It is shown that a fundamental question of revealed preference theory, namely whether the weak axiom of revealed preference (WARP) implies the strong axiom of revealed preference (SARP), can be reduced to a Hamiltonian cycle problem: A set of bundles allows a preference cycle of irreducible length if and only if the convex monotonic hull of these bundles admits a Hamiltonian cycle. This leads to a new proof to show that preference cycles can be (...) of arbitrary length for more than two but not for two commodities. For this, it is shown that a set of bundles satisfying the given condition exists if and only if the dimension of the commodity space is at least three. Preference cycles can be constructed by embedding a cyclic $(L-1)$ -polytope into a facet of a convex monotonic hull in $L$ -space, because cyclic polytopes always admit Hamiltonian cycles. An immediate corollary is that WARP only implies SARP for two commodities. The proof is intuitively appealing as this gives a geometric interpretation of preference cycles. (shrink)

We consider choice correspondences that assign a subset to every choice set of alternatives, where the total set of alternatives is an arbitrary finite or infinite set. We focus on the relations between several extensions of the condition of independence of irrelevant alternatives on one hand, and conditions on the revealed preference relation on sets, notably the weak axiom of revealed preference, on the other hand. We also establish the connection between the condition of independence of irrelevant (...) alternatives and so-called strong sets; the latter characterize a social choice correspondence satisfying independence of irrelevant alternatives. (shrink)

We interpret solution rules on a class of simple allocation problems as data on the choices of a policy maker. We analyze conditions under which the policy maker’s choices are (i) rational (ii) transitive-rational, and (iii) representable; that is, they coincide with maximization of a (i) binary relation, (ii) transitive binary relation, and (iii) numerical function on the allocation space. Our main results are as follows: (i) a well-known property, contraction independence (a.k.a. IIA) is equivalent to rationality; (ii) every contraction (...) independent and other-c monotonic rule is transitive-rational; and (iii) every contraction independent and other-c monotonic rule, if additionally continuous, can be represented by a numerical function. (shrink)

This chapter sharpens the book’s criticism of exclusivist responsible to religious multiplicity, firstly through close critical attention to arguments which religious exclusivists provide, and secondly through the introduction of several new, formal arguments / dilemmas. Self-described ‘post-liberals’ like Paul Griffiths bid philosophers to accept exclusivist attitudes and beliefs as just one among other aspects of religious identity. They bid us to normalize the discourse Griffiths refers to as “polemical apologetics,” and to view its acceptance as the only viable form of (...) pluralism. This reasoning may seem initially plausible, but on closer examination his and other’s defence of the reasonableness of exclusivist responses to religious multiplicity fall apart. Informed by our study of luck-leaning theological explanations of religious difference and the counter-inductive thinking they exemplify, I argue that exclusivist responses to religious multiplicity are best explained by personal and group bias, and that a discourse between exclusivist authors or sects is beyond the pale of reasonable disagreement. Our study of descriptive (psychological) and prescriptive (religious) fideism in the first sections of Chapter Five suggests that we turn back to formal features of doxastic methods (i.e., of how people process), features that may be straightforwardly tested for in studies utilizing scales of religious orientation. These formal features allow us to better recognize not only the multiplicity of models of faith that religious adherents adhere to, but also that the relationship between forms of fideism is scalar: there is a spectrum of views running from rationalism to fideism, and at the fideistic end from moderate to strong forms of religious fideism. I further explain why developing tests and markers for a high degree of fideistic orientation is important to all those who study religion. The second half of the chapter turns to criticism or censure of exclusivist attitudes to religious multiplicity, in contrast to apologetic defenses of exclusivism. While we have examined the close connections between fideism and fundamentalism, and again between fundamentalism and exclusivism in earlier chapters, a sharper focus reveals an important but little-recognized distinction reflected in the literature: the distinction between religion-specific (or particularist) and mutualist exclusivism. The mutualist doesn’t talk just about the right of adherents of one specific religion to assert exclusivism, but the adherents of any and all “home” religions. I argue that some previously unrecognized problems for the reasonableness of exclusivist responses to religious multiplicity are brought to light when we make the distinction between the two basic ways to understand the claim that exclusivists are making. I put particularist (Barth, Lindbeck, Plantinga) and mutualist (Griffiths, Gellman, Margalit, D’Costa) defenses of exclusivism on the horns of a dilemma, and argue that despite the popularity it presently enjoys among post-liberal theologians, a close examination reveals that the very conceptual coherence of mutualist exclusivism is in serious doubt. (shrink)

One of the most distinctive and intriguing developments of modern set theory has been the realization that, despite widely divergent incentives for strengthening the standard axioms, there is essentially only one way of ascending the higher reaches of infinity. To the mathematical realist the unexpected convergence suggests that all these axiomatic extensions describe different aspects of the same underlying reality.

This paper discusses a sequence of extensions ofNFU, Jensen's improvement of Quine's set theory “New Foundations” (NF) of [16].The original theoryNFof Quine continues to present difficulties. After 60 years of intermittent investigation, it is still not known to be consistent relative to any set theory in which we have confidence. Specker showed in [20] thatNFdisproves Choice (and so proves Infinity). Even if one assumes the consistency ofNF, one is hampered by the lack of powerful methods for proofs of consistency and (...) independence such as are available for use withZFC; very clever work has been done with permutation methods, starting with [18] and [5], and exemplified more recently by [14], but permutation methods can only be applied to show the consistency or independence of unstratified sentences (see the definition ofNFUbelow for a definition of stratification). For example, there is no method available to determine whether the assertion “the continuum can be well-ordered” is consistent with or independent ofNF. There is one substantial independence result for an assertion with nontrivial stratified consequences, using metamathematical methods: this is Orey's proof of the independence of the Axiom of Counting fromNF(see below for a statement of this axiom).We mention these difficulties only to reassure the reader of their irrelevance to the present work. Jensen's modification of “New Foundations” (in [13]), which was to restrict extensionality to sets, allowing many non-sets (urelements) with no elements, has almost magical effects. (shrink)

This paper discusses a sequence of extensions ofNFU, Jensen's improvement of Quine's set theory “New Foundations” (NF) of [16].The original theoryNFof Quine continues to present difficulties. After 60 years of intermittent investigation, it is still not known to be consistent relative to any set theory in which we have confidence. Specker showed in [20] thatNFdisproves Choice (and so proves Infinity). Even if one assumes the consistency ofNF, one is hampered by the lack of powerful methods for proofs of consistency and (...) independence such as are available for use withZFC; very clever work has been done with permutation methods, starting with [18] and [5], and exemplified more recently by [14], but permutation methods can only be applied to show the consistency or independence of unstratified sentences (see the definition ofNFUbelow for a definition of stratification). For example, there is no method available to determine whether the assertion “the continuum can be well-ordered” is consistent with or independent ofNF. There is one substantial independence result for an assertion with nontrivial stratified consequences, using metamathematical methods: this is Orey's proof of the independence of the Axiom of Counting fromNF(see below for a statement of this axiom).We mention these difficulties only to reassure the reader of their irrelevance to the present work. Jensen's modification of “New Foundations” (in [13]), which was to restrict extensionality to sets, allowing many non-sets (urelements) with no elements, has almost magical effects. (shrink)

Related Works: Original Paper: M. Randall Holmes. Strong Axioms of Infinity in NFU. J. Symbolic Logic, Volume 66, Issue 1 , 87--116. Project Euclid: euclid.jsl/1183746361.

Related Works: Original Paper: M. Randall Holmes. Strong Axioms of Infinity in NFU. J. Symbolic Logic, Volume 66, Issue 1, 87--116. Project Euclid: euclid.jsl/1183746361.

The purpose of this communication is to present some recent advances on the consequences that forcing axioms and large cardinals have on the combinatorics of singular cardinals. I will introduce a few examples of problems in singular cardinal combinatorics which can be fruitfully attacked using ideas and techniques coming from the theory of forcing axioms and then translate the results so obtained in suitable large cardinals properties.The first example I will treat is the proof that the proper forcing axiom (...) PFA implies the singular cardinal hypothesis SCH, this will easily lead to a new proof of Solovay's theorem that SCH holds above a strongly compact cardinal. I will also outline how some of the ideas involved in these proofs can be used as means to evaluate the “saturation” properties of models of strong forcing axioms like MM or PFA.The second example aims to show that the transfer principle ↠ fails assuming Martin's Maximum MM. Also in this case the result can be translated in a large cardinal property, however this requires a familiarity with a rather large fragment of Shelah's pcf-theory.Only sketchy arguments will be given, the reader is referred to the forthcoming [25] and [38] for a thorough analysis of these problems and for detailed proofs. (shrink)

An online survey of 654 Australians found that the NP seniors is associated with positive personal characteristics of health and well-being such as ‘like to travel’, ‘lead an involved and active life’, ‘are vibrant and full of purpose’. Older people is also associated with positive characteristics, but somewhat less so than seniors and more socially oriented. Older people are seen to ‘benefit the workforce through their experience’, ‘have wisdom and can always be turned to for advice’, ‘play an important role (...) in their extended family’s life’. By contrast, the characteristics of those typically referred to by the elderly are negative in that the referents are incompetent or impose a burden on society, cf. ‘are frail and fall more often’, ‘are often victims of mental and physical abuse’, ‘are unable to look after themselves and depend on others for help’. The referents of old people and oldies have no particular set of characteristics assigned to them; perhaps that is why they only figure in the one characteristic ‘are tight-fisted with money’ that itself is not strongly associated with any one of the five NPs. (shrink)

This study aims to determine the paradigm shift of scientists who use inner reason to external reason (mind), a concept initiated by Aristotle. The change allegedly occurred because of the strict laws of science. Philosophers basically talk about a topic broadly and deeply about inner reason, while scientists are more focused and narrower (outer reason). Data are obtained from six articles closely related to reason, mind, and brain, then explored and presented by six expert panels for data analysis using the (...) N Vivo 12 QSR tool. The study shows a very strong correlation between the philosophical factor and reason. The results of the cluster analysis describe various comprehensive topics discussed by philosophers regarding reason which are correlated with inner reason and God, while the scientific discussion shows a very strong correlation between the brain and the alpha band. The alpha band is a condition that exists in brain waves. The cluster analysis results illustrate that scientists' discussions are focused and narrow on the brain. Thus, there has been a paradigm shift, where scientists now use outer reason to solve problems in life rather than applying inner reason. An interesting finding from this paper is that philosophers refer to reason as a noun, which means that reason is matter. This information is helpful because until now, based on a literature search, there have been no articles from scientists explaining that reason is a matter. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Call for New Theological Reflection on the Sacramental Character of Marriage and the Thought of St. ThomasLawrence J. WelchTheologians across the theological spectrum have called attention to the urgent need for a new reflection on the theological and sacramental character of marriage. Peter Hünermann, known for his strong criticism of magisterial teachings on marriage, and the late Cardinal Carlo Caffarra, known for his equally strong defense (...) of them, have both drawn attention to this need. At an international symposium in September 2015, held in Rome prior to the Ordinary Synod of Bishops on Marriage and the Family, Hünermann gave a presentation entitled "On the Specific Theological Character of the Sacrament of Matrimony."1 The symposium aimed at providing a critical and scholarly discussion of new and constructive perspectives for the Church doctrine on marriage and family life in time for the 2015 synod on the family.2 Some of Hünermann's work from this paper also came to be known from an interview in Commonweal magazine where he summarized some of the main points of his symposium presentation.3 In the interview, he also revealed that before the 2015 synod he [End Page 845] was invited to speak with Pope Francis about the theology of marriage. Understandably, this meeting heightened interest in the German theologian's thought.Hünermann argues that "the specific character of the sacrament of marriage, which is very closely connected to the dying of the marriage bond,... has scarcely been the object of theological reflection, [and] is almost unknown in the consciousness of the bishops." 4 Hünermann appeals to St. Thomas as a way forward for understanding the theological character of marriage. This appeal is situated within a wider examination5 that offers an elaboration and new interpretation of "the specific dogmatic characteristics of the sacrament of matrimony that emerge in today's situation from a critical comparison of the encyclical Casti connubii and the Catholic theological tradition, especially the theology of St. Thomas."6 Sharply critical of the encyclical, Hünermann sees it as having saddled the Church with a legalistic concept of marriage elevated above history that is too far removed from the Catholic theological tradition and St. Thomas's theology of marriage.The year before his death, Cardinal Caffarra gave the 2016 graduation address at the John Paul II Institute for Marriage and Family in Washington, DC.7 Among the challenges he identified for the institute to address was the [End Page 846] need for theological reflection on the sacramental character of marriage. Referring to his earlier work, he pointed out that theology after the Council of Trent "lost the awareness of sacramental ontology, of the real transformation produced by the sacrament in the persons of the spouses [res et sacramentum]."8 Furthermore, according to Caffarra, the "theology of the conjugal covenant was supplanted by the notion of a contract, as a human act by which two persons commit to one another." The sacramental character was thought of as consisting of the assurance of divine graces given to fulfill the contract. Caffarra claimed that, "consequently, the words of Jesus 'What God has joined together, let not man put asunder,' lost all their realistic force. Absolute indissolubility, once the sacrament was perfected [=a ratified, consummated marriage], became essentially indefensible."9The primary interest of this paper is to respond to the call for a renewed theological reflection on the specific character of the sacrament of marriage. I wish to take up Caffarra's suggestion to focus on the sacramental character (res et sacramentum) on the one hand, and on the other hand, Hünermann's suggestion that a kind of ressourcement from St. Thomas Aquinas's theology of marriage can be of great help for a fresh theological reflection on the specific character of the sacrament of marriage. Although I agree with Hünermann that a renewed consideration of the thought of St. Thomas can be a way forward, I differ from him on how it can be. Hünermann notices that St. Thomas speaks of the grace of the sacrament of marriage as a helping grace.10 St. Thomas does indeed speak this way of the... (shrink)

Saunders Mac Lane has drawn attention many times, particularly in his book Mathematics: Form and Function, to the system of set theory of which the axioms are Extensionality, Null Set, Pairing, Union, Infinity, Power Set, Restricted Separation, Foundation, and Choice, to which system, afforced by the principle, , of Transitive Containment, we shall refer as . His system is naturally related to systems derived from topos-theoretic notions concerning the category of sets, and is, as Mac Lane emphasises, one that is (...) adequate for much of mathematics. In this paper we show that the consistency strength of Mac Lane's system is not increased by adding the axioms of Kripke–Platek set theory and even the Axiom of Constructibility to Mac Lane's axioms; our method requires a close study of Axiom H, which was proposed by Mitchell; we digress to apply these methods to subsystems of Zermelo set theory , and obtain an apparently new proof that is not finitely axiomatisable; we study Friedman's strengthening of , and the Forster–Kaye subsystem of , and use forcing over ill-founded models and forcing to establish independence results concerning and ; we show, again using ill-founded models, that proves the consistency of ; turning to systems that are type-theoretic in spirit or in fact, we show by arguments of Coret and Boffa that proves a weak form of Stratified Collection, and that is a conservative extension of for stratified sentences, from which we deduce that proves a strong stratified version of ; we analyse the known equiconsistency of with the simple theory of types and give Lake's proof that an instance of Mathematical Induction is unprovable in Mac Lane's system; we study a simple set theoretic assertion—namely that there exists an infinite set of infinite sets, no two of which have the same cardinal—and use it to establish the failure of the full schema of Stratified Collection in ; and we determine the point of failure of various other schemata in . The paper closes with some philosophical remarks. (shrink)

In a recent paper, Andy Clark (2008) has argued that the literature on embodied cognition reveals a tension between two prominent strands within this movement. On the one hand, there are those who endorse what Clark refers to as body-centrism, a view which emphasizes the special contribution made by the body to a creature’s mental life. Among other things, body centrism implies that significant differences in embodiment translate into significant differences in cognition and consciousness. On the other hand, there are (...) those who endorse what Clark calls extended functionalism, a view which sees the mind as the joint product of the computational resources presented by (i) intracranial processing, (ii) bodily input, and (iii) environmental scaffolding. As such, extended functionalism allows for the possibility that any contribution of the body to cognition and consciousness can be compensated for by the other two contributing factors. While Clark’s sympathies lie with the latter approach, we argue in favour of the former. In particular, we focus on consciousness and argue that the unique contribution the body makes to a creature’s manifold of phenomenal experience cannot be compensated for, in the manner, and on the scale, that Clark envisages. (shrink)

We show that either PFA + or Martin's maximum implies Fleissner's Axiom R, a reflection principle for stationary subsets of P ℵ 1 (λ). In fact, the "plus version" (for one term denoting a stationary set) of Martin's axiom for countably closed partial orders implies Axiom R.

New technologies could facilitate new ways of cheating. This emerging scenario places academic integrity policy in higher education institutions as critical. Academic integrity scholars have designed conceptual frameworks to analyze academic integrity policy. The body of the literature on academic integrity policy analysis includes studies developed in North America, Europe, and Australia. However, insight into several regions of the world is lacking. This pioneering study in the Chilean context analyzes documents addressing academic integrity at forty-three accredited universities. Using a qualitative (...) research design, we framed this policy analysis in the five core elements of exemplary academic integrity policy: access, approach, responsibility, detail, and support. The findings revealed challenges with accessing documents online, a strong presence of legal language that might not be understandable to all students, and a scarcity of information about review cycles. The punitive approach was prevalent, with a significant focus on students’ conduct. Signs of collaboration and mechanisms for promoting academic integrity cultures were nearly absent. The documents primarily targeted students and the roles of other stakeholders concentrated on the enforcement of sanctions and misconduct investigations. The analysis also showed the use of general definitions to describe academic integrity breaches, inconsistency across the system in defining plagiarism and a lack of guidance to address contract cheating and unauthorized use of generative artificial intelligence. The findings also highlighted the unavailability of institutional support to teach, learn, and research with integrity or references to research-based practices. We propose twelve practical recommendations for policymakers and academic integrity advocates. (shrink)

We suggest a new approach for addressing the problem of establishing an axiomatic foundation for large cardinals. An axiom asserting the existence of a large cardinal can naturally be viewed as a strong Axiom of Infinity. However, it has not been clear on the basis of our knowledge of ω itself, or of generally agreed upon intuitions about the true nature of the mathematical universe, what the right strengthening of the Axiom of Infinity is—which large cardinals (...) ought to be derivable? It was shown in the 1960s by Lawvere that the existence of an infinite set is equivalent to the existence of a certain kind of structure-preserving transformation from V to itself, not isomorphic to the identity. We use Lawvere's transformation, rather than ω, as a starting point for a reasonably natural sequence of strengthenings and refinements, leading to a proposed strong Axiom of Infinity. A first refinement was discussed in later work by Trnková—Blass, showing that if the preservation properties of Lawvere's tranformation are strengthened to the point of requiring it to be an exact functor , such a transformation is provably equivalent to the existence of a measurable cardinal. We propose to push the preservation properties as far as possible, short of inconsistency. The resulting transformation V→V is strong enough to account for virtually all large cardinals, but is at the same time a natural generalization of an assertion about transformations V→V known to be equivalent to the Axiom of Infinity. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Current State of Vico ScholarshipDavid L. MarshallGiambattista Vico is one of those chameleon figures in the history of ideas who is so intellectually rich that he can be constantly reinvented. It is indicative of the rich ambiguity of his thought that two of the most prominent intellectual historians working today should have come to opposite conclusions about his relationship to the master-category of eighteenth-century intellectual history: for Mark (...) Lilla, Vico was a Counter-Enlightenment thinker; for Jonathan Israel, he was a figure in the Radical Enlightenment.1 Vico’s fungibility gives reason for pause. Someone who can be folded into all manner of intellectual projects may be suspect. But Vico is more colonizing than colonized and, thus, the diversity of his receptions is evidence of creativity, and not merely malleability. The only way to deal with Vico is to dive into the multiplicity of plausible interpretations and find in them the makings of a new line of inquiry. Vico’s moment of flourishing in the Anglophone world came initially in the 1960s and 1970s, but if the diversity and quality of receptions in the last five years is anything to go by then we can say that Vico remains—especially in Italian, French, and German— an intellectual historical provocateur.This review essay surveys such literature and makes a single recurring observation: the various specifications of Vico’s place in intellectual history come into alignment as dimensions of what one might term Vico’s reinvention of rhetoric. As a professor of rhetoric in a culture that possessed—for [End Page 141] the most part—very weak oratorical institutions, Vico found himself in a particularly paradoxical situation. Recent research on Vico suggests that this paradox worked itself out in Vico’s thought in a number of highly interesting ways. First, Vico constitutes an opportunity for intellectual historians of the scientific revolution by offering a simultaneously rhetorical and pragmatic gloss of the early modern logic of experiment. Second, for intellectual historians of religion, Vico constitutes a study in how early moderns could examine the rhetorical functioning of theological vocabularies without necessarily committing themselves to the independent existence of the referents of those vocabularies. Third, for intellectual historians of Enlightenment, Vico confirms that encyclopedism was not a merely French practice in the eighteenth century and that the kind of omnicompetence implicit in encyclopedic multidisciplinarity had roots in rhetorical criticism. Fourth, intellectual historians of Counter-Enlightenment cannot easily fold Vico into their narratives, in part because his legal works (which have been read as a call for cultural retrenchment in response to early modern skepticism) are in fact an account of how Greek rhetoric found its analogue in Roman jurisprudence. Fifth, for historians of the idea of language, Vico demonstrates that there were powerful alternatives in early modernity to the dominant contractualist account of the origin of language (offered by Hobbes, Locke, and others) that were rhetorical and yet did not emphasize the priority of speech over writing.When it appeared in 1961, Nicola Badaloni’s Introduzione a G.B. Vico was the most sophisticated attempt to locate Vico in the Neapolitan philosophical tradition. In many ways, it remains the best attempt at contextualizing a thinker who is notoriously difficult to situate among his contemporaries. John Robertson’s recent Case for the Enlightenment has many virtues (not least its revealing supposition that Vico ought to be read alongside Hume), but as an attempt at contextualization Robertson’s work is not as rich as Badaloni’s.2 In particular, Badaloni did a great deal to reconstruct the history of natural philosophical inquiry at Naples in the seventeenth and eighteenth centuries. In Badaloni’s description, Naples was a place in which a strong culture of natural philosophical investigation set the foundation for concepts such as experimentalism and pantheism. Furthermore, Badaloni argued that, although such concepts originated in natural philosophy, they cross-pollinated with ideas prominent in the Neapolitan schools of jurisprudence—particularly probabilism. In the [End Page 142] broadest terms, Badaloni argued that Vico’s intellectual project was an examination of the pantheistic principle that Jovis omnia plena (“all things are made of Jove”) in the domains of law, poetry, and history... (shrink)

Writing, the exigency of writing: no longer the writing that has always (through a necessity in no way avoidable) been in the service of the speech or thought that is called idealist (that is to say, moralizing), but rather the writing that through its own slowly liberated force (the aleatory force of absence) seems to devote itself solely to itself as something that remains without identity, and little by little brings forth possibilities that are entirely other: an anonymous, distracted, deferred, (...) and dispersed way of being in relation, by which everything is brought into question – and first of all the idea of God, of the Self, of the Subject, then of Truth and the One, then finally the idea of the Book and the Work so that this writing (understood in its enigmatic rigor), far from having the Book as its goal rather signals its end: a writing that could be said to be outside discourse, outside language. – Maurice Blanchot ( The Infinite Conversation , xi) The Compendium * Beginning with the idea and practice of writing, and moving to the subject or self, then to truth and the One, and arriving at the Book and the Work, Blanchot’s words reflect the trajectory of the following work of writing. True to the embeddedness of the subject in the work of writing, the term “Compendium” has been a metonym for me over the past few years as I have thought about the concept of totality alongside its expression in figures such as the One, the Whole, or the All. In the following I aim to share some of the content of this metonym, and to enrich it by making some distinctions. 1 Here the term “Compendium” will refer to a concept of totality that is ontological (pertaining to being, and the copula) and also textual (pertaining to the symbolic, and the signifier-signified relationship). The Compendium is a figure for thinking the world as a Book, in the broadest sense—an approach to reality that is by no means new, but one that is due for renewal. 2 In partial answer to the question of the Compendium we will say that the word ‘Compendium’ stands in for expressions which seek to totalize, or concepts which seek to approach the concept of ‘everything,’ particularly when these expressions are bound up in the question of the Book (both the book as a physical object and the Book as a metaphysical figure: a way of thinking about the work in and of writing). The question of the Compendium is strongly associated with the physical and metaphysical form of the Book, like the mysterious and symbolic books which are opened in the Biblical book of Revelation, the book of life and the book of death, which together constitute an important couplet. 3 Parataxis & Hypotaxis There are two helpful distinctions that will bring us closer to an answer to the question “What is a Compendium?” The first distinction is between two figures in and for writing: parataxis and hypotaxis . Typically paired in contrast to one another as literary techniques, with parataxis indicating a side-by-side placement of textual elements and hypotaxis referring to subordinate arrangements of textual elements, the two figures can be understood as having a philosophical significance in addition to their practical function as devices for writers. For us these two terms will remain between philosophical theory and writing practice, and serve as a perspective for our writing and creation of texts. Here I take texts to refer to anything from the concrete written words in a book, to the ontological text of the world that we experience. Parataxis , as a figural way of thinking about the ontological structure of texts, refers to texts which are tightly woven and interdependent – texts within which each sentence bears the weight of the entire work. Parataxis often involves repetition, great density, and fragility. One of the best examples of this sort of text is Theodor Adorno’s posthumous magnum opus , Aesthetic Theory . In addition to the text itself, the translation history of the book may also help us to better understand parataxis and its relation to hypotaxis . The final published version of Aesthetic Theory , in German, was a text that Adorno intended to revise and rewrite, but this intention was never realized because of his untimely death. Where the German text of Aesthetic Theory certainly exemplifies the concept of parataxis , the first English edition took this densely woven text and carved Adorno’s lengthy paragraphs and lengthy sentences into manageable ‘bite-sized’ pieces of English text. The first translator took further liberty and inserted headings and new paragraph breaks where there were none in the original. Aesthetic Theory was eventually retranslated by Robert Hullot-Kentor and is now available in a form that is much more faithful to the original work. 4 The pertinent idea that this translation history points to is the distinction between parataxis and hypotaxis . Where parataxis describes texts which are repetitive, densely woven, and often fragile, hypotaxis describes texts which are hierarchical and in which the primary relation is linear – the latter of which is very similar to the first English translation of Aesthetic Theory . On the other hand, the original German text that Adorno wrote was very dense, often repetitive, and contained long sections of text unbroken by paragraphs or headings. This example of parataxis was then turned towards hypotaxis through the initial translation which took a text that was, in many ways, nonhierarchical and nonlinear, and artificially subjected it to a hierarchy that was not its own (and here I take the word of Fredric Jameson who comments on the two translations in a note at the beginning of his book Late Marxism ). 5 The point here is not about translation, but rather the distinction between parataxis and hypotaxis precisely as they are figures for discourse, written or otherwise. The concept of parataxis looks far more postmodern and rhizomic than the concept of hypotaxis which remains very modern and arborescent. This is a more figural way of talking about the distinction. However, if we wanted to take a more precise and analytical approach we could say that on the level of form parataxis involves a relationship between sentences and paragraphs in which each part bears an equally crushing responsibility to present the whole content of the text. As well, on the level of content, parataxis requires that each concept in a work take on the full conceptual weight of the total work. Continuing the analysis, we could say that parataxis describes texts in which there is no (or very little) linear or causal move from antecedent to consequent, whether in content or form. Instead, parataxis describes texts which weave together concepts via conjugations or associations. The concept of hypotaxis , on the other hand, requires that texts submit themselves to hierarchy, one example of which is logical argumentation. The contingency of the conclusion upon premises in hypotaxis is certainly distinct from the repetition, re-presentation, and conjugation of concepts in parataxis , and I think that this is evident in the difference between the writing styles prevalent in contemporary Analytic philosophy and Continental philosophy. It is not the case that the distinction between parataxis and hypotaxis absolutely corresponds with the writing styles of Continental and Analytic philosophy (respectively). There are thinkers who take exception to this pattern, such as Badiou’s more formal approach in the discourse of Continental philosophy to give one example. However, when Analytic philosophy takes its writing lessons from the sciences, and seeks to do philosophy via the clean linear move from antecedent to consequent, then I think that Analytic philosophy writes with hypotaxis in mind. On the other hand, when Continental (particularly German and French) philosophy takes its writing lessons from narrative or poetry then Continental philosophy writes with parataxis in mind. It is not fair to say that all those writing Continental philosophy are looking to narrative and poetry for stylistic direction, just as it is not the case that all those writing Analytic philosophy have mathematics and science as their writing format, however there are some striking ways in which the differing epistemologies of Continental and Analytic philosophy encourage writing with parataxis and hypotaxis in mind (respectively). For some, writing with parataxis or hypotaxis in mind is a conscious decision and a product of stylistic self-consciousness, and for others it is an unconscious discursive and epistemic requirement that must be met in order to be involved in a particular discourse. Before moving on to our second distinction, and then an examination of the question of the Book, it is important to point out that both totality and figurations like the One, the Whole, and the All, come out of very human desires to totalize or to actualize our being-towards-totality. The relationship between identity and totality then can be construed, with Heidegger in mind, as striving toward wholeness, completion, or fulfillment, each of which is a quality of compendia. 6 Compilation & Selection The first distinction between parataxis and hypotaxis pertains to both form and content, and to both the mechanics of writing and the ideas to which writing refers. The second distinction pertains to both as well. In the process of writing and in the process of perception as well, there is a tension between compilation and selection . To begin with, in the work of theory-writing there is compilation, and this is because writing theory requires a broad perspective and certain measure of totalization. On the other hand, writing theory requires that the writer select an idea or a combination of ideas to individuate out of a radical and infinite multiplicity of identities and combinations. The concern here is not primarily for the writing of a theory about a specific idea, like a secondary work or a reference text. But rather the concern is with the writing of grand theories: Marx and Marxism, Derrida and Deconstruction, Husserl and Phenomenology, Sartre and Existentialism, Saussure and Structuralism —each of which strives along a trajectory towards being all-encompassing, whether it intends to or not. Today, we could even say that Speculative Realism has embarked on this journey, and perhaps now we could say that the discourse of Speculative Realism has reached the inevitable point after which a grand theory leaves the hands of its writer or writers and becomes a possession of the collective consciousness of the academy, or (perhaps now) the mass consciousness of the blogosphere—and this is a true pharmakon , a poison and a cure, a blessing and a curse. 7 When we write theory, whether the scope is that of a grand theory or a particular theory, we write in the tension between compilation (making good on the desire to be all encompassing) and selection (being required to decide and discern and to judge what is included in the work and what is deleted or appended or abridged or given over to ellipses). Generally speaking, the work of theory-writing often comes out of a desire to totalize, that is, to develop a theory of everything that is able to apprehend new experiences and ideas while still remaining whole. I grant that this is not a universal desire, and that not everyone who sits down to write a work (or book) of theory does so because of their will-to-totality, but it remains that this drive to totalize does condition a great many writers of theory (especially those who seek to develop grand theories like those mentioned previously). At the beginning of his book of interviews, Between Existentialism and Marxism , Sartre is quoted as saying, after completing the first volume of his Critique of Dialectical Reason : “I no longer feel the need to make long digressions in my books, as if I were forever chasing after my own philosophy. It will now be deposited in little coffins, and I will feel completely emptied and at peace—as I felt after Being and Nothingness . A feeling of emptiness: a writer is fortunate if he can attain such a state. For when one has nothing to say, one can say everything .” 8 This is where our two initial distinctions come to bear on the being-towards-totality as it is expressed in the concrete practice of writing: the first being between parataxis and hypotaxis , and the second being between compilation and selection. Where this second distinction is concerned there is a certain paradox at play given that selection is inescapable, and compilation is unachievable. Selection is inescapable (with the figure of the Compendium in mind) because, even when the imperative to compile is followed to excruciating lengths, selection still has the last word. This is why the Compendium is a figure rather than some material thing that can actually be accomplished or actualized. No matter how far one goes along with the will-to-archive and the will-to-compile, it is only ever a question of minimizing selection and never eliminating it. This leads to the second point, which is that total compilation is unachievable. The closest thing to total compilation that we have before us is the ontological and textual fabric of the world. Even in the case of the world, compilation cannot be enacted in a total fashion because of the need to include both the sphere of the actual and the sphere of the possible or potential. This as another way in which compilation is always-already selection, and further evidence that total compilation is practically impossible. Discursive Figuration and Total Writing Rather than figuration referring to a figure of speech or an image, here the term points to a way in which to think about the work of writing, both the work put into writing, and the work that is the result of writing: the finished yet incomplete final piece. As figures or figurations, the Book and the Compendium are ways of thinking about the work of writing and the human desire for the wholeness, completion, and fulfillment that are made manifest in the completed form of the book (whether a published or printed or saved document put to rest by the author). These two figures bear more strongly upon works that seek to be all-encompassing, and works that strive towards expressions of totality such as the One, the Whole, or the All. Moving on to the topic of the subtitle, and on a more prescriptive note, I would say that there is more hope for theory-writing to be found in parataxis than hypotaxis . Part of the reason for this claim is the poststructuralist critique of hierarchies, and yet another part is the compelling line of thinking called “weak thought” (in theology by John D. Caputo, and in philosophy by Gianni Vattimo, among others). 9 The consequences of these two convictions are such that if one is to strongly assert the truth of a grand theory without leaving the realm of hierarchy-critique and weak thought, then one must write paradoxically with parataxis in mind, and in so doing write weakly and non-hierarchically. This does not mean avoiding a sort of topography or topology when writing theory, rather it means avoiding both subjugation and oppression in thought by pursuing a nonviolent sort of ontology. In order to do this, theory writing does not present itself as an exercise in logical analysis where one mechanically moves from a set of premises (via contingency) to the inevitable conclusion (via necessity). Instead, theory approaches the idea of a Compendium. Given that the figural Compendium places parataxis and compilation above hypotaxis and selection, then the question becomes: is placing one part of a binary term before another not just another way of selecting, or another expression of hypotaxis ? Counter to the urge to resign oneself to the reign of selection, with some qualification one can nonetheless write without deciding whether selection and hypotaxis should be subservient to compilation and parataxis (which is to say that writing-without-decision is somewhere between and beyond possibility and impossibility). This dilemma can be disarmed by stating that theory writing is not about primacy, and not about having-decided-beforehand, both stylistically and also where content is concerned. This is the paradox of writing: always striving along a trajectory ( telos ) towards totality via parataxis and compilation, but always being drawn back to finitude and making selections, and placing one idea before another with hypotaxis in mind. In light of this paradox, the question of the Compendium as a figure for discourse and a figural Book has resonance with Jacques Derrida’s essay on Edmund Jabès’ Book of Questions , found in his Writing and Difference . The Question of the Book “Little by little the book will finish me.” 10 Derrida quotes Jabès, and proceeds to outline the reflexive relationship between the author of the book and the book itself, each of which are subjected to the other through a sort of chiasmus, both ontological and textual (not that the two are entirely separable). The Book, for Derrida like Blanchot in the introductory quotation, “infinitely reflects itself” and “develops as a painful questioning of its own possibility”, and in light of this we can draw an association with the painful tension between the practical reality of selection and the ideal trajectory of compilation. 11 This tension in writing, between the will to total compilation and the necessity of abridgment, is an ontological tension between part and whole just as it is a textual tension between signifier and signified. The ontological tension in writing that Derrida expresses in his essay on Jabès is between everything and nothing – a contradiction which Derrida finds in Jabès’ Book of Questions and also in the divine, in God. When one writes between compilation and selection one writes towards totality, and here we can follow Derrida who states that the lapse in signification, presumably in the signifier-signified discrepancy, is a “ rupture with totality itself” and furthermore that this lapse cannot be rectified through deductive reason or even philosophical discourse. 12 This rupture with totality, found in the troubled relation between signifier and signified, can also tell us a lot about the Book and about writing. Given an understanding of writing as an ontological act that strives towards (but never accomplishes) totality, we can see the written book as the manifested and given body of that striving. Perhaps in other disciplines or even other schools of philosophy there is a cultural climate within which the article is prized above the book, but I am fairly confident, especially when referring to the grand theories of Continental thought, that there is a respect for the book as a uniquely meaningful object capable of apprehending totality. Derrida writes, Between the too warm flesh of the literal event and the cold skin of the concept runs meaning. This is how it enters into the book. Everything enters into, transpires in the book. This is why the book is never finite. It always remains suffering and vigilant. 13 Here the vitality of the literal event is compromised by the deadening weight of the concept, and the figure of the Book assists in this lapse of meaning. The Book is a totalizing object, much like the figure of the Compendium, and yet this totalization lacks its final object of completed totality both because the figural Book is necessarily incomplete, and because the physical book is always-already a product of selection. Instead of achieving its end of being a place where everything takes place, it suffers from the lapse of writing, the discrepancy between event and concept. Derrida continues his exposition on Jabès by bringing to light yet another reflexive relation, a reversal of the relationship between the Book and the world. Derrida writes that, for Jabès, “the book is not in the world, but the world is in the book.” 14 In addition to what was stated before, I take figuration to mean that the concepts employed, such as the Book or the Compendium, are not subject to the supposed rigor of analysis that is so prized by Enlightenment or Capitalist realisms. The figure of the Book and the figure of the Compendium cannot be held accountable to standards imported from scientific method, given an understanding that these standards require a concept to be replicable, consistent, falsifiable, measurable, and so on… This is an important point to make, especially in the present atmosphere within which theory must justify itself under conditions that are not its own. Instead of being held to these standards, figuration serves as a way in which to think about writing that leaves thought open to idealistic speculation, imperfect analogies, and most importantly the ever-present gain and loss that occur in the relationship between thought and being. By extension the figural way of addressing writing indulges in enough generalization to accommodate the excess/lack relationship between the ideal form of the Book or the Compendium, and the manifested and given body of a text (as it is practically completed and closed). Here we speak against the hostile atmosphere which would have theory submit itself to hierarchical rigor, rather than Blanchot’s “enigmatic rigor”, by being explicit about the discursive conditions and epistemic conditions under which theory operates. To write with parataxis in mind is, to a certain degree, to write with weakness as one’s methodology (with weak thought being in opposition to hypotaxis and hierarchy as much as weak thought can be in opposition to anything). Rather than asserting the strength of hierarchical theory, and rather than employing antagonistic argumentation with the goal of refutation different discursive and epistemic conditions for theory writing must be cultivated (and these are by no means new). First the critical and theoretical spirit reveals itself as being concerned with the task of complication—especially the complication and critique of binaries, dichotomies, dualities, polarities, paradoxes, parallaxes, hybridities, and especially antinomies. Second, theory positions itself as a sort of showing or revealing, rather than being ultimately focused on coming to full agreement or disagreement. This is where figuration can help theory-writing, both by placing emphasis on teleologies and trajectories (like parataxis and compilation), and by shifting focus away from pure primacy, power, or absolute origin. Figuration then, assists theory writing by placing the concern of theory outside of the concerns of the hard or soft sciences, and into the realm of thought or the idea. To speak of ‘the’ Compendium or ‘the’ Book, here, is to generalize not regarding the perfect form of the Compendium or Book, but to engage speculatively with an abstract idea which remains singular and yet complicated by multiplicity. The question of the Book that Derrida asks through Jabès is a question of everything and nothing, totality and nonbeing, and this question is a concern for writing and a concern for the figure of the Compendium so defined by the tension between compilation and selection, and parataxis and hypotaxis . On the note of nonbeing, we can look to the final page of Derrida’s first essay on Jabès in Writing and Difference and notice the introduction of his neologism, différance (with an ‘a’). Derrida writes: Life negates itself in literature only so that it may survive better. So that it may be better. It does not negate itself any more than it affirms itself: it differs from itself, defers itself, and writes itself as différance . Books are always books of life (the archetype would be the Book of Life kept by the God of the Jews) or of afterlife (the archetype would be the Books of the Dead kept by the Egyptians). 15 This introduction of différance into the equation of the Book, alongside ontological affirmation and negation, hearkens back to the discussion of the symbolic lapse earlier in his essay. Differing and deferring, the Book is always a Book of Life and a figure for the intersection of the vital (life) and the total in writing. In a way, the writer of the Book may be someone who lives life, and in another way the writer of the book-as-object may be someone who engages in the act of writing, both practically (by inscribing words on paper, or typing script on a computer) and ontologically or symbolically (by investing their existence and inexistence into a work worthy of the figural Book). In addition to the writer as writer, the writer also serves as an editor, and the editorial role alongside the idea of the Compendium shows the editor to be one who collects and compiles, while being restrained by eventual selection and decision. Beyond this the editor of works and texts, in both the Book and the world, is engaged in a process of inscribing notation—of annotating (on) the Compendium. Eternal commentary is a feature of the textual Compendium, just as open-ended totality describes the ontological Compendium. The writer as writer does not simply write texts, but rather engages in a profoundly ontological act of inscribing their existence into the world, and the writer as editor does not merely annotate or alter texts as they are, but rather comments upon the text of the world. In/Conclusion So as we create texts, and as we write and create theory, let us be and remain attentive to the figure of the Compendium and the figure of the Book. These two concurrent metonymies are essential for total writing (grand theories, etc.), and may be forgettable for those concerned with fragmentary or hierarchical writing (which are valid in their own right). From the ontological and symbolic text of the world and phenomenological experience, to concrete texts such as books or mixed media, the figure of the Compendium and the figure of the Book are important for the actualization of the human will to be all-encompassing. The figure of the Compendium teaches writers of theory that the repetition, density, and fragility of parataxis offers a strong sort of weakness which does not become yet another variety of oppressive and hegemonic thought. Rather than write with hypotaxis in mind, subjugating one thought to another via cause and effect or antecedent and consequent, I would hope that theory-writing could guiltlessly indulge in the dialectical and contradictory conjugation of ideas, and take this as a legitimate methodology. Rather than being ashamed of showing resonances or giving way to abridgment or ellipses, it is my own authorial (but not authoritative) conviction that one need not give up on totalizing and constructing grand theories because of the fact that complete totalization is impossible, and one need not give up on totalizing and constructing grand theories because of the worry of violence, for the Book and the Compendium lack their completed object and are ever incomplete trajectories. NOTES * UPDATED 7/19/13: we've updated the HTML version to reflect the (correct) PDF version. Our apologies to the author—eds. 1. I would like extend thanks to Dr. Peter Schwenger of the University of Western Ontario for his comments on this paper and his hospitality as it was presented as a Theory Session at the Centre for Theory and Criticism on October 26th 2012. I would also like to thank Andrew Weiss for conversation and critique. 2. I should clarify my use of the term ‘figure’ at the outset. Given the use of the term by Jean-Francois Lyotard in Discourse, Figure (and also Gilles Deleuze in Francis Bacon ), I should state clearly that my use of the term will not correspond to the term ‘figure’ understood as the representation of an object. Instead, my use of the term ‘figure’ and its variations (‘figural’, ‘figurative’, ‘figuration’) will refer to the illustrative or metaphorical use of the Compendium or the Book as models or ways of thinking about writing and discourse. 3. Cf. Revelations 20:12-15. 4. Theodor Adorno, Aesthetic Theory , Trans. Robert Hullot-Kentor (London & New York: Continuum Press, 1997). 5. Fredric Jameson, Late Marxism: Adorno, or the Persistence of the Dialectic (London & New York: Verso, 1990), ix-x. 6. I have written about this concept of being-towards-totality elsewhere in two pieces of writing: the first is called Notes on the Compendium (an unfinished draft) which addresses some very wide theoretical concerns, being structured as a sort of itinerary or archive, and the second is Dialectics Unbound (Punctum Books, 2013) which outlines a concept of totality without the violence of totalization. While these works are more concerned with ontological totality, here I would like to focus on the idea of the Compendium as a textual totality. 7. Cf. Louis Morelle, “Speculative Realism: After Finitude and Beyond, A vade mecum” in Speculations: Journal of Speculative Realism . Issue 3 (Brooklyn, New York: Punctum Books, 2012), 241-272. 8. Jean-Paul Sartre, Between Existentialism and Marxism . Trans. John Matthews (London & New York: Verso, 1974), 9. 9. Cf. John D. Caputo, The Weakness of God (Indiana: Indiana University Press, 2006). 10. Jacques Derrida, “Edmond Jabès and the Question of the Book” in Writing and Difference . Trans. Alan Bass (Chicago: University of Chicago Press, 1978), 65. 11. Ibid, 65. 12. Ibid, 71. 13. Ibid, 75. 14. Ibid, 76. 15. Ibid, 78. (shrink)

I conducted my own comparative and empirical study on the presence, absence, and uses of dignity as a bioethical principle. My study revealed the difference between the Anglo-American region and Europe, as well as the internal diversity in the European countries, which demonstrated a lack of unity and consistency in both the scope and the perception of the concept. The information and analyses presented in this work confirm these observations and conclusions while highlighting the strong presence of the (...) principle of dignity in the law almost everywhere in the world. However, this relative omnipresence of the notion of dignity is less evident in the field of bioethics, which is my sole interest. All of which resulted in referring back to the words of Ruth Macklin “Dignity is a useless concept,” albeit in the form of a question: is dignity a useless, perhaps even harmful, concept, as it is a source of confusion and misunderstanding rather than of clarity? (shrink)

In legal methodology (usul al-fiqh), the problem of the defining istiḥsān and the legitimacy of its definition is among the critical discussion topics. To overcome the rigorism of law, istiḥsān was used by the founder scholars of Ḥanafī school of law and Malik b. Anas - however this use received various objections. Although the Mālikī scholars also used istiḥsān strong criticisms of istiḥsān have been directed on the Ḥanafīs. After the severe criticism of Muḥammad b. Idrīs al-Shāfiʿī, the Ḥanafī (...) scholars carried out various intellectual activities to define istiḥsān and to prove that it is legitimate. This process -which started especially with Abū’l-Ḥasan al-Karkhī and Abū Bakr al-Jaṣṣāṣ, revealed a rich accumulation with the contribution of the legal theorists in other school of laws. It is known that al-Karkhī's definition of istiḥsān has become widespread among the legal theorists, and the legitimacy of istiḥsān in the works of legal theory was based on his definition. Al-Karkhī's considerations on the legaliticamy of using istiḥsān can be traced in his student al-Jaṣṣāṣ, in the following centuries, Abū Zayd al-Dabūsī, Abū l-‘Usr al-Bazdawī and al-Sarakhsī’s works. Al-Jaṣṣāṣ' explanations on the legitimacy of istiḥsān begin with the criticism of Imam al-Shāfiʿī's against istiḥsān. He provides the proof of legitimacy for istiḥsān in divided two sub-headings. Al-Jaṣṣāṣ, who deals with istiḥsān in two parts as word and meaning, argues that there is no disagreement about the use of istiḥsān and that all mujtahids accept istiḥsān, and even al-Shāfiʿī, who opposes to the use of istiḥsān, employs istiḥsān in this sense. The type of istiḥsān on which there is a deabte is the istiḥsān used in relation to its meaning. Al-Jaṣṣāṣ states that this use is a qiyas operation; he justifies his point of view by referring to the works of Muḥammad b. Hasan al-Shaybānī. Indeed, when we look at how al-Shaybānī explained the istiḥsān’s examples in his works, it is seen that there are two conflicting juristic analogy (qiyas) made in many examples. Moreover, al-Shaybānī openly considered some types of istiḥsān part of qiyas by stating that some examples “can be included in this type of istiḥsān” Ḥanafī scholars wanted to break the hostile atmosphere toward istiḥsān by defining and evaluating the istiḥsān in a way that their opponents could accept. The definition of Istiḥsān “to abandon the judgment given to similar ones due to stronger evidence.” has been generally accepted. In this definition, istiḥsān is defined by associating with qiyas, and referred to an istihsan that is presented as the more substantial evidence, and qiyas is the weaker evidence. Although it is appropriate to define istiḥsān in relation to qiyas, the claim that in the definition istiḥsān is put in stronger place than qiyas might casuse to some the contradictions- in particular when the example’s of al-Shaybānī are taken into consideration. Because in most cases, when qiyas conflicts with istiḥsān, istiḥsān is taken. But in an opposite case, qiyas might be taken. Apart from these, there are examples of the types of istiḥsān that al-Karkhī has classified in the works of al-Shaybānī, but sometimes there are also strange situations such as taking the qiyas by istiḥsān. This also means that the term is not sufficiently defined. The negative attitude towards istiḥsān in some Shāfiʿī circles and the criticisms against the legitimacy of istiḥsān continued in the works of the fiqh method. Istiḥsān is defined as making a judgment without evidence by Shāfiʿī circles. Therefore, they did not accept the abandonment of qiyas, which is a sharī proof, because of istiḥsān, which is a non-sharī notable proof. Based on the examples given by the users of istiḥsān, Ibn Ḥazm, one of the Ẓāhirītes, claims that istiḥsān opens the door to arbitrariness. According to him, a situation that is accepted as istiḥsān according to Ḥanafīs can be taken as istiḥsān according to Mālikīs. This creates an apparent contradiction. There are some valid points in the assessment of Ibn Ḥazm. Because while it is seen that the istiḥsān of Mālikīs is criticized in al-Shaybānī's book named al-Ḥujjah, it can be also found that the istiḥsān of Ḥanafīs is charged in the works of Abū’l-Walīd al-Bājī, one of the Mālikīs. The criticism toward istiḥsān was continued by Shāfiʿīs such as Abū Isḥāq al-Shīrāzī, Imam al-Haramayn al-Juwaynī and Abū Ḥāmid al-Ghazālī. While al-Juwaynī sees istiḥsān as a method based on the lust of the soul, not istinbat/legal deduction, al-Ghazālī understands istiḥsān as a personal comment. The main reason for the negative attitude towards istiḥsān is that the content based on the definitions, has been neglected most of the time. However, when we look at the works of al-Shaybānī, it can be seen that there is a proof of istiḥsān contrary to what is believed-and that this can be sometimes a work, sometimes a necessity, sometimes another comparison, or sometimes a custom. (shrink)

This research aims, first of all, to establish that Abû Hanîfa's (d. 150/767) positive view on the issue of performing wudû’ with nabîdh of date is correct, and then to reveal Abû Hanîfa's dalîls on this subject. The issue of wudû’ with nabîdh of date is controversial among early Hanafî jurists, and the jurist who expressed a positive opinion on this issue is Abû Hanîfa, the founding imam of the madhhab. The opinion that wudû’ can be performed with nabîdh of (...) date is the strong opinion of Abû Hanîfa mentioned in zâhir al-riwâya. The riwâya reported by Nûh bin Abi Maryam (d. 173/789) stating that Abû Hanîfa reneged on this view is not strong enough to oppose the view in zâhir al-riwâya. For this reason, it is not a correct approach to ignore the view in zâhir al-riwâya based on this riwâya. As a matter of fact, Abû Hanîfa's view of zâhir al-riwâya is conveyed in many of the classical Hanafî texts such as Mukhtasar al-Karkhi and Mukhtasar al-Tahâwî. Although the majority of Hanafî jurists preferred the view of Abû Yûsuf (d. 182/798), a significant group of Hanafî jurists such as Jassâs (d. 370/981), Kâshânî (d. 587/1191) and ‘Aynî (d. 855/1451) He supports Abû Hanîfa's view. Therefore, there are two views on the issue in Hanafî fıqh. In the literature, the dalîls of Abû Hanîfa's view is not available as a whole in a single source, but is scattered in many Hanafî fiqh sources. The Hanafî jurist Jassâs is the one who deals with the mentioned dalîls in the most comprehensive way in his many works. For this reason, the subject was examined by focusing on Jassâs's dalîls. Jassâs' istidlâls regarding the issue of wudû’ with nabîdh of date also mean defending Abû Hanîfa against other Hanafî jurists such as Abu Yusuf and Imâm Muhammad (d. 189/805). Jassâs' insistent attitude on this issue and his passionate counter-answers prove how much he deserves the title of defense. For the relevant determination, Hanafî fiqh classics are centered. Because the jurists who argue that wudû’ can be made with the nabîdh of date are among the Hanafî jurists. Then, the positive and negative approaches of the jurists about the nabîdh of date are given. Starting from the early Hanafî jurists, the views of the sahâbîs, the tâbi'ûn and many later jurists on the subject are included. The approach of the four madhhabs of fiqh is also examined in this section. Then, the istidlâls of Jassâs, which is the main subject of the research, were emphasized. It is seen that Jassâs' istidlâls have three main pillars: âya, hadîth and idjma. As a âya, the 6th âya of the sûra of Mâida, as a hadîth, the hadîth of ‘Abd Allâh bin Mas'ûd (r.a.) and as a idjma, the the sahâbîs idjma tries to showas references. The most controversial dalîl is undoubtedly the hadiths of Ibn Mas'ud (r.a.). Jassâs opposes those who claim that the hadîth is da‘îf and discusses the hadîth with its detailed tarîks and argues that this hadîth is sahîh. (shrink)

The big five personality traits and entrepreneurial mindset are crucial individual-level elements that determine entrepreneurial intention. This study examines the impact of big five personality traits and EM, on EI using the theory of planned behavior. Besides, this study examined the role of entrepreneurial self-efficacy and attitude toward entrepreneurship influences EI. To achieve the research objectives, a quantitative approach was used. Structural equation modeling and path analysis were conducted using SmartPLS software. Data were collected from 270 respondents through online questionnaires. (...) Findings of the study revealed that big five personality traits influence ESE and ATE which led to EI. Finally, the moderating role of entrepreneurial passion was also found to have strong effect on influence ESE and ATE. This study offers evidence and insights that academics, educators, and others involved in the creation or expansion of entrepreneurial knowledge can use as a reference point. (shrink)

Kant’s ‘Refutation of Idealism’ plainly has an anti-Cartesian conclusion: ‘inner experience in general is only possible through outer experience in general’ (B278). Due to wide-spread preoccupation with Cartesian skepticism, and to the anti-naturalism of early analytic philosophy, most of Kant’s recent commentators have sought to find a purely conceptual, ‘analytic’ argument in Kant’s Refutation of Idealism – and then have dismissed Kant when no such plausible argument can be reconstructed from his text. Kant’s argument supposedly cannot eliminate all relevant alternatives, (...) and so cannot justify its strong modal claims. Kant based his arguments on an inventory of our basic cognitive capacities to employ our forms of intuition and our forms of judgment. Kant provides a variety of considerations and arguments to determine what our cognitive capacities are. This involves ‘transcendental reflection’, which Kant held is absolutely crucial for judging matters a priori (A263/B319). I argue that there is a level of philosophical reflection on our own cognitive capabilities and their preconditions that is significantly richer than has been noticed by recent commentators, and that is a precondition of Kant’s transcendental reflection proper. I explicate certain thought experiments Kant proposes in order for us to recognize some our basic, characteristic cognitive capabilities, and the limits and requirements they entail for the nature and objects of human knowledge. These thought experiments involve a kind of reflection on who we as cognizant subjects are, on what our basic cognitive capabilities are. Engaging in this kind of reflection reveals that Kant’s transcendental arguments are significantly stronger and more persuasive than has been recognized in recent commentary. (shrink)

Architecture and Deconstruction Case of Peter Eisenman and Bernard Tschumi -/- Introduction Towards deconstruction in architecture Intensive relations between philosophical deconstruction and architecture, which were present in the late 1980s and early 1990s, belong to the past and therefore may be described from a greater than before distance. Within these relations three basic variations can be distinguished: the first one, in which philosophy of deconstruction deals with architectural terms but does not interfere with real architecture, the second one, in which (...) a collaboration between Jacques Derrida and a group of architects interested in his concepts is commenced, and the third one, in which completed or only designed objects or new concepts of deconstruction created by architects gain their supremacy over philosophy. The following book analyses these three possible ways, first of all with the reference to Peter Eisenman and Bernard Tschumi. -/- Peter Eisenman -/- Misreading… and Other Errors -/- The issue of relations between Peter Eisenman’s work and philosophy of deconstruction may be referred to his activity more than ten years preceding his direct collaboration with Jacques Derrida (in 1985) and organisation of the exhibition Deconstructivist Architecture at Museum of Modern Art in New York (in 1988). As soon as at the stage of designing the first houses (House I-III, 1967-1970), which almost entirely inscribed in formalistic aesthetics of Modernism, the architect analysed the problem of architecture dependence on its assumptions. All his later designs may be treated as consequence of this initial interest in relations between practice and theory, and at the same time as an introduction to manipulations later on led at the level of metaphysics of architecture. Beginning with the issue of presence, considered in comments to House VI (1972), the number of ideas having their analogies in philosophy of deconstruction increased. The text entitled The End of the Classical: The End of the Beginning, The End of the End (1984), in which Eisenman criticised questions of representation in architecture, its delusive strive for truth and comparably unattainable attempts at ultimate definition of elementary rules, should be acclaimed the breaking point. This attitude was extended by numerous strategies disturbing architecture rules defined at metaphysical level in an essay Moving Arrows, Eros, and Other Errors: an Architecture of Absence (1986). The issue of Eisenman’s passage from formalism to deconstruction has already been much discussed in the literature (Rosalind Krauss, Thomas Patin among others), still it should be mentioned that the threads similar to Derrida’s concept included in Eisenman’s writing reveal untranslatability of architecture and philosophy. -/- Choral Works or Separate tricks -/- In 1985-1986 a series of seven disputes between Jacques Derrida and Peter Eisenman took place. The pretext for them were designs concerning Parc de la Villette in Paris. The situation of many months of collaboration between a notable philosopher of the second half of the 20th c. and an architect that already had a huge theoretical oeuvre, ended up with a publication of a large volume entitled Chora L Works and it became at the same time a vast study area for historians of contemporary architecture and philosophers. Derrida’s contribution to concept works were his considerations over the idea of chôra, the properties related to this concept were about to be reflected in shapes of the park. Therefore, Chora L Works became an example of the abilities of contemporary art, both in its capability of translation from philosophical ideas to artistic forms and its resistance to tradition of representing in architecture some phenomena and values originating outside this discipline. In the final period of their collaboration both interlocutors started to polemicise with each other more decidedly, what became a separate part of their thought exchange. The exchange of letters between Derrida and Eisenman at the turn of 1989 ended up the period of their direct contacts, nevertheless, at this time precisely a large group of experts in issues of deconstruction joined the discussion and extended the revealed in the former dispute problems into more than ten years of further considerations and publications. Except for a long text by Jeffrey Kipnis, who had participated in the meetings of the philosopher and the architect, there appeared also comments of researchers of artistic theories (K. Michael Hays, Thomas Patin), philosophers (Andrew Benjamin), and even experts in Greek literature (Maria Theodorou or Ann Bergren). Following these debates a contemporary reflection on architecture has saturated with indeed numerous concepts originating in philosophy of deconstruction. -/- Architecture which imitates mute philosophy -/- The series of Jacques Derrida and Peter Eisenman meetings, which took place in the period of 1985-1987, induced many authors to make comments. Some of them (Jeffrey Kipnis, Ann Bergren, Maria Theodorou) developed the subject of chôra which was introduced to the discussion by Derrida. The problem that was about to be solved was the question of tying up the concept of chôra with architecture, including Eisenman’s architecture and the series of meetings within frames of Chora L Works project. Kipnis on this occasion paid attention to chôra and its character of anachronia which infects any being created within chôra. In other words any event has its counterpart (analogon) in another, earlier event. He demonstrated the similarity of structure of many events and statements from the times of Derrida and Eisenman’s meetings to the almost identical behaviour of figures in Plato’s dialogue Timaeus. The loss of beginning present in this phenomenon was appropriate to both features of chôra and the effects of typical analyses of philosophy of deconstruction. Bergren’s analyses focused on accentuating gender of chôra, which, according to this author, had been neglected hitherto in discussions. She collated chôra descriptions with characteristics of women in myths, early Greek epic and philosophy and she arrived at a conclusion that chôra has features of a single woman and a married one at the same time. And yet Theodorou’s studies showed that in the Homeric epics chôra is not treated as an idea but is related with single things and events. The other part of the comments (represented by Andrew Benjamin and K. Michael Hays’ utterances) concerns Eisenman’s attitude to tradition which was treated as a variety of iteration understood philosophically. Benjamin commenced his considerations at the point of closeness between a definition of tradition and a concept of chôra understood as perpetuation (placement). A problematic issue was for him Eisenman’s complex relation to tradition based on its contest and affirmation at the same time. Overcoming the simple subordination to tradition – according to Benjamin – was based on awareness of the role of repetition in culture not known before. Hays made an attempt to explain the pleasure and torment of repetition with the support of Sigmund Freud and Roland Barthes’ concepts. According to Hays repetitions are attempts of a single being to a certain primal state perceived as free of any tension. In a similar way Rosalind Krauss explained a motif of a grate present in Modernistic art and also exceptionally frequent in Eisenman’s work. -/- Annex Architecture is still writing Balzac novels. Peter Eisenman and literature -/- Architecture’s approach to writing, script or literature, present within Peter Eisenman’s work, is an exceptional phenomenon, furthermore a complex one. The article considers four possible relations. The first one relates to Eisenman’s characteristics as a person extremely gifted with the ability to wordplay, which very ‘play’ reveals skills to create architectural images. In the second approach the attention has been paid to Eisenman’s interests – in the first period of his oeuvre – in linguistic works by Noam Chomsky and his transformational-generative grammar. The third kind of relations applied to overcoming the need for autonomy of architecture (and of modernist aesthetics at the same time) and renew interests in questions of meaning in architecture. The fourth sort of relations occurred when Eisenman started to create reflections of historic or literary narrations in architecture – ‘stone stories’ and architectural fictions of their kind. -/- Bernard Tschumi -/- From perversion to deconstruction In Bernard Tschumi’s writings from the 1970s and 1980s we can find a transposition of important threads of post-structuralist ideas deriving from Georges Bataille, Roland Barthes and Jacques Derrida’s works. The analysis of the architect’s writings also shows roots in Phillippe Sollers, Michel Foucault and Denis Hollier’s works. The analysis of borrowed elements from the beginnings of Tschumi’s theoretical activity may be helpful in explaining the contents of his later writings motre inspired by philosophy of deconstruction. The set of his earliest views was inspired by Marxism, Neo Marxism and French Structuralism, mainly by the writings of Henri Levebre and Guy Debord. From the thought of Levebre Tschumi took interest for city as not only a question of urbanistics but also a political issue. From Debord’s concepts he borrowed a conviction about the role of situational violation for changes in the society structure. Some of these beliefs were preserved in his own concepts of architecture as an event. From this period derived also his will to change conservative elements of social structure not by means of political revolution but of theoretical and creative activity. Tschumi acknowledged that the effective way of the proceedings towards achieving his aims would be accepting the role of both a critical intellectualist and architecture expert who would not hide away his left-wing orientation. The speculations defined by the architect as ‘revolting analyses’ were about to characterise contradictions which tear the society apart, penetrate architecture and constitute the basis of culture. Spreading away of the conscience of false assumptions hidden away in various disciplines could have weakened cohesion of a conservative society and influence the will to change among the elites. This way the beginnings of political revolution were rooted in philosophy of architecture. In 1977 Tschumi published his text entitled The Pleasure of Architecture inspired by Roland Barthes’s The Pleasure of the Text, it also included some concepts derived from Georges Bataille and Jacques Derrida. First of all the author used Barthes’s concept which made an assumption that literary activity is pervaded by the spirit of resistance towards social rules, and Tschudi transferred this remark onto architecture. From the ideas of Bataille, acquainted via Holier’s work, he derived his belief that two concepts of space, a conceptual one (defined as Pyramid) and a sensual one (defined as Labirynth), not losing their distinct features, they join in the concept of experienced space which exceeds contradictions. The exceeding itself was defined as the basic rule of architecture and it was referred to situations in which architecture not only negates social needs, but also disavows its own tradition. Crossing the borders applies not only to political issues or permanent rules of the very discipline but also interfering with other fields (especially literature and film). The fact that architecture is associated with organising events turned Tschumi’s attention to questions of violence that result from upsetting architectural order of a given building by its users and the one hand, and on the other from forcing the users to specific acts imposed by this very order. The analysis of the concepts used by Tschumi in his early writings indicates that they are close to definitions that would occur in his reflection in the following years influenced by philosophy of deconstruction. -/- Approaching deconstruction Tschumi in his theories developed in the 1980s presumed that the current social world had undergone a deep process of decay, and the reaction against which ought to be based on ordering-up actions, and also preserving the main outline of disintegration of the whole and its elements in the state of conflict. The statements concerning the nature of the contemporary to Tschumi social relations were applied by him to the world of architecture, this led him to coming up with designing strategies that took into consideration the destabilised character of conditions in which works of architecture were created. New ways of conduct invented by Tschumi drew their inspiration from literature and research on literature, psychoanalysis, structural linguistics, structuralism and post structuralism, and eventually also deconstruction philosophy. The proposed methods were opposed by their author both to functionalism continuity trends and postmodern architecture. Tschumi’s proposals contradicted any forms of conservatism or traditionalism in political sphere as well as in reference to tendencies in architecture. They were not simple contradictions of social or architectural rules, they intrude them from the inside, weaken or escalate the already existing incongruities, they move the boundaries between the areas. Revolutionary illusions about the possibility of radical changes were replaced with strategies which completed, tainted or test former rules in the series of formal games of permutation and combination. Quite different from avant-garde formalism Tschumi’s games were not about maintaining the autonomy of a given area, but on the contrary – polluting it with other areas’ influences. Tschumi enjoyed demonstrating illusions of architecture concerning simple relations between form and function, or between form and meaning. Making use of Freud, Lacan and Foucault’s research he introduced a category of “madness” into architecture allowing an observation that the recognised norms are nothing but merely ones of many possible principles of behaviour, and their recognised status resulted from unjustified hindering innovativeness which is crucial for architecture. To reborn architecture’s capability of changing Tschumi also made use of Barthes’s discoveries concerning rules of narration and works by writers who applied in their writing knowledge on linguistics. Making a work’s author unclear by various mechanical transformations of its elements was however apparent only, and formal rigours imposed on the process of designing liberated possibilities difficult to obtain in more traditional creative action. Another mode of acting introduced by Tschumi was combining his work of elements deriving from outside architecture; joining space records with notation of motion and events accompanying architectural objects among others. These architectural and extra-architectural elements were not unified, on the contrary their heterogenous and conflictual character was stressed. This is how shock, anxiety and instability, typical for live in great metropolises, infiltrated architecture. Taking some ideas of deconstruction philosophy as a pattern Tschumi also took into critical consideration in his essays traditional in architecture oppositions between form and figuration, or theory and practice. By combining various inspirations he eventually worked out an idea of architectural event, which he understood as a series of actions contesting its own field, redefining its sources, principles and elements. An event, understood in this way, was not so much producing works as rather creating conditions of their production and at the same time designing the society different from a hierarchic one. -/- Park of deconstruction Among numerous philosophical strategies of deconstruction most frequently used was questioning the practice of strong opposition of two reasons. In many cases Bernard Tschumi’s writings just consider functioning of the conflict juxtaposition of the ideas of structure and ornament or theory and practice in history of architecture. Violation of traditional relations between terms of this kind, both old and modern, raised Jacques Derrida’s objections, when he was induced for the first time to co-operate with architects’ milieu. During this long lasting thought exchange the philosopher eventually acknowledged Bernard Tschumi’s arguments for reasoning the encroachment of architecture’s fundamental rules. Deconstruction applied in architecture was not a simple transposition or analogy of practices that had been applied by philosophy of deconstruction. We may even say that considering architectural terms became an important formula of deconstruction. Architecture understood in philosophical way became something beyond the practice and theory of its own discipline, a sort of metaphysics of both philosophy and architecture. The deliberate encroachment of simplicity of dividing architecture into theory and practice, for the first time became a clear aim for Tschumi in his drawings and texts entitled The Manhattan Transcripts. The contents of this series of works was a record of characteristic features of this New York district in such a way that not only objects were the subject of the record but also relations between objects, people and events. The record was about to take into consideration a conflict character of elements of this representation and at the same time to avoid applying to them the rule of mimetism. The record became a form of reflection over the very record by an increased control over the ways of representation. Architecture which was considered in the The Manhattan Transcripts was not directed to fulfill the needs of inhabitation or production, it was rather related with hitherto usually marginalised liminal situations: building ostentatiously big monuments, religious cult, war etc. Architecture operating in these relations focused also the attention on the included in it continuous tendency to overpass its own restrictions, the role of violence as its not recognised factor, or the meaning of excess and shock in its operation. Architecture moving from reason towards madness became even more visible in the design of Parisian Parc de la Villette, whose pavilions were defined as folies (in French it means both small park buildings and follies). The park was supposed to be on the one hand a reflection of traditional society disintegration while on the other it questioned basic rules of producing a work of architecture. The traditional rules of designing, based on ordering up, were replaced with the strategies of dysfunction and dissociation. In Tschumi’s opinion methods of this kind may be equivalent of what Derrida named différance. Instead of aiming at mergence, any diversity, plays or variations were strengthen. Tschumi’s texts, in which he explained his attitude, were completed by Derrida’s extent statement entitled Point de folie – Maintenant l’architecture. Derrida’s article is the most significant of all his statements on architecture as a form of thinking and activity. According to the philosopher, architecture should divide space (in French defined as espacement), what enables both thinking and action – it arranges the space of an event. Tschumi’s buildings, defined as folies, in an essential way destabilise any created order, and at the same time they refresh it. Derrida’s statement suggests that architecture may become both metaphor of an order merging a language or a society but also of inner forces which deconstruct and reconstruct it. Therefore architecture is at the same time a construction, a deconstruction and a reconstruction. Parc de la Villette stands out in this system with its attempt to step beyond the scheme of an easy repetition and its heading for chances of achieving more radical otherness. -/- Conclusion Destruction as construction. Paradoxes of deconstruction in architecture -/- Scepticism about persistence and common importance of fundamental values of human culture evinced in philosophers and writers’ works as early as in Greek antiquity, nevertheless it was not expressed so strongly as in the second half of the 20th century. Especially in Heidegger’s work Being and Time (although originated in 1927, still influential in all later philosophy) the following states were characterised: the state of losing the ground (Abgrund), of being out of sight (Unheimlichkeit) and of being out of dwelling (Un-zuhause-sein) – as the basis of self-confidence of conscious being there (Dasein). The entire criticism of philosophy of home and dwelling draws the inspiration from this early writing of the German philosopher, it combines crisis of basic terms of metaphysics with social conditions which are dictated by living in large metropolis. The crisis of both metaphysical foundation and home appears to be similar to the situation of weakening the relations between a man and his dwelling in extensively expanding cities. Whereas philosophy, as well as many disciplines of social sciences, have diagnosed for a long time the destabilisation of fundamental ideas of Western culture and crucial changes in the ways of dwelling, architecture itself occurred to be “the last fortress of metaphysics” (J. Derrida). Among contemporary architects, Peter Eisenman and Bernard Tschumi were the ones who engaged most decidedly in the issues of critical analysis of architecture foundation and its social role. Both the architects noticed new formulas of contemporary social and individual existence, tremendously different from the entire history, and at the same time they affirmed lack of adequacy of architecture concepts to new situations. Both Eisenman and Tschumi used to describe the existing architecture as a tool for consolidation of highly integrated and hierarchised societies, and also as a discipline extremely uncoincidental with the current character of social life based on ideas of freedom and diversity. The means to transform architecture and make a factor of further social changes out of it, was a concept that accentuated revealing the inner contradictions of this discipline, and considering them in designing strategies. Eisenman’s activity, in regard of what has just been noticed, was focused on questioning the basic rules of traditionally comprehended architecture, especially the rule of purpose. The American architect noticed that the concept of architecture as fulfilment the need of location, hides away the fact that the location has to be constantly reconsidered, and hence it is overtaken by change (dislocation). Therefore new concept of architecture propounded architectural activity to translocate the concept of location – more than before – but also to change its status perpetually. Such comprehended architecture should claim, as its main purpose, the constant revision of this purpose and create itself anew permanently. Even Eisenman’s earliest designs of houses nos. I-IV broke with such values as the sense of safety, closeness and familiarity, and just on the contrary they accentuated senses of strangeness, homelessness and loss of confidence. The contradictions within architecture noticed by Tschumi referred to combination of intellectual and sensual values in architecture, when their non-appropriation was defeated by an additional condition, namely the way of experience based on pleasure of excess, marked by insanity. The features of folly were especially visible in his designs of gardens, where the order of planning was mixed with sensual experience introduced by particular elements (both the ones created by nature, and the buildings defined as folies). Parc de la Villette designed by the French architect in Paris put in question not only the common understanding of purpose in architecture but also the ideas of order and integrity, as its plan was based on the combination of independent layers with records of grids of points, various lines and planes. The architecture that collides inadequate elements with each other was supposed to be a kind of an event with no beginning and no end. The architecture treated as an event became a form of a space weakened articulation that maintains its diversity and lack of accordance of the elements building it up. The analyses of Eisenman and Tschumi’s theoretical writings indicate how much the aims of architecture have actually changed; instead of supporting social persistence, the architecture is rather intensifying contradictions, and instead of providing people with the sense of safety, it sublimes danger. From simple acts of defamiliarisation, increasing the distance to itself and enhancing the role of theory, through discomfort, anxiety, not feeling someone at home, weirdness, excess, shock and violence, architecture reached the edge of stability and uncertainty, only to make an attempt at penetrating what is impossible and unutterable, and recording what cannot become the subject of any records. -/- . (shrink)

Providing high-quality education for students with emergent proficiency in the language of instruction (referred to here as multilingual students) presents a challenge to inclusion for educational systems the world over. In Austria, a new German language support model was implemented in the school year 2018/19 which provides language support in separate classrooms up to 20 h a week. Since its implementation, the model has been strongly criticized for excluding multilingual students from the mainstream classroom, which is argued to reinforce the (...) educational disadvantages that they face. The study presented here provides unprecedented qualitative insight into how schooling for students within the so-called German language support classes (GLSC) was organized during the COVID-19 pandemic. It builds on results of a previous large-scale quantitative study (n= 3,400 teachers), which was conducted during the first lockdown (spring 2020) and indicated a high risk of exclusion for marginalized students, especially for multilingual students in GLSC. To gain deeper insights into the situation of these students during school closures, 37 teachers who work in these classes at both primary and lower-secondary schools in Vienna were interviewed, of which 18 interviews were considered for analysis. The interviews focus on the situation during the first and second school closures in the city of Vienna. A thematic analysis of the interview data reveals teachers’ perceptions of aspects which harmed or promoted inclusion for students in GLSC during these periods of school closure. Teachers’ perceptions of the most harming factors for students included strong language barriers between teachers and students, restricted access to technical equipment and supportive learning spaces, and low parental engagement. A development that promoted inclusion of these students was the option to allow them to come to school during the second school closure. Since existing studies on the schooling of students during school closures have hardly addressed the situation of students in GLSC, this study contributes to closing this research gap. (shrink)

We construct creature forcings with strong Axiom A that specialize a given Aronszajn tree. We work with tree creature forcing. The creatures that live on the Aronszajn tree are normed and have the halving property. We show that our models fulfill ℵ1=d

Set Theory in Philosophy of Mathematics

Direct download (3 more)  

 

Export citation  

 

Bookmark   1 citation  

This paper is a sequel to Tzouvaras :571–601, 2010), where a local version of ZFC, LZFC, was introduced and examined and transitive models of ZFC with properties that resemble large cardinal properties, namely Mahlo and Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi_1^1}$$\end{document}-indescribable models, were considered. By analogy we refer to such models as “large models”, and the properties in question as “large model properties”. Continuing here in the same spirit we consider further large model properties, that resemble (...) stronger large cardinals, namely, “elementarily embeddable”, “extendible” and “strongly extendible”, “critical” and “strongly critical”, “self-critical” and “strongly self-critical”, the definitions of which involve elementary embeddings. Each large model property ϕ gives rise to a localization axiom Locϕ saying that every set belongs to a transitive model of ZFC satisfying ϕ. The theories LZFCϕ = LZFC + Locϕ are local analogues of the theories ZFC+“there is a proper class of large cardinals ψ”, where ψ is a large cardinal property. If sext is the property of strong extendibility, it is shown that LZFCsext proves Powerset and Σ1-Collection. In order to refute V = L over LZFC, we combine the existence of strongly critical models with an axiom of different flavor, the Tall Model Axiom. V = L can also be refuted by TMA plus the axiom GC saying that “there is a greatest cardinal”, although it is not known if TMA + GC is consistent over LZFC. Finally Vopěnka’s Principle and its impact on LZFC are examined. It is shown that LZFCsext + V P proves Powerset and Replacement, i.e., ZFC is fully recovered. The same is true for some weaker variants of LZFCsext. Moreover the theories LZFCsext+V P and ZFC+V P are shown to be identical. (shrink)

THE ART OF CAUSAL CONJECTURE Glenn Shafer Table of Contents Chapter 1. Introduction........................................................................................ ...........1 1.1. Probability Trees..........................................................................................3 1.2. Many Observers, Many Stances, Many Natures..........................................8 1.3. Causal Relations as Relations in Nature’s Tree...........................................9 1.4. Evidence............................................................................................ ...........13 1.5. Measuring the Average Effect of a Cause....................................................17 1.6. Causal Diagrams..........................................................................................20 1.7. Humean Events............................................................................................23 1.8. Three Levels of Causal Language................................................................27 1.9. An Outline of the Book................................................................................27 Chapter 2. Event Trees............................................................................................... .....31 2.1. Situations and Events...................................................................................32 2.2. The Ordering of Situations and Moivrean Events.......................................35 2.3. Cuts................................................................................................ ..............39 2.4. Humean Events............................................................................................43 2.5. (...) Moivrean Variables......................................................................................49 2.6. Humean Variables........................................................................................53 2.7. Event Trees for Stochastic Processes...........................................................54 2.8. Timing in Event Trees.................................................................................56 2.9. Intersecting Event Trees...............................................................................60 2.10. Notes on the Literature...............................................................................61 Chapter 3. Probability Trees...........................................................................................63 3.1. Some Types of Probability Trees.................................................................64 ii 3.2. Axioms for the Probabilities of Moivrean Events.......................................68 3.3. Zero Probabilities....................................................................................... ..70 3.4. A Sample-Space Analysis of the Event-Tree Axioms.................................72 3.5. Probabilities and Expected Values for Variables.........................................74 3.6. Martingales......................................................................................... .........79 3.7. The Expectation of a Variable in a Cut........................................................83 3.8. Conditional Expected Value and Conditional Expectation.........................87 Chapter 4. The Meaning of Probability...........................................................................91 4.1. The Interpretation of Expected Value..........................................................92 4.2. The Interpretation of Expectation................................................................95 4.3. The Long Run..............................................................................................98 4.4. Changes in Belief.........................................................................................101 4.5. The Empirical Validation of Probability......................................................106 4.6. The Diversity of Uses of Probability...........................................................108 4.7. Notes on the Literature.................................................................................110 Chapter 5. Independent Events.......................................................................................113 5.1. Independence........................................................................................ .......114 5.2. Weak Independence.....................................................................................118 5.3. The Principle of the Common Cause...........................................................121 5.4. Conditional Independence............................................................................128 5.5. Notes on the Literature.................................................................................133 Chapter 6. Events Tracking Events.................................................................................135 6.1. Tracking............................................................................................ ...........137 6.2. Tracking and Conditional Independence.....................................................142 6.3. Stochastic Subsequence...............................................................................143 6.4. Singular Diagrams for Stochastic Subsequence...........................................147 6.5. Conjunctive and Interactive Forks...............................................................149 Chapter 7. Events as Signs of Events..............................................................................153 iii 7.1. Sign................................................................................................ ..............154 7.2. Weak Sign................................................................................................ ....159 7.3. The Ethics of Causal Talk............................................................................160 7.4. Screening Off...............................................................................................16 2 Chapter 8. Independent Variables...................................................................................167 8.1. Unconditional Independence........................................................................170 8.2. Conditional Independence............................................................................175 8.3. Independence for Partitions.........................................................................177 8.4. Independence for Families of Variables......................................................182 8.5. Individual Properties of the Independence Relations...................................186 Chapter 9. Variables Tracking Variables........................................................................189 9.1. Tracking and Conditional Independence: A Summary...............................190 9.2. Strong Tracking............................................................................................ 192 9.3. Strong Tracking and Conditional Independence..........................................198 9.4. Stochastic Subsequence...............................................................................201 9.5. Functional Dependence................................................................................203 9.6. Tracking in Mean.........................................................................................204 9.7. Linear Tracking............................................................................................ 207 9.8. Tracking by Partitions..................................................................................210 9.9. Tracking by Families of Variables...............................................................212 Chapter 10. Variables as Signs of Variables...................................................................215 10.1. Sign................................................................................................ ............219 10.2. Linear Sign................................................................................................ .222 10.3. Scored Sign................................................................................................ 225 10.4. Families of Variables.................................................................................227 Chapter 11. AnTheory of Event Trees.............................................................229 11.1. Event Trees as Sets of Sets........................................................................230 11.2. Event Trees as Partially Ordered Sets........................................................232 iv 11.3. Regular Event Trees...................................................................................240 11.4. The Resolution of Moivrean Variables......................................................244 11.5. Humean Events and Variables...................................................................246 Chapter 12. Martingale Trees..........................................................................................247 12.1. Examples of Decision Trees......................................................................249 12.2. The Meaning of Probability in a Decision Tree.........................................253 12.3. Martingales......................................................................................... .......257 12.4. The Structure of Martingale Trees.............................................................261 12.5. Probability and Causality...........................................................................265 12.6. Lower and Upper Probability.....................................................................269 12.7. The Law of Large Numbers.......................................................................272 12.8. Notes on the Literature...............................................................................274 Chapter 13. Refining............................................................................................ ...........275 13.1. Examples of Refinement............................................................................277 13.2. A Constructive Definition of Finite Refinement.......................................281 13.3. Axioms for Refinement..............................................................................282 13.4. Lifting Moivrean Events and Variables.....................................................288 13.5. Refining Martingale Trees.........................................................................288 13.6. Grounding........................................................................................... .......294 Chapter 14. Principles of Causal Conjecture..................................................................299 14.1. The Diversity of Causal Explanation.........................................................302 14.2. The Mean Effect of the Happening of a Moivrean Event..........................305 14.3. The Effect of a Humean Variable..............................................................311 14.4. Attribution and Generality.........................................................................316 14.5. The Statistical Measurement of the Effect of a Cause...............................319 14.6. Measurement by Experiment.....................................................................320 14.7. Using Our Knowledge of How Things Work............................................322 v 14.8. Sampling Error...........................................................................................329 14.9. The Sampling Frame..................................................................................329 14.10. Notes on the Literature.............................................................................330 Chapter 15. Causal Models.............................................................................................3 31 15.1. The Causal Interpretation of Statistical Prediction....................................333 15.2. Generalizing to a Family of Exogenous Variables....................................337 15.3 Some Joint Causal Diagrams......................................................................339 15.4. Causal Path Diagrams................................................................................342 15.5. Causal Relevance Diagrams.......................................................................346 15.6. The Meaning of Latent Variables..............................................................352 15.7. Notes on the Literature...............................................................................357 Chapter 16. Representing Probability Trees...................................................................359 16.1. Three Graphical Representations...............................................................361 16.2. Skeletal Simplifications.............................................................................368 16.3. Martingale Trees in Type Theory...............................................................371 Appendix A. Huygens’s Probability Trees.....................................................................379 Huygens’s Manuscript in Translation..................................................................380 Appendix B. Some Elements of Graph Theory..............................................................385 B1. Undirected Graphs........................................................................................385 B2. Directed Graphs............................................................................................38 6 Appendix C. Some Elements of Order Theory...............................................................393 C1. Partial and Quasi Orderings.........................................................................393 C2. Singular and Joint Diagrams for Binary Relations.......................................394 C3. Lattices............................................................................................ .............395 C4. The Lattice of Partitions of a Set..................................................................396 Appendix D. The Sample-Space Framework for Probability.........................................399 D1. Probability Measures....................................................................................399 D2. Variables........................................................................................... ...........400 vi D3. Families of Variables...................................................................................401 D4. Expected Value............................................................................................402 D5. The Law of Large Numbers.........................................................................405 D6. Conditional Probability................................................................................406 D7. Conditional Expected Value........................................................................407 Appendix E. Prediction in Probability Spaces................................................................409 E1. Conditional Distribution...............................................................................411 E2. Regression on a Single Variable...................................................................412 E3. Regression on a Partition or a Family of Variables......................................415 E4. Linear Regression on a Single Variable.......................................................418 E5. Linear Regression on a Family of Variables................................................422 Appendix F. Sample-Space Concepts of Independence.................................................425 F1. Overview............................................................................................ ...........426 F2. Independence Proper.....................................................................................432 F3. Unpredictability in Mean..............................................................................434 F4. Simple Uncorrelatedness..............................................................................437 F5. Mixed Uncorrelatedness...............................................................................438 F6. Partial Uncorrelatedness...............................................................................440 F7. Independence for Partitions..........................................................................442 F8. Independence for Families of Variables.......................................................445 F9. The Basic Role of Uncorrelatedness.............................................................448 F10. Dawid’s Axioms.........................................................................................449 Appendix G. Prediction Diagrams..................................................................................453 G1. Path Diagrams............................................................................................ ..454 G2. Generalized Path Diagrams..........................................................................462 G3. Relevance Diagrams.....................................................................................466 G4. Bubbled Relevance Diagrams......................................................................475 Appendix H. Abstract Stochastic Processes...................................................................479 vii H1. Probability Conditionals and Probability Distributions...............................477 H2. Abstract Stochastic Processes......................................................................479 H3. Embedding Variables and Processes in a Sample Space.............................480 References.......................................................................................... ..............................491. (shrink)

Sextus Empiricus does not reveal anything of himself as distinct from ‘the Sceptic’ except in a passing and incidental way. He does not refer to his contemporaries, nor to his country, nor to any personal experiences, in such a way as to provide a definite picture of his life and times. The few references he makes to his involvement in the medical profession are as perplexing as they are enlightening. The only attachments which Sextus strongly identifies with in his extant (...) writings are the demands of the Pyrrhonean philosophy. (shrink)

The method of morphisms is a well-known application of Dialectica categories to set theory. In a previous work, Valeria de Paiva and the author have asked how much of the Axiom of Choice is needed in order to carry out the referred applications of such method. In this paper, we show that, when considered in their full generality, those applications of Dialectica categories give rise to equivalents of either the Axiom of Choice or Partition Principle —which is a (...) consequence of $\textbf{AC}$ whose precise status of its relationship with$\textbf{AC}$ itself is an open problem for more than a hundred years. (shrink)

Strongly positive uses of terms that designate an absence, a cognitive or ontological impossibility or a sensory privation are among the persistent conceptual figures of Benjamin’s thought. This article analyses the moves by which Benjamin gave his concept of ‘the expressionless’ its intriguing semantic meaning and moral value. Drawing on the poetics and philosophy of the sublime from Greek antiquity through modern times, the article reveals key historical reference points of Benjamin’s concept and, furthermore, his strategy of advocating a (...) novel theory of the sublime as an antithesis to, or an interruption of, the beautiful by selectively integrating older traditions with theorems previously unrelated to these traditions. (shrink)

This book reveals the French scientific contribution to the mathematical theory of nonlinear oscillations and its development. The work offers a critical examination of sources with a focus on the twentieth century, especially the period between the wars. Readers will see that, contrary to what is often written, France's role has been significant. Important contributions were made through both the work of French scholars from within diverse disciplines, and through the geographical crossroads that France provided to scientific communication at the (...) time. This study includes an examination of the period before the First World War which is vital to understanding the work of the later period. By examining literature sources such as periodicals on the topic of electricity from that era, the author has unearthed a very important text by Henri Poincaré, dating from 1908. In this work Poincaré applied the concept of limit cycle to study the stability of the oscillations of a device for radio engineering. The “discovery” of this text means that the classical perspective of the historiography of this mathematical theory must be modified. Credit was hitherto attributed to the Russian mathematician Andronov, from correspondence dating to 1929. In the newly discovered Poincaré text there appears to be a strong interaction between science and technology or, more precisely, between mathematical analysis and radio engineering. This feature is one of the main components of the process of developing the theory of nonlinear oscillations. Indeed it is a feature of many of the texts referred to in these chapters, as they trace the significant developments to which France contributed. Scholars in the fields of the history of mathematics and the history of science, and anyone with an interest in the philosophical underpinnings of science will find this a particularly engaging account of scientific discovery and scholarly communication from an era full of exciting developments. (shrink)

In economics, it has often been claimed that testing choice data for violation of certain axioms-particularly if the choice data is observed under laboratory conditions-allows conclusions about the validity of certain preference axioms and the neoclassical maximization hypothesis. In this paper I argue that these conclusions are unfounded. In particular, it is unclear what exactly is tested, and the interpretation of the test results are ambiguous. Further, there are plausible reasons why the postulated choice axioms should not hold. Last, these (...) tests make implicit assumptions about beliefs that further blur the interpretations of the results. The tests therefore say little if anything about the validity of certain preference axioms or the maximization hypothesis. (shrink)

This paper is about pairing relation algebras as well as fork algebras and related subjects. In the 1991-92 fork algebra papers it was conjectured that fork algebras admit a strong representation theorem . Then, this conjecture was disproved in the following sense: a strong representation theorem for all abstract fork algebras was proved to be impossible in most set theories including the usual one as well as most non-well-founded set theories. Here we show that the above quoted conjecture (...) can still be made true by choosing an appropriate set theory as our foundation of mathematics. Namely, we show that there are non-well-founded set theories in which every abstract fork algebra is representable in the strong sense, i.e. it is isomorphic to a set relation algebra having a fork operation which is obtained with the help of the real pairing function. Further, these non-well-founded set theories are consistent if usual set theory is consistent. Finally, we will discuss related developments in propositional multi-modal logics of quantification and substitution, in algebraic logic e.g. cylindric algebras, the so called finitization problem, and applications to a logic introduced and studied in Tarski-Givant [42]. In particular, representable, weakly higher order cylindric algebras are finitely axiomatizable in a set theory which admits the axiom of foundation for finite sets. (shrink)

The strong correlation between people’s socioeconomic position and health within high income countries is a well-documented fact. A person’s occupation, income and education level tell us a lot about that person’s prospects on a long and healthy life, such that we can speak of a ‘social gradient in health’, or a ‘socioeconomic health gap’. This association is often perceived to be unjust. Therefore, it is generally thought that governments should aim to reduce socioeconomic health inequalities. However, this idea needs (...) ethical justification, for it is not evident if and why exactly these inequalities are unjust. For instance, are inequalities in health unjust per se? Or because the underlying socioeconomic inequalities are unjust? And does justice require equal health levels, or a minimum level of health? What complicates the issue, is that the width of the health gap, or the steepness of the social gradient, depends on what health measures are used. Overall, the more subjective the measure, the greater the inequalities appear to be. But are all these measures equally morally relevant? This dissertation aims to give a better understanding of these philosophical questions. It does so by investigating the question of what we should understand by health in the first part, after which it addresses the question of how to evaluate socioeconomic health inequalities in the light of justice. The introduction begins with a description of the phenomenon of socioeconomic health inequalities, and how it has been addressed by politicians, epidemiologists and philosophers in the past and today. The chapter continues by formulating the central question of the dissertation – that of which health inequalities should be focused in the light of a concern with social justice. It explicates how this dissertation contributes to answering that question, by discussing the potential relation between the conceptualisation of health and justice evaluations, and by discussing which questions are addressed in each of the following chapters. The chapter 2 addresses the question of how health is conceptualised in the philosophical and public heath literature, and how theoretical concepts of health differ. It proposes to approach health concepts as a Wittgensteinian family of thick concepts and argues that while theories on health generally argue in favour of one specific concept, a comparison of concepts shows that we may need different concepts of health given the variety of health practices. By explicating the differences between five concepts of health, this chapter argues that each captures aspects of health that all seem relevant when we talk and think about health. Classifying these concepts based on their distinctions reveals them as members of a conceptual family: each of the discussed concepts differs from the others in at least one respect and resembles the others in several respects. Moreover, the discussion of the concepts shows that ‘health’ always both describes a condition and values that condition at the same time. Having both descriptive and evaluative dimensions, we can see health concepts as ‘thick concepts’. Given this evaluative dimension, it is important to reflect on the question of what understanding of health guides specific practices. Moreover, the distinctions revealed by the classification can serve as a conceptual toolbox for reflection on the assumptions and purposes of health practices. How such reflection could work is illustrated by a brief exploration of what health aspects are focused upon in three specific health practices. Chapter 3 presents a study into the question of how health is conceptualised by ordinary citizens and to what extent conceptualisations of health differ between socioeconomic groups. By making use of the method of concept mapping, this study analyses how different socioeconomic groups formulate their own answers regarding the question ‘what does health mean to you?’. It presents concept maps of health for three different socioeconomic groups living in the city of Utrecht that reveal that all groups have a multidimensional understanding of health. An interpretation of the concept maps reveals nuanced differences between groups. The multiple aspects of health were also ranked by importance. It appears that each group assigned most importance to mental health. All in all, the study shows that people in lower socioeconomic groups are more likely to show a conceptualisation of health that refers to 1) the absence of health threats, 2) a person within his/her circumstances, 3) the value of functional notions, and 4) an accepting attitude towards life. Chapter 4 addresses the question of what the theoretical and empirical study to concepts of health could imply for health equity practices. It does so by exploring further the suggestions made in chapters 2 and 3. Regarding the question of which health aspects should guide health equity policies, this chapter discusses the question of whether we should primarily look at subjective or objective health measures, and whether a universal or relative standard of health should be central. While justice-related concerns of impartiality and equal treatment may seem to favour an objective perspective and a universal health standard, it appears that we have good reason to account for the subjective perspective as well. It is also argued that a concern for recognition and participatory parity gives room for relative health standards. Th room for relative health standards confronts us with the question of how to deal with mechanisms like adaptive preferences that the concept maps reveal. It proposes a way out, by arguing for society-relative health standards. Chapter 5 examines the question of whether inequalities in health should be evaluated ‘directly’, thus independently of a distribution of their social determinants. It proposes a sufficientarian perspective, such that the central question of evaluation is that of whether everyone is – or can be – healthy enough. By discussing two sufficientarian approaches to health and social justice – by Powers & Faden and by Nussbaum – this chapter distinguishes two ways of setting a threshold level for health. Both approaches appear to provide an unsatisfactory basis for justice evaluations and lead us away from direct evaluation if we try to settle health minima that are less arbitrary. In anticipation to chapters 6 and 7, it is argued that the perspective of sufficient health for relational equality escapes this arbitrariness: compared to that of a decent human life, it better helps to answer both the question of what socioeconomic health inequalities a society is due to avoid, and the question of when socioeconomic health inequalities are unjust considering their consequences. Chapter 6 discusses to what extent Daniels’s theory of health justice provides a satisfactory answer to the question of what health inequalities a society is due to avoid. Daniels proposes an indirect evaluative approach by arguing that we should evaluate socioeconomic health inequalities in the light of Rawls’s principles of justice as fairness. That is, if socioeconomic inequalities are in accordance with fair equality of opportunity and with the difference principle, the corresponding health inequalities would be just. It is shown that the suggestion that Rawls’s principles regulate the social determinants of health neglects that not all social determinants of health belong to society’s basic structure as conceived of by Rawls and are thereby not subjected to the principles of justice. To acknowledge the social mechanisms leading to socioeconomic health inequalities in their full complexity, it is argued that we should broaden our understanding of society’s structure in accordance with Young’s notion of social structural processes. This renders the question of what health inequalities a society is due to avoid into a question of what we can expect from the side of the various actors that uphold the social structures that produce socioeconomic health inequalities. Lastly, it is discussed how a shift to Young’s theory completes the shift to non-ideal theorising that seem already initiated by Daniels, and that with this, the distinction between direct and indirect evaluation dissolves. Chapter 7 discusses to what extent equality in health is of instrumental value for a society of free and equals. It thus takes up the idea proposed in chapter 5, that an evaluation of the consequences of health inequalities is also due. Taking relational equality as an evaluative framework reveals three ways in which inequalities in life expectancy threaten this ideal. That is, via unequal risks to stigmatisation, unequal risks to unemployment and the risk of unequal pension enjoyments. It is thereby shown that these risks are especially great for those lower down the socioeconomic strata. It thus concludes that equality in health is of instrumental value to relational equality. The chapter continues to argue that our instrumental approach opens a new perspective: to mitigate the identified injustices by changing society, rather than by reducing inequalities in health. This is argued to be an advantage in the light of the realistic assumption that of the socioeconomic health inequalities will persist. The paper thus offers a complementary approach to both the evaluation and the mitigation of the injustice of socioeconomic inequalities in health. The discussion chapter summarises the central findings of the analyses of health concepts and discusses questions regarding the philosophical and practical merits of comparing theoretical health concepts, the need for developing new health measures or concepts and the importance or nonsense of studying citizen’s views on health. Repeating this for the dissertation’s second part, the central findings of the chapters on justice evaluation are summarised and followed by a discussion of questions and issues that have remained unaddressed so far. Here, central points of discussion are my take on rules of distribution, the distinction of direct and indirect evaluation, the role of ideal and non-ideal theory, the idea of relational equality, and personal responsibility for health. The chapter concludes by noting that also in the light of justice evaluations, all commonly used health measures are relevant for justice. Therefore, my recommendations for policy and further research entail that inequalities in each of these measures deserve attention by both policymakers and researchers. Specifically, policymakers and researchers should give attention to how exactly each of these health inequalities come about, in such a way that a discussion about the question of who can be assigned responsibility to alleviate them is well-informed; and both should give attention to the effects of health inequalities on the opportunities for people to live on equal standing, in such a way that when these opportunities are diminished, actions can be considered to aim to restore relational equality. (shrink)

Set theory deals with the most fundamental existence questions in mathematics—questions which affect other areas of mathematics, from the real numbers to structures of all kinds, but which are posed as dealing with the existence of sets. Especially noteworthy are principles establishing the existence of some infinite sets, the so-called “arbitrary sets.” This paper is devoted to an analysis of the motivating goal of studying arbitrary sets, usually referred to under the labels of quasi-combinatorialism or combinatorial maximality. After explaining what (...) is meant by definability and by “arbitrariness,” a first historical part discusses the strong motives why set theory was conceived as a theory of arbitrary sets, emphasizing connections with analysis and particularly with the continuum of real numbers. Judged from this perspective, the axiom of choice stands out as a most central and natural set-theoretic principle (in the sense of quasi-combinatorialism). A second part starts by considering the potential mismatch between the formal systems of mathematics and their motivating conceptions, and proceeds to offer an elementary discussion of how far the Zermelo—Fraenkel system goes in laying out principles that capture the idea of “arbitrary sets”. We argue that the theory is rather poor in this respect. (shrink)

We propose an extension of Aczel's constructive set theory CZF by an axiom for inductive types and a choice principle, and show that this extension has the following properties: it is interpretable in Martin-Löf's type theory. In addition, it is strong enough to prove the Set Compactness theorem and the results in formal topology which make use of this theorem. Moreover, it is stable under the standard constructions from algebraic set theory, namely exact completion, realizability models, forcing as (...) well as more general sheaf extensions. As a result, methods from our earlier work can be applied to show that this extension satisfies various derived rules, such as a derived compactness rule for Cantor space and a derived continuity rule for Baire space. Finally, we show that this extension is robust in the sense that it is also reflected by the model constructions from algebraic set theory just mentioned. (shrink)

Technical reasoning refers to making inferences about how to use tools. The degree of technical reasoning is indicated by the bias of the gaze on the functional part of the tool when in use. Few studies have examined whether technical reasoning differs between familiar and unfamiliar novel tools. In addition, what effect the intention to use the tool has on technical reasoning has not been determined. This study examined gaze shifts in relation to familiar or unfamiliar tools, under three conditions, (...) among 14 healthy adults. The cumulative fixation time on the functional part of the tool served as a quantitative indicator of the degree of technical reasoning. The two-way analysis of variance for tools and conditions revealed that the cumulative fixation time significantly increased under free viewing and use conditions, compared to lift conditions. Relative to the free viewing condition, cumulative fixation time for unfamiliar tools significantly decreased in the lift condition and significantly increased in the use condition. Importantly, the results showed that technical reasoning was performed in both the use and the free viewing conditions. However, technical reasoning in the free viewing condition was not as strong as in the use condition. The difference between technical reasoning in free viewing and use conditions may indicate the difference between automatic and intentional technical reasoning. (shrink)

Blood supplies have become indexes of national security and the public good. While blood shortages can provoke anxiety, controversies continue to erupt in many countries over proper donor screening, especially with reference to HIV. This article sketches these dynamics in several global settings, focusing especially on activist efforts by gay men to reform exclusionary blood donor guidelines. The contours of the debate recall familiar conflicts between the putative demands of public health and the rights of individuals in the era (...) of AIDS. However, if gay activists marshal a discourse of individual rights vis-a-vis forms of institutional exclusion, they also seek a broader shift in social and cultural understandings of gay identity. To capture this complex interplay of citizenship and sociality, risk and responsibility, the article introduces the notion of `vital publics' to refer to the peculiar associational form represented by blood supplies. Vital publics are kinds of embodied association elicited through the generalized exchange of body — in this case, blood. Hailed to `give life' by the jargon of the pervasive social marketing of varied blood service systems, activists seek to contribute to the life of the `vital public' that transfusion medicine calls into being. (shrink)