It is well-established that topos theory is inherently connected with intuitionistic logic. In recent times several works appeared concerning so-called complement-toposes, which are allegedly connected to the dual to intuitionistic logic. In this paper I present this new notion, some of the motivations for it, and some of its consequences. Then, I argue that, assuming equivalence of certain two definitions of a topos, the concept of a complement-classifier is, at least in general and within the conceptual framework (...) of category theory, not appropriately defined. For this purpose, I first analyze the standard notion of a subobject classifier, show its connection with the representability of the functor Sub via the Yoneda lemma, recall some other properties of the internal structure of a topos and, based on these, I critically comment on the notion of a complement-classifier. (shrink)

This article examines the distinction between active matter and active materials, and it offers foundational remarks toward a system of classification for active materials. Active matter is typically identified as matter that exhibits two characteristic features: self-propelling parts, and coherent dynamical activity among the parts. These features are exhibited across a wide range of organic and inorganic materials, and they are jointly sufficient for classifying matter as active. Recently, the term “active materials” has entered scientific use as a complement, (...) supplement, and extension of “active matter.” At the same time, new work in the philosophy of science has considered the problem of how to classify the products of synthetic and laboratory processes, and the extent to which the aims of classifying natural kinds compare and contrasts with the aims of classifying these synthetic kinds. In this article, I apply those considerations to the problems of classifying and characterizing active materials. In doing so, I also argue for a conception of active materials’ coherent dynamical activity as multiscale, rather than emergent, and I discuss how the special non-equilibrium status of active materials factors in to classificatory concerns. (shrink)

Dini's theorem says that compactness of the domain, a metric space, ensures the uniform convergence of every simply convergent monotone sequence of real-valued continuous functions whose limit is continuous. By showing that Dini's theorem is equivalent to Brouwer's fan theorem for detachable bars, we provide Dini's theorem with a classification in the recently established constructive reverse mathematics propagated by Ishihara. As a complement, Dini's theorem is proved to be equivalent to the analogue of the fan theorem, weak König's lemma, (...) in the original classical setting of reverse mathematics started by Friedman and Simpson. (shrink)

In one approach to classifying island phenomena, there is a group that answers to the following description. ADJUNCT ISLAND CONDITION If an XP is in an adjunct position, nothing may move out of it. In the influential approach to this condition in Huang, “adjunct” position is defined in terms that reference argument structure and its reflection in phrasemarker geometry. This definition groups together subject phrases and modifying phrases, contrasting them with phrases in “complement” position. The subsequent bounding theories in (...) Lasnik and Saito and Chomsky build on this basic idea, but attempt to spread it to a wide variety of island effects, including those characterized by early versions of Chomsky’s Subjacency condition. Central to their approaches is the notion of “lexical governor,” which is responsible for making the complement/non-complement cut — only phrases that are governed by a suitably lexical Xo are “complements,” and the island conditions are defined, then, over all the others. This part of the system has fallen into disuse partly, I suspect, because characterizing the “lexical” versus “non-lexical” distinction never found itself grounded in something more general, and partly because it became unwieldy in the increasing richness of post-Pollock representations of phrase-markers. This paper adopts the view that there is an island condition like that in, which groups together subjects and adjuncts, but it does not attempt to define these phrases on the basis of a “lexical governor.” Instead, let us adopt a characterization of “adjunct” that is wholly geometric: An adjunct is a phrase whose sister is also a phrase and whose mother is not its projection. This will put together “subject” phrases and modifier phrases under the standard assumption that these are both necessarily sisters to phrases rather than heads. Thus it will single out the boxed phrases in. (shrink)

As a complement to his version of Euclid’s Optics, the Portuguese mathematician Francisco the Melo (1490-1536) wrote a short treatise on the principles of vision that also included a summary description of the components of the eye. Combining arguments of geometric and anatomical nature, that text helps us to understand some of the conflicting ideas of the Renaissance period, before Kepler, but it also invites us to reread the contributions of a number of authors from the Middle Ages, with (...) a particular focus on Alhacen and Witelo. Although Melo's theory of vision cannot be classified as exactly groundbreaking, it presents many interesting and singular peculiarities. In particular the way in which Melo justifies the existence of rays emitted by the eye while incorporating, at the same time, some elements of the intromission theories, and the clear steps he gives to single out the perpendicular ray in the mechanism behind a faithful and distinct vision. (shrink)

Machine learning classifiers are increasingly used to inform, or even make, decisions significantly affecting human lives. Fairness concerns have spawned a number of contributions aimed at both identifying and addressing unfairness in algorithmic decision-making. This paper critically discusses the adoption of group-parity criteria (e.g., demographic parity, equality of opportunity, treatment equality) as fairness standards. To this end, we evaluate the use of machine learning methods relative to different steps of the decision-making process: assigning a predictive score, linking a classification to (...) the score, and adopting decisions based on the classification. Throughout our inquiry we use the COMPAS system, complemented by a radical simplification of it (our SAPMOC I and SAPMOC II models), as our running examples. Through these examples, we show how a system that is equally accurate for different groups may fail to comply with group-parity standards, owing to different base rates in the population. We discuss the general properties of the statistics determining the satisfaction of group-parity criteria and levels of accuracy. Using the distinction between scoring, classifying, and deciding, we argue that equalisation of classifications/decisions between groups can be achieved thorough group-dependent thresholding. We discuss contexts in which this approach may be meaningful and useful in pursuing policy objectives. We claim that the implementation of group-parity standards should be left to competent human decision-makers, under appropriate scrutiny, since it involves discretionary value-based political choices. Accordingly, predictive systems should be designed in such a way that relevant policy goals can be transparently implemented. Our paper presents three main contributions: (1) it addresses a complex predictive system through the lens of simplified toy models; (2) it argues for selective policy interventions on the different steps of automated decision-making; (3) it points to the limited significance of statistical notions of fairness to achieve social goals. (shrink)

In this article, the meaning of concept of sharʿī science gained in the conception of education, which was established in Islamic civilization, was studied. The main problem of the research is to evaluate the idea of education in Islamic Civilization, which is closely related to the concept of sharʿī science, with a false perception that it consists entirely of religious education. The beginning of Islamic Civilization is traced back to descent of the Qur'an. The conception of education that started to (...) emerge after this period is based on the understanding of the Qur'an and hadiths at first. In later times, a wide variety of fields, such as language, literature, logic, wisdom, riyāzat, nature, and astronomy, have been included in the concept of education to encompass the whole existence of the entity. In the following centuries, these fields, which were included in the course curriculum of the madrasahs, were examined in detail in the works of classification of sciences. Therefore, the false perception needs to be reconsidered. For this reason, the article focuses on how the concept of sharʿī science is defined. Historical data analysis method was used to solve the problem. The claim of the article is that the concept of shar′i science has wide perspective to cover the world of meaning, mind and essence of man. As a result, this article, it was determined that the concept of sharʿī science has a meaning to cover the majority of information fields that are subject to instruction in our educational conception.Summary: The formation of the conception of education in Islamic civilization has emerged in the long term through a scientific process. During this time, a rich curriculum on the concept of education was shaped. The sciences that form the curriculum have been diversified in later periods compared to the early periods of Islam. With the advent of the different sciences, which provided this diversification and which were not at first, all the existing sciences were classified according to different perspectives by the ulama (muslim scholars). In the classifications, which have important contributions to the conception of education, the sciences were tried to be introduced and their position in the education life was tried to be explained. The sciences classified have not been dealt with against each other but rather to complement each other in different ways. The distinction of sciences in classification; different approaches such as linguistically, religious, secular, mental, transportation, philosophical and sharʿī have been developed.The concept of sharʿī science, which can be expressed as a general definition of the sciences, is given in almost all of the works related to the classification of sciences, even under the name or different titles. When we look at the classification, it is seen that sharʿī sciences are handled in four different approaches. As the first approach, the sharʿī sciences are among the main elements of main division in the classification. Here, the sharʿī sciences, in general, with the linguistic sciences and mental sciences were included in the top title. In the second approach, there are works in their classification that do not include the sharʿī sciences and the distinction between it. In addition, these works collect the sciences within this scope under other scientific compositions or other names. In the third approach, among the works that give information about the general of the sciences, there are those who mentioned all together without classifying these sciences and others. In the last approach, the sharʿī sciences are seen as the upper description of the knowledge fields that are included in the teaching, which covers the majority of the other sciences except for the linguistic sciences.The approaches presented in the classification of sciences indicate the diversity of the issue. In order to have better understanding of the issue, it is useful to look closely at the meaning of the concept of sharʿī sciences. At this point, three definitions of 2nd, 4th and 12th centuries are given respectively. Firstly, for Jābir b. Hayyān sharʿī science is the most useful politics in terms of religion and the world, because it contains the benefits of the world's interests after death.Secondly, al-Ghazali (d. 505/1111) describes the sharʿī science as the knowledge learned from Şārī ʿ and prophets, but not by the experience and hearing. According to this, the sharʿī science is defined as the knowledge of the sunnah that only gives information about revelation. The information fields outside this definition are also considered as the sciences, which are instrumental in reaching to sharʿī science.The perspective of the third definition of sharʿī science is given by Saçaklızāde (d. 1145/1732). He lists the three definitions made before the time of his life from the specific (hās) to the general (ām). Saçaklızāde gave the aforementioned definition of al-Ghazali in the first sense of the concept of sharʿī science. He points out that the meaning given here is allocated. The second definition belongs to Molla Husraw (d. 885/1480). According to him, the sharʿī science is the sciences that can be reached through the sciences of the Şārīʿ. In other words, it is the sciences that are not used except for obtaining the sciences obtained from Şārīʿ itself. This meaning is a bit more extensive since there are no records as described in al-Ghazali. This definition is also included in the sciences benefited from it. Although it is not the first, there is usūl-i fiqh (Islamic legal theory) within this meaning.In the third definition, sharʿī science is the sciences that form the basis for things arising from Şārīʿ or originating from Şārīʿ. This definition belongs to Ibn Hajar el-Haytamī. He did not consider the partial allocation of the second meaning as given above, and included all the instrument sciences in the definition of sharʿī science. Based on the definitions he gave, three sharʿī science approaches made before the time he lived were listed from specific to general. Thus, in a sense, he depicts the general shape of the sharʿī science perspective. With the approach to generalization, we can say that a sharʿī science perspective that encompasses the majority of the fields involved in education is developing. In the third meaning of sharʿī science, it is seen that the majority of the fields of knowledge in education and training are gathered under one roof. The most important factor gathering the sciences together is the effort to understand the purpose of Şārīʿ, who owns the whole area of existence. The fields of knowledge and sciences needed to achieve this aim can be included in the definition of sharʿī science. The effort to understand the purpose of Şārīʿ is also at the center of the idea of Islamic education. Since there are various dimensions of being, each step taken to understand and learn them is directed in a way to Şārīʿ itself. Whether it is language and literary sciences or other sciences, such as mathematics, physics and philosophies, the aim is to recognize and understand Şārīʿ for the collection of things that fall within the scope of all educational activities. With sharʿī science approach, teaching the whole of the area of existence owned by Allah is possible within the concept of education. In the works written for the education curriculum, it is seen that the perspective covering the majority of the sciences in the definition of third sharʿī science is preserved. First of all, the meaning integrity of the sharʿī science concept has been determined. In the definitions of three different periods given here, it is seen that the approach to the sciences, which are the subject of instruction in education is not exclusive but inclusive. Especially because of the width in the third sense, the majority of the instrument sciences and mental science fields in the curriculum are included in the definition of sharʿī science. (shrink)

While business as a social activity has involved communities of persons embedded in dense relational networks and practices for thousands of years, the modern legal, theoretical psychological, and moral foundations of business have progressively narrowed our understanding of practical wisdom. Although practical wisdom has recently regained ground in business ethics and management studies, thanks mainly to Anscombe's recovery of virtue ethics, Anscombe herself once observed that it lacks, and has even neglected, a moral psychology that genuinely complements the nuanced philosophical (...) perspective of a virtue‐centered moral philosophy. Herein, we offer one way to fill this gap by suggesting two opposing psychological paradigms, namely the inter‐processual self and the autonomous self, which are classified according to the assumptions they make about the self, human agency and action more broadly, as well as how they relate to practical wisdom. Upon presenting these moral psychologies, we will bring this proposal into conversation with business ethics to show how the IPS paradigm can enable and support virtuous management. (shrink)

SummaryThe relationship between travel, travel narrative, and the enterprise of natural history is explored, focusing on activities associated with the early Royal Society. In an era of expanding travel, for colonial, diplomatic, trade, and missionary purposes, reports of nature's effects proliferated, both in oral and written forms. Naturalists intent on compiling a comprehensive history of such phenomena, and making them useful in the process, readily incorporated these reports into their work. They went further by trying to direct the course of (...) travel to suit their ends, but the complex story of how travel influenced the direction of study cannot be told without acknowledging the influence of objects acquired in a random fashion, arriving in a miscellany off returning ships. Travel writing complemented the activity of documenting nature's history, supplementing the range of available testimony. Such accounts of travel became an accepted source for information, cross-references, and queries, ostensibly eliminating error and advancing knowledge. The difficulty of identifying and classifying objects added to the importance of these reports; furthermore, the scope for attending to prodigies created the grounds for accepting tales of marvels and monsters. The fluid exchange between travel, narrative, and natural history often masked rather than exposed problems of belief, testimony, and evidence, perpetuating an economy of error in which knowledge was both advanced and retarded. (shrink)

In this article we show that it is possible to completely classify the degrees of r.e. bases of r.e. vector spaces in terms of weak truth table degrees. The ideas extend to classify the degrees of complements and splittings. Several ramifications of the classification are discussed, together with an analysis of the structure of the degrees of pairs of r.e. summands of r.e. spaces.

AbtractTechnologies both new and old provide us with a wide range of cognitive artifacts that change the structure of our cognitive tasks. After a brief analysis of past classifications of these artifacts, I shall elaborate a new way of classifying them developed by focusing on an aspect that has been previously overlooked, namely the possible relationships between these objects and the cognitive processes they involve. Cognitive artifacts are often considered as objects that simply complement our cognitive capabilities, but this (...) “complementary view” seems to be an oversimplification. Assuming an “interaction-centered approach”, this article identifies three essential ways in which cognitive artifacts carry out their function: complementing, constituting and substituting our cognitive processes, and builds a taxonomy of these objects that is grounded on these relations. In so doing, it also addresses the chaotic set of different micro-functions carried out by cognitive artifacts, which have not thus far been dealt with, sorting these functions into three corresponding categories. The second part of the article analyzes in greater detail how cognitive artifacts work in our cognitive life, identifying a new kind of functions, called semi-proper functions, and providing a new definition of cognitive artifact based on the previous analysis of these objects. (shrink)

Let ${\mathfrak{M}}$ be a nonstandard model of Peano Arithmetic with domain M and let ${n \in M}$ be nonstandard. We study the symmetric and alternating groups S n and A n of permutations of the set ${\{0,1,\ldots,n-1\}}$ internal to ${\mathfrak{M}}$ , and classify all their normal subgroups, identifying many externally defined such normal subgroups in the process. We provide evidence that A n and S n are not split extensions by these normal subgroups, by showing that any such complement (...) if it exists, cannot be a limit of definable sets. We conclude by identifying an ${\mathbb{R}}$ -valued metric on ${\tilde{S}_n = S_n /B_S}$ and ${\tilde{A}_n = A_n /B_A}$ (where B S , B A are the maximal normal subgroups of S n and A n identified earlier) making these groups into topological groups, and by showing that if ${\mathfrak{M}}$ is ${\mathfrak\aleph_1}$ -saturated then ${\tilde{S}_n}$ and ${\tilde{A}_n}$ are complete with respect to this metric. (shrink)

Introduction Paul Boshears The following excerpt from Paul Amitai's In Between States: Field notes and speculations on postwar landscapes (2012) confounds its reader. Presenting an alternate history of the State of Israel as a space station orbiting Earth, the excitement of possibilities crackles across the texts and images. Like Chris Marker's La Jeteé , the accompanying static images distort the viewer's temporality: are these archaeological items, images from a past, or a future? Why isn't this our future? In Between States (...) can also be seen as complementing Larissa Sansour's provocative science fiction works, Space Exodus (2009) which "documents" the Palestinian space program, and her Nation Estate (2012), in which Palestine is relocated into a skyscraper. Amitai's vision opens onto an intergalactic diaspora, wherein the refugees of World War II are given the stars as Western Europe continues to fight over terrestial colonies. —PFB Auditorium, Hoechst AG headquarters, Industriepark-Höchst, 2011. In 1941 an investigation by the US Justice Department exposed a marriage cartel between John D. Rockefeller’s Standard Oil (now ExxonMobil) and I.G. Farben. The two corporations had formed a joint operation in 1927 called Standard IG Farben. It was revealed that the two had shared patents in order to control prices and markets in their respective regions. Standard was accused of hiding patents from the US Navy and supplying fuel to German submarines, which lead to charges of criminal conspiracy. The Pentagon intervened, requesting that President Roosevelt stop the investigation in order to protect war production and oil supply. Roosevelt agreed, and the Senate committee investigating the matter, headed by Senator Harry Truman, was halted. Standard Oil paid a fine of $5000 and promised to stop supplying fuel to the enemies. Auditorium, Hoechst AG headquarters, Industriepark-Höchst, 2011. Furious at the decision to terminate the investigation of acts he considered treason, Truman initiated a new inquiry into Standard Oil’s war-time practices after succeeding Roosevelt as president in 1945. With the chief executives of I.G Farben simultaneously on trial at Nuremburg, Truman brokered a deal with the Allies that reduced or withdrew criminal charges leveled against both corporations in exchange for Standard Oil and I.G. Farben’s sponsorship of one of Truman’s most ambitious postwar projects—the relocation of the Jewish people. Detail, Sanofi-Aventis advertisement, 2011. The third critical player in this bold experiment was the nascent North Atlantic Space Agency. Formed by Allied forces using the seized assets and engineering expertise of Hitler’s hitherto classified space program (conquer Earth, then the stars), the North Atlantic Space Agency was a pre-NATO foray into interstellar nation building, with orbital occupation as the first point of order. By 1947, NASA was nearly ready to deploy the first manned space station. Standard Oil and I.G. Farben’s advanced fuel refinement capacities and deep, war-enriched financial resources allowed NASA to speed up their launch schedule significantly. Detail, Sanofi-Aventis advertisement, 2011. Diplomatic efforts to establish a Jewish homeland in Palestine were failing to gain traction, while post-colonial England held its ground on immigration restrictions and bands of Jews and Arabs battled over territory on the ground. More immediate was the issue of temporarily housing Holocaust survivors and refugees across scorched Europe. Leaders of the continental nations demonstrated, at best, reluctance to accommodate the Jews, who in turn were, at the least, resistant to returning to the same bloody cocktail from which they had fled. Truman used the impasse to advance a plan for NASA’s space station to be put to use as a temporary Jewish outpost, an orbital displaced persons camp, to be operated by the US Army. Detail, Infaserv Höchst advertisement, 2011. Final preparations advanced rapidly. Viewing the orbital displaced persons (ODP) camp as a solution to their immigration problem both at home and abroad, England came on board as a willing partner. Spaceship Exodus was positioned for takeoff on German farmland 20 kilometers southwest of Frankfurt. On December 30, 1947, one month after the UN General Assembly voted down the separation plan for Palestine, Exodus rocketed into the atmosphere hauling the first module of barracks designed to house 1,500 refugees. Transport vehicles arrived shortly thereafter, loaded down with leftover wartime military rations and 3,000 Jews of Russian and Polish origin. Detail, Infaserv Höchst advertisement, 2011. "The camp is the space that is opened when the state of exception begins to become the rule."—Giorgio Agamben, Homo Sacer , trans. Daniel Heller-Roazen, (Stanford: Stanford University Press, 1995), 96. Detail, Infaserv Höchst advertisement, 2011. The ODP camp proved to be a longer-term solution than originally envisioned. Additional installations were positioned to form swollen clusters of interlocking units – sleeping quarters, schools, clinics, canteens. The UN was brought in to monitor the camp following two chaotic years of US Army control in which food shortages, pandemic diseases, and rampant black market trade had brought the camp to near total collapse. No less bureaucratic or ineffectual, the UN relief agency at least had prior experience facilitating contexts of a similar magnitude and could potentially predict outcomes. Detail, Infaserv Höchst advertisement, 2011. What had been unexpected was the degree to which the camp would evolve into its own self-regulated, hive-like ecosystem where previously accepted rules of conduct were not applicable. The ODP camp was an exceptional space, a riverboat casino, an offshore research lab of social experimentation and entrepreneurial innovation. No longer Earth-bound, touching soil knotted by prescripts of Talmudic law, the camp residents were able to rationalize loopholes and detonate barriers standing in the way of absolute production. The Jewish archipelago was renamed Israel after the ancient homeland. If the temple couldn’t be rebuilt in the motherland, a post-national rhizome would sprout up in its stead. Eyes everywhere, beyond all borders. More information on the project at the author's site. (shrink)

This paper uses two case studies to explore an interest-relative view of taxonomy and how it complements kind pluralism in biology. First, I consider the ABC island bear, which can be correctly classified into more than one species. I argue that this classificatory pluralism can be explained by reference to the range of alternative explanatory interests in biology. In the second half of the paper, I pursue an interest-relative view of classification more generally. I then apply the resultant view to (...) a second case study: whether whales are fish. I argue that this question is not one about scientific vs folk usage, as has been assumed. I also develop a new view: that Fish should be rejected as a category, both from the point of view of biological science, and from the point of view of folk taxonomy. Along the way, I use the interest-relative view to shed light on the circumstances under which higher taxa should be accepted as legitimate categories for biological science. (shrink)

In his Critical corpus, Kant makes two seemingly inconsistent claims concerning the highest good and its relation to the postulates of immortality and God. On the one hand, he argues that the highest good is a duty to be promoted that must therefore be possible by human powers (‘ought implies can’). On the other hand, he asserts that the highest good is an “unconditioned object” of practical reason that can only be attained on the ground of the postulates of immortality (...) and the aid of God. In order to resolve this apparent conflict in Kant’s claims, I intend to argue in this paper that Kant implicitly classifies the highest good as a wide obligation (imperfect duty), which is to be promoted in the world by human agency but goes beyond the limits of human powers and must be assisted and complemented by the postulates of immortality and God. To do so, I argue that the highest good stems from the moral law since the moral law embodies the ground of absolute goodness and holiness that is never fully achievable by rational agents and thus can generate duties that are impossible to attain. In parallel, I argue that two of the components of the highest good, namely moral worthiness and distribution of happiness, are classified as wide obligations that the moral law commands us to pursue infinitely and with the aid of God. In sum, I try to resolve the initial conflict by suggesting that the highest good as an infinite progress towards the holiness demanded by the moral law signifies a wide obligation, which is not achievable merely by human agency but fundamentally requires the postulates of immortality and the existence of God as a complementing and assisting ground. (shrink)

Descartes holds that ideas have or contain _objective reality_ of their objects, so that the idea of the sun is the sun itself existing in the intellect. In this paper, I examine this obscure thesis which grounds the disagreement about Descartes’ commitment to direct or indirect realism. I suggest that, importantly, both readings are correct to a certain extent. I argue that the view of objective reality Descartes develops bears the earmarks of both direct and indirect realist views but must (...) be classified as a third alternative combining some central features of both. I elaborate first on the direct realist interpretations of Descartes’ objective reality and explain their most significant shortcomings. My interpretation of objective identity comes in the form of attributing to Descartes a view about identity and persistence of objects known as _sortalism_. I argue that Descartes’ objective identity turns out to be much like the Aristotelian view of _formal identity_, yet without the forms. By way of discussing the case of Theseus’ ship, I point out how Cartesian sortalism, contrary to other versions of sortalism, allows us to analyze the puzzle as a tension between two distinct yet independently legitimate criteria of identity. It is this sortalist insight that helps to render Descartes’ account of objective identity consistent. This point also grounds my argument that we need not consider direct and indirect realism as logical complements, contrary to the received wisdom. (shrink)

The Hungarian Nominal Functional Sequence combines the methods of syntactic cartography with evidence from compositional semantics in a comprehensive exploration of the structure of Noun Phrases. Proceeding from the lexical core to the top of DP, it uses Hungarian as a window on the underlying universal functional hierarchy of Noun Phrases, but it also regularly complements and supports the analysis with cross-linguistic evidence. The book works out a minimal map of the extended NP in the sense that the proposed hierarchy (...) only has projections which host overt material and it does not draw on semantically empty word order projections. Topics which receive special attention include the syntax of classifiers, demonstratives, proper names, possessive NPs and plural pronouns. (shrink)

Scientific explanation is an important goal of scientific practise. Philosophers have proposed a striking diversity of seemingly incompatible accounts of explanation, from deductive-nomological to statistical relevance, unification, pragmatic, causal-mechanical, mechanistic, causal intervention, asymptotic, and model-based accounts. In this dissertation I apply two novel methods to reexamine our evidence about scientific explanation in practise and thereby address the fragmentation of philosophical accounts. I start by collecting a data set of 781 articles from one year of the journal Science. Using automated text (...) mining techniques I measure the frequency and distribution of several groups of philosophically interesting words, such as "explain", "cause", "evidence", "theory", "law", "mechanism", and "model". I show that "explain" words are much more common in scientific writing than in other genres, occurring in roughly half of all articles, and that their use is very often qualified or negated. These results about the use of words complement traditional conceptual analysis. Next I use random samples from the data set to develop a large number of small case studies across a wide range of scientific disciplines. I use a sample of "explain" sentences to develop and defend a new general philosophical account of scientific explanation, and then test my account against a larger set of randomly sampled sentences and abstracts. Five coarse categories can classify the explanans and explananda of my cases: data, entities, kinds, models, and theories. The pair of the categories of the explanans and explanandum indicates the "form" of an explanation. The explain-relation supports counterfactual reasoning about the dependence of qualities of the explanandum on qualities of the explanans. But for each form there is a different "core relation" between explanans and explanandum that supports the explain-relation. Causation, modelling, and argument are the core relations for different forms of scientific explanation between different categories of explanans and explananda. This flexibility allows me to resolve some of the fragmentation in the philosophical literature. I provide empirical evidence to show that my general philosophical account successfully describes a wide range of scientific practise across a large number of scientific disciplines. (shrink)

Chapter 1 First Person Access to Mental States. Mind Science and Subjective Qualities -/- Abstract. The philosophy of mind as we know it today starts with Ryle. What defines and at the same time differentiates it from the previous tradition of study on mind is the persuasion that any rigorous approach to mental phenomena must conform to the criteria of scientificity applied by the natural sciences, i.e. its investigations and results must be intersubjectively and publicly controllable. In Ryle’s view, philosophy (...) of mind needs to adopt an antimentalist stance to achieve this aim. Antimentalism not only definitively rejects the idea that mind is a substance separated from the body, it also denies that mental phenomena radically differ from physical phenomena by virtue of several unique features. Most problematically, mental phenomena have a conscious character (mental states are related to specific qualitative feelings) and are accessible only to the first-person (only the subject knows directly what s/he is experiencing inside his/her mind). Ryle takes a strong stance on antimentalism going so far as to maintain that an approach to mind which aims to meet the criteria of scientificity set by the natural sciences must avoid any reference to internal, unobservable mental states. In his view (which is considered a specifically philosophical version of psychological behaviorism and also addresses questions put forward in psychological research), mental states can be redescribed in terms of behavioral dispositions. In this chapter, we address the historical roots of the antimentalist view and analyze its relation to the later tradition of research on mind. We show that, compared to the antimentalist stance, functionalism and cognitivism take a step back when they maintain that direct reference to mental states is necessary since mental states cause and therefore explain human behavior. This step backwards is often interpreted as a return to mentalism. However, this is only partially true. Indeed, we suggest that these later traditions retain one important element of Ryle’s antimentalism, i.e. the idea that mental states must be uniquely identified using external and publicly observable criteria, while excluding any reference to introspection and those qualitative dimensions of a mental state, which are accessible only to the first-person. According to the perspective we put forward, this epistemological stance has continued to influence contemporary research on mind and current philosophical and psychological theories which both tend to exclude the subjective qualities of human experience from their accounts of how the mind works. The issue we raise here is whether this is legitimate or whether subjective qualities do play a role with respect to the way our mind works. The conclusion of this chapter anticipates the argument the book makes in in favor of this latter position, starting from a particular angle, i.e. the problem of how we categorize concepts related to our internal states. -/- Chapter 2 The Misleading Aspects of the Mind/Computer Analogy. The Grounding Problem and the Thorny Issue of Propriosensitive Information -/- Abstract. After the crisis of behaviorism, cognitivism and functionalism became the predominant models in the field of psychology and of philosophy, respectively. Their success is mainly due to the new key they use for interpreting mental processes: the mind/computer analogy. On the basis of this analogy, mental operations are seen as cognitive processes based on computations, i.e. on manipulations of abstract symbols which are in turn understood as informational unities (representations). This chapter identifies two main problems with this model. The first is how these symbols can relate to and communicate with perception and thus allow us to identify and classify what we perceive through the senses. Here we limit ourselves to presenting this issue in relation to the classical symbol grounding problem originally put forward by Harnad on the basis of Searle’s Chinese room argument. An attempt to address the problem raised here will be made in chap. 3. The second point we discuss in relation to the mind/computer analogy concerns the idea of information it fosters. Indeed, following this analogy, information is something available in the external world which can be captured by the senses and transmitted to the central system without being influenced or modified by the procedures of transmission. This perspective does not take into account that – unlike computers – in living beings information is acquired by means of the body. As Ulric Neisser has already pointed out, the body is itself an informational source that provides us with additional sensory experience that influences (modifies or complements) the information extracted from the external world by the senses. To develop this line of analysis and to determine exactly what information is provided by the body and how this might influence cognition, we examine Sherrington’s and Gibson’s positions. Moving on from their views, we qualify bodily information in terms of ‘proprioception’. We use ‘proprioception’ in a broad sense to describe any kind of experience we have of our internal states (including postural information as well as sensations related to the general state of the body and its parts). Following Damasio’s and Craig’s studies, we further elaborate this position, arguing that living beings are equipped with an internal propriosensitive monitoring system which maps all the changes that constantly occur in our body and that give us perceptual (‘proprioceptive’ or propriosensitive) information about what happens inside us. Moreover, relying on Goldie’s and Ratcliffe’s view, we show that emotional information can also be considered as a form of ‘proprioception’ which contributes to determining everything we perceive. This analysis leads us to the second main thesis of this book: ‘proprioception’ is a form of internal perception and it is an essential component of the sensory information we can access and use for all cognitive purposes. -/- Chapter 3 Semantic Competence from the Inside: Conceptual Architecture and Composition -/- Abstract. Concepts are essential constituents of thought: they are the instruments we use to categorize our experience, i.e. to classify things and group them together in homogeneous sets. Here we define concepts as the internal mental information (representations) that allows us, among other things, to master words in natural language. By analyzing the way in which individuals master word meanings we explore a number of hypotheses regarding the nature of concepts. Following Diego Marconi’s research, we differentiate between two kind of abilities that underpin lexical competence – so-called ‘referential’ and ‘inferential competence’ – and we suggest that, in order to support these abilities, concepts must also include two corresponding kinds of information, i.e. inferential and referential information. We point out that the most widely used and acknowledged theories of concepts do not make this distinction, instead broadly characterizing the information used for categorization in terms of propositionally described feature lists. However, we show that while feature lists can explain inferential competence, they do not account for referential competence. To address the issue of referential competence we examine Ray Jackendoff’s hypothesis that to account for the possibility of linking perceptual and conceptual information we need to assume the existence of a (visual) representation that encodes the geometric and topological properties of objects and bridges the gap between the percept and the concept. Furthermore, we analyze the extension of this work by Jesse Prinz who introduced the notion of a proxytype, a perceptual representation of a class of objects that incorporates structural and parametric information related to their appearance. However, as we point out, proxytypes can only explain the relationship between perception and concepts with respect to instances that can be perceived through the senses and that belong to the same class by virtue of their physical similarity. We suggest that this notion be extended to include larger conceptual classes. To accomplish this, we further develop Mark Johnson, George Lakoff and Jean Mandler’s idea of a schematic image and argue that conceptual representations include a perceptual schema. Perceptual schemata are non-linguistic, structured experiential gestalts (patterns or maps) that make use of information taken from all sensory modalities, including body perception. They accomplish a quasi-conceptual function: they allow us to recognize and to classify different instances. In this work, we hypothesize that perceptual schemata are an essential component of concepts, but not identical to them. Instead, we suggest that concepts include both perceptual and propositional information with perceptual schemata providing the ‘perceptual core concept’ that grounds related propositional information. -/- Chapter 4 In the Beginning There Were Categories. The Bodily Origin of Prelinguistic Categorical Organization: The Example of Folkbiological Taxonomies -/- Abstract. Studies of categorization in psychology and the cognitive sciences have made use of the notions of ‘category’ and ‘concept’ without precisely defining what is meant by either; in fact, often these terms have been used as synonyms, making it difficult to address specific issues related to conceptual development. This chapter begins by discussing the definitions of, as well as the distinctions between, ‘categories’ and ‘concepts’ in the classical philosophical tradition (Aristotle, Kant and Husserl). We introduce our view of categories with reference to Husserl. Categorization is defined as the way in which our experience is originally (pre-linguistically) organized in a passive and fully unconscious manner on the basis of universal structuring principles. Conceptualization is explained as a later process in which the earlier categorical macro-classes are further subdivided into more specific and detailed sets; this later process also relies on linguistic learning and exposure to culture. On the basis of Ray Jackendoff, Jean Mandler, George Lakoff and Mark Johnson’s work, we hypothesize that categorization is a two-step process that begins with the formation of homogeneous sets of entities partitioned into regions that describe the ontological boundaries of the objects that humans perceive (categories) and continues at a later stage with the development of more specific classifications (concepts). In this chapter, we mainly address three related issues: Why should we assume that there is categorical organization which precedes the development of a conceptual system? How do categories and concepts relate to each other? Shall we hypothesize that categories are innate or that they are formed before concepts on the basis of information and organizational structure available at a very early developmental stage? We show that categorical partitions are necessary for categorization and, following Mandler, that the general categories we form at an early age do not match our adult superordinate concepts. As for the third issue, we argue that there might be no need to assume that categories are innately present in the human mind, since their formation can be explained – at least in certain cases – by basic mechanisms that work on body (propriosensitive) information. This hypothesis will not be discussed in general, but in relation to a particularly relevant example of categorical partition, i.e. the folk-biological dichotomy between ANIMATE/INANIMATE. This is compared with other dichotomies that derive from it, but are not directly categorical such as LIVING/NON-LIVING and BIOLOGICAL/NON-BIOLOGICAL. -/- Chapter 5 Internal States: From Headache to Anger. Conceptualization and Semantic Mastery -/- Abstract. Here we ask if we can also apply the distinction between referential and inferential competence we introduced in Chapter 3 to words that do not refer to things that are perceived using the external senses, especially to words/concepts that denote bodily experiences (such as pain, thirst, hunger, etc.) or emotions. We introduce and discuss the hypothesis that – even though such words/concepts do not refer to intersubjectively identifiable entities in the external world – they do have a kind of referent that can be accessed via direct perception, more specifically ‘proprioception’, as we have defined it in terms of all propriosensitive information we can consciously access. In the first part of the chapter, we specifically consider terms denoting bodily experiences such as ‘pain’ or ‘hunger’ and argue that their referents are identified and classified from a first-personal point of view on the basis of four main characteristics: their specific intensity, their localization in the body, their co-occurrence with other signals and above all their specific qualitative sensations. Emotions are addressed in the second part of the chapter. We suggest that there is a continuity between bodily experiences and emotions. In particular, we argue for a perceptual theory of emotions in line with that proposed by James and Lange at the end of the 19th century and developed more recently by authors such as Damasio (see also chap. 2§5, §6). The hypothesis we put forward is that the referential information that supports the categorization of emotions and therefore also our mastery of terms referring to emotions consists in the perception (i.e. the ‘proprioception’) of those bodily states and changes in bodily states which constitute our emotional experience. In the context of this discussion we examine some objections to this line of reasoning that arise from a cognitivist perspective and following authors such as Oatley, Johnson-Laird and Frijda, we distinguish between basic emotions that can be identified and classified solely on the basis on how they feel and complex emotions whose identification and classification additionally depends on cognitive factors. To describe how emotions are identified and classified on the basis of how they feel, we rely on Marcel and Lambie’s distinction between an ‘emotion state’ and an ‘emotion experience’. Both notions indicate kinds of feelings that we consciously experience. However, they describe first-order and second order emotion awareness respectively. The emotion state is the feeling we have of the bodily states and changes that occur when we are experiencing an emotion, while the emotion experience is the fully developed and integrated emotion we both experience and are, with reflection, aware of experiencing. On the basis of this differentiation, we also show that the same characteristics that aid in the identification and classification of bodily experiences (specific qualitative sensations; somatic localization; specific intensity; presence/absence of specific concomitant sensations) can also be used for the identification and classification of emotions – at least basic emotions. In the last two sections of the chapter we present some clinical evidence on the semantic competence of people who suffer from Alexithymia and Autism Spectrum Disorder which supports the conclusions of our preceding analyses. -/- Chapter 6 The ‘Proprioceptive’ Component of Abstract Concepts -/- Abstract. In this chapter, we address the issue of whether the mastery of abstract words requires only inferential knowledge and thus, if the concepts that support the mastery of abstract words include only linguistic information. We start by differentiating the notions of ‘abstract’ and ‘general’ which are often erroneously confused. We then identify a strict definition of abstract, as contrasted with ‘concrete’, that applies to words or concepts whose referent cannot be experienced by the senses. We argue that abstract words/concepts would be better described as theoretical, because they are usually conceived as structured sets of inferential knowledge expressed linguistically; that is, as small theories. Pointing out parallels with Carnap’s analysis of this issue in philosophy of science, we hypothesize that words/concepts denoting non-observable entities are not all ‘equally theoretical’, because their link to sensory experience can be stronger or weaker. We revive the distinction, inspired by Quine, between theoretical and intertheoretical concepts/words. This distinction relies on the fact that the former – unlike the latter – retains a strong, although indirect, connection with perception. In Quine’s discussion, perception is understood uniquely in terms of observability, i.e. of external sensory experience. Here we argue, however, that bodily, ‘proprioceptive’ (i.e. propriosensitive) experience can also serve to referentially ground theoretical (i.e. abstract) concepts/words. We frame this issue using the example of the theoretical concept ‘freedom’ and Lakoff’s hypothesis that this concept is developed on the basis of bodily information. We contrast this with the example of ‘democracy’ which more closely resembles an intertheoretical concept/word. Furthermore, we show that one of the classical views put forward in psycholinguistic research to explain how abstract concepts are mentally represented – i.e. Paivio’s Dual Coding Theory – points in the same direction as our analysis. The same is true of Barsalou’s work suggesting that we use internal information to understand at least some abstract words. To sustain this position, we put forward two lines of evidence: the first comes from psycholinguistic studies while the second examines deficits of semantic competence exhibited by people with Autism Spectrum Disorder. On the basis of our analysis, we put forward a classification that distinguishes between different kinds of concreteness and different degrees of abstraction: concepts/words referring to body experiences and basic emotions are described as analogous to concrete concepts/words because they are grounded in perceptual (i.e. propriosensitive) experience, while abstract concepts/words are considered more or less abstract depending on whether they are intratheoretical (and rely entirely on inferential information) or theoretical (and are partially grounded in perceptual – or more often in propriosensitive perceptual – information). In the last section of the chapter we consider two scales that have been used in psycholinguistic research to measure the degree of concreteness vs. abstractness of words and we show that – used conjointly – they can provide a measure of the internal vs. external grounding of specific words. (shrink)

§1. I will start with a quick definition of descriptive set theory: It is the study of the structure of definable sets and functions in separable completely metrizable spaces. Such spaces are usually called Polish spaces. Typical examples are ℝn, ℂn, Hilbert space and more generally all separable Banach spaces, the Cantor space 2ℕ, the Baire space ℕℕ, the infinite symmetric group S∞, the unitary group, the group of measure preserving transformations of the unit interval, etc.In this theory sets are (...) classified in hierarchies according to the complexity of their definitions and the structure of sets in each level of these hierarchies is systematically analyzed. In the beginning we have the Borel sets in Polish spaces, obtained by starting with the open sets and closing under the operations of complementation and countable unions, and the corresponding Borel hierarchy. After this come the projective sets, obtained by starting with the Borel sets and closing under the operations of complementation and projection, and the corresponding projective hierarchy.There are also transfinite extensions of the projective hierarchy and even much more complex definable sets studied in descriptive set theory, but I will restrict myself here to Borel and projective sets, in fact just those at the first level of the projective hierarchy, i.e., the Borel (), analytic () and coanalytic () sets. (shrink)

The principle-based approach is a methodology to classify and analyse argumentation semantics. In this paper we classify seven of the main alternatives for argumentation semantics using a set of new robustness principles. These principles complement Baroni and Giacomin’s original classification and deal with the behaviour of a semantics when the argumentation framework changes due to the addition or removal of an attack between two arguments. We distinguish so-called persistence principles and monotonicity principles, where the former deal with the question (...) of whether a labelling or extension of an argumentation framework under a given semantics persists after a change, and the latter with the question of whether new labellings or extensions are created after a change. We furthermore show in which sense labelling-based and extension-based semantics lead to subtly different principles and results. Our results can be used for choosing a semantics for a particular application, or to guide the search for new argumentation semantics, but they have been used also in the design of algorithms. (shrink)

The Common Anatomy Reference Ontology (CARO) is being developed to facilitate interoperability between existing anatomy ontologies for different species, and will provide a template for building new anatomy ontologies. CARO has a structural axis of classification based on the top-level nodes of the Foundational Model of Anatomy. CARO will complement the developmental process sub-ontology of the GO Biological Process ontology, using it to ensure the coherent treatment of developmental stages, and to provide a common framework for the model organism (...) communities to classify developmental structures. Definitions for the types and relationships are being generated by a consortium of investigators from diverse backgrounds to ensure applicability to all organisms. CARO will support the coordination of cross-species ontologies at all levels of anatomical granularity by cross-referencing types within the cell type ontology (CL) and the Gene Ontology (GO) Cellular Component ontology. A complete cross-species CARO could be utilized in other ontologies for cross-product generation. (shrink)

As AI algorithms advance and produce surprising outputs, the question of imagination arises. Can we classify their output as imaginative? And what is their effect on human imagination? Apparently, algorithms follow Kant’s explanations on human imagination, thereby pushing us to update our understanding of imagination by taking into account the co-shaping between humans and their technologies. Such a new understating is offered in this article based on the theories of Don Ihde and Bernard Stiegler. With Ihde, imagination is conceived as (...) tightly linked to perception. Imagination evolves from the modernist task of seeking new points-of-view to a new mode in which technologies present imaginative layers of information on top of reality. With Stiegler, imagination is regarded as tightly linked to memory. He demonstrates how imagination complements memory, serves as a condition to memory/technology and at the same time how imagination itself is conditioned by memory/technology. In this article I develop a new synthesis: imagination as composed of perception and memory. This is the foundation of my layered model of digital imagination. In this model, the task of AI algorithms is the filling in of the layers with data. By producing endless possibilities, these technologies “automate” the Kantian “free play” of imagination, allowing us to examine more options and focus on the best of them. The model reserves the production of meaning to humans. Our role as humans is to generate meaning to the link between layers and establish new layers. (shrink)

Research on fairness in machine learning (ML) has been largely focusing on individual and group fairness. With the adoption of ML-based technologies as assistive technology in complex societal transformations or crisis situations on a global scale these existing definitions fail to account for algorithmic fairness transnationally. We propose to complement existing perspectives on algorithmic fairness with a notion of transnational algorithmic fairness and take first steps towards an analytical framework. We exemplify the relevance of a transnational fairness assessment in (...) a case study on a disaster response system using images from online social media. In the presented case, ML systems are used as a support tool in categorizing and classifying images from social media after a disaster event as an almost instantly available source of information for coordinating disaster response. We present an empirical analysis assessing the transnational fairness of the application’s outputs-based on national socio-demographic development indicators as potentially discriminatory attributes. In doing so, the paper combines interdisciplinary perspectives from data analytics, ML, digital media studies and media sociology in order to address fairness beyond the technical system. The case study investigated reflects an embedded perspective of peoples’ everyday media use and social media platforms as the producers of sociality and processing data-with relevance far beyond the case of algorithmic fairness in disaster scenarios. Especially in light of the concentration of artificial intelligence (AI) development in the Global North and a perceived hegemonic constellation, we argue that transnational fairness offers a perspective on global injustices in relation to AI development and application that has the potential to substantiate discussions by identifying gaps in data and technology. These analyses ultimately will enable researchers and policy makers to derive actionable insights that could alleviate existing problems with fair use of AI technology and mitigate risks associated with future developments. (shrink)

Any fundamental examination of managerial practices must consider a philosophical conundrum at the heart of market exchange. Economically, the opportunity for profit seems to demand somebody else’s loss, and ethically, we must not take advantage of others’ misfortune. In a market system involving a multiplicity of stakeholders, profit opportunities may arise in which relationships between winners and losers are distant, indirect, or even nonexistent; their motives are multivalent; and their market participation may be intentional or accidental. Reflecting two decades later (...) upon several cases arising from the 9/11/2001 terrorist attacks, this paper describes several examples of profiting from loss that demonstrate the ubiquity and variety of the problem. It also invokes numerous bodies of literature that demonstrate the inherent complexity and interdisciplinarity of the problem and the absence of determinative principles to answer the question of when it is justifiable to profit from loss. The paper positions casuistry, the ancient philosophical art of case analysis that resembles modern business pedagogy, as a complement to ethical theory. The Loss Agency-Division of Benefits framework developed in the paper demonstrates the value of philosophy to managerial practices when economic theory is insufficient for ethically classifying and evaluating forms of profiting from loss. (shrink)

We prove that for any computably enumerable degree c, if it is cappable in the computably enumerable degrees, then there is a d.c.e. degree d such that c d = 0′ and c ∩ d = 0. Consequently, a computably enumerable degree is cappable if and only if it can be complemented by a nonzero d.c.e. degree. This gives a new characterization of the cappable degrees.

In this paper, I address the problem wherein the same English word permits one of its complement positions to be satisfied by phrases of different categories. A well-known example of such an English word is the copula to be, whose complements include adjective phrases, noun phrases, prepositional phrases and adverbial phrases. I provide a way to treat such words, in particular verbs, as single lexical items through a conservative extension of the usual treatment of word classification as a pair (...) comprising a part of speech category and a complement list. I then show how a further conservative extension of complement lists permits a satisfactory formalization of doubly complemented English verbs which are synonymous under a permutation of their complements. These verbs include, but are not limited to, so-called double object constructions. (shrink)

It is well known that in Bishop-style constructive mathematics, the closure of the union of two subsets of ℝ is ‘not’ the union of their closures. The dual situation, involving the complement of the closure of the union, is investigated constructively, using completeness of the ambient space in order to avoid any application of Markov's Principle.

Classifying Madness (Springer, 2005) concerns philosophical problems with the Diagnostic and Statistical Manual of Mental Disorders, more commonly known as the D.S.M. The D.S.M. is published by the American Psychiatric Association and aims to list and describe all mental disorders. The first half of Classifying Madness asks whether the project of constructing a classification of mental disorders that reflects natural distinctions makes sense. Chapters examine the nature of mental illness, and also consider whether mental disorders fall into natural kinds. The (...) second half of the book addresses epistemic worries. Even supposing a natural classification system to be possible in principle, there may be reasons to be suspicious of the categories included in the D.S.M. I examine the extent to which the D.S.M. depends on psychiatric theory, and look at how it has been shaped by social and financial factors. I aim to be critical of the D.S.M. without being antagonistic towards it. Ultimately, however, I am forced to conclude that although the D.S.M. is of immense practical importance, it is unlikely to come to reflect the natural structure of mental disorders. (shrink)

In 2014, the editorial board of BMC Medical Ethics came together to devise sections for the journal that would give structure to the journal help ensure that authors’ research is matched to the most appropriate editors and help readers to find the research most relevant to them. The editorial board decided to take a practical approach to devising sections that dealt with the challenges of content management. After that, we started thinking more theoretically about how one could go about classifying (...) the field of medical ethics. This editorial elaborates and reflects on the practical approach that we took at the journal, then considers an alternative theoretically derived approach, and reflects on the possibilities, challenges and value of classifying the field more broadly. (shrink)

The so-called paradoxes of material implication have motivated the development of many non-classical logics over the years, such as relevance logics, paraconsistent logics, fuzzy logics and so on. In this note, we investigate some of these paradoxes and classify them, over minimal logic. We provide proofs of equivalence and semantic models separating the paradoxes where appropriate. A number of equivalent groups arise, all of which collapse with unrestricted use of double negation elimination. Interestingly, the principle ex falso quodlibet, and several (...) weaker principles, turn out to be distinguishable, giving perhaps supporting motivation for adopting minimal logic as the ambient logic for reasoning in the possible presence of inconsistency. (shrink)

We show that the Lascar group $\operatorname {Gal}_L$ of a first-order theory T is naturally isomorphic to the fundamental group $\pi _1|)$ of the classifying space of the category of models of T and elementary embeddings. We use this identification to compute the Lascar groups of several example theories via homotopy-theoretic methods, and in fact completely characterize the homotopy type of $|\mathrm {Mod}|$ for these theories T. It turns out that in each of these cases, $|\operatorname {Mod}|$ is aspherical, i.e., (...) its higher homotopy groups vanish. This raises the question of which homotopy types are of the form $|\mathrm {Mod}|$ in general. As a preliminary step towards answering this question, we show that every homotopy type is of the form $|\mathcal {C}|$ where $\mathcal {C}$ is an Abstract Elementary Class with amalgamation for $\kappa $ -small objects, where $\kappa $ may be taken arbitrarily large. This result is improved in another paper. (shrink)

Two algebraic structures, the contrapositionally complemented Heyting algebra (ccHa) and the contrapositionally |$\vee $| complemented Heyting algebra (c|$\vee $|cHa), are studied. The salient feature of these algebras is that there are two negations, one intuitionistic and another minimal in nature, along with a condition connecting the two operators. Properties of these algebras are discussed, examples are given and comparisons are made with relevant algebras. Intuitionistic Logic with Minimal Negation (ILM) corresponding to ccHas and its extension |${\textrm {ILM}}$|-|${\vee }$| for c|$\vee (...) $|cHas are then investigated. Besides its relations with intuitionistic and minimal logics, ILM is observed to be related to Peirce’s logic and Vakarelov’s logic MIN. With a focus on properties of the two negations, relational semantics for ILM and |${\textrm {ILM}}$|-|${\vee }$| are obtained with respect to four classes of frames, and inter-translations between the classes preserving truth and validity are provided. ILM and |${\textrm {ILM}}$|-|${\vee }$| are shown to have the finite model property with respect to these classes of frames and proved to be decidable. Extracting features of the two negations in the algebras, a further investigation is made, following logical studies of negations that define the operators independently of the binary operator of implication. Using Dunn’s logical framework for the purpose, two logics |$K_{im}$| and |$K_{im-{\vee }}$| are discussed, where the language does not include implication. The |$K_{im}$|-algebras are reducts of ccHas and are different from relevant algebraic structures having two negations. The negations in the |$K_{im}$|-algebras and |$K_{im-{\vee }}$|-algebras are shown to occupy distinct positions in an enhanced form of Dunn’s kite of negations. Relational semantics for |$K_{im}$| and |$K_{im-{\vee }}$| is provided by a class of frames that are based on Dunn’s compatibility frames. It is observed that this class coincides with one of the four classes giving the relational semantics for ILM and |${\textrm {ILM}}$|-|${\vee }$|⁠. (shrink)

Mortensen studies dual intuitionistic logic by dualizing topos internal logic, but he did not study a sequent calculus. In this paper I present a sequent calculus for complement-topos logic, which throws some light on the problem of giving a dualization for LJ.

Work on a computer program called SMILE + IBP (SMart Index Learner Plus Issue-Based Prediction) bridges case-based reasoning and extracting information from texts. The program addresses a technologically challenging task that is also very relevant from a legal viewpoint: to extract information from textual descriptions of the facts of decided cases and apply that information to predict the outcomes of new cases. The program attempts to automatically classify textual descriptions of the facts of legal problems in terms of Factors, a (...) set of classification concepts that capture stereotypical fact patterns that effect the strength of a legal claim, here trade secret misappropriation. Using these classifications, the program can evaluate and explain predictions about a problem’s outcome given a database of previously classified cases. This paper provides an extended example illustrating both functions, prediction by IBP and text classification by SMILE, and reports empirical evaluations of each. While IBP’s results are quite strong, and SMILE’s much weaker, SMILE + IBP still has some success predicting and explaining the outcomes of case scenarios input as texts. It marks the first time to our knowledge that a program can reason automatically about legal case texts. (shrink)

We examine, from a constructive perspective, the relation between the complements of S, T, and S ∩ T in X, where X is either a metric space or a normed linear space. The fundamental question addressed is: If x is distinct from each element of S ∩ T, if s ϵ S, and if t ϵ T, is x distinct from s or from t? Although the classical answer to this question is trivially affirmative, constructive answers involve Markov's principle and (...) the completeness of metric spaces. (shrink)

By a classifying topos for a first-order theory , we mean a topos such that, for any topos models of in correspond exactly to open geometric morphisms → . We show that not every first-order theory has a classifying topos in this sense, but we characterize those which do by an appropriate ‘smallness condition’, and we show that every Grothendieck topos arises as the classifying topos of such a theory. We also show that every first-order theory has a conservative extension (...) to one which possesses a classifying topos, and we obtain a Heyting-valued completeness theorem for infinitary first-order logic. (shrink)

Let E be an analytic equivalence relation on a Polish space. We introduce a framework for studying the possible “reasonable” complete classifications and the complexity of possible classifying invariants for E, such that: (1) the standard results and intuitions regarding classifications by countable structures are preserved in this framework; (2) this framework respects Borel reducibility; and (3) this framework allows for a precise study of the possible invariants of certain equivalence relations which are not classifiable by countable structures, such as (...) E1. In this framework we show that E1 can be classified, with classifying invariants which are κ-sequences of E0-classes where κ=b, and it cannot be classified in such a manner if κshrink)

Computably enumerable equivalence relations received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility \. This gives rise to a rich degree structure. In this paper, we lift the study of c-degrees to the \ case. In doing so, we rely on the Ershov hierarchy. For any notation a for a non-zero computable ordinal, we prove several algebraic properties of the degree structure induced by \ on the \ equivalence relations. (...) A special focus of our work is on the existence of infima and suprema of c-degrees. (shrink)

In this volume, leading philosophers of psychiatry examine psychiatric classification systems, including the Diagnostic and Statistical Manual of Mental Disorders, asking whether current systems are sufficient for effective diagnosis, treatment, and research. Doing so, they take up the question of whether mental disorders are natural kinds, grounded in something in the outside world. Psychiatric categories based on natural kinds should group phenomena in such a way that they are subject to the same type of causal explanations and respond similarly to (...) the same type of causal interventions. When these categories do not evince such groupings, there is reason to revise existing classifications. The contributors all question current psychiatric classifications systems and the assumptions on which they are based. They differ, however, as to why and to what extent the categories are inadequate and how to address the problem. Topics discussed include taxometric methods for identifying natural kinds, the error and bias inherent in DSM categories, and the complexities involved in classifying such specific mental disorders as "oppositional defiance disorder" and pathological gambling. -/- Contributors George Graham, Nick Haslam, Allan Horwitz, Harold Kincaid, Dominic Murphy, Jeffrey Poland, Nancy Nyquist Potter, Don Ross, Dan Stein, Jacqueline Sullivan, Serife Tekin, Peter Zachar. (shrink)

Let us say that any (Turing) degree d > 0 satisfies the minimal complementation property (MCP) if for every degree 0 < a < d there exists a minimal degree b < d such that a ∨ b = d (and therefore a ∧ b = 0). We show that every degree d ≥ 0′ satisfies MCP. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim).

Through contact algebras we study theories of mereotopology in a uniform way that clearly separates mereological from topological concepts. We identify and axiomatize an important subclass of closure mereotopologies called unique closure mereotopologies whose models always have orthocomplemented contact algebras , an algebraic counterpart. The notion of MT-representability, a weak form of spatial representability but stronger than topological representability, suffices to prove that spatially representable complete OCAs are pseudocomplemented and satisfy the Stone identity. Within the resulting class of contact algebras (...) the strength of the algebraic complementation delineates two classes of mereotopology according to the key ontological choice between mereological and topological closure operations. All closure operations are defined mereologically if and only if the corresponding contact algebras are uniquely complemented while topological closure operations highly restrict the contact relation but allow not uniquely complemented and nondistributive contact algebras. Each class contains a single ontologically coherent theory that admits discrete models. (shrink)

Classify and Label is a philosophical treatment of classification in the social sciences and everyday life, focusing on its moral, social, and political implications. This book stands at the intersection of philosophy of the social sciences, feminist philosophy, philosophy of sex, and social and political philosophy.

A complement clause is used instead of a noun phrase; for example one can say either I heard [the result] or I heard [that England beat France]. Languages differ in the grammatical properties of complement clauses, and the types of verbs which take them. Some languages lack a complement clause construction but instead employ other construction types to achieve similar ends; these are called complementation strategies. The book explores the variety of types of complementation found across the (...) languages of the world, their grammatical properties and meanings. Detailed studies of particular languages, including Akkadian, Israeli, Jarawara, and Pennsylvania German, are framed by R. M. W. Dixon's introduction, which sets out the range of issues, and his conclusion, which draws together the evidence and the arguments. This book will interest scholars of typology, language universals, syntax, information structure, and language contact in departments of linguistics and anthropology, as well as advanced and graduate students taking courses in these subjects. (shrink)

A finer-grained delineation of a given explanandum reveals a nexus of closely related causal and non- causal explanations, complementing one another in ways that yield further explanatory traction on the phenomenon in question. By taking a narrower construal of what counts as a causal explanation, a new class of distinctively mathematical explanations pops into focus; Lange’s characterization of distinctively mathematical explanations can be extended to cover these. This new class of distinctively mathematical explanations is illustrated with the Lotka-Volterra equations. There (...) are at least two distinct ways those equations might hold of a system, one of which yields straightforwardly causal explanations, but the other of which yields explanations that are distinctively mathematical in terms of nomological strength. In the first, one first picks out a system or class of systems, finds that the equations hold in a causal -explanatory way; in the second, one starts with the equations and explanations that must apply to any system of which the equations hold, and only then turns to the world to see of what, if any, systems it does in fact hold. Using this new way in which a model might hold of a system, I highlight four specific avenues by which causal and non- causal explanations can complement one another. (shrink)

I show that words with indefinite implicit complements occasion a dilemma for their model theory. There has been only two previous attempts to address this problem, one by Fodor and Fodor (1980) and one by Dowty (1981). Each requires that any word tolerating an implicit complement be treated as ambiguous between two different lexical entries and that a meaning postulate or lexical rule be given to constrain suitably the meanings of the various entries for the word. I show that (...) the positing of such an ambiguity runs counter to the facts and propose an alternative solution which does not appeal to ambiguity, meaning postulates or lexical rules. Indeed, I show that the dilemma posed by indefinite implicit complements is posed by all implicit complements and that a general solution to the problem of implicit complements follows from an independently motivated, single treatment of five other problems, that of subcategorization, that of phrasal projections of words, that of defining a model theoretic structure for phrase structure grammars, that of complement polyvalence and that of complement polyadicity. (shrink)