We develop a general algebraic and proof-theoretic study of substructural logics that may lack associativity, along with other structural rules. Our study extends existing work on substructural logics over the full Lambek Calculus [34], Galatos and Ono [18], Galatos et al. [17]). We present a Gentzen-style sequent system that lacks the structural rules of contraction, weakening, exchange and associativity, and can be considered a non-associative formulation of . Moreover, we introduce an equivalent Hilbert-style system and show that the logic associated (...) with and is algebraizable, with the variety of residuated lattice-ordered groupoids with unit serving as its equivalent algebraic semantics. Overcoming technical complications arising from the lack of associativity, we introduce a generalized version of a logical matrix and apply the method of quasicompletions to obtain an algebra and a quasiembedding from the matrix to the algebra. By applying the general result to specific cases, we obtain important logical and algebraic properties, including the cut elimination of and various extensions, the strong separation of , and the finite generation of the variety of residuated lattice-ordered groupoids with unit. (shrink)

Although there are important moral arguments against cloning human beings, it has been suggested that there might be exceptional cases in which cloning humans would be ethically permissible. One type of supposed exceptional case involves infertile couples who want to have children by cloning. This paper explores whether cloning would be ethically permissible in infertility cases and the separate question of whether we should have a policy allowing cloning in such cases. One caveat should be stated at the beginning, however. (...) After the cloning of a sheep in Scotland, scientists pointed out that using the same technique to clone humans would, at present, involve substantial risks of producing children with birth defects. This concern over safety gives compelling support to the view that it would be wrong to attempt human cloning now. Thus, we do not reach the debate about exceptional cases unless the issue of safety can be set aside. I ask the reader to consider the possibility that in the future humans could be cloned without a significantly elevated risk of birth defects from the cloning process itself. The remainder of this paper assumes, for sake of argument, that cloning technology has advanced to that point. Given this assumption, would cloning in the infertility cases be ethically permissible, and should it be legally permitted? (shrink)

Purely parallel neural networks can model object recognition in brief displays – the same conditions under which illusory conjunctions have been demonstrated empirically. Correcting errors of illusory conjunction is the “tag-assignment” problem for a purely parallel processor: the problem of assigning a spatial tag to nonspatial features, feature combinations, and objects. This problem must be solved to model human object recognition over a longer time scale. Our model simulates both the parallel processes that may underlie illusory conjunctions and the serial (...) processes that may solve the tag-assignment problem in normal perception. One component of the model extracts pooled features and another provides attentional tags that correct illusory conjunctions. Our approach addresses two questions: How can objects be identified from simultaneously attended features in a parallel, distributed representation? How can the spatial selectional requirements of such an attentional process be met by a separation of pathways for spatial and nonspatial processing? Our analysis of these questions yields a neurally plausible simulation of tag assignment based on synchronizing feature processing activity in a spatial focus of attention. (shrink)

Some defenders of the view that there is a common morality have conceived such morality as being universal, in the sense of extending across all cultures and times. Those who deny the existence of such a common morality often argue that the universality claim is implausible. Defense of common morality must take account of the distinction between descriptive and normative claims that there is a common morality. This essay considers these claims separately and identifies the nature of the arguments for (...) each claim. It argues that the claim that there is a universal common morality in the descriptive sense has not been successfully defended to date. It maintains that the claim that there is a common morality in the normative sense need not be understood as universalist. This paper advocates the concept of group specific common morality, including country-specific versions. It suggests that both the descriptive and the normative claims that there are country-specific common moralities are plausible, and that a country-specific normative common morality could provide the basis for a country's bioethics. (shrink)

Ethical controversy over transplantation of human fetal tissue has arisen because the source of tissue is induced abortions. Opposition to such transplants has been based on various arguments, including the following: rightful informed consent cannot be obtained for use of fetal tissue from induced abortions, and fetal tissue transplantation might result in an increase in the number of abortions. These arguments were not accepted by the National Institutes of Health (NIH) Human Fetal Tissue Transplantation Research Panel. The majority opinion of (...) the panel stated that abortion and fetal tissue use are entirely separate issues, and that tissue use is ethically acceptable because it can be morally insulated from the issue of abortion. In support of this view, panel members and others have replied to the arguments put forward by opponents of fetal tissue use. However, replies to the two arguments mentioned above have been unsatisfactory, and the shortcomings of those replies are identified herein. Examination of the arguments pro and con suggests that fetal tissue use cannot be completely insulated from the issue of abortion. Thus, in seeking an ethical justification for fetal tissue transplantation we must consider reasons other than those put forward by the NIH panel. In this paper it is argued that whatever wrong is involved in using fetal tissue from induced abortions must be balanced against the benefits for patients, and it is on this basis that fetal tissue transplantation can be ethically justified. (shrink)

A bold argument that constitutional states are not weaker because their powers are divided -- they are often stronger because they solve collective action problems rooted in speech and communication.

The notion of strong measure zero is studied in the context of Polish groups and general separable metric spaces. An extension of a theorem of Galvin, Mycielski and Solovay is given, whereas the theorem is shown to fail for the Baer–Specker group Zω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb{Z}^{\omega}}}$$\end{document}. The uniformity number of the ideal of strong measure zero subsets of a separable metric space is examined, providing solutions to several problems of Miller and Steprāns (...) :52–59, 2006). (shrink)

Many adoptees face a number of challenges relating to separation from biological parents during the adoption process, including issues concerning identity, intimacy, attachment, and trust, as well as language and other cultural challenges. One common health challenge faced by adoptees involves lack of access to genetic-relative family health history. Lack of GRFHx represents a disadvantage due to a reduced capacity to identify diseases and recommend appropriate screening for conditions for which the adopted person may be at increased risk. In this (...) article, we draw out common features of traditionally understood “health disparities” in order to identify analogous features in the context of adoptees’ lack of GRFHx. (shrink)

In this paper, I accomplish a conceptual task and a historical task. The conceptual task is to argue that (1) Einstein’s Principle of Separability (henceforth “separability”) is not a supervenience principle and that (2) separability and entanglement are compatible. I support (1) by showing that the conclusion of Einstein’s incompleteness argument would still follow even if one assumes that the state of a composite system does not supervene on the states of the subsystems, and by showing that (...) what Einstein says in “Quantum Mechanics and Reality” (1948) strongly suggests that separability is not a principle about how subsystem states relate to the state of composite systems. I support (2) by showing that if separability was incompatible with entanglement, then Einstein’s argument would be incoherent in a trivial way. Thus, by arguing for (1) and (2) I directly challenge what has been, and still is, a very common reading of separability. The historical task is to offer the first detailed review of the different ways in which separability has been defined by physicists and philosophers in the last 60 years. Among other things, such a review distinguishes three different definitions of the principle, and shows that since the 1990s and up until the present date, it became standard to take separability (as presented by Einstein) to be a supervenience principle. (shrink)

Professor Weil’s thesis seems largely correct with respect to the United States, whose law on religious establishment I regularly teach. Funding is central to American debates over religious establishment. The fight over religious establishments in Virginia, which inspired both James Madison’s “Memorial and Remonstrance against Religious Assessments” and Thomas Jefferson’s “An Act for Establishing Religious Freedom,” was over whether persons could be forced to pay taxes to support religious instruction. Financial concerns were at the root of church-state debates in the (...) nineteenth century, when Protestants repeatedly rebuffed Catholics who wanted funding for Catholic private schools. Many state constitutions still have what are known as mini-Blaine Amendments that forbid public funding for religious institutions. Whether proponents of a strong separation between church and state in the United States are fighting the same battles as proponents of a strong separation of church and state in France is nevertheless problematic. The French revolutionaries had to subordinate a reactionary church. The American revolutionaries merely had to negotiate peace treaties among the different sects that supported the Declaration of Independence. Separation of church and state in the United States is best conceptualized as a division of labor among liberal institutions rather than a means for purging anti-liberal religion from the liberal public sphere. (shrink)

Ontological separation plays a key role in Aristotle’s metaphysical project: substances alone are ontologically χωριστόν. The standard view identifies Aristotelian ontological separation with ontological independence, so that ontological separation is a non-symmetric relation. I argue that there is strong textual evidence that Aristotle employs an asymmetric notion of separation in the Metaphysics—one that involves the dependence of other entities on the independent entity. I argue that this notion allows Aristotle to prevent the proliferation of substance-kinds and thus to secure (...) the unity of his metaphysical system. (shrink)

The term ‘emergence’ often causes confusion in science and philosophy, as it is used to express at least two quite different concepts. We can label these concepts _strong_ _emergence_ and _weak emergence_. Both of these concepts are important, but it is vital to keep them separate.

For Christian theology, the survival of the soul after the death of the body is a matter of fact. However, its philosophical explanation is probably the most peculiar issue of Thomas Aquinas’ radically Aristotelianaccount of body-soul. For both Augustine and Avicenna – who, together with Aristotle, can be considered the main sources of thirteenth century philosophy – the certainty of the immaterial soul’s ability to survive independently from the body was so strong that, coining their very own notions of (...) human spiritual substance, they described it as only partially implied in the act of the body’s information. This account was able to mediate between Aristotle’s idea of the soul as a form of the body and the Neoplatonic theory of the soul as an independent substance.... (shrink)

One diagnosis of Bell's theorem is that its premise of Outcome Independence is unreasonably strong, as it postulates one common screener system that purports to explain all the correlations involved. This poses a challenge of constructing a model for quantum correlations that is local, non-conspiratorial, and has many separate screener systems rather than one common screener system. In particular, the assumptions of such models should not entail Bell's inequalities. We prove that the models described do not exist, and hence, (...) the diagnosis above is incorrect. (shrink)

The meaning of sustainability is the subject of intense debate among environmental and resource economists. Perhaps no other issue separates more clearly the traditional economic view from the views of most natural scientists. The debate currently focuses on the substitutability between the economy and the environment or between “natural capital” and “manufactured capital”—a debate captured in terms of weak versus strong sustainability. In this article, we examine the various interpretations of these concepts. We conclude that natural science and economic (...) perspectives on sustainability are inconsistent. The market-based Hartwick-Solow “weak sustainability” approach is far removed from both the ecosystem-based “Holling sustainability” and the “strong sustainability” approach of Daly and others. Each of these sustainability criteria implies a specific valuation approach, and thus an ethical position, to support monetary indicators of sustainability such as a green or sustainable Gross Domestic Product (GDP). The conflict between “weak sustainability” and “strong sustainability” is more evident in the context of centralized than decentralized decision making. In particular, firms selling “services” instead of material goods and regarding the latter as “capital” leads to decisions more or less consistent with either type of sustainability. Finally, we discuss the implications of global sustainability for such open systems as regions and countries. Open systems have not been dealt with systematically for any of the sustainability criteria. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Separating the Human from the Divine Cesáreo Bandera University ofNorth Carolina at Chapel Hill Myths are hard to die. One such myth concerns what happened with poetry in general, that is to say, imaginative literature or literary fiction, in the transition from the Middle Ages to the Renaissance and beyond. Its basic outline was developed during the nineteenth century. J. E. Spingarn, for example, echoes such a myth in (...) his History of Literary Criticism in the Renaissance, first published in 1899, which has gone through many editions and reprintings since then. In it we read the following: The first problem of Renaissance criticism was the justification of imaginative literature. The existence and continuity of the aesthetic consciousness, and perhaps, in a less degree, of the critical faculty, throughout the Middle Ages, can hardly be denied; yet distrust of literature was keenest among the very class of men in whom the critical faculty might be presupposed, and it was as the handmaid of philosophy, and most of all as the vassal of theology, that poetry was chiefly valued.... The Renaissance was thus confronted with the necessity ofjustifying its appreciation of the vast body of literature which the Revival of Learning had recovered for the modern world. (3) Speaking of Savonarola's De Divisione ac Utilititate Omnium Scientiarum, written about 1492, he concludes as follows: In fine, as a reformer, he represents for us the religious reaction against the paganization of culture by the humanists. But the forces against him were too strong. Even the Christianization of culture effected during the next century by the Council of Trent was hardly more than temporary. Humanism, which represents 74Cesáreo Bandera the revival of ancient pagan culture, and rationalism, which represents the growth of the modem spirit in science and art, were currents too powerful to be impeded by any reformer, however great. (14) This general picture of the historical standing and the fate of literary fiction as we move from the Middle Ages into the modern era, is still very much with us, even though it is ill at ease with, or flatly contradicted by, undeniable historical facts. For example, the incredible notion of a "paganization of culture by the humanists" would have horrified somebody as profoundly Christian as Petrarch and, later on, Erasmus, who criticized the scholastics "in the name of a purer and simpler mode of piety and religious devotion" (Mazzeo 17). Or the mistaken idea that modern rationalism was much more hospitable to poetry than the old scholastic one. For from the seventeenth century on, as J. F. West has pointed out, the whole tide of [scientific] opinion was running strongly against poetry, metaphor, and poetic prose. The philosophers generally saw them as an obstacle to truth. Hobbes regarded metaphor as one of the hindrances to straight thinking. Rousseau thought that the philosophy of Descartes had 'cut the throat of poetry'; and John Locke, late in the century, openly regarded poetry as made up of 'pleasant pictures and agreeable visions in the fancy,' but basically misleading. (114) It is indeed true that in medieval scholasticism poetry occupies the lowest rank in the hierarchical structure of the arts and sciences. But it does have a place there. It would have never occurred to Thomas Aquinas, for example, to expel it from that position as something dangerous, something to be avoided. In fact, as he tells us at the beginning of the Summa Theologica, theology itself, the highest of the sciences, does not consider it below its dignity to make use of metaphor and other poetic devices propter utilitatem ac necessitatem. And yet it is precisely that kind of violent expulsion ofpoetic fiction that will be attempted during the Renaissance. In the words of Russell Fraser, "it is in the Renaissance, and not the Middle Ages that the artist is driven from the commonwealth" (39). It was then that the "war against poetry" intensified to fever pitch. It is, therefore, an error to imagine that those in the sixteenth and seventeenth centuries who bitterly attacked poetic fiction in general and the theater in particular as a very dangerous threat to religion and morality, were fanatic hold-overs from a medieval past... (shrink)

It is proposed that the multiple enhancer elements associated with locus control regions and super‐enhancers recruit RNA polymerase II and efficiently assemble elongation competent transcription complexes that are transferred to target genes by transcription termination and transient looping mechanisms. It is well established that transcription complexes are recruited not only to promoters but also to enhancers, where they generate enhancer RNAs. Transcription at enhancers is unstable and frequently aborted. Furthermore, the Integrator and WD‐domain containing protein 82 mediate transcription termination at (...) enhancers. Abortion and termination of transcription at the multiple enhancers of locus control regions and super‐enhancers provide a large pool of elongation competent transcription complexes. These are efficiently captured by strong basal promoter elements at target genes during transient looping interactions. -/- . (shrink)

The two theories that revolutionized physics in the twentieth century, relativity and quantum mechanics, are full of predictions that defy common sense. Recently, we used three such paradoxical ideas to prove “The Free Will Theorem” (strengthened here), which is the culmination of a series of theorems about quantum mechanics that began in the 1960s. It asserts, roughly, that if indeed we humans have free will, then elementary particles already have their own small share of this valuable commodity. More precisely, if (...) the experimenter can freely choose the directions in which to orient his apparatus in a certain measurement, then the particle’s response (to be pedantic—the universe’s response near the particle) is not determined by the entire previous history of the universe. Our argument combines the well-known consequence of relativity theory, that the time order of space-like separated events is not absolute, with the EPR paradox discovered by Einstein, Podolsky, and Rosen in 1935, and the Kochen-Specker Paradox of 1967 (See [2].) We follow Bohm in using a spin version of EPR and Peres in using his set of 33 directions, rather than the original configuration used by Kochen and Specker. More contentiously, the argument also involves the notion of free will, but we postpone further discussion of this to the last section of the article. Note that our proof does not mention “probabilities” or the “states” that determine them, which is.. (shrink)

We introduce three families of diagonal reflection principles for matrices of stationary sets of ordinals. We analyze both their relationships among themselves and their relationships with other known principles of simultaneous stationary reflection, the strong reflection principle, and the existence of square sequences.

Uniform sequential continuity, a property classically equivalent to sequential continuity on compact sets, is shown, constructively, to be a consequence of strong continuity on a metric space. It is then shown that in the case of a separable metric space, uniform sequential continuity implies strong continuity if and only if one adopts a certain boundedness principle that, although valid in the classical, recursive and intuitionistic setting, is independent of Heyting arithmetic.

This paper explores and rehabilitates the value of decisional privacy as a conceptual tool, complementary to informational privacy, for critiquing personalized choice architectures employed by self-tracking technologies. Self-tracking technologies are promoted and used as a means to self-improvement. Based on large aggregates of personal data and the data of other users, self-tracking technologies offer personalized feedback that nudges the user into behavioral change. The real-time personalization of choice architectures requires continuous surveillance and is a very powerful technology, recently coined as (...) “hypernudging.” While users celebrate the increased personalization of their coaching devices, “hypernudging” technologies raise concerns about manipulation. This paper addresses that intuition by claiming that decisional privacy is at stake. It thus counters the trend to solely focus on informational privacy when evaluating information and communication technologies. It proposes that decisional privacy and informational privacy are often part of a mutually reinforcing dynamic. Hypernudging is used as a key example to illustrate that the two dimensions should not be treated separately. Hypernudging self-tracking technologies compromise autonomy because they violate informational and decisional privacy. In order to effectively judge whether technologies that use hypernudges empower users, we need both privacy dimensions as conceptual tools. (shrink)

This is a version of a paper delivered at the Beckett centenary conference held at University College Cork, May 26-27, 2006. It was subsequently published under the title ‘Stellar Separation orMachine? Badiou and Deleuze and Guattari on Beckett’ in Beckett Re-Membered: After the Centenary, edited by James Carney,Mi chael O’Sullivan, Leonard Madden and Karl White, pp. 92-107, ISBN 1443835005. This is a pre-publication version of the paper as it appeared in the latter publication. OPENING PARAGRAPH: In the most important study (...) to date of the respective use of Beckett’s writings in the work of Deleuze and Badiou, Jean-Jacques Lecercle concludes by surmising that “Perhaps the close proximity, in the French edition, of Deleuze’s essay, ‘The Exhausted’, to Beckett’s own text, is indeed more than a fortunate coincidence: perhaps it is a symptom”.1 For, Lecercle, despite his long-term support for Deleuze and indeed despite his misgivings concerning Badiou’s characteristically strong reading of Beckett, decides that there may be, after all, something more compelling in the Badiou than in the less consistent Deleuze. This may also be, he suggests, attributable to Deleuze’s own modernism as a writer, which, though it gives him greater access to, and understanding of, the materiality of Beckett’s writing, also in the final analysis, renders his reading of Beckett somewhat orthodox. By contrast, the defiantly declarative and unhesitatingly dogmatic reading advanced by Badiou, is able to disclose strikingly original insights, not least because of the co-implication and reversibility of the readings of Badiou-Beckett and Beckett-Badiou. This essay seeks to examine the symptomatology of one text in particular as it operates and produces or is indicative of symptoms in the work of Badiou and Deleuze respectively. (shrink)

independence facts implied by a particular directed acyclic graph; an alternative equivalent rule has been proposed by Lauritzen et al. (1990). Geiger et al. (1990) have shown that d-separation is atomic-complete for independence statements..

The view that the soul can exist separately from the body is commonly associated with dualism. Since Plato’s Phaedo (Phd.) argues that the soul is immortal and survives the death of the body, there seems to be reason to call Plato, in that dialogue at least, a ‘dualist’. Yet, as we know, there are many kinds of dualism, so we have thereby not said very much. Let me therefore start with some distinctions. First of all, we can distinguish between two (...) kinds of dualism which say that the soul is a different kind of substance from the body. On one version, call it ‘strong’ substance dualism, no properties of mind can also be properties of body. Mind is defined as a kind of thing that uniquely has a certain property or set of properties, say consciousness, just as body is defined by its unique properties, say spatial extension. This would seem to be Descartes’ view. On another version, call it ‘weak’ substance dualism, no essential or defining properties of mind are also properties of body. This leaves it open whether the mind and body may share some accidental or non-defining properties. Finally, there is an even weaker kind of dualism which we may call property dualism. According to this view, there are mental properties which are distinct from and irreducible to bodily properties.4 However, these mental properties may or not be properties of an underlying substance that also has bodily properties. In other words, the same thing may have both mental and bodily properties, so having mental properties is not enough to make something a different kind of substance. (shrink)

We study the partial orderings of the form ⟨P,⊂⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\langle \mathbb{P}, \subset\rangle}$$\end{document}, where X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document} is a binary relational structure with the connectivity components isomorphic to a strongly connected structure Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Y}}$$\end{document} and P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{P} }$$\end{document} is the set of substructures of X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} (...) \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {X}}$$\end{document} isomorphic to X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document}. We show that, for example, for a countable X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document}, the poset ⟨P,⊂⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\langle \mathbb {P}, \subset\rangle}$$\end{document} is either isomorphic to a finite power of P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{P} }$$\end{document} or forcing equivalent to a separative atomless σ-closed poset and, consistently, to P/fin. In particular, this holds for each ultrahomogeneous structure X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document} such that X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document} or Xc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}^{c}}$$\end{document} is a disconnected structure and in this case Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Y}}$$\end{document} can be replaced by an ultrahomogeneous connected digraph. (shrink)

Two questions often shape our view of the world. On the one hand, we ask what there is, on the other hand, we ask what there ought to be. Empirical research and normative theory, the methodological traditions concerned with these questions, entered a difficult relationship, from at least as early as around the time of the advent of modern sciences. To this day, there remains a strong separation between the two domains, with both tending to neglect discourses and results (...) from the other. Contrary to a verdict of strict segregation between »is« and »ought«, there are, nowadays, various attempts to integrate both theoretical approaches. This calls for a newly intensified discourse on the relation between empirical research and normative theory. In this volume, scholars from different disciplines – including psychology, sociology, economics, and philosophy – discuss possible desired or undesired influences on, and limits of, the integration of these two approaches. (shrink)

This article argues that Habermas’s division of the process of Western modernization into cultural modernity (a pure normative sphere) and social-economic modernization (a pure technical-logical or instrumental sphere) and his use of this theoretical-political standpoint in order to ground a model of radical political democracy as an impartial, neutral, impersonal and formal procedural juridical-political paradigm based on the dialectics between institutionalization and spontaneity lead to strong institutionalism in politics. The notion of modern social systems or institutions as structures of (...) impartial, neutral, formal and impersonal proceduralism with a technical-logical or instrumental sense, constitution and evolution implies their non-political and non-normative understanding, depoliticizing them. As a consequence, institutions (especially political and economic ones) become self-referential and self-subsisting structures-subjects which are centralized and managed by institutional elites and technicians from a technical-logical standpoint-dynamics. We argue that a model of radical political democracy must overcome such separation between cultural modernity and social-economic modernization, politicizing the social systems and making them normative-political institutions-subjects streamlined and defined by social struggles between conflicting social classes, their hegemony and counterpoints. (shrink)

In [20] Krajíček and Pudlák discovered connections between problems in computational complexity and the lengths of first-order proofs of finite consistency statements. Later Pudlák [25] studied more statements that connect provability with computational complexity and conjectured that they are true. All these conjectures are at least as strong as $\mathsf {P}\neq \mathsf {NP}$ [23–25].One of the problems concerning these conjectures is to find out how tightly they are connected with statements about computational complexity classes. Results of this kind had (...) been proved in [20, 22].In this paper, we generalize and strengthen these results. Another question that we address concerns the dependence between these conjectures. We construct two oracles that enable us to answer questions about relativized separations asked in [19, 25] (i.e., for the pairs of conjectures mentioned in the questions, we construct oracles such that one conjecture from the pair is true in the relativized world and the other is false and vice versa). We also show several new connections between the studied conjectures. In particular, we show that the relation between the finite reflection principle and proof systems for existentially quantified Boolean formulas is similar to the one for finite consistency statements and proof systems for non-quantified propositional tautologies. (shrink)

In his book on P max [7], Woodin presents a collection of partial orders whose extensions satisfy strong club guessing principles on ω | . In this paper we employ one of the techniques from this book to produce P max variations which separate various club guessing principles. The principle (+) and its variants are weak guessing principles which were first considered by the second author [4] while studying games of length ω | . It was shown in [1] (...) that the Continuum Hypothesis does not imply (+) and that (+) does not imply the existence of a club guessing sequence on ω | . In this paper we give an alternate proof of the second of these results, using Woodin's P max technology, showing that a strengthening of (+) does not imply a weakening of club guessing known as the Interval Hitting Principle. The main technique in this paper, in addition to the standard P m a x machinery, is the use of condensation principles to build suitable iterations. (shrink)

A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated with arbitrary forcing classes. The relationships between the resulting principles and related principles, such as the corresponding forcing axioms and the corresponding fragments of the strong reflection principle, are analyzed, and consequences are presented. Some of these consequences are “exact” versions of diagonal stationary reflection principles of sets of ordinals. We also separate some of these diagonal strong reflection principles from (...) related axioms. (shrink)

Important examples of $\Pi^0_1$ classes of functions $f \in {}^\omega\omega$ are the classes of sets (elements of ω 2) which separate a given pair of disjoint r.e. sets: ${\mathsf S}_2(A_0, A_1) := \{f \in{}^\omega2 : (\forall i < 2)(\forall x \in A_i)f(x) \neq i\}$ . A wider class consists of the classes of functions f ∈ ω k which in a generalized sense separate a k-tuple of r.e. sets (not necessarily pairwise disjoint) for each k ∈ ω: ${\mathsf S}_k(A_0,\ldots,A_k-1) := (...) \{f \in {}^\omega k : (\forall i < k) (\forall x \in A_i) f(x) \neq i\}$ . We study the structure of the Medvedev degrees of such classes and show that the set of degrees realized depends strongly on both k and the extent to which the r.e. sets intersect. Let ${\mathcal S}^m_k$ denote the Medvedev degrees of those ${\mathsf S}_k(A_0,\ldots,A_{k-1})$ such that no m + 1 sets among A 0,...,A k-1 have a nonempty intersection. It is shown that each ${\mathcal S}^m_k$ is an upper semi-lattice but not a lattice. The degree of the set of k-ary diagonally nonrecursive functions $\mathsf{DNR}_k$ is the greatest element of ${\mathcal S}^1_k$ . If 2 ≤ l < k, then 0 M is the only degree in ${\mathcal S}^1_l$ which is below a member of ${\mathcal S}^1_k$ . Each ${\mathcal S}^m_k$ is densely ordered and has the splitting property and the same holds for the lattice ${\mathcal L}^m_k$ it generates. The elements of ${\mathcal S}^m_k$ are exactly the joins of elements of ${\mathcal S}^1_i$ for $\lceil{k \over m}\rceil \leq i \leq k$. (shrink)

This paper aims to come to grips with the rich philosophy of Charles Taylor by focusing on his concept of ‘strong evaluation’. I argue that a close examination of this term brings out more clearly the continuing tensions in his writings as a whole. I trace back the origin of strong evaluation in Taylor’s earliest writings, and continue by laying out the different philosophical themes that revolve around it. Next, the focus is on the separate arguments in which (...) strong evaluation is central, uncovering several methodological conflicts in Taylor’s strategies. Arguing against most of his commentators, I suggest that a distinction should be drawn between the philosophical anthropological, moral, and ontological implications of strong evaluation. As a result, the contribution of this paper is threefold. First, it clarifies the issue of strong evaluation by distinguishing the different arguments in which Taylor employs the concept. Second, it makes the case for multiple tensions within Taylor’s methods. Third, as a consequence, this analysis not only enables us to evaluate the potential and limits of his subject-centered philosophy but also separates his objectivist claims from his theories of human subjectivity, opening up the question of the metaphysical status of his ontological view. (shrink)

We outline two points of criticism. Firstly, we argue that robots do constitute a separate category of beings in people's minds rather than being mere depictions of non-robotic characters. Secondly, we find that (semi-)automatic processes underpinning communicative interaction play a greater role in shaping robot-directed speech than Clark and Fischer's theory of social robots as depictions indicate.

All spaces are assumed to be separable and metrizable. We show that, assuming the Axiom of Determinacy, every zero-dimensional homogeneous space is strongly homogeneous (i.e. all its non-empty clopen subspaces are homeomorphic), with the trivial exception of locally compact spaces. In fact, we obtain a more general result on the uniqueness of zero-dimensional homogeneous spaces which generate a given Wadge class. This extends work of van Engelen (who obtained the corresponding results for Borel spaces), complements a result of van Douwen, (...) and gives partial answers to questions of Terada and Medvedev. (shrink)

Kant’s attempts to formulate a conception of the harmony of nature and freedom have two logical presuppositions. The first presupposition is separation of ought and is, which provides a logical formulation of the separation of freedom and nature. Kant might well have settled on the view that the separation between nature and freedom cannot be bridged. Why did Kant attempt to overcome said separation? The second presupposition of Kant’s project to bridge nature and freedom involves an ought→can inference, stating that (...) moral obligation implies the possibility of its fulfillment. There are at least two ways this inference can be understood. There is a weak sense of the inference, stating that no one is obliged to do the impossible. There is also a very strong sense of the inference, stating that if a moral obligation is found to obtain, it must then be possible to fulfill it. Kant interprets the ought→can inference in this strong as well as in the weak sense. Nature, the law-governed totality of what exists, must be understood as able to provide a suitable field for moral realization. The isomorphism between the lawfulness of nature and that of moral freedom animate Kant’s account of moral judgment, and will provide the main focus of the current investigation. Kant conceives of nature and freedom as twin kingdoms, thus providing a theoretical model validating this ought→can inference. The weaker sense of this ought→can inference does justice to moral judgment without requiring the awesome task of bridging nature and freedom. Why, then, should we maintain the strong ought→can inference in our post-Kantian situation? I suggest that Kant’s insistence on the strong ought→can inference may yield an ethical approach to the ever more powerful ways in which human beings technologically transform nature, including human nature itself. (shrink)

Atoms and molecules are particular kinds of restricted n-body systems, which generally behave as quasi-separable, unlike other n-body systems, e.g., Newtonian ones. The Coulomb repulsion and the Pauli exclusion principle in atoms and molecules are responsible for that separability. Additionally, chemical bonds, especially covalent bonds, enhance the separability of molecules. Independent particle models do not describe atoms and molecules since first-order energy corrections are high. However, these corrections obtained by the first-order perturbation or mean-field strongly converge, implying a (...) one-electron effective potential description. Consequently, stable states of atoms and molecules can be reasonably described by one-electron effective potentials, which strongly differ from other n-body problems. We discuss the peculiarities of the correlation motion of generic systems in the context of the four fundamental forces. In particular, we have shown that the two components (attraction and repulsion) of the electromagnetic force confer a relatively low correlation motion to atoms and molecules. We discuss the physical and chemical nature of atoms and molecules, comparing the degrees of separability between different systems. For example, the separability of Newtonian systems is generally possible in particular classes of restricted systems due to relative mass differences. However, for atoms and molecules, the separability is much broader. (shrink)

Ethical analyses, professional guidelines and legal decisions support the equivalence thesis for life-sustaining treatment: if it is ethical to withhold treatment, it would be ethical to withdraw the same treatment. In this paper we explore reasons why the majority of medical professionals disagree with the conclusions of ethical analysis. Resource allocation is considered by clinicians to be a legitimate reason to withhold but not to withdraw intensive care treatment. We analyse five arguments in favour of non-equivalence, and find only relatively (...) weak reasons to restrict rationing to withholding treatment. On the contrary, resource allocation provides a strong argument in favour of equivalence: non-equivalence causes preventable death in critically ill patients. We outline two proposals for increasing equivalence in practice: (1) reduction of the mortality threshold for treatment withdrawal, (2) time-limited trials of intensive care. These strategies would help to move practice towards more rational treatment limitation decisions. (shrink)

We prove that the two-variable fragment of first-order logic has the weak Beth definability property. This makes the two-variable fragment a natural logic separating the weak and the strong Beth properties since it does not have the strong Beth definability property.

Recently there has been a surge of interest in the intersection between epistemology and action theory, especially in principles linking rationality in thought and rationality in action. Recently there has also been a surge of interest in the epistemic significance of perceived peer disagreement: what, epistemically speaking, is the rational response in light of disagreement with someone whom one regards as an epistemic peer? The objective of this paper is to explore these two issues—separately, but also in connection with one (...) another. I turn first to the idea that the normative standing of our actions depends on the normative standing of our beliefs. I endorse this idea. More precisely, I endorse a principle according to which sufficiently high credence in success conditions for a given goal-directed action is a necessary condition on rational execution of that action. I then turn to the debate concerning the epistemic significance of perceived peer disagreement. The basic issue is whether such disagreement is always epistemically significant in the sense of serving as a defeater of the initial credences of the disagreeing parties. Conformists argue that this is so while non-conformists deny it. I present a new argument against a brand of non-conformism that I call “strong non-conformism”. The key premise is the principle that sufficiently high credence in success conditions for a given goal-directed action is a necessary condition on rational execution of that action. I argue that, given this principle, strong non-conformism fails to yield the verdict that the epistemic requirement on rational action is violated in a case where, intuitively, it is violated. This is because strong non-conformism has it that disagreement with a perceived peer does not act as a defeater in the relevant case. Conformism fares better. (shrink)

Nearly thirty years ago, Robert Alexy in his book The Concept and Validity of Law as well as in other early articles raised non-positivistic arguments in the Continental European tradition against legal positivism in general, which was assumed to be held by, among others, John Austin, Hans Kelsen and H.L.A. Hart. The core thesis of legal positivism that was being discussed among contemporary German jurists, just as with their Anglo- American counterparts, is the claim that there is no necessary connection (...) between law and morality. Robert Alexy has argued, however, that the law, besides consisting conceptually of elements of authoritative issuance and social efficacy, necessarily lays a claim to substantial correctness, which is derived from analytical arguments. Furthermore, if this claim to substantial correctness necessarily requires the incorporation of moral elements into law, then the ‘necessary connection thesis’, as defended by non-positivism, can be justified. Some of the most significant objections to this sort of claim, stemming from the Anglo-American world, are those introduced by Joseph Raz. In his ‘Reply’ to Robert Alexy, Raz raises at least three interesting criticisms, including, first, the ambiguity of ‘legal theory in the positivistic tradition’, second, the indeterminate formulations of the ‘separation thesis’, and, third, the necessary claim of law to legitimate authority as a moral claim. As a point of departure, I will argue that Raz’s three criticisms are misleading. For they do not enhance our understanding of the genuine compatibility or incompatibility between legal positivism and non-positivism. Despite the frequently reformulated theses of legal positivism and the various kinds of opponents responding thereto, the essential divergence between legal positivism and non-positivism was and remains the answer to the question of the relation between law and morality. Furthermore, I will clarify that in the strictest sense there can be three and only three logically possible positions concerning the relation between law and morality: the connection between them is either necessary, or impossible (i. e. they are necessarily separate), or contingent (i. e. they are neither necessarily connected nor necessarily separate). The first position is non-positivistic, while the latter two positions are, indeed, both positivistic, but in different forms: one may be called ‘exclusive’ legal positivism, the other ‘inclusive’ legal positivism. I will continue by showing that these three positions stand to one another in the relation of contraries, not contradictories, and that, taken together, they exhaust the logically possible positions concerning the relation between law and morality, never mind the tradition or authority from which these positions are derived. Raz mentions, however, many changeable formulations of the separation thesis, which even leads him to acknowledge ‘necessary connections between law and morality’. One who is trying to understand legal positivism would no doubt be puzzled by this claim. Nevertheless, I will argue that this is an alternative strategy of legal positivism, and it points to naturalistically oriented view. Although this necessary separation between law and morality, understood naturalistically, strikes one as strengthening the separation, in the end it leads to a weakened notion of necessity. This weakened necessary separation thesis, however, cannot be justified through the so-called claim of the law to legitimate authority, defended by Raz, for it is difficult to answer the question of whether a normally justified but factual authority can gain legitimate authority. Finally, the necessary connection between law and morality in a strong sense can still be justified by the claim of law to correctness, as per Alexy’s argument. (shrink)

I critically examine the view that Descartes’s independence conception (IC) of substance plays a crucial role in his “separability argument” for substance dualism. I argue that IC is a poisoned chalice. I do so by considering how an IC-based separability argument fares on two different ways of thinking about principal attributes. On the one hand, if we take principal attributes to be universals, then a separability argument that deploys IC establishes a version of dualism that is unacceptably (...) strong. On the other hand, if we take principal attributes to be tropes, then IC introduces challenges which undermine the argument. This is partly because the assumption of tropes makes it possible to distinguish several versions of substance dualism, versions which differ with respect to their degree of generality. I argue that taking principal attributes to be tropes makes it challenging to establish any of these versions by way of an IC-based separability argument. I conclude the paper by suggesting a way forward for the proponent of the separability argument. (shrink)

Philosophers investigating questions of animal ethics tend to draw on animal cognition research while subscribing to strong positions regarding animal minds, and philosophers pursuing the question of animal minds frequently draw conclusions from the arguments of ethical philosophers. Despite this exchange, animal mind and animal ethics research have developed in fundamentally different directions. One reason for this divison lies in the institutional distinction between theoretical and practical philosophy. This anthology brings these fields and their philosophical approaches closer together, mapping (...) their surprising ideological and methodological overlap. (shrink)

Kevin Vallier’s book, Liberal Politics and Public Faith. Beyond Separation, constitutes an essential reading for anyone interested in public reason liberalism and in the debate concerning the role of religion in contemporary democratic societies. Vallier argues for a strong version of convergence in public justification, aiming at defending an account of liberalism friendly towards religion and religious citizens. Against traditional forms of liberalism built on the idea of neutrality and embodied in a secularized view of social institutions, Vallier’s goal (...) is to reconcile public reason liberalism with religion by showing that his theory “realizes foundational liberal values while according religion a prominent and powerful role in public life” .The topic of Vallier’s book is clearly of fundamental importance. That of the supposedly needed separation between religion and the state is not only one of the most long-standing issues in political philosophy, but it is also extremely r .. (shrink)

We discuss several axiomatizations of set theory in first order predicate calculus with epsilon and a constant symbol W, starting with the simple system K(W) which has a strong equivalence with ZF without Foundation. The other systems correspond to various extensions of ZF by certain large cardinal hypotheses. These axiomatizations are unusually simple and uncluttered, and are highly suggestive of underlying philosophical principles that generate higher set theory.

Uniformism about the epistemology of modality is the view that there is only one basic route to modal knowledge; non-uniformism is the view that there are several. Non-uniformism is becoming an increasingly popular stance, but how can it be defended? I prise apart two ways of understanding the uniformism/non-uniformism conflict that are mixed up in the literature. I argue that once separated, it is evident that they lead up to two different non-uniformist theses that need to be argued for in (...) very different ways. In particular, one construal allows only for a weak thesis about the actual lay of the current theoretical land in modal epistemology, while the other allows for a strong thesis that can be defended without reliance on claims about the alleged goodness or badness of individual accounts of modal justification. I argue that philosophers inclined towards non-uniformism ought to go for the strong, rather than the weak, thesis. (shrink)

This thesis is divided into three parts, the first and second ones focused on combinatorics and classification problems on discrete and geometrical objects in the context of descriptive set theory, and the third one on generalized descriptive set theory at singular cardinals of countable cofinality.Descriptive Set Theory (briefly: DST) is the study of definable subsets of Polish spaces, i.e., separable completely metrizable spaces. One of the major branches of DST is Borel reducibility, successfully used in the last 30 years to (...) solve and compare many classification problems. One of our goals is the classification of knots, very familiar and tangible objects in everyday life, which also play an important role in modern mathematics. The study of knots and their properties is known as knot theory. Our plan is to gain insight into knots using discrete objects, such as linear and circular orders. This approach was already exploited in [6]. The first part of this work is therefore devoted to countable linear orders and the study of the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results. We also expand our research to the case of circular orders.Another objective of this first part is to extend the notion of convex embeddability on countable linear orders. We provide a family of quasi-orders of which embeddability is a particular case as well. We study these quasi-orders from a combinatorial point of view and analyse their complexity with respect to Borel reducibility. Furthermore, we extend the analysis of these quasi-orders to the set of uncountable linear orders.The second part of the project deals with classification problems on knots and $3$ -manifolds. The goal here is to apply the results obtained in the first part to the study of proper arcs and knots, establishing lower bounds for the complexity of some natural relations between these geometrical objects. We also obtain some combinatorial results which are particularly interesting when we restrict to the set of wild proper arcs and wild knots, classes which haven’t received much attention so far. These parts are included in the two preprints [4, 5] in collaboration with my supervisor Alberto Marcone, Luca Motto Ros (University of Torino), and Vadim Weinstein (University of Oulu).The second part of this work also includes the classification of non-compact $3$ -manifolds up to homeomorphism (the case of compact $3$ -manifolds has already been solved: indeed, there are only countably many $3$ -manifolds up to homeomorphism; see [7]), and that of Cantor sets of $\mathbb {R}^3$ up to conjugation (answering to Question 5.5 of [3]). Here we resort to algebraic tools. Stone duality gives a neat way to go back-and-forth between totally disconnected Polish spaces and countable Boolean algebras (see [1]). The main ingredient is the Stone space of all ultrafilters on a Boolean algebra. In this work we introduce a weaker concept which we call “blurry filter”. Using blurry filters instead of ultrafilters enables one to extend the class of spaces under consideration beyond totally disconnected. As an application of this method, we show that both homeomorphism on non-compact $3$ -manifolds and conjugation of Cantor sets in $\mathbb {R}^3$ are completely classifiable by countable structures. These results are part of an upcoming paper in collaboration with Vadim Weinstein.The last part of this thesis concerns the natural generalization of descriptive set theory that occurs when countable is replaced by uncountable, called Generalized Descriptive Set Theory (briefly: GDST). In particular, we focus on the case of GDST for a singular cardinal $\kappa $ of countable cofinality. The goal here is to study the generalizations of the Perfect Set Property and the Baire Property to subsets of spaces of higher cardinalities, like the power set $\mathcal {P}(\kappa )$. We consider the question under which large cardinal hypotheses classes of definable subsets of these spaces possess such regularity properties, focusing on rank-into-rank axioms, like I2, and classes of sets definable by $\Sigma _1$ -formulas with parameters from various collections of sets. The obtained results are included in [2], a joint work with my co-supervisor Vincenzo Dimonte and Philipp Lücke (University of Hamburg).Abstract prepared by Martina IannellaE-mail: [email protected]: https://air.uniud.it/handle/11390/1262824. (shrink)

You have thoughts, feelings and desires. You remember your past and imagine your future. Sometimes you make a special effort, other times you are content to simply relax. All of these things are true about you. But do you exist? Is your sense of self an illusion, or is there something in the world that we can point to and say: ‘Ah, yes – that is you’? If you are familiar with the contemporary science of mind, you will know that (...) the concept of a substantive self, separate from the mere experience of self, is unpopular. But this stance is unwarranted. Research on attention points to a self beyond experience, with its own powers and properties. (shrink)

Over the last few decades, our theories of fundamental physics have become increasingly detached from empirical data. Recently, Richard Dawid has argued that the progressive separation of theory from experiment is concomitant with a number of changes in the methodology of the discipline. More precisely, Dawid has argued that the new methods of fundamental physics amount to a form of non-empirical confirmation, and that physical theories may therefore be confirmed even in the absence of empirical data. In this paper, I (...) critically engage with Dawid's views on non-empirical physics. My main target is the excessively central role that, in my view, the notion of non-empirical confirmation plays on Dawid's analysis. I will therefore argue that, while non-empirical methods may legitimately be employed in physics, those are not always deployed with the purpose of confirming scientific theories. Non-empirical arguments may also be used in order to ground pragmatic choices regarding what theories deserve to be further developed—and this is an aspect of the work that non-empirical methods perform that cannot be solely understood in terms of Dawid's notion of non-empirical confirmation. I support these claims by making use of a case-study from the early history of particle physics. The case-study concerns a theory of the strong force that J. J. Sakurai introduced in 1960. As we shall see, both the genesis of Sakurai's theory as well as the arguments that he used to defend it provide direct support for my own views on the role that non-empirical methods play in physics. Finally, I conclude the paper by introducing a notion that I believe is useful in making sense of the manner in which the pragmatic and the epistemic dimensions of non-empirical reasoning relate to each other, namely the notion of a cognitive attitude. -/- . (shrink)

We give a solution stated in the title to problem 3 of part 1 of the problems listed in the book of Eklof and Mekler [2], p. 453. There, in pp. 241-242, this is discussed and proved in some cases. The existence of strongly λ-free ones was proved earlier by the criteria in [5] and [3]. We can apply a similar proof to a large class of other varieties in particular to the variety of (non-commutative) groups.