prohibition was provisional and it was based on certain reasons. Because there are many narratives bearing information that this prohibition was due to several reasons and this is a situation which needs to be considered. Accordingly, there are three reasons, nearly all of which are attributed to judgement of the Companions. These were the facts that domesticated donkey was used in transportation; it used to eat filth and it was slaughtered/consumed without distributing booty/paying taxes. The seeking of the Companions for any reason for this prohibition indicates that they needed to comprehend this prohibition and that the prohibition is not absolute and constant.There is no explanation neither in the resources where the narratives are included nor in the annotation about when, where, why and in which context the prohibition regarding the predatory animals was realized. It is highly possible to assume that the Prophet prohibited these animal as they eat carcass. Another interesting issue within this regard is the fact that there are narratives and views indicating permissibility of eating hyena, which is a predatory, while predatory animals are forbidden in the narratives. Statements of the Prophet related to permissibility of eating hyena, which are considered authentic by traditionists and information about the Arabs who used to eat hyena and some of the Companions who praised eating hyena indicate that urf (custom) has a primary and decisive role about permissibility of eating meats. Regarding this matter about the hyenas, the narratives pointing out some Companions like ʿĀʾisha bint Abī Bakr and Ibn ‘Abbās who viewed prohibition of animals other than the prohibited animals in the Qur’an as inapplicable and other issues referring to the dispute indicate that prohibition of the Prophet Muḥammadfor predators can not be accepted as an absolute and unquestionable prohibition. Some of the prohibitions mentioned in ḥadīth narratives, except these animals, stem from the way of feeding and slaughtering of some animals. It is understood that consuming meat and milk of the animals that eat filth is prohibited in order to abstain from the things harming human health and mujassam (killing an animal with an arrow, etc. by fastening it as a target) is prohibited as carcass is banned and it is not permissible to torture and harm animals. Some of the prohibitions are related to the some animals, which were allowed and banned to slaughter by the Prophet. As the Prophet commanded some animals to be slaughtered and some animals not, meat of these animals was considered as forbidden. There is a dispute among the scholars, whilst there is not any statement of the Prophet about whether the animals included in this group can be eaten or not. It is seen that the Prophet ordered to slaughter some of the animals and prohibited to slaughter some other animals based on several reasons. (shrink)

The aim of J.-L. Marion’s article is to revisit the important debate on the place of Augustine in the history of metaphysics. Often, quibbles arise upon considering the use of substance (substantia) by Augustine, not only as approximative of essentia and as synonymous with ousia, but in deciding whether in so doing Augustine effectuates a ‘metaphysical turn’. While he elsewhere argues that Augustine is a pre-metaphysical thinker, in this article Marion focuses on showing the diverse range of usages of the (...) term substance in the Augustinian corpus. Marion observes: first, whenever substance seems a fixed definition, the term allows for equivocity; second, God is substance in an indeterminate sense or by negation; third, human beings are substances fundamentally to capture the mutability of human existence. As such, Marion concludes, the Augustinian use of substance is insufficient to inelude Augustine in the history of metaphysics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:IntroductionF. S. [email protected] and Richard [email protected] state that there are no sound bites or video clips from classical antiquity is to repeat the obvious. But it is a surprise perhaps to realize how seldom we can recall our field’s most influential scholars even of the very recent past through such now commonplace media. Moreover, the chance to view and hear personal reflections articulated by any such figures about their (...) career, influences, and impact is rare indeed. It was precious opportunities of this type that Pat Thane, Alastair Reid, and Michael Thompson had the foresight to capture from the mid-1980s by developing a video Interviews with Historians series between 1985 and 1996.1 The series was produced by the Publications Department of the Institute of Historical Research at the University of London. In each instance (eventually a total of twenty-eight), a leading historian is interviewed—usually in a studio—by a younger colleague in the same field; three cameras are used, one long shot and one close-up of each participant.2The interview with Sir Moses Finley was one of the first two made (in October 1985) and, as it turned out fortuitously, only months before his sudden death in June 1986 at age 74. The interviewer is Keith Hopkins (a youthful 51), Finley’s one-time graduate student, who had himself just become Cambridge’s professor of ancient history, the position that Finley occupied from 1970 to 1979. They talked in the studio for approximately one hour, and Alastair Reid then edited the master tape with notable skill [End Page 167] to shorten the interview to thirty-five minutes; once both participants had given their approval, the interview was released.3 Meantime, the hour-long U-Matic master tape was archived, but otherwise forgotten. Fortunately, however, in response to inquiries made by Richard Talbert during summer 2013, the Institute proved able to retrieve the tape and—despite its fragility and long outmoded format—to arrange for a successful transfer of the interview to DVD by Soho Broadcast, London.4Our original intention was to offer a transcript of the edited thirty-five-minute version,5 but once the hour-long tape surfaced, we decided instead to offer the interview in its entirety. Our transcript (below, p. 179) inevitably has its limitations and can make no claim to substitute for the video itself.6 It cannot reproduce the unfailingly good-humored atmosphere throughout the interview, nor the range of tones and emphases, nor Finley’s New York accent, nor the marked variations in the pace at which he makes his points, nor of course his constant, characteristic gestures. The variations in pace have influenced how we resolved to punctuate some passages, an unavoidably subjective exercise. Above all, however, we have resisted the recurrent temptation to “clean up” the conversation, so that repetitious, inconsequential, and incomplete remarks are eliminated, and readers are left with a text that more readily approximates to standard written prose.7 Au contraire, our transcript consciously aims to preserve the untidiness and immediacy of the interview; in consequence, very little in the way of repetitive and inconsequential remarks has been omitted.The transcript must be approached, therefore, as the opportunity to listen in on a cordial conversation. One might fairly wonder how far Hopkins had settled in advance with Finley the directions that it might take. No more than minimally, we may suspect, beyond their mutual acknowledgment of the general scope and purpose outlined by the series organizers—hence Hopkins’ unfailing deference towards Finley and his [End Page 168] successive cues to advance the conversation instructively. But recalling the stage where Hopkins asks, “How did you come to cross the Atlantic?” and Finley blithely declines to offer more than the briefest response, we can only speculate whether this was a prearranged rejection of a question which it was reasonable for Hopkins to pose but which Finley preferred not to pursue; or whether Hopkins failed to anticipate quite such a rapid, firm rebuff, and so had to introduce a fresh line of questioning sooner than expected. After all, if Finley had opted to take up the... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Enigmatic Lady PudentillaVincent HuninkRoman literature, like Roman society in general, was dominated by males. From this “men’s world” only a few women seem to stand out as individuals. Hence it is not surprising that whenever a Roman text presents a marked female personality, the relevant data from the text are readily used by scholars to reconstruct her biography.This is certainly the case for Aemilia Pudentilla, the wife of (...) the famous orator and Platonic philosopher Apuleius of Madauros, who lived in Africa in the third quarter of the second century a.d. Between the lines of his extant speech Pro Se de Magia, commonly known as the Apology, Apuleius seems to provide much information about his wife. And in fact, we do not know, about any other woman from this period and this province, even approximately as much as we know about Pudentilla.Thus Pudentilla has become quite popular among modern historians of her place and time, perhaps even more so than her husband. She appears in many studies on the social and economic history of the Roman Empire.1 In 1992 Andreas Gutsfeld devoted a lengthy article expressly to her, in which he attempted a reconstruction of her manifold possessions and her commercial activities, in the context of the economic mentality of the upper class to which she belonged. Even more recently, Elaine Fantham (1995) has attempted to correct Apuleius’ picture of his wife and to examine the situation from Pudentilla’s point of view.Relevant and interesting as these approaches may be, some caution seems due here. It must be realized that we know absolutely nothing about Pudentilla from any other, independent source: every single detail is derived from Apuleius’ speech. More important, however, is [End Page 275] that the Apology is not an official document but a judicial speech, which is, moreover, characterized by a strongly literary color. Historians have not always taken these special circumstances sufficiently into account.Discussion below reviews the most important pieces of information about Pudentilla provided by the text and considers them in relation to the aims and strategies of the speaker. In the end, this will prove to be of some consequence for the portrait of Pudentilla.There is a crucial problem concerning her, which lies at the heart of the speech. Apuleius’ opponents have suggested that she must have been out of her mind to agree in marrying the much younger, impoverished philosopher Apuleius. Under the influence of magical powers, so they suggested, she was robbed by Apuleius of a great capital (e.g., 67.4).2 He, on the contrary, asserts that she had rational, sensible, and practical arguments to marry him, and that she lost no money to him. So we immediately see two conflicting images of Pudentilla: she is considered either as a bewitched hysteric or as a prudent and responsible lady. Who is the real Pudentilla?Hard FactsAn entirely reliable answer to this question will always remain out of reach, since we only have Apuleius’ account to go by. Nonetheless, in practice some pieces of information may be taken or inferred from his text. Surely, it contains some elements which seem beyond reasonable doubt.First, the “previous history” to the marriage, as presented by Apuleius at 66–73, seems clear and plausible.Apuleius says that he was a friend of Pontianus, Pudentilla’s elder son. On his way to Alexandria, he fell ill in the town Oea, where Pontianus lived. He was forced to stay there for the winter, and there he met Aemilia Pudentilla. She had been a widow for fourteen years by then. From her marriage to Sicinius Amicus she had two sons, Pontianus and Pudens. The boys’ grandfather was legally in charge of them and, moreover, could decide on the inheritance of their father. Being well [End Page 276] aware of this, he put pressure on Pudentilla to marry his second son. Pudentilla, however, had rejected that idea and remained a widow. Only after this grandfather’s death had she become freer to act, as Pontianus had become the legal tutor of his younger brother. She then decided she would remarry, mainly for specific, medical reasons. Pontianus offered... (shrink)

The most important reason underlying the success of the Crusaders taking Antakya from Muslims and entering the Syrian and Palestinian territories is undoubtedly the division among the Muslims. This division was not only among the dynasties, but also the cities. The Muslim rulers of Damascus have sat up alliances with the Crusaders to protect themselves from neighboring Muslim rulers. Of course, this alliance was more of a role for the Crusaders, making it easier for them to hold on to the (...) region, and strengthening them by acquiring new lands. Damascus's opposition posture caused power and time loosing to Muslim rulers, which served the Crusaders and to take the advantage of this controversy. Damascus continued its opponent position after Saladin (d. 589/1193), and quarrels within the dynasty caused the Crusaders to breathe deeply and as well as Jerusalem to fall into the hands of the Crusaders for a while again. During the Mamluks period, Damascus, who showed his opposing face for a short period of time, but afterwards he attained peace and obedience and also occupied comply with Rukn al-Dīn Baybars al-Bunduqdārī (d. 676/1277). In this article we will analyze the opposing stance of Damascus and his role in the Crusades. Summary: Pearl of Syria, Damascus has a rebellious and oppositional aspect as well. This feature of the city came into prominence further with the coming of the Crusaders to the region. Its oppositional stance and uncompromising aspect sometimes played into the hands of the Crusaders unintentionally. When the Crusaders first came to the surrounding of Antakya, the governor of Damascus, Duqāq did not provide the necessary support to Yaghisiyan who was encircled in Antakya by the Crusaders, due to his inexperience, jealousy and his hostile competition with his brother, Ridvan who is emir of Aleppo. Thus, the Crusaders used this opportunity.Atabeg of Duqāq, Tughtakīn who started to command the city after the death of Duqāq did not support especially Mawdūd who struggled against the Crusaders in Urfa, adequately. Besides, he was accused of getting Mawdūd killed by another separatist power of the region, the Assassins in the great mosque of the city. On top of it, he allied with the Crusaders, because he was troubled with the commander Porsuk sent to the region by the Sultan of Great Saljūq Empire, Mohammed Tapar. He caused the heroic warrior, Porsuk to be defeated near Tel-Dānis by the Crusaders and to die in Al Jazīrah after a short time.Soon after the above events, ‘Imāduddīn Zengī focused on Damascus and tried to establish the Islamic unity. The son of the ruler Böri, called Ismail became isolated because of the poor administration in the city. He resorted to inviting Zangī to the city. However, Ismail was killed by the opponents before the arrival of Zangī, so no result could be accomplished. Later, Zangī focused on the city again. Although he mercilessly treated the resisters in Ba’lebek after occupying there to demotivate the community of Damascus, he faced the serious resistance of the forces of Damascus. While Zangī spent all his energy to Damascus, the king of Jerusalem, Foulque improved his policy for Syria to some extent and could reestablish communication with the states of the Crusaders. The community Damascus helped the Crusaders and eased their work unintentionally once more.The Mamlūk called Uner began to govern Damascus on behalf of the forces of Bori who lost their influence in the city. Uner who developed a close relationship with the Crusaders to prevent the dominance of Zangī in the city did not hesitate to send an envoy to them. He promised to give Banyas to the Crusaders in return for moving Zangī away from Damascus. After the Franks accepted the proposal of Uner, Zangī remained in between the forces of Damascus and the Crusaders and was obliged to recede to Aleppo. In this way, the Crusaders occupied the castle of Banyas. Several locations until Buzaa were seized by the Crusaders in Antakya who found the opportunity.Zangī was martyred in front of Jaabar castle in 541/1146, so his son Nūr al-dīn became the new ruler of Damascus. Nevertheless, the following incidents caused Nūr al-dīn and Uner to get closer to each other, and the Crusaders had to move away from Damascus. First, the administrator of Havran under the control of Uner rose against his governor and turned to the Crusaders. Besides, the Second Crusade in Damascus contributed to the association of Damascus and Aleppo for a while. Following the elimination of both endangers, the association of Damascus and Aleppo resumed. Uner established a close contact with the Crusaders and made a two-year agreement with them to prevent Nūr al-dīn from seizing the city. Uner died after some time, but almost nothing changed. The new governor of the city Mucīruddin ‘Abaq kept the association of the Crusaders. An operation of Nūr al-dīn against the city was averted with the help of the Crusaders again. Mucīruddin got closer to the Crusaders after their help. Their close relationship was strengthened with the mutual visits of the committees of the Crusaders and Damascus. The Artuquid governor Timurtāsh decided to organize a military expedition to Jerusalem after a little while. However, Mucīruddin who worried about the possible dissolution of their association with the Crusaders stopped supporting him, so Timurtāsh failed in his expedition. Mucīruddin improved his relations with the Crusaders further and started to pay tribute to them following their invasion of ‘Asqalān’s in 548/1153. Even, ‘Abaq offered officially his commitment to Jerusalem. Even though the spoilt Crusaders plundered and destroyed the surrounding of Damascus, they kept the administrators of Damascus with them. Moreover, they went further and offered them to give Ba’lebek to them in return for moving Nūr al-dīn away from Damascus. Such acts provoked the community of Damascus who opposed to the dynasty of Bori in the city afterward. Nūr al-dīn welcomed this opportunity and seized Damascus in 549/1154 by means of the public without giving any chance to coming of the Crusaders. Damascus was governed by Nūr al-dīn for approximately twenty years. A disagreement arose among the community of Zangī in the city after the decease of Nūr al-dīn in 569/1174, thus leading to the dominance of Ṣalādīn Ayyubi in the city. The Ayyubids began to govern Damascus, but internal conflicts started among them with the death of Ṣalādīn in 589/1193. Similarly, Damascus was the focus of these conflicts. The Ayyubids in Egypt were the other party of the disagreement. Unfortunately, the Crusaders benefited from such rivalries. When the senior member of the family al-Adil dominated Damascus in 592/1196, the Crusaders who increased their domain had seized Beirut. Egypt and Damascus got closed temporarily during the Fifth Crusade. After the Crusaders withdrew from Damietta, two brothers, al-Muazzam and al-Kᾱmil fought with each other again. Damascus and Egypt chose the Khwarezmian dynasty and Friedrich in Sicilia as ally, respectively. Unexpected death of al-Muazzam during the preparations for the Sixth Crusade resulted in the siege of Damascus by the forces of Egypt. Friedrich reached Akkā over the course of the siege. al-Kᾱmil who played for time to seize Damascus delivered Jerusalem to the Crusaders. Later, the internal conflicts about the new dynasty which arose in Damascus weakened the Ayyubids and made the Crusaders advantageous. Finally, Damascus found tranquility with the dominance of Baybars in the city. (shrink)

A brief discussion is offered of what it means to say that a set of statements provides D-N explanation with special emphasis given to approximative D-N explanation. An idealized theory is seen to provide approximative D-N explanation. An ideal case provides explanation only if postulates are offered which connect the ideal antecedent condition with actual conditions. Such postulates will help in accounting for deviations between what the consequent of the ideal case entails and what actually occurs. Three ways are presented (...) for deciding on the acceptability of idealizations: (i) as actual conditions more closely approximate the ideal antecedent conditions specified in an ideal case, the more closely actual cases ought to approximate the consequent of the ideal case; (ii) the additional postulates connecting ideal antecedent conditions with actual conditions ought to account for deviations between what is entailed by an idealized theory and what actually occurs; and (iii) an idealized theory is explained by a more general theory when certain state variables in the more general theory are given extreme values. It is argued that (iii) is not a necessary condition for the acceptability of idealizations. (shrink)

This paper proposes a formalization of the class of sentences quantified by most, which is also interpreted as proportion of or majority of depending on the domain of discourse. We consider sentences of the form “Most A are B”, where A and B are plural nouns and the interpretations of A and B are infinite subsets of \. There are two widely used semantics for Most A are B: \ > C \) and \ > \dfrac{C}{2} \), where C denotes (...) the cardinality of a given finite set X. Although is more descriptive than, it also produces a considerable amount of insensitivity for certain sets. Since the quantifier most has a solid cardinal behaviour under the interpretation majority and has a slightly more statistical behaviour under the interpretation proportional of, we consider an alternative approach in deciding quantity-related statements regarding infinite sets. For this we introduce a new semantics using natural density for sentences in which interpretations of their nouns are infinite subsets of \, along with a list of the axiomatization of the concept of natural density. In other words, we take the standard definition of the semantics of most but define it as applying to finite approximations of infinite sets computed to the limit. (shrink)

Shared conceptualization, in the sense we take it here, is as recent a notion as the Semantic Web, but its relevance for a large variety of fields requires efficient methods of extraction and representation for both quantitative and qualitative data. This notion is particularly relevant for the investigation into, and construction of, semantic structures such as knowledge bases and taxonomies, but given the required large, often inaccurate, corpora available for search we can get only approximations. We see fuzzy description logic (...) as an adequate medium for the representation of human semantic knowledge and propose a means to couple it with fuzzy semantic networks via the propositional Łukasiewicz fuzzy logic such that these suffice for decidability for queries over a semantic-knowledge base such as “to what degree of sharedness does it entail the instantiation C(a) for some concept C” or “what are the roles R that connect the individuals a and b to degree of sharedness ε.” . (shrink)

-/- Continuous first-order logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures (such as fields, group, and graphs) to various natural classes of complete metric structures (such as probability algebras, Hilbert spaces, and Banach spaces). With research in continuous first-order logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention. Is there an interesting set of axioms yielding a completeness result? -/- The primary purpose (...) of this article is to show that a certain, interesting set of axioms does indeed yield a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely) satisfiable if (and only if) it is consistent. From this result it follows that continuous first-order logic also satisfies an approximated form of strong completeness, whereby Σ⊧φ (if and) only if Σ⊢φ ∸2−n for all n < ω. This approximated form of strong completeness asserts that if Σ⊧φ, then proofs from Σ, being finite, can provide arbitrarily better approximations of the truth of φ. -/- Additionally, we consider a different kind of question traditionally arising in model theory—that of decidability. When is the set of all consequences of a theory (in a countable, recursive language) recursive? Say that a complete theory T is decidable if for every sentence φ, the value φ T is a recursive real, and moreover, uniformly computable from φ. If T is incomplete, we say it is decidable if for every sentence φ the real number φ T o is uniformly recursive from φ, where φ T o is the maximal value of φ consistent with T. As in classical first-order logic, it follows from the completeness theorem of continuous first-order logic that if a complete theory admits a recursive (or even recursively enumerable) axiomatization then it is decidable. (shrink)

The Qur’an has been transmitted as both a written text and an oral recital. This has led to the development of a reading tradition that permits numerous different vocalisations to be made upon the basic skeletal text of the established ʿUthmānī codex. Ibn al-Jazarī chose ten early readers whom he felt were most representative of this tradition and whose readings are treated as canonical up until this day. One of these, the Kufan linguist al-Kisāʾī has been characterised in the literature (...) as more focused on the grammar of the Qur’an than his reader peers. This article explores al-Kisāʾī’s process of ikhtiyār when deciding between various possible readings. The sample for analysis consists of Kisāʾī’s tafarrudāt, the approximately fifty cases in which his reading differs from the other nine readers. By comparing his reading with the comments of early scholars of Qur’anic linguistics, especially his near-contemporary al-Farrāʾ, it is possible to construct a typology of the suspected principal reasons for al-Kisāʾī’s tafarrudāt. Not only are many of these based on grammatical preferences, but they demonstrate a significant degree of consistency. Furthermore, analysis of a cluster of readings with implications for the interpretation of the sharīʿa provides evidence for a subtle exegetical dimension to al-Kisāʾī’s work as a reader-grammarian. (shrink)

Vagueness is epistemic, according to some. Vagueness is ontological, according to others. This article deploys what I take to be a compromise position. Predicates are coined in specific contexts for specific purposes, but these limited practices do not automatically fix the extensions of predicates over the domain of all objects. The linguistic community using the predicate has rarely considered, much less decided, all questions that might arise about the predicate’s extension. To this extent, the ontological view is correct. But a (...) predicate that applies in some contexts can be reasonably extended to other contexts where it is initially vague. This process of development approximates the cognitive remedy for vagueness that the epistemic view prescribes. The process is piecemeal and inductive, akin to what von Wright described as the molding of concepts. Vagueness cannot be understood apart from the backdrop of classification, for vagueness is classification gone awry. Hence these pages explore the classification of particulars, both its clear successes and vague failures. How we classify unique particulars is the theme of Sections 2 and 3, which are primarily descriptive. Section 2 identifies a way of classifying particulars that pervades discourse of all sorts, and Section 3 illustrates its use in a field notorious for vagueness: ethics. Why a certain particular should (or should not) be classified in a certain way is a normative question, however, and it occupies Sections 4 and 5. Section 4 proposes a norm for strong arguments by analogy, and Section 5 illustrates how the norm might resolve vagueness in one kind of ethical dispute. This norm, which has a strong probabilistic component, is one way of affirming that probability is a guide to life. (shrink)