The assertion by Simmons and Park that the dynamical map associated with the Bloch equations of nuclear magnetic resonance is not completely positive is wrong.

In this rejoinder to a critique by Raggio and Primas of our paper, “On Completely Positive Maps in Generalized Quantum Dynamics,” we acknowledge that, contrary to our original assertion, the Bloch equations are indeed completely positive. We then explain briefly why this modification of our analysis does not alter its main conclusions.

Several authors have hypothesized that completely positive maps should provide the means for generalizing quantum dynamics. In a critical analysis of that proposal, we show that such maps are incompatible with the standard phenomenological theory of spin relaxation and that the theoretical argument which has been offered as justification for the hypothesis is fallacious.

The role of completely positive mappings in quantum dynamics and measurement theory is reanalyzed in light of the possibility of a generalized dynamics.

There has been a long-standing and sometimes passionate debate between physicists over whether a dynamical framework for quantum systems should incorporate not completely positive (NCP) maps in addition to completely positive (CP) maps. Despite the reasonableness of the arguments for complete positivity, we argue that NCP maps should be allowed, with a qualification: these should be understood, not as reflecting ‘not completely positive’ evolution, but as linear extensions, to a system’s entire (...) state space, of CP maps that are only partially defined. Beyond the domain of definition of a partial-CP map, we argue, much may be permitted. (shrink)

This chapter provides a background for a virtue ethical map of Hume and Nietzsche. A map offers an interpretation of a terrain or subject matter that is “stylized,” “abstract,” and “simplified. A complete map of Nietzsche and Hume, whether or not it involves a virtue ethical map of their ethics, ideally requires a thoroughly explicated conception of their metaphysical perspective. The chapter offers instead a very abstract map of the main issues and the author's general position. Of great importance for (...) a virtue ethical map of Hume and Nietzsche is their emphasis on psychology. Psychological interpretation must not be confused with an “individualistic” interpretation, according to which persons are viewed as if they were not shaped by their cultures. Indeed Nietzsche frequently draws the attention to the virtues of different ages which may be embryonic in earlier ages. (shrink)

Positive logics are $\{ \wedge, \vee, \to \}$-fragments of intermediate logics. It is clear that the positive fragment of $Int$ is not structurally complete. We give a description of all hereditarily structurally complete positive logics, while the question whether there is a structurally complete positive logic which is not hereditarily structurally complete, remains open.

GPS position data prediction can effectively alleviate urban traffic, population flow, route planning, etc. It has very important research significance. Using swarm intelligence optimization algorithm to predict geographic location has important research strategies. Flower pollination algorithm is a new swarm intelligence optimization algorithm and easy to implement and has other characteristics; more and more scholars have continuously improved it and applied it to more fields. Aiming at the fact that FPA leads to the local optimal value in cross-pollination, the chaotic (...) mapping strategy is proposed to optimize related issues that the population is not rich enough in the self-pollination process. The improved flower pollination algorithm has better advantages in testing function convergence and geographic location prediction effect. (shrink)

Walter Map was a twelfth-century courtier and royal servant. He was a prolific writer, but De Nugis Curialium is the only surviving work confidently attributed to him. The book is a collection of short stories and anecdotes about the court, religion and history. Map's references demonstrate that he read widely, not only biblical and theological works, but also classical authors such as Horace, Virgil, Ovid and Juvenal. The only surviving manuscript of the work is a fourteenth-century copy once belonging to (...) the monk John Wells of Ramsey Abbey. The Cambridge bibliographer M. R. James would have been attracted to the breadth of Map's referencing, and the author's light-hearted writing style which was intended to entertain. James' 1914 Oxford publication corrected the earlier work of Thomas Wright who published an edition for the Camden Society in 1850. (shrink)

Global justice is, at its core, about moral obligations to distant others. But which obligations ought to be included is a matter of considerable debate. In the discussion that follows I will explicate and challenge two objections to the inclusion of foundationally positive obligations in our account of global justice. The first objection is based on the proposition that negative obligations possess and positive obligations lack a property necessary for a moral demand to be a matter justice. The (...) second objection is that even the most trivial positive obligation becomes overly burdensome when applied to the global arena. And, though I do not offer any particular substantive account of positive obligations to distant others; I assess some of the implications that would arise were positive obligations to distant others to be included in our account of global justice. (shrink)

Fix a finite ordinal \ and let \ be an arbitrary ordinal. Let \ denote the class of cylindric algebras of dimension \ and \ denote the class of relation algebras. Let \\) stand for the class of polyadic algebras of dimension \. We reprove that the class \ of completely representable \s, and the class \ of completely representable \s are not elementary, a result of Hirsch and Hodkinson. We extend this result to any variety \ between (...) polyadic algebras of dimension \ and diagonal free \s. We show that that the class of completely and strongly representable algebras in \ is not elementary either, reproving a result of Bulian and Hodkinson. For relation algebras, we can and will, go further. We show the class \ is not closed under \. In contrast, we show that given \, and an atomic \, then for any \, \ is a completely representable \. We show that for any \, the class of completely representable algebras in certain reducts of \s, that happen to be varieties, is elementary. We show that for \, the the class of polyadic-cylindric algebras dimension \, introduced by Ferenczi, the completely representable algebras coincide with the atomic ones. In the last algebras cylindrifications commute only one way, in a sense weaker than full fledged commutativity of cylindrifications enjoyed by classical cylindric and polyadic algebras. Finally, we address closure under Dedekind-MacNeille completions for cylindric-like algebras of dimension \ and \s for \ an infinite ordinal, proving negative results for the first and positive ones for the second. (shrink)

Positive modal algebras are the$$\left\langle { \wedge, \vee,\diamondsuit,\square,0,1} \right\rangle $$-subreducts of modal algebras. We prove that the variety of positive S4-algebras is not locally finite. On the other hand, the free one-generated positive S4-algebra is shown to be finite. Moreover, we describe the bottom part of the lattice of varieties of positive S4-algebras. Building on this, we characterize structurally complete varieties of positive K4-algebras.

In the article "Podstawy analizy metodologicznej kanonów Milla" [2] Jerzy Łoś proposed an operator that refered sentences to temporal moments. Let us look, for example, at a sentence ‘It is raining in Toruń’. From a logical point of view it is a propositional function, which does not have any logical value, unless we point at a temporal context from a fixed set of such contexts. If the sentence was considered today as a description of a state of affairs, it could (...) be true. If it was considered yesterday, it could be false. 1 The operator enables us to connect any sentence p with any temporal context t. Such a complex sentence we read as: a sentence p is realized at a temporal context t (a point of time, an interval of some kind, etc). (shrink)

The 1948 constitution of the World Health Organization (WHO) defines health as ‘a state of complete physical, mental and social well-being and not merely the absence of disease or infirmity’. It was a bold and revolutionary health idea to gain international consensus in a period characterized by fervent anti-communism. This article explores the genealogy of the health definition and demonstrates how it was possible to expand the scope of health, redefine it as ‘well-being’, and overcome ideological resistance to progressive and (...) international health approaches. The first part of the article demonstrates how the health definition was composed through a trajectory of draft ideas from scholars in the history of medicine, as well as political actors working to promote national health insurance. The definition was authored by League of Nations veteran Raymond Gautier, but secretly drew heavily on medical historian Henry E. Sigerist’s controversial book Socialized Medicine in the Soviet Union (1937). The second part analyses how it was possible to resist the ideological pushback against the WHO and secure US ratification. The WHO’s progressive constitution was not simply a deviation from dominant health ideas, but a direct outcome of the entrenched health conflict. The genealogy is based on original archival material from international organizations and US government archives. The article contributes to understandings of the political controversies surrounding the WHO and to scholarship on understandings of health. It also illustrates how influential health ideas cross the boundaries between politics and health sciences, as well as the boundaries between domestic health policy and global health. (shrink)

No-cloning theorem says that there is no unitary operation that makes perfect clones of non-orthogonal quantum states. The objective of the present paper is to examine whether an imperfect cloning operation exists or not in a C*-algebraic framework. We define a universal \ -imperfect cloning operation which tolerates a finite loss \ of fidelity in the cloned state, and show that an individual system’s algebra of observables is abelian if and only if there is a universal \ -imperfect cloning operation (...) in the case where the loss of fidelity is less than \ . Therefore in this case no universal \ -imperfect cloning operation is possible in algebraic quantum theory. (shrink)

It is almost universally believed that in quantum theory the two following statements hold: all transformations are achieved by a unitary interaction followed by a von-Neumann measurement; all mixed states are marginals of pure entangled states. I name this doctrine the dogma of purification ontology. The source of the dogma is the original von Neumann axiomatisation of the theory, which largely relies on the Schrődinger equation as a postulate, which holds in a nonrelativistic context, and whose operator version holds only (...) in free quantum field theory, but no longer in the interacting theory. In the present paper I prove that both ontologies of unitarity and state-purity are unfalsifiable, even in principle, and therefore axiomatically spurious. I propose instead a minimal four-postulate axiomatisation: associate a Hilbert space \ to each system \; compose two systems by the tensor product rule \; associate a transformation from system \ to \ to a quantum operation, i.e. to a completely positive trace-non-increasing map between the trace-class operators of \ and \; evaluate all joint probabilities through that of a special type of quantum operation: the state preparation. I then conclude that quantum paradoxes—such as the Schroedinger-cat’s, and, most relevantly, the information paradox—are originated only by the dogma of purification ontology, and they are no longer paradoxes of the theory in the minimal formulation. For the same reason, most interpretations of the theory interpret the same dogma, not the strict theory stripped of the spurious postulates. (shrink)

This paper formulates a notion of independence of subobjects of an object in a general (i.e. not necessarily concrete) category. Subobject independence is the categorial generalization of what is known as subsystem independence in the context of algebraic relativistic quantum field theory. The content of subobject independence formulated in this paper is morphism co-possibility: two subobjects of an object will be defined to be independent if any two morphisms on the two subobjects of an object are jointly implementable by a (...) single morphism on the larger object. The paper investigates features of subobject independence in general, and subobject independence in the category of C∗ - algebras with respect to operations (completely positive unit preserving linear maps on C∗ - algebras)as morphisms is suggested as a natural subsystem independence axiom to express relativistic locality of the covariant functor in the categorial approach to quantum field theory. (shrink)

"Ever Since This World Began" from Love Dog (Penny-Ante Editions, 2013) by Masha Tupitsyn continent. The audio-essay you've recorded yourself reading for continent. , “Ever Since the World Began,” is a compelling entrance into your new multi-media book, Love Dog (Success and Failure) , because it speaks to the very form of the book itself: vacillating and finding the long way around the question of love by using different genres and media. In your discussion of the face, one of the (...) themes of Love Dog , I think there is something to be said about the surfaces media create and how you constantly manipulate them in your work. This seems important for thinking also about your book LACONIA: 1,200 Tweets on Film ; a book on film written in tweets, interposing already three sets of expectations and pushing the boundaries of each medium's faciality, it's surface tension. In Love Dog , is there another kind of facial interaction? Perhaps the discursive faces of approaching love as topic and love as method? If so, how did/do these intersect for you, do/did they drive the creation of this book? MASHA TUPITSYN With LACONIA and Love Dog , I wanted to pay homage to the work modernism has done on subjective time and chronological time by carrying that experiment over into the digital economy. Because LACONIA is a time-based work of cultural criticism that employs the aphorism to look at 21 st century American culture, it is also an archival work of cultural mourning and memory. And in Love Dog , which is also a work about mourning as it relates to love, I wanted to think with all my senses, and to reflect that in the writing itself by using a multi-media form. LACONIA tackled the sound bite and the promotional image--the everyday language of consumer culture--which often wants to communicate ideological agendas through the repetition of a single image or reductive phrase. I had always been interested in the approaches of artists like Barbara Kruger and Jenny Holzer and essayistic, typographical filmmakers, like Chris Marker and Godard. In both cases, I felt it was important to try to compose a book in which deep—critical—thinking happens in so-called immediate, informal, and disposable contexts. That is, in places where you are either not supposed to be serious or are not required to take things seriously. To me the most intervention is needed in every day instances of culture and representation. In order to do that, I had to utilize and interrogate the very structures I was critiquing. In other words, the writing had to materialize in that live, digital, public space. It couldn’t simply happen at home on a piece of paper or in a word document on my computer that no one could see until it was finished. It had to unfold in real time, amidst everything else. And it had to literally be surrounded by the cultural landscape I wanted to assess. In both LACONIA and Love Dog , I wanted to know how and if we can get away from what we cannot get away from? From which there is no respite. Given this, I don’t think hypertexts can really be called hypertexts anymore. Hypertexts are simply the world today. This is not only the way we read the world now. It is the way the world reads. Likewise, interfaciality, as you put it, works on a number of levels for me, both on and off the page. There is my relation to epistemological and phenomenological surfaces—the screen, the body, the face, the voice, gender; the official story. Then there is the way this dovetails formally, and to which the digital adds yet another dimension. It’s also where sound comes into Love Dog (giving the book a sound; giving tonality to the book’s ideas and feelings). As Anne Carson pointed out in her essay “The Gender of Sound,” the two are connected, and of course so are love and gender. In “Ever Since This World Began,” I wanted to think about the phenomenology of the voice, which is why I visualize the sonic in the book and why in my writing about faces, I look at the tonal aspects (the things a face voices and a voice faces) of a face. This was standard to do when images and faces were “silent” in the silent era. Those images/faces were extraordinarily audible. The greatest screen face, to me, is still Falconetti’s in Dreyer’s The Passion of Joan of Arc . We can hear her face—even though there is no actual sound on screen of her speaking. The internet is a similarly “silent” space where actual voices are lacking. So intertextuality goes with interfaciality. I’ve also talked a lot about how categorization worked when it came to the reception of my first book, Beauty Talk & Monsters . How despite the fact that Beauty Talk is a text that crisscrosses form and content in a variety of ways, not pinpointing its exact genre—choosing one genre over another—only made things worse. Fiction was the category people were most adverse to me using, even though of course there is a lot of fiction in the book. Part of how fiction works in Beauty Talk is in the reader not knowing exactly where the fiction resides. In Godard’s 1967 film, Weekend , for example, everything matters. Everything is political, whether it’s real or imaginary, film or reality. In Weekend , life is not a game and neither is the game a game. The game is really life. Either everything is important or nothing is. But many people want clear answers and demarcations so that they can decide what is important and what is not important. My use of the “I,” subjective criticism, made everything “real” in Beauty Talk . But fiction is in the construction. It is in the blending. This is why I perforate the movie screen and connect the onscreen and the offscreen; the official story and the backstory. Although I don’t think there is a difference between onscreen and offscreen anymore. Nor is there a dialectic. It’s all screen all the time now. Non-fiction, on the other hand, was more tolerated as a moniker. Unlike Love Dog , Beauty Talk wasn’t explicitly or tangibly (what is tangible is a question in all these books) working with digital forms or within this digital economy, so some people resisted the book’s hypertextuality or intertextuality because they couldn’t see its other forms, if that makes sense. It was a problem of invisibility; of how to make something appear (this is where Nietzsche, big presence in Love Dog , comes in—the nature of appearances). Something people don’t necessarily want to see. Some readers couldn’t see the way forms were interfacing in that book. On the surface, Beauty Talk was simply a text about media culture—the domination of entertainment as a mode of being and knowing—and most readers could only see that one side of the book. But as Godard puts it in Wim Wenders’ documentary about the future of cinema, Room 666 , “Films are made, images are made, when there’s no one looking. That’s what the invisible is, that which we don’t see. That’s what the incredible is, that which we don’t see. And cinema shows you that which we don’t see, the incredible.” We are living in the aftermath of narrative and temporal collapse, which means we don’t read or feel in the same way. I began to use digital forms in my writing because I don’t see us as traditional book people anymore. I would add that power also resides in the invisible, in the things we make invisible by making them visible. Or it did for a long time. The new face of power is quickly becoming so-called transparency, which is even more corrupt because even though we now live in a behind-the-scenes culture, and see and know how the mechanisms of power and corruption operate, we still don't change. The world still doesn't change. Finally, another important thing that Godard says in Room 666 that relates to Love Dog is: “I’m here in front of the camera, and yet in my body and in my head, I’m behind it. My world is the imaginary and the imaginary is a journey between forwards and backwards.” This idea of visible/invisible, foresight and hindsight , backwards and forwards is an important dialectic in relation to time and the idea of the destinal. This is why I wanted Love Dog to travel, literally, figuratively, and discursively. You have to be open to not knowing. To epistemological, geographical, chronological, and emotional aporias. In Love Dog my story is both visible and invisible to me. Sometimes I could see where I was going. Other times I was completely in the dark existentially. Truth procedure, which love is, as bell hooks and Badiou tell us, requires expedition and openness to possibility. Unless you want a story you already know, but that is not truth procedure. So I tried to create this backwards and forwards journey in the book—this sense of travel and motion, hope and doubt—by jumping between forms, media, time; traveling to different places, texts, and emotional registers. The book’s “Time-Jump series,” which mostly takes the form of music—songs—but also a series of “green” videos that I shot, is the most obvious tribute to this idea of subjective and chronological time. continent. Your work aligns with writers that play with the form of their language, or have assumed the role of performance artist at some point: Kathy Acker, Chris Kraus, Avital Ronell, and Anne Carson to name a few representing varied approaches that show up in Love Dog . At the risk of ossifying the work, or missing the point—as these experimental modes of writing stack-up in piles of published works, do they approach a genre? MASHA As I noted in my book Life As We Show It , in Chelsea Girls the poet Eileen Myles points out, “You can’t get money without a category.” More importantly, you can’t get a category—or respect, rank—without a clear genre. This makes genre and gender an obvious pair. The two words are even linked etymologically and both genre and gender concern taxonomies of legitimacy—of sorting through what and who is valuable. So the words share common prejudices. The things one does not want to read is often synonymous with who one doesn't want to read about. Therefore a break-up of or with genre is maybe the genre or anti-genre that could be said to link these writers. Avital Ronell breaks up with philosophical tradition and modes of inquiry. Like Nietzsche, she revaluates methods of evaluation, testing out things you are not supposed to use philosophy to test (and, by the same token, testing philosophy in ways it’s not supposed to be tested), like drugs and stupidity—where philosophy fails and we fail philosophy. And Chris Kraus does something similar in her experimental fiction, using different forms to put female subjectivity “to the test,” so to speak. All these female writers and thinkers have tried to destabilize the systems that have been set up in (and against) writing. Thus missing the mark with genre, even intentionally, means that we have missed the point in some sense as writers and thinkers. And that to me is a good thing, however difficult. We’ve started at the wrong point and gone somewhere else instead. We’ve acknowledged that writing and thinking are also about failure, and that failure is always embedded in the act of writing and in our reasons for writing. So that missing the point is also the point. Derrida insisted: “We must invent a name for those ‘critical’ inventions which belong to literature while deforming its limits.” But how can you give something that resists and deforms, a name? Wouldn’t the name also be deformed? Isn't this why the aforementioned writers get hyphenated descriptors like ficto-criticism? Do we need a proper name to be able to read something carefully? I don’t think so. I don’t need it as a reader. I’ve always taken a work on its own terms. But for most people, if you don’t have an address, people don’t know how to find you. A lot of time, they won’t even know how to look. And in some cases, they’ll think you’re not even worth finding. You are not on the map because you have to literally make the map in order to exist. In her essay, “The Gender of Sound” Carson asks, “Why is female sound bad to hear?” I think for the same reason something uncategorizable (pedagogically, creatively, racially, and sexually)—Other—is hard to read. *For an audio recording of Florida , read by Masha Tupitsyn click here . continent. : We're also curious to hear know how you see the significance of 'performance' (and why the label sticks to the shoes of these authors like toilet paper) in describing this kind of writing work? MASHA I think I responded to the parenthetical portion of this question in my previous answer. As far as how performance relates to Love Dog , in Acker’s Don Quixote , which is another big presence in the book, she writes, “there is no other reality than anthropomorphism.” In Don Quixote , the dog is human and the human is dog. Which brings us to the title of Love Dog and the totemic function of the dog in the book: giving human things animal characteristics and animal things human characteristics. Rather than investing all our human love ideals into dogs, which we do constantly as a culture of dog lovers, I wanted to put the dog into love. It is the difference between the consumption of love as a patriarchal institution or status position and the essence of a type of radical and liberatory relation that would benefit humans in their bonds with other humans. So the dog in Love Dog is not simply the book’s cover or performative affect, so to speak. Love has always needed the dog, which is why the dog is the very embodiment of belief in love . Recall Argos The Great Dog and Odysseus. Argos is the only one who remembers and recognizes the ragged and old Odysseus even after his 20-year absence. So love is the high ideal and the dog, both common and dependable, is the bridge between the sacred and the profane. The dog is the house of love. And because Love Dog is a digital project, it seemed impossible to think about the post-human, technology, the virtual, or difference (which Badiou says is essential to love in In Praise of Love ) without thinking about animal-being and being-animal. Instead of simply “performing” these ideas and characteristics as literary affects, I’m interested in being-becoming. Which means the book’s tropes, leitmotifs, series, and even its titles are in service of that truth procedure. In other words, I actually want to live this way, not just write this way. And, more importantly, I want to live this way not just think this way. So Love Dog became both my totem animal and my autobiographical animal. This made the book organic, anthropomorphic—beyond literary. See the trailer to Masha Tupitsyn's new book available now from Penny Ante Editions. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Philosophy, Dissent, and Nonconformity, 1689–1920Bruce KuklickAlan P. F. Sell. Philosophy, Dissent, and Nonconformity, 1689–1920. Cambridge: James Clark & Co., 2004. Pp. 296. Cloth, £50.00This is a competent, clearly written, and authoritative exploration of its topic, in some respects a labor of love, for the author is both a pastor and a student of theology. Sell comprehensively examines the proliferation of dissenting academies and nonconformist colleges of England and (...) Wales, with some excursions into the Scottish scene, from the Toleration Act of 1689 through the early twentieth century. For the 230 years of this study, a great variety of schools, many of which had only a brief moment of existence, and most of which were barely funded, offered training for the ministers of over a dozen protestant denominations in Britain. Often one man provided instruction in subjects as diverse as mathematics, science, and literature—as well as religious fields.Sell does not focus on ministerial training or even theology, but the way in which the nonconforming religious élite expounded on and was taught philosophy. Thus, one sees how a diverse group that surely had sectarian needs in mind was also interested in grasping how thinkers outside its belief system approached basic problems of human existence. Over time Descartes and other continental rationalists, Locke and the Cambridge Platonists, Kant and Hegel, and the nineteenth-century British idealists were taught by the dissenting professoriate. In summarizing its interpretation, Sell presents a history of modern Anglo-European philosophy as it was refracted in the minds of (some) English-speaking Protestants. Their emphases are not unexpected: empiricism is somewhat devalued, and rationalistic and a priori modes of thinking perhaps inflated. The ethical implications of epistemology and metaphysics are most carefully explicated, and what is taken to be most strategic for [End Page 211] Reformed theology is underscored. Overall, if one is tempted to generalize (as Sell himself does not), the positions reached are credible and not out of line with the philosophical cutting edge of each era.For the most part the dissenters were not themselves creative philosophers of the first rank, but Sell rightly puts forward (206) a short list of thinkers at these schools who have genuine claims to merit, and my own very short list would include Richard Price, James Martineau, and Robert Mackintosh.The author uses diverse strategies to give readers a sense of the effort of these mostly forgotten men. To some extent the book is a biographical compendium, with brief sections on individual or paired thinkers. But Sell also offers coverage by denomination, and he adds a series of discussions by topics—on an assortment of recurring dilemmas in moral philosophy and on apologetics. A final and most useful feature of the book is a trio of indices, in addition to the very full notes and a complete bibliography, mainly of the writings of the many authors cited. Two of the indices are standard, but helpful, lists of persons and topics; the third one is a compendium of all the academies Sell treats, as well as their denominational affiliation, and the duration of their existences.Philosophy, Dissent, and Nonconformity has the defects of its virtues. It is encyclopedic in nature, available for reference but unlikely to be read as a synthetic book, except by devotees of a certain kind of historical philosophical theology. The author also presumes his readers are unlikely to tackle the volume unless they have a prior attraction. That is, the book is written without much contextual explication, and attention to the needs of the non-specialist certainly would have made the volume of wider interest. The work is still relatively brief, under 300 pages, and because of its character, I would have liked to have seen a series of maps that pinpointed the whereabouts of the dissenting schools, giving the reader a visual sense of when and where they arose and declined among particular denominations, and that informed us of what the relations were among the successive professors who defined the learning.Bruce KuklickUniversity of PennsylvaniaCopyright © 2005 Journal of the History of Philosophy, Inc.... (shrink)

We systematically study the completion of choice problems in the Weihrauch lattice. Choice problems play a pivotal rôle in Weihrauch complexity. For one, they can be used as landmarks that characterize important equivalences classes in the Weihrauch lattice. On the other hand, choice problems also characterize several natural classes of computable problems, such as finite mind change computable problems, non-deterministically computable problems, Las Vegas computable problems and effectively Borel measurable functions. The closure operator of completion generates the concept of total (...) Weihrauch reducibility, which is a variant of Weihrauch reducibility with total realizers. Logically speaking, the completion of a problem is a version of the problem that is independent of its premise. Hence, studying the completion of choice problems allows us to study simultaneously choice problems in the total Weihrauch lattice, as well as the question which choice problems can be made independent of their premises in the usual Weihrauch lattice. The outcome shows that many important choice problems that are related to compact spaces are complete, whereas choice problems for unbounded spaces or closed sets of positive measure are typically not complete. (shrink)

Several paleontologists have recently challenged the explanatory adequacy of the modern synthetic theory of evolution. Their position is that, contrary to the prevailing view that evolutionary change is gradual, the fossil record manifests long periods of species stasis punctuated by periods of rapid species formation. And, they argue, this punctuated equilibria pattern challenges the gradualist, adaptationist and extrapolationist assumptions of the modern synthetic theory of evolution and supports a hierarchical, non-extrapolationist view of evolution. In this paper I argue that the (...) challenge rests on an inadequate characterization of the modern synthetic theory and that, even accepting punctuated equilibria and an irreducible evolutionary hierarchy, the modern synthetic theory is adequate to explain evolutionary change at all levels of the hierarchy. (shrink)

It is frequently argued that home birth is morally irresponsible because it involves the taking of risks on behalf of the fetus. Against this position, I argue three things. First, the fact that home birth involves risks does not necessarily entail that choosing or attending one is morally unacceptable, irresponsible or wrong. Second, parents have a prima facia prerogative to decide on behalf of their fetuses and children whether risks should be taken. While this prima facia prerogative can be overridden, (...) reasonable and widely accepted criteria for doing so are not met in the case of home birth. Third, since the current attitudes and behaviours of physicians with regard to home birth constitute a de facto morally and socially unjustifiable overriding of an informed parental decision, physician autonomy should be restricted so as to preserve the autonomy of the medical consumer. (shrink)

Benton Stidd has defended the position that punctuationists are not wrong about the inadequacy of the synthetic theory of evolution for explaining evolution. The thrust of his defense is that arguments to the contrary by Thompson involve a rational reconstruction along logical empiricist lines, which is insensitive to historical and social forces in a way that the Kuhnian Weltanschauung view that he espouses is not. I argue in this paper that Stidd has entirely misunderstood my arguments, that the soundness of (...) my arguments does not depend on acceptance of logical empiricism , and that Stidd fails to establish that punctuated equilibria is a new "paradigm". (shrink)

The paper provides a critical review of the debate on the foundations of Computer Ethics (CE). Starting from a discussion of Moor’s classic interpretation of the need for CE caused by a policy and conceptual vacuum, five positions in the literature are identified and discussed: the “no resolution approach”, according to which CE can have no foundation; the professional approach, according to which CE is solely a professional ethics; the radical approach, according to which CE deals with absolutely unique issues, (...) in need of a unique approach; the conservative approach, according to which CE is only a particular applied ethics, discussing new species of traditional moral issues; and the innovative approach, according to which theoretical CE can expand the metaethical discourse with a substantially new perspective. In the course of the analysis, it is argued that, although CE issues are not uncontroversially unique, they are sufficiently novel to render inadequate the adoption of standard macroethics, such as Utilitarianism and Deontologism, as the foundation of CE and hence to prompt the search for a robust ethical theory. Information Ethics (IE) is proposed for that theory, as the satisfactory foundation for CE. IE is characterised as a biologically unbiased extension of environmental ethics, based on the concepts of information object/infosphere/entropy rather than life/ecosystem/pain. In light of the discussion provided in this paper, it is suggested that CE is worthy of independent study because it requires its own application-specific knowledge and is capable of supporting a methodological foundation, IE. (shrink)

In a now classic paper published in 1991, Alberch introduced the concept of genotype–phenotype (G!P) mapping to provide a framework for a more sophisticated discussion of the integration between genetics and developmental biology that was then available. The advent of evo-devo first and of the genomic era later would seem to have superseded talk of transitions in phenotypic space and the like, central to Alberch’s approach. On the contrary, this paper shows that recent empirical and theoretical advances have only sharpened (...) the need for a different conceptual treat- ment of how phenotypes are produced. Old-fashioned metaphors like genetic blueprint and genetic programme are not only woefully inadequate but positively misleading about the nature of G!P, and are being replaced by an algorithmic approach emerging from the study of a variety of actual G!P maps. These include RNA folding, protein function and the study of evolvable soft- ware. Some generalities are emerging from these disparate fields of analysis, and I suggest that the concept of ‘developmental encoding’ (as opposed to the classical one of genetic encoding) provides a promising computational–theoretical underpinning to coherently integrate ideas on evolvability, modularity and robustness and foster a fruitful framing of the G!P mapping problem. (shrink)

In the current scientific and political discourse surrounding the transformation of the scientific publication system, significant attention is focused on Diamond Open Access (OA). Diamond OA is characterized by no charges for readers or authors and relies on monetary allowances and voluntary work. This article explores the potential and challenges of Diamond OA journals, using Germany as a case study. Two key questions are addressed: first, the current role of such journals in the scientific publication system is determined through bibliometric (...) analysis across various disciplines. Second, an investigation is conducted to assess the sustainability of Diamond OA journals and identify associated structural problems or potential breaking points. This investigation includes an in-depth expert interview study involving 20 editors of Diamond OA journals. The empirical results are presented using a landscape map that considers two dimensions: 'monetized and gift-based completion of tasks' and 'journal team size.' The bibliometric analysis reveals a substantial number of Diamond OA journals in the social sciences and humanities, but limited adoption in other fields. The model proves effective for small to mid-sized journals, but not for larger ones. Additionally, it was found that 23 Diamond OA journals have recently discontinued their operations. The expert interviews demonstrate the diversity within the landscape and the usefulness of the two dimensions in understanding key differences. Journals in two of the four quadrants of the map exemplify sustainable conditions, while the other two quadrants raise concerns about long-term stability. These concerns include limited funding leading to a lack of division of labor and an excessive burden on highly committed members. Gift-like contributions, while appealing, also present challenges as potential donors not only decide whether to contribute but also how to contribute, potentially creating friction between the gift and the journal's requirements. Furthermore, journals in the lower right quadrant often rely on third-party funding, necessitating a transformation once the funding expires. Common pathways for sustaining operations include lobbying for funding at the journal's home institution or increasing reliance on gift-based completion of tasks. These findings underscore the need for the development of more sustainable funding models to ensure the success of Diamond OA journals. (shrink)

Using the perspective of situated cognition we studied how people interact with a physical map to help them navigate through an unfamiliar environment. The study used a mixture of cognitive ethnography and traditional experimental methods. We found that the difference between high and low performing navigators showed up in the speed they completed their task and also in the way they use maps. High performers plan routes using a survey method whereas low performers use a route strategy. We suggest (...) that when people are given a task that does not match their cognitive style they try to transform the task to better suit their cognitive abilities and cognitive style. (shrink)

Love is an essential biological, psychological, sociological, and religious phenomenon. Using various conceptual models, philosophers have often distinguished between different types of love, such as self-love, romantic love, friendship love, love of God, and neighborly love. Psychologists and neuroscientists on the other hand have thus far focused predominantly on understanding the emotions and behavioral and neural mechanisms associated with romantic love and parental love. We do not yet know how the models construed by philosophers are related to actual experiences of (...) love, and to which extent they are merely nominal creations connecting phenomena that in fact have little to do with each other. We lack empirical knowledge of how different types of love are experienced as embodied feelings, and how these experiences are related to one another. Here we distinguished between 27 different types of love. Using self-report methods, we measured 1) how subjective feelings of different types of love are topographically embodied; 2) how different types of love are associated with self-reported emotional valence, strength of the bodily and mental experience, association with touch, time elapsed since last experienced, and controllability; and 3) how similar different types of love feel. Our study provides the first mapping of embodied experiences associated with different types of love. The results show that the subjective feelings associated with the love types form a continuum from strongly to weakly felt loves. (shrink)

We show how to encode, by classical structures, both the objects and the morphisms of the category of complete metric spaces and uniformly continuous maps. The result is a category of, what we call, cognate metric spaces and cognate maps. We show this category relativizes to all models of set theory. We extend this encoding to an encoding of complete metric structures by classical structures. This provide us with a general technique for translating results about infinitary logic on (...) classical structures to the setting of infinitary continuous logic on continuous structures. Our encoding will also allow us to talk about not only the relations between complete metric structures, but also the potential relations between complete metric structures, i.e. those which are satisfied in some larger model of set theory. For example we will show that given any two complete metric structures we can determine if they are potentially isomorphic by looking at any admissible set which contains them both. (shrink)

Here is an account of logical consequence inspired by Bolzano and Tarski. Logical validity is a property of arguments. An argument is a pair of a set of interpreted sentences (the premises) and an interpreted sentence (the conclusion). Whether an argument is logically valid depends only on its logical form. The logical form of an argument is fixed by the syntax of its constituent sentences, the meanings of their logical constituents and the syntactic differences between their non-logical constituents, treated as (...) variables. A constituent of a sentence is logical just if it is formal in meaning, in the sense roughly that its application is invariant under permutations of individuals.1 Thus ‘=’ is a logical constant because no permutation maps two individuals to one or one to two; ‘∈’ is not a logical constant because some permutations interchange the null set and its singleton. Truth functions, the usual quantifiers and bound variables also count as logical constants. An argument is logically valid if and only if the conclusion is true under every assignment of semantic values to variables (including all non-logical expressions) under which all its premises are true. A sentence is logically true if and only if the argument with no premises of which it is the conclusion is logically valid, that is, if and only if the sentence is true under every assignment of semantic values to variables. An interpretation assigns values to all variables. (shrink)

Scientific realism is typically associated with metaphysics. One current incarnation of such an association concerns the requirement of a metaphysical characterization of the entities one is being a realist about. This is sometimes called “Chakravartty’s Challenge”, and codifies the claim that without a metaphysical characterization, one does not have a clear picture of the realistic commitments one is engaged with. The required connection between metaphysics and science naturally raises the question of whether such a demand is appropriately fulfilled, and how (...) metaphysics engages with science in order to produce what is called “scientific metaphysics”. Here, we map some of the options available in the literature, generating a conceptual spectrum according to how each view approximates science and metaphysics. This is done with the purpose of enlightening the current debate on the possibility of epistemic warrant that science could grant to such a metaphysics, and how different positions differently address the thorny issue concerning such a warrant. (shrink)

As a scientific discipline and profession, law has been for centuries at the heart of social and political power of many Western societies. Professors of law, as influential representatives of the profession, are important powerbrokers between academia, politics and the corporate world. Their influence is based on scientific reputation, institutional mandates inside and outside academia or privileged network connections with people in powerful positions. In this study, based on a full sample of all Swiss law professors in the years 1957, (...) 1980 and 2000, we contrast two theories of the distribution of power among law professors: Bourdieu’s thesis on the trade-off between scientific reputation and -academic institutional power vs. the thesis of an opposition between a group of established incumbents and socio-demographically marginal challengers who try to gain access to the profession. We show that among Swiss law professors the endowment with scientific capital is not opposed to the possession of institutional power within academia. Our findings reveal rather an opposition between a challenging group of professors devoid of resources and an incumbent fraction with a high amount of scientific, institutional and social capital alike. In the conclusion we discuss a series of explanations of this specific power structure, including the specific status scientific reputation and social capital can have for law professors. (shrink)

Recently, the increasing interest in responsible leadership (RL) has produced a research field rich in theoretical and conceptual potential, with diverse research foci, theoretical foundations, and methodological approaches. While these developments have demarcated the field from other leadership-oriented disciplines, they have equally courted fragmentation and ambiguity in terms of the field’s positioning within the greater body of leadership studies. To map the theoretical, methodological, and empirical state of the art of the RL field, we outline recent developments and delineate important (...) research gaps and directions for future theory development and empirical research. We emphasize the transition of RL research from micro-level perspectives with normative roots to research spanning multiple levels of analysis, vis-à-vis both antecedents and outcomes. We discuss the implications of our mapping, highlighting the necessity of not only conceptualizing RL across multiple levels of analysis, but also to actively focus on interactions among RL antecedents and outcomes across these levels. Through these, we aim to contribute to the field by strengthening its conceptual foundations and anchoring it more clearly within leadership studies overall. (shrink)

A deductive system is said to be structurally complete if its admissible rules are derivable. In addition, it is called hereditarily structurally complete if all its extensions are structurally complete. Citkin (1978) proved that an intermediate logic is hereditarily structurally complete if and only if the variety of Heyting algebras associated with it omits five finite algebras. Despite its importance in the theory of admissible rules, a direct proof of Citkin’s theorem is not widely accessible. In this paper we offer (...) a self-contained proof of Citkin’s theorem, based on Esakia duality and the method of subframe formulas. As a corollary, we obtain a short proof of Citkin’s 2019 characterization of hereditarily structurally complete positive logics. (shrink)

In this article, drawing on the discursive psychology of Rom Harré, we show how mapping the exchange of words among people might disclose a complex reality; not merely that which farmers explicitly talk ‘about’ but the reality implicitly at stake within the communication. More specifically, we show how discourses involving modern farmers reveal an underlying placing in an abstract space, having sub-spaces defined by the life-orientation, sense of self and according self-positioning of modern people. In this way, we construct a (...) road map of a set of ‘individualities’ characterizing the life of modern farmers: an individuality of citizenship, an individuality of geographies and an individuality of experience. Consequently, farmers face the problem that this multiplicity of individuality prevents them from communicating, as we will call it, univocally in the public by contrast to the univocal voices of other established social groups. We will analyse the structure of that problem by viewing diverse relations between the authority and the authenticity of different partners in the conversation on land use. (shrink)

Husserl's two notions of "definiteness" enabled him to clarify the problem of imaginary numbers. The exact meaning of these notions is a topic of much controversy. A "definite" axiom system has been interpreted as a syntactically complete theory, and also as a categorical one. I discuss whether and how far these readings manage to capture Husserl's goal of elucidating the problem of imaginary numbers, raising objections to both positions. Then, I suggest an interpretation of "absolute definiteness" as semantic completeness and (...) argue that this notion does not suffice to explain Husserl's solution to the problem of imaginary numbers. (shrink)

Given two (positive) equivalence relations ∼ 1 , ∼ 2 on the set ω of natural numbers, we say that ∼ 1 is m-reducible to ∼ 2 if there exists a total recursive function h such that for every x, y ∈ ω, we have $x \sim_1 y \operatorname{iff} hx \sim_2 hy$ . We prove that the equivalence relation induced in ω by a positive precomplete numeration is complete with respect to this reducibility (and, moreover, a "uniformity property" (...) holds). This result allows us to state a classification theorem for positive equivalence relations (Theorem 2). We show that there exist nonisomorphic positive equivalence relations which are complete with respect to the above reducibility; in particular, we discuss the provable equivalence of a strong enough theory: this relation is complete with respect to reducibility but it does not correspond to a precomplete numeration. From this fact we deduce that an equivalence relation on ω can be strongly represented by a formula (see Definition 8) iff it is positive. At last, we interpret the situation from a topological point of view. Among other things, we generalize a result of Visser by showing that the topological space corresponding to a partition in e.i. sets is irreducible and we prove that the set of equivalence classes of true sentences is dense in the Lindenbaum algebra of the theory. (shrink)

Most research on metaphors that construe time as motion (motion metaphors of time) has focused on the question of whether it is the times or the person experiencing them (ego) that moves. This paper focuses on the equally important distinction between metaphors that locate times relative to ego (the ego-based metaphors Moving Ego and Moving Time) and a metaphor that locates times relative to other times (sequence is relative position on a path). Rather than a single abstract target domain TIME, (...) these two kinds of temporal metaphor metaphorize different kinds of temporal concept—perspective-specific vs. perspective-neutral temporal concepts. Recognition of this distinction enhances the explanatory potential of conceptual metaphor theory (Lakoff and Johnson 1980). An example involves the interaction of deixis and the temporal reference crosslinguistically of vocabulary with the spatial meanings in-front and behind. More generally, this approach refines our ability to describe the temporal concepts involved in motion metaphors of time. Such temporal concepts are present not only in the target domains, but also in the source domains of motion metaphors of time, where we find space-to-time metonymy, which may play a role in motivating the metaphors. In order to distinguish such metonymy from metaphor, we need to characterize metaphor as a mapping across frames rather than domains. (shrink)

A case study of Chinese grandparents’ transnational caregiving experiences in Canada highlights two issues that have received limited attention in the broader feminist care literature: elderly persons are usually positioned as receivers rather than providers of care; and transnational care studies focus on women migrating as part of “global care chains,” rather than on elderly family members migrating to meet the caring needs of adult kin who work in market economies that do not recognize caring responsibilities. The paper concludes by (...) arguing that the distribution of care responsibilities needs to be one of the pillars in the pursuit of transnational social justice. (shrink)

With the advent of the severe acute respiratory syndrome-Corona Virus type 2 pandemic, the theme of emotion recognition from facial expressions has become highly relevant due to the widespread use of face masks as one of the main devices imposed to counter the spread of the virus. Unsurprisingly, several studies published in the last 2 years have shown that accuracy in the recognition of basic emotions expressed by faces wearing masks is reduced. However, less is known about the impact that (...) wearing face masks has on the ability to recognize emotions from subtle expressions. Furthermore, even less is known regarding the role of interindividual differences in emotion processing. This study investigated the perception of all the six basic emotions, both as a function of the face mask and as a function of the facial expressions’ intensity in terms of participants’ uncertainty in their responses, misattribution errors, and perceived intensity. The experiment was conducted online on a large sample of participants. Participants completed the 20-item Toronto Alexithymia Scale and the Autistic Spectrum Quotient and then performed an emotion-recognition task that involved face stimuli wearing a mask or not, and displaying full or subtle expressions. Each face stimulus was presented alongside the Geneva Emotion Wheel, and participants had to indicate what emotion they believed the other person was feeling and its intensity using the GEW. For each combination of our variables, we computed the indices of ‘uncertainty’, ‘bias’, and ‘perceived intensity’. We found that face masks increase uncertainty for all facial expressions of emotion, except for fear when intense, and that disgust was systematically confused with anger. Furthermore, when faces were covered by the mask, all the emotions were perceived as less intense, and this was particularly evident for subtle expressions. Finally, we did not find any evidence of a relationship between these indices and alexithymic/autistic traits. (shrink)

It would be a mistake to imagine that the problem of the Cartesian circle lies in Descartes’ suggestion that we cannot know anything unless we know God. It is true that this thought seems fatal to his enterprise; for if we cannot know anything prior to knowing that God exists, then it follows that we cannot know the arguments that prove God’s existence. However the problem of the Cartesian circle does not consist in this logical error. It consists, rather, in (...) the fact that Descartes’ attempts to deal with the charge of circular reasoning seem so inadequate. It is implausible that Descartes simply failed to appreciate the point, for the objection is a very simple one, requiring no special vocabulary nor any advanced logical apparatus. He addressed the problem twice in the replies to his critics and went over it again in the Principles of Philosophy. Despite these qualifications, Descartes was not able to lay out his position with sufficient clarity to satisfy his reviewers or to prevent the publication of a bewildering variety of interpretations. The question then becomes, if Descartes understood the objection, why did he not deal with it more effectively. (shrink)

Determinism is the thesis that a future state is completely determined by a past state of something - thus its future course is fixed when the initial state is given. Before the discovery of quantum mechanics many people thought the universe was deterministic; rather like a huge clock. Indeterminacy is when something is NOT deterministic, that is the initial state does not completely determine all subsequent ones. Indeterminacy is an important topic and doubly so for those involved in (...) social simulation. Due my interest in these issues and the rather low level of insight provided by the chapters in this book, I will briefly summarise some of the issues as they relate to social simulation first, and relate it to the book later. (shrink)

Since its publication in 1936, Walter Benjamin’s “Artwork” essay has become a canonical text about the status and place of the fine arts in modern mass culture. Benjamin was especially concerned with the ability of new technologies—notably film, sound recording, and photography—to reproduce works of art in great number. Benjamin could not have foreseen the explosion of imagery and media that has occurred during the past fifty years. Does Benjamin’s famous essay still speak to this new situation? That is the (...) question posed by the editors of this book to a wide range of leading scholars and thinkers across a spectrum of disciplines in the humanities. The essays gathered here do not hazard a univocal reply to that question; rather they offer a rich, wide-ranging critique of Benjamin’s position that refracts and reflects contemporary thinking about the ethical, political, and aesthetic implications of life in the digital age. (shrink)

In “The Blessing of Departure—Exchange of Populated Territories The Lieberman Plan as anExercise in Demographic Transformation,” Prof. Timothy Waters offers a strong endorsement of the right of ethnic majorities within a state to redefine their state's boundaries in ways consistent with the majority's right to self-determination and to opt out of a political union with minority groups, regardless of the latter's' political preferences. Applied to the Israeli context, Waters concludes that parts of the Lieberman Plan—a plan advocating the redrawing of (...) Israel borders, inter alia, in ways which exclude some areas populated by Israeli citizens belonging to the Arab-Palestinian minority —does not run afoul of international law . This short response challenges two points that are central to Waters’s analysis. First, that the right to self-determination of peoples—in particular, the right to external self-determination —is subject to temporal or contextual limitations. The right is fully applicable only in exceptional and formative moments in the life of a nation—e.g., during the formation of a new polity or the collapse of an existing political arrangement , and when states systematically fail to respect the basic interest of some of the groups that comprise its populace—i.e., in response to extraordinary situations of groups exclusion or oppression. Second, even if Waters is correct and an ongoing right to self-determination—including, a right to secede from existing states—is available to ethnic groups comprising diverse national societies, the invocation of such a right must necessarily be limited by other positive rules of international law designed to protect group and individual interests. Specifically, Waters’s concept of self-determination as a right of a preliminary nature, that overrides other human rights , is debatable. (shrink)

We investigated how the structure of the brain network relates to the stability of perceptual alternation in binocular rivalry. Historically, binocular rivalry has provided important new insights to our understandings in neuroscience. Although various relationships between the local regions of the human brain structure and perceptual switching phenomena have been shown in previous researches, the global organization of the human brain structural network relating to this phenomenon has not yet been addressed. To approach this issue, we reconstructed fiber-tract bundles using (...) diffusion tensor imaging and then evaluated the correlations between the speeds of perceptual alternation and fractional anisotropy (FA) values in each fiber-tract bundle integrating among 84 brain regions. The resulting comparison revealed that the distribution of the global organization of the structural brain network showed positive or negative correlations between the speeds of perceptual alternation and the FA values. First, the connections between the subcortical regions stably were negatively correlated. Second, the connections between the cortical regions mainly showed positive correlations. Third, almost all other cortical connections that showed negative correlations were located in one central cluster of the subcortical connections. This contrast between the contribution of the cortical regions to destabilization and the contribution of the subcortical regions to stabilization of perceptual alternation provides important information as to how the global architecture of the brain structural network supports the phenomenon of binocular rivalry. (shrink)

For a ring R, Hilbert’s Tenth Problem $HTP$ is the set of polynomial equations over R, in several variables, with solutions in R. We view $HTP$ as an enumeration operator, mapping each set W of prime numbers to $HTP$, which is naturally viewed as a set of polynomials in $\mathbb {Z}[X_1,X_2,\ldots ]$. It is known that for almost all W, the jump $W'$ does not $1$ -reduce to $HTP$. In contrast, we show that every Turing degree contains a set W (...) for which such a $1$ -reduction does hold: these W are said to be HTP-complete. Continuing, we derive additional results regarding the impossibility that a decision procedure for $W'$ from $HTP$ can succeed uniformly on a set of measure $1$, and regarding the consequences for the boundary sets of the $HTP$ operator in case $\mathbb {Z}$ has an existential definition in $\mathbb {Q}$. (shrink)

In the last decades, research in science mapping has delivered several powerful techniques, based on citation or textual analysis, for charting the intellectual organization of research fields. To map the social network underlying science and scholarship, by contrast, science mapping has mainly relied on one method, co-authorship analysis. This method, however, suffers from well-known limitations related to the practice of authorship. Moreover, it does not perform well on those fields where multi-authored publications are rare. In this study, a new method (...) for mapping the social structure of research fields is advanced, based on the analysis of the acknowledgments of academic publications. We first discuss the standard account of the function of acknowledgments in scholarly communication, then we introduce a new interpretative framework in which the acknowledgments are intended as positioning signals exchanged by researchers. Next, we provide the formal definition of the four acknowledgments-based networks that stand at the core of the method, and we test it on a humanities field, analytic philosophy. Results show that acknowledgement-based networks allow to reconstruct the fine-grained social structure of analytic philosophy from different perspectives. Furthermore, by comparing the citation-based maps of the field with the acknowledgments-based networks, it permits to shed light on the relationship between the intellectual and social layer of analytic philosophy. We conclude by presenting practical limitations of the method and by sketching some further research lines. (shrink)

Mature representations of number are built on a core system of numerical representation that connects to spatial representations in the form of a ‘mental number line’. The core number system is functional in early infancy, but little is known about the origins of the mapping of numbers onto space. Here we show that preverbal infants transfer the discrimination of an ordered series of numerosities to the discrimination of an ordered series of line lengths. Moreover, infants construct relationships between individual numbers (...) and line lengths that vary positively, but not between numbers and lengths that vary inversely. These findings provide evidence for an early developing predisposition to relate representations of numerical magnitude and spatial length. A central foundation of mathematics, science and technology therefore emerges prior to experience with language, symbol systems, or measurement devices. (shrink)