We study smooth classes without the algebraic closure property. For such smooth classes we investigate the simplicity of the class of generic structures, in the context of Robinson theories.

In connection with the work of Anscombe, Macpherson, Steinhorn and the present author in [1] we investigate the notion of a multidimensional exact class (R-mec), a special kind of multidimensional asymptotic class (R-mac) with measuring functions that yield the exact sizes of definable sets, not just approximations. We use results about smooth approximation [24] and Lie coordinatization [13] to prove the following result (Theorem 4.6.4), as conjectured by Macpherson: For any countable language$\mathcal {L}$and any positive integerdthe (...) class='Hi'>class$\mathcal {C}(\mathcal {L},d)$of all finite$\mathcal {L}$-structures with at mostd4-types is a polynomial exact class in$\mathcal {L}$, where a polynomial exact class is a multidimensional exact class with polynomial measuring functions. (shrink)

This article puts forward a novel class of Bézier smooth semi-supervised support vector machines(BS4VMs) for classification. As is well known, semi-supervised support vector machine is introduced for dealing with quantities of unlabeled data in the real world. Labeled data is utilized to train the algorithm and then adapting it to classify the unlabeled data. However, the objective semi-supervised function is not differentiable globally. It is required to endure heavy burden in solving two quadratic programming problems with inversion matrix (...) operation. To solve this problem, the interpolation Bézier functions for replacing the non-smooth term have been investigated. Firstly, the development of the novel BS4VMs classifier is introduced. Then, the non-linear model and convergence analysis are presented. To show how the BS4VMs can be practically implemented, experiments on synthetic and real data sets are offered. The theoretical analysis and experiments comparisons clearly illustrate the BS4VMs are superior to the proposed methods in both cross-validation classification accuracy and calculating time. (shrink)

A new three-order piecewise function was used to smoothen the model of Support Vector Machine( SVM) and a Third-order Piecewise Smooth SVM( TPSSVM) was proposed. By theory analyzing, approximation accuracy of the smooth function to the plus function is higher than that of the available. When dealing with the multi-class problem, a coding method of multi-class classification based on one-against-rest was proposed. Principal Component Analysis( PCA) was employed to extract the main features of face image set, (...) and multi-class classification of smooth SVM was used for face recognition. The experimental results on ORL and FERET face databases show that the recognition rate of smooth SVM for multi-class classification is better than the traditional identification methods. (shrink)

Let be a class of models with a notion of ‘strong’ submodel and of canonically prime model over an increasing chain. We show under appropriate set-theoretic hypotheses that if K is not smooth , then K has many models in certain cardinalities. On the other hand, if K is smooth, we show that in reasonable cardinalities K has a unique homogeneous-universal model. In this situation we introduce the notion of type and prove the equivalence of saturated with (...) homogeneous-universal. (shrink)

A new smooth method for solving the support vector machine classification (SVC) is presented. Since the objective function of the unconstrained SVC is non-smooth, we apply the smooth technique and replace the SVC function with Bézier function and get a class of Bézier smooth support vector machines (BSSVM). The fast Newton-Armijo algorithm is used to solve the BSSVM. Theoretical analysis and numerical results illustrate that this smooth SVM model improves in efficiency and accuracy compared (...) with other smooth methods. (shrink)

We study classes of right-angled Coxeter groups with respect to the strong submodel relation of a parabolic subgroup. We show that the class of all right-angled Coxeter groups is not smooth and establish some general combinatorial criteria for such classes to be abstract elementary classes (AECs), for them to be finitary, and for them to be tame. We further prove two combinatorial conditions ensuring the strong rigidity of a right-angled Coxeter group of arbitrary rank. The combination of these (...) results translates into a machinery to build concrete examples of AECs satisfying given model-theoretic properties. We exhibit the power of our method by constructing three concrete examples of finitary classes. We show that the first and third classes are nonhomogeneous and that the last two are tame, uncountably categorical, and axiomatizable by a single Lω1,ω-sentence. We also observe that the isomorphism relation of any countable complete first-order theory is κ-Borel reducible (in the sense of generalized descriptive set theory) to the isomorphism relation of the theory of right-angled Coxeter groups whose Coxeter graph is an infinite random graph. (shrink)

A study of smooth classes whose generic structures have simple theory is carried out in a spirit similar to Hrushovski 147; Simplicity and the Lascar group, preprint, 1997) and Baldwin–Shi 1). We attach to a smooth class K0, of finite -structures a canonical inductive theory TNat, in an extension-by-definition of the language . Here TNat and the class of existentially closed models of =T+,EX, play an important role in description of the theory of the K0,-generic. We (...) show that if M is the K0,-generic then MEX. Furthermore, if this class is an elementary class then Th=Th). The investigations by Hrushovski and Pillay , provide a general theory for forking and simplicity for the nonelementary classes, and using these ideas, we show that if K0,, where {,*}, has the joint embedding property and is closed under the Independence Theorem Diagram then EX is simple. Moreover, we study cases where EX is an elementary class. We introduce the notion of semigenericity and show that if a K0,-semigeneric structure exists then EX is an elementary class and therefore the -theory of K0,-generic is near model complete. By this result we are able to give a new proof for a theorem of Baldwin and Shelah 1359). We conclude this paper by giving an example of a generic structure whose first-order theory is simple. (shrink)

The class of recursive functions over the reals, denoted by , was introduced by Cristopher Moore in his seminal paper written in 1995. Since then many subsequent investigations brought new results: the class was put in relation with the class of functions generated by the General Purpose Analogue Computer of Claude Shannon; classical digital computation was embedded in several ways into the new model of computation; restrictions of were proved to represent different classes of recursive functions, e.g., (...) recursive, primitive recursive and elementary functions, and structures such as the Ritchie and the Grzergorczyk hierarchies.The class of real recursive functions was then stratified in a natural way, and and the analytic hierarchy were recently recognised as two faces of the same mathematical concept.In this new article, we bring a strong foundational support to the Real Recursive Function Theory, rooted in Mathematical Analysis, in a way that the reader can easily recognise both its intrinsic mathematical beauty and its extreme simplicity. The new paradigm is now robust and smooth enough to be taught. To achieve such a result some concepts had to change and some new results were added. (shrink)

This chapter discusses three different ways of talking about mood enhancement. First, if we do want to enhance, what is good enhancement? Second, if one wants to enhance, what is the usefulness of enhancement? Third, if we want to enhance, what might be the beneficial (or harmful) effects? To illustrate the conceptual analysis in this chapter, two classes of drugs to enhance mood are used. First is the class of selective serotonin reuptake inhibitors (SSRIs) and the other class (...) is of beta blocking agents, which are claimed to be good as “memory‐smoothing” drugs. Three different ways of using the terms “good” or “bad” are shown to be in play in mood enhancement: instrumental goodness and badness, utalitarian goodness and badness, and benefactorial goodness and badness. Mood‐improving and memory‐smoothing drugs may serve different purposes, which are linked to the general purpose of improving the mood or smoothing memories. (shrink)

A large literature on South Korean economic development has presented one dominant narrative on Korean modernity, essentially that of a smooth and peaceful process of modernity brought about by the immutable logic of the market and by a gradual expansion of the middle class and civil society. This essay presents another narrative which stresses the role of social struggles in this process. Korea's transition to modernity has been marked by a high level of social conflicts and by clashes (...) between modernity and tradition and between external and national values. In this process, history and tradition did not simply give way to modernity but have been continuously rediscovered and reappropriated for new social struggles. Korea's modernity has been woven out of these political, social and cultural materials rather than simply out of the universal fabric of capitalism. (shrink)

The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary particle, (...) neutrino, on the ground of energy conservation in quantum mechanics, afterwards confirmed experimentally. Bohr recognized his defeat and Pauli’s truth: the paradigm of elementary particles (furthermore underlying the Standard model) dominates nowadays. However, the reason of energy conservation in quantum mechanics is quite different from that in classical mechanics (the Lie group of all translations in time). Even more, if the reason was the latter, Bohr, Cramers, and Slatters’s argument would be valid. The link between the “conservation of energy conservation” and the problem of hidden variables is the following: the former is equivalent to their absence. The same can be verified historically by the unification of Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics in the contemporary quantum mechanics by means of the separable complex Hilbert space. The Heisenberg version relies on the vector interpretation of Hilbert space, and the Schrödinger one, on the wave-function interpretation. However the both are equivalent to each other only under the additional condition that a certain well-ordering is equivalent to the corresponding ordinal number (as in Neumann’s definition of “ordinal number”). The same condition interpreted in the proper terms of quantum mechanics means its “unitarity”, therefore the “conservation of energy conservation”. In other words, the “conservation of energy conservation” is postulated in the foundations of quantum mechanics by means of the concept of the separable complex Hilbert space, which furthermore is equivalent to postulating the absence of hidden variables in quantum mechanics (directly deducible from the properties of that Hilbert space). Further, the lesson of that unification (of Heisenberg’s approach and Schrödinger’s version) can be directly interpreted in terms of the unification of general relativity and quantum mechanics in the cherished “quantum gravity” as well as a “manual” of how one can do this considering them as isomorphic to each other in a new mathematical structure corresponding to quantum information. Even more, the condition of the unification is analogical to that in the historical precedent of the unifying mathematical structure (namely the separable complex Hilbert space of quantum mechanics) and consists in the class of equivalence of any smooth deformations of the pseudo-Riemannian space of general relativity: each element of that class is a wave function and vice versa as well. Thus, quantum mechanics can be considered as a “thermodynamic version” of general relativity, after which the universe is observed as if “outside” (similarly to a phenomenological thermodynamic system observable only “outside” as a whole). The statistical approach to that “phenomenological thermodynamics” of quantum mechanics implies Gibbs classes of equivalence of all states of the universe, furthermore re-presentable in Boltzmann’s manner implying general relativity properly … The meta-lesson is that the historical lesson can serve for future discoveries. (shrink)

continent. 2.1 (2012): 40–43. Lance Olsen is a professor of Writing and Literature at the University of Utah, Chair of the FC2 Board of directors, and, most importantly, author or editor of over twenty books of and about innovative literature. He is one of the true champions of prose as a viable contemporary art form. He has just published Architectures of Possibility (written with Trevor Dodge), a book that—as Olsen's works often do—exceeds the usual boundaries of its genre as it (...) explores his interests in narrative theory and pedagogy. The book is a kind of “anti-textbook;” a performative polemic against the stale, conservative and monolithic conception of the literary that so often dominates institutional discourse around creative writing. The following interview takes the occasion of AoP's publication as a chance to speak with Olsen about the book itself as well as to engage with larger, unanswerable, questions about the futures and intersections of literature and education. —Ben Segal INTERVIEW: 1) First, I want to start before the beginning, with the title. I’m really fascinated by the concept it conjures. Can you say something about innovative/experimental/(choose your adjective) literature in relation to both ideas around architecture and possibility? Innovative or experimental are tremendously fraught adjectives, needless to say. But for the purposes of my book, they modify a fiction concerned with the questions: What is fiction? What can it do, and how, and why? Now, of course, what looks “innovative” or “experimental” to one at 17 may not be what looks “innovative” or “experimental” to one at 27 or 57, and what looks “innovative” or “experimental” in 1812 may not be what looks “innovative” or “experimental” in 2012. A certain existential and historical perspectivism is always at work. But I think it’s fair to say that innovative and experimental usually refer to a narrativity that includes a self-reflective awareness of and engagement with theoretical inquiry, concerns, and obsessions, as well as a sense of being in conversation with fiction across space and time. One can't create challenging writing in a vacuum; it has to challenge in relation to something. So contemporary writers interested in the subject are not only in pursuit of the innovative, but are also always-already writing subsequent to it—writing, that is, in its long wake. Architectures of Possibility conceives of creativity as a possibility space, a locale just outside our comfort zones where we can and should take multiple chances in order to imagine in new ways, explore fresh strategies for finding and cultivating ideas, re-view what it is we’re doing and why, better understand what Samuel Beckett meant when he wrote: “Try again. Fail again. Fail better.” It reminds us that there are other ways of narrating our worlds and ourselves than those we have inherited from the entertainment industry, the government, academia, previous writing, and so on. 2) AoP seems to be directed at several audiences (and purposes) simultaneously. What I mean is that it seems at times a polemic in favor of innovative literature, at other times a creative writing textbook, and still other times a guide to the network of publishers, journals, and programs that make up the current world of non-mainstream literary art in the U.S. In my mind, Architectures is a theorized anti-textbook about writing. Most textbooks on the subject (think of Janet Burroway’s Writing Fiction: A Guide to Narrative Craft , taught in most creative-writing classroom across the country) orchestrate how to construct conventional stories. They instruct from a place of power how to generate familiar stories that are repeated so often that many of us begin to take them as the primary model for narrativity, if not unconsciously as a kind of truth. The result, as Brian Kiteley points out in 3 A.M. Epiphany (one of the only other alternative textbooks about innovative writing around, by the way, and a tremendous repository of exercises), is merely competent texts. Architectures problematizes that gesture by outlining what conventional narrativity looks like, urging writers to think about its ideology of form as well as content, and invites them to imagine writing, not as a set of relatively stable conventions, but, rather, as a possibility space where everything can and should be thought, tried, challenged. It thereby rhymes with Roland Barthes’s definition of literature: the question minus the answer—which is to say Architectures poses complications to the act of writing rather than solutions. 3) One of the most notable things about the book is the use of interviews. This is also one of the reasons that I think the book works so well for a variety of audiences—that anyone with even a passing interest in the state and future of literature will have an interest in your conversation with people like Ben Marcus, Samuel Delany, and Lydia Davis. I was hoping you could just talk a little about how you chose these subjects to interview, how you edited the interview material, and which answers you received struck you the most. Experimentalism , like realism , wants to appear in the plural. The idea of gathering more than forty interviews (with the help of my awesome collaborator, Trevor Dodge, himself a fine innovative author) represents an attempt to suggest that: the wide, rich, exciting opportunities inherent in the term. There are interviews with younger writers, elder statesmen in the field, publishers, editors, hypermedia artists, comic book makers, and so on: Joe Wenderoth, Carole Maso, Scott McCloud, Nick Montfort, Kathy Acker, et al. Trevor and I decided to do flash interviews: short, concentrated Q&As, each focusing on a particular troubling of writing. We only lightly edited the results to match the manuscript’s overall style, and every interview arrived as a surprise housing several unexpected insights. Three brief examples: Michael Mejia, when asked about what he dreads when setting about writing: “Dread is an interesting word here. I associate it less with loathing or aversion, I suppose, than with a kind of productive fear. Do I dread a project’s failure? Sure, who doesn’t? Who wants to waste time on something that comes to nothing, or is unreadable? But then, what do these terms mean, and who or what defines a work as a ‘failure,’ as ‘waste,’ as ‘unreadable’? Should a work actually try to interrogate and exceed these conceptual limitations? My tendency is to write into dread in order to reveal to myself, as much as to any reader that may come after, the varied complacencies that make other, mostly more conventional writings, readable. It’s at the frontier between readability (security) and unreadability (terror) that I want to live creatively.” Carole Maso, when asked what she’d like a sentence to accomplish: “I think a sentence can if allowed carry emotional and intellectual states as they flee, as they come and go, an escaping essence difficult to hold in other ways. In this way I think the sentence can work as a phrase of music does, sounding something large and elusive in us. Alternatively it can provide sometimes a stability, an essence, a moment of being. Unlike music the sentence also of course carries language with all its potential for meaning making and memory traces and association with it as well. I probably love the accretion of sentences most—those patterns, that shimmer, that resonance.” Shelley Jackson, when asked what is innovative about the innovative: “The purpose of the innovative is, I think, to wake us up. We are not quite alive, most of the time; we occupy a sort of cartoon version of our lives, its lines made smooth by repetition. Writing can open the seams in that world, reintroduce us to the real lives that we have forgotten. Maybe all good writing is innovative in some sense, in that it shows or tells or makes you feel something you never felt before—something for which you have no cartoon ready.” 4) You talk a little about N. Katherine Hayles’s concept of Media Specific Analysis and propose the supplemental notion of Medium Specific Generation—basically taking Hayles and applying her thought from the perspective of the writer. I’ve been trying to develop somewhat related theoretical frameworks, so I was really excited to come upon this section of the book. I’m wondering if you can talk a little more about this idea and, in general, about the potentials that you see as being opened up by writers engaging with and exploiting different media as literary platforms? “Lulled into somnolence by five hundred years of print,” Hayles urges in her (at least for me) transformative 2004 essay, “Print is Flat, Code is Deep,” “literary analysis should awaken to the importance of media-specific analysis, a mode of critical attention which recognizes that all texts are instantiated and that the nature of the medium in which they are instantiated matters.” She goes on to argue critics should learn to become more attuned to the materiality of the medium under investigation—which is to say a story isn’t a story isn’t a story. Rather, the “same” story remediated through film is intrinsically different from that story remediated through conventionally printed books is intrinsically different from that story remediated through hypermedia. “Materiality,” Hayles goes on, “is reconceptualized as the interplay between a text’s physical characteristics and its signifying strategies, a move that entwines instantiation and signification at the outset.” My point in Architectures is simply to emphasize Media Specific Generation: the idea that when writing you should be cognizant, not only of the thematics of the text you are working on, and, as it were, the internal components of its narrativity (character, language, plot, etc.), but also of the material embodiment those components take, and, perhaps more important, the material embodiment those components can take. The idea that the way texts matter matters isn’t something usually addressed in any significant way in creative-writing classrooms and textbooks. It may almost go without saying such experimentation with typography, layout, and white space has a long tradition—certainly one that tracks back at least as far as Guillaume Apollinaire’s early twentieth-century Calligrammes , Laurence Sterne’s textually ribald eighteenth-century Tristram Shandy , although one could arguably plot a hypothetical trajectory that reaches to ancient Greek romances like Achilles Tatius’ second-century Leucippe and Clitophon . Experiments into atomic materiality and digital immateriality bracket the definition of “book” at the same time they highlight Michael Martone’s prediction of its present future as increasingly viral, collaborative, and ephemeral. Or, as Matthew Battles points out: the future of the “book” has already arrived, and it is “ethereal and networked” rather than “an immutable brick.”While conventional writing and reading practices are conceptualized as private, individual, relatively fixed experiences, many of the new forms indicate that writing and reading—from production through dissemination—are rapidly becoming public, collective, incrementally unfixed experiences. That strikes me as an astonishing set of opportunities for a writer to investigate. 5) Another concept you elaborate in AoP is that of limit texts, basically texts that, once you read them, change what you imagine as the shape/horizon/potential of literature. You provide a fantastic reading list of limit texts at the end of AoP. I was hoping you could talk about a few of them in terms of how they specifically operate as limit texts for you—how they expand your understanding of what literature could be or do. Karl Jaspers coined the word Grenzsituationen (border/limit situations) to describe existential moments accompanied by anxiety in which the human mind is forced to confront the restrictions of its existing forms—moments that make us abandon, fleetingly, the securities of our limitedness and enter new realms of self-consciousness. Death, for example. Limit texts are a variety of disturbance that carries various elements of narrativity to their brink so the reader can never quite imagine them in the same terms again. Once you’ve taken one down from the shelf, you’ll never be able to put it back up again. They won’t leave you alone. They will continue to work on your imagination long after you’ve read them. Simply by being in the world, they ask us to embrace difficulty, freedom, radical skepticism. One of the most important for me is Samuel Beckett’s The Unnamable . Instead of establishing conventional setting and building traditional character, from its first words it unsettles both: “Where now? Who now? When now?” That first trio of question marks broadcasts the thematics of the writing (“novel” may be too strong a word) that will follow: it is all about a voice (or, perhaps, voices, about the grammatical mistake of the first-person pronoun), a consciousness (maybe, again, too strong a word), often genderless, removed from place and chronology and socioeconomic reality, hovering in a state of perpetual aporia. All it knows is what it doesn’t know, and its not-knowing is blackly, sardonically comic. The Unnamable is the embodiment of an unreliable narrator—a subject position that can’t trust itself, let alone be trusted by a reader. It contradicts, takes back, digresses, undoes what it just did, forgets, lies, hallucinates gloriously. The language is abstract, disembodied, devoid of sensory data, grayish rather than painterly in texture. Without knowing this passage is from a novel, a reader might well conclude s/he were reading a patch of (anti-)Cartesian philosophy. It might be helpful to conceive of what Beckett is doing as post-genre writing, then, or perhaps what Raymond Federman referred to as critifiction—a mode that blurs conventional distinctions between theory and narrative. In completely different register, and much more recently, Anne Carson’s Nox blew me away. It takes the form of an elegy for her older brother, whom she didn’t know well and who died unexpectedly while on the run from the law in Europe. The thing itself arrives in a box that simulates a thick book, as well as the brother’s textual coffin. Open it, and inside you discover, not a codex, but an accordioned series of “pages” that folds out into an arrangement that suggests an ancient scroll (Carson is, perhaps illuminatingly, a professor of classics) made up of shards of her brother’s letters, old photographs, tickets, Carson’s observations, Catullus’ poem 101 (the one addressed to the Roman poet’s dead brother, a doubling of Carson’s situation), and extensive dictionary entries on all the words that compose that poem. The aggregate produces a collage about the impossibilities of aggregates, the impossibilities of understanding fully, of capturing absences in language. At times Nox feels less an example of what most readers consider a book than something closer to a three-dimensional work of assemblage art. It’s a beautiful mechanism for contemplating Media Specific Analysis, for urging us all to be more extreme. 6) Finally, I want to talk a little about pedagogy and institutions. I’m less interested in questions like “Are MFA programs good for writers?” than in questions about how your role as teacher informs your understanding of literature and your writing practice. I’m also very curious about your take on how commercially marginal literary art is largely patronized by large state institutions and at the same time often imagines itself as a critical and even possibly revolutionary practice. How have your own positions within universities and university-affiliated organizations shaped your thinking about them and about innovative literature? I can imagine in many ways it might make you even more critical. And (I know, another ‘and’...) how does AoP (especially given its relation to Rebel Yell , your previous text on creative writing) reflect your personal history and experience as a teacher and member of communities that are largely defined by institutions? In the classroom, I try to generate the pedagogical field I would have liked to have inhabited as a student, but didn’t. Roland Barthes has a lovely line about this: “We need to substitute for the magisterial [classroom] space of the past (the word delivered by the master from the pulpit above with the audience below, the flock, the sheep, the herd)—a less upright, less Euclidean space where no one, neither teacher nor students, would ever be in his final place.” Easier said than done, of course, but an important life project for all who think of themselves as educators. My own classroom, my own writing, and Architectures of Possibility itself attempt to create the sort of possibility space where, as I mentioned at the outset of our interview, everything should be thought, tried, challenged; where everything rhymes with Roland Barthes’s definition of literature: the question minus the answer. I’m not sure I could write what I’m writing now without the conversations I have almost daily with my students, the conversations they have with each other, the conversations we all have with the texts we study. Especially in light of the paradigm shift over the last, say, quarter century from academia as intellectual exploration to academia as McDonaldized trade school, the irony isn’t lost on me concerning the discrepancy between the safe harbor innovative authors find there and the cultural critiques those authors launch through their writing and pedagogical work. In 2001, I quit my full professorship at one institution precisely because of my disappointment over what had happened to the learning environment there. I had no intentions of reentering the field. In 2007, however, the University of Utah approached me, and I found myself in an environment much more hospitable to the sort of work I want to do—teaching experimental narrative theory and practice. It isn’t by any means a simple irony. One could easily argue innovative writing and pedagogy represents the trace of the paradigm Barthes suggests, and that trace is tremendously productive in all kinds of ways. Innovative writing has never and will never change the world in any large, macrocosmic way. But we’ve all had our lives changed, one by one, by an encounter with a difficult, rich, resonant piece of prose, poetry, music, art, you name it. We’ve all had our lives changed at the ahistorical, microcosmic moment by a class we’ve taken, a teacher we’ve studied with, to such an extent that we became, quite literally, different people. I just came across a stunning set of sentences from Derrida on the topic: “What is education? The death of the parents.” That’s what we’re all up to in the innovative, be it in written texts or the texts we call our classrooms or the texts we call our politics: trying to disrupt what both can and can’t be disrupted, trying to undo what both can and can’t be undone, continuously. (shrink)

This paper details a “metadisciplinary” applied ethics course jointly taught and pioneered by a biologist, psychologist, and ethicist on the subject of Assisted Reproduction. Contrasted with a transdisciplinary approach (whose content involves themes or issues that span traditional disciplinary lines) and a multidisciplinary approach (which involves experts from several disciplines working side by side), a metadisciplinary approach involves both of these former characteristics while incorporating a continuous, critical appreciation for the strengths and weaknesses of the contrasting methods and scopes of (...) each discipline’s methods of inquiry. This paper details the kinds of subjects that lend themselves to metadisciplinary approaches (e.g. applied ethics subjects which are real-world, complex, and studied by various disciplines), staffing guidelines for a smoothly functioning core team, how to plan and prepare the day-to-day of such a course to prevent a diffuse lesson structure, assignment and evaluation guidelines, and an appraisal of the value of such a class. The authors argue that while fundamental research may be conducted along traditional disciplinary lines, solutions to the complex problems of contemporary society require people who are equipped with problem-solving skills whose relevance spans disciplinary boundaries. (shrink)

In this dissertation we explore projective Fraïssé theory and its applications, as well as limitations, to the study of compact metrizable spaces. The goal of projective Fraïssé theory is to approximate spaces via classes of finite structures and glean topological or dynamical properties of a space by relating them to combinatorial features of the associated class of structures. Using the framework of compact metrixable structures, we establish general results which expand and help contextualize previous works in the field. Many (...) proofs in the domain of projective Fraïssé theory are carried out in a context dependent fashion and have thus far eluded clean generalizations. A reason is to be found in the lack of a clear understanding of which spaces are amenable to be studied via projective Fraïssé limits. We give both positive and negative results in this direction. We isolate a combinatorial condition which entails a correspondence between finite structures and regular quasi-partitions of compact metrizable spaces. This correspondence greatly aids the combinatorial-toplogical translation. We apply this machinery to study a class of one-dimensional compact metrizable spaces, which we call smooth fences. To this end, we isolate a class of finite structures—finite partial orders whose Hasse diagram is a forest—whose projective Fraïssé limit approximates a distinctive smooth fence with remarkable properties. We call it the Fraïssé fence and characterize it topologically by carefully exploiting the bridge between the combinatorial and topological worlds. We explore homogeneity and universality features of the Fraïssé fence and the properties of its spaces and endpoints, and provide some results on the dynamics of its group of homeomorphisms. The dissertation is partially based on [1, 2]. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:134 Feminist Studies 41, no. 1. © 2015 by Gabeba Baderoon Focal Length Gabeba Baderoon I take out the black and white photos I brought with me from Cape Town and haven’t looked at for years and stand them next to one another on the dining room table. In one, my mother in her white coat at the hospital looks up from her notes, distracted, in the grainy matte (...) finish you could ask for in the eighties instead of gloss. Here she is, younger, standing by the window, holding the telephone with its spiraling black cord to her ear, the curtain slanting to the side as she turns away from the camera. I take down from the wall the framed collection of Rafi’s baby photos I’d found wrapped in tissue paper among the tablecloths in the sideboard we inherited from his parents and line us up with each other. There he is, his face fitting into his mother’s shoulder; his brother holding him with hands under the armpits the way he was told; posing by a white door in a hooded woolen coat, his head reaching just above the handle. When I unwrapped them, the tissue paper had only one set of creases, untouched since she packed them for their long journey. In the soft focus of faded paper, I am standing with my back to a VW Beetle I know is pale green, my hands tucked behind me against the bumper, the license plate showing the number from the time before we moved from Uitenhage to Cape Town. In this one, I am on my mother’s lap, leaning against her like gravity. In the photo the focus shifts between my face and my mother’s. She is looking at me, like my father who is taking the picture. My face is clear and hers slightly blurred, as though his eyes are moving between us, as though the camera cannot capture the eye’s oscillation between two people one loves at the same time. One photo had been folded into three, bent once and then again to fit into a pocket, close enough to the skin to warm the paper, and then smoothed out again to fit into a frame. In it, I am turning sideways toward the camera—someone must have called my name—and a line creases just Gabeba Baderoon 135 beneath my eyes. Folded, hidden, forgotten, memory doesn’t come to me straight. The pleat of the curtain as she leans against it, his face in the crook of her shoulder as though he would never leave, me turning toward my name, the paper keeping its original crease. Poetry for Beginners In the evening poetry class for beginners in the community hall during the introductions a girl looking down behind her hair and a thick brown coat she doesn’t take off breathes in deep and risking something says fast my boyfriend’s in prison and I’m here to find out how to write to him through the bars and someone laughs and she pulls herself back into her coat and from inside looks past us and the next week doesn’t come back and I think of her for years and what poetry is I think of her long pause at the beginning her silence before and her silence after and I think this is my origin where poetry is risk, is betrayal and the memory of the first question how not to be alone 136 Gabeba Baderoon ID Photos In the small caravan parked permanently next to the Traffic Department with the handwritten sign ID Photos Taken Here its wheels rusted into place the young old photographer with dreadlocks and a tired poet’s face is shaking his head from side to side muttering some version of no just before me a woman in a long black skirt and black veil unties the loop of fabric knotted behind her head and her face briefly emerges the young old photographer sees everything hundreds of unclaimed photos line the inside of his caravan the making of identity interrupted and turned into small sad signs of something else we don’t look at... (shrink)

This paper details a “metadisciplinary” applied ethics course jointly taught and pioneered by a biologist, psychologist, and ethicist on the subject of Assisted Reproduction. Contrasted with a transdisciplinary approach (whose content involves themes or issues that span traditional disciplinary lines) and a multidisciplinary approach (which involves experts from several disciplines working side by side), a metadisciplinary approach involves both of these former characteristics while incorporating a continuous, critical appreciation for the strengths and weaknesses of the contrasting methods and scopes of (...) each discipline’s methods of inquiry. This paper details the kinds of subjects that lend themselves to metadisciplinary approaches (e.g. applied ethics subjects which are real-world, complex, and studied by various disciplines), staffing guidelines for a smoothly functioning core team, how to plan and prepare the day-to-day of such a course to prevent a diffuse lesson structure, assignment and evaluation guidelines, and an appraisal of the value of such a class. The authors argue that while fundamental research may be conducted along traditional disciplinary lines, solutions to the complex problems of contemporary society require people who are equipped with problem-solving skills whose relevance spans disciplinary boundaries. (shrink)

We consider the relation between the uniform interpolation property and the elimination of non-standard quantifiers (the bisimulation quantifiers) in the context of the ?-calculus. In particular, we isolate classes of frames where the correspondence between these two properties is nicely smooth.

In lieu of an abstract, here is a brief excerpt of the content:The Transformative Journey of TransplantationValen KeeferThe moisture from the ocean floated effortlessly through the air as it glided over the rocky cliff. The steady stream of mist covered my face and frizzy hair with beaded water droplets. I had been sitting on a bench alone for hours admiring the Northern California coast at a magnificent overlook featuring a bird’s-eye view of the endless sea and campground I called home (...) for the past month. The stunning mountain landscape behind me, the soothing colors of the coastal shrubbery, and the smell of eucalyptus made for a trifecta of surreal beauty. The ocean disappeared from my view and I became engulfed in the precipitation and felt like I was suspended in a cloud. I was soaking in every moment as it was the last day of my solo RV trip.The fog slowly separated and exposed bits and pieces of the ocean again and then a breathtaking rainbow came into sight. Each end appeared to be touching either side of the campground like it was giving it a hug. I was eye-level with the center and highest point of the rainbow, arching above our home on wheels. I stood on the bench with my arms wide open, embracing nature and the gift of life in all its glory. This moment would not have possessed such deep meaning if it wasn’t for the journey that came before it—the transformative journey of transplantation.Some may think of transplantation as a singular event when in reality, it’s a lifelong journey that can start with a diagnosis many years prior. My transplant journey began when I was diagnosed with polycystic kidney disease (PKD) at 10-years-old. Being diagnosed with a hereditary disease that has deeply impacted multiple generations of our family and with no known treatment or cure was a lot to carry as a child.My youth was full of love from my parents and filled with illness and the limitations and long-term impacts of growing up with multiple chronic illnesses. My education on PKD was the brutal real-life experiences of enduring it firsthand—with no support groups, resources, or internet to seek answers. I always felt different during a time when you’d do anything to fit in. I couldn’t play sports and had to sit on the sidelines in gym class. I was often in the nurse’s office, hospital, or recovering from a surgery. I hid my scars and unattractive body while changing in gym class. Friendships were really hard. Relationships were even harder.Growing up with chronic illnesses takes away from the fun of dreaming. It’s like that bright future full of endless possibilities is blocked by a huge mountain you know you have to summit first with no supplies, no friends, and no paved path to follow.Complications from PKD followed me from high school right into college, when I spent almost a year in the hospital. Both of my kidneys were removed, I was on dialysis, had pancreatitis, received over 70 blood transfusions, survived an internal bleed, and was in dire need of a lifesaving kidney transplant.At 19-years-old, I was too sick to be placed on the transplant waiting list, but needed a kidney to survive. My parents were living at the Ronald McDonald House, wondering if they would be the next ones to lose their teenage daughter. A close family friend forever changed our lives when she restored my health by selflessly donating her kidney to me. While it was an arduous path to transplantation, in some ways, the journey was just beginning.Fifteen years following my kidney transplant and summiting what I thought was going to be the most challenging mountain of my health journey, I found myself back on death’s doorstep with another battle ahead. I was in need of a second miracle, this time a lifesaving liver transplant. It was PKD again. The bile ducts in my liver were so gnarly that they looked like limbs of an oak tree rather than the desired smooth straw-like appearance. Their malformations led to chronic liver infections and multiple sepsis... (shrink)

This paper reports completeness results for dyadic deontic logics in the tradition of Hansson’s systems. There are two ways to understand the core notion of best antecedent-worlds, which underpins such systems. One is in terms of maximality, and the other in terms of optimality. Depending on the choice being made, one gets different evaluation rules for the deontic modalities, but also different versions of the so-called limit assumption. Four of them are disentangled, and compared. The main observation of this paper (...) is that, even in the partial order case, the contrast between maximality and optimality is not as significant as one could expect, because the logic remains the same whatever notion of best is used. This is established by showing that, given analogous properties for the betterness relation, the same system is sound and complete with respect to its intended modelling. The chief result of this paper concerns Åqvist’s system F supplemented with the principle of cautious monotony. It is established that, under the maximality rule, F + is sound and complete with respect to the class of models in which the betterness relation is required be reflexive and smooth . From this, a number of spin-off results are obtained. First and foremost, it is shown that a similar determination result holds for optimality; that is, under the optimality rule, F + is also sound and complete with respect to the class of models in which the betterness relation is reflexive and smooth . Other spin-off results concern classes of models in which further constraints are placed on the betterness relation, like totalness and transitivity. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Michael L. MarkPatrice Madura Ward-SteinmanI met Michael Mark at the first Philosophy of Music Education conference held at Indiana University in the summer of 1990. I was a doctoral student at IU then and had studied the writings of many of the conference presenters and so the experience of hearing and meeting them in person was a heady one, indeed. I will never forget those impressions of Phil Alperson, (...) Wayne Bowman, Allen Britton, David Elliott, Peter Kivy, Gerard Knieter, Thomas Regelski, Bennett Reimer, John Shepherd, Ann Stokes, Eleanor Stubley, Keith Swanwick, and many others.I was interested in meeting Michael after hearing his response to the presentation of one of my favorite IU professors of musicology, Austin Caswell. Caswell’s provocative paper, “How We Got into Canonicity and What it has Done to Us: An American Music Historian’s View of Music in Academia,” claimed that “the effect of canonicity on American musical life is destructive,” while Michael’s response was characterized by his style of writing that I came to recognize over the decades as distinct, calm, logical, methodical, and based in an extraordinarily wide and deep wealth of historical knowledge. While I greatly admired my rebellious and passionate professor’s views and temperament which were not unlike my own, I also appreciated hearing Michael’s measured and thoughtful response. Thus began my friendship with Michael, who, I learned, was not only a professor [End Page 92] and dean at Towson State University but also an avid big band woodwind doubler who showed interest in my doctoral research in the art of vocal jazz improvisation. That friendship lasted for almost twenty-eight years and we enjoyed memorable reunions at other conferences. For example, there was the ISPME conference held at UCLA where he invited me to dinner with his good friend and connoisseur of fine wines, Bennett Reimer, and the ISPME conference in Helsinki where, after I tripped and severely broke my ankle, requiring surgery, Michael, Estelle Jorgensen, Iris Yob, and two then-doctoral students (Kasia Bugaj and Leonard Tan) visited me in the Helsinki hospital.When I began teaching at the University of Southern California in 1995, it was fortuitous that Michael’s brother, Brian, lived in the Los Angeles area. His frequent visits allowed him to make several guest lectures to my graduate research methods classes, very welcome opportunities. After one of those lectures, I relayed the history of my family’s ballroom in the Chicago area that was open for business with big band music from 1929 until 1967. He asked if I had any artifacts from Madura’s Danceland, and when I mentioned my father’s stacks of dusty record books, newsletters, photos, and posters in our basement, he became very enthusiastic and told me that I had a “gold mine” of an archive with which to write a book about the place! As a trained quantitative researcher, I began to explore the record books to analyze trends in band pay over the Depression and World War II years.1 Over the next ten years, with help from Michael’s regular prodding and encouragement, I organized the large archive into the history of Madura’s Danceland.2 I owe this personally important accomplishment to Michael Mark.Michael invited me (in his endearing way which I could not refuse) to coauthor a music education textbook with him3 and our writing partnership went so smoothly that he invited me to co-author the 4th edition of his Contemporary Music Education.4 Although our writing styles and areas of expertise were very different, I learned much from his narrative approach which included illustrative scenarios, interviews, and the informal use of contractions, a style of writing that was not second nature for me. We wrote both books without meeting in person, except to celebrate the publication of the first at the Metropolitan Art Museum café in New York with our beloved spouses, Lois Mark and David Ward-Steinman.Dr. Michael L. Mark will long be remembered for his many books, chapters, and articles on the history of music education and his many symposium presentations; for his university teaching and administrative achievements; and for his... (shrink)

§ 1. Introduction. In this communication we present some recent results on the classification of Polish metric spaces up to isometry and on the isometry groups of Polish metric spaces. A Polish metric space is a complete separable metric space.Our first goal is to determine the exact complexity of the classification problem of general Polish metric spaces up to isometry. This work was motivated by a paper of Vershik [1998], where he remarks : “The classification of Polish spaces up to (...) isometry is an enormous task. More precisely, this classification is not ‘smooth’ in the modern terminology.” Our Theorem 2.1 below quantifies precisely the enormity of this task.After doing this, we turn to special classes of Polish metric spaces and investigate the classification problems associated with them. Note that these classification problems are in principle no more complicated than the general one above. However, the determination of their exact complexity is not necessarily easier.The investigation of the classification problems naturally leads to some interesting results on the groups of isometries of Polish metric spaces. We shall also present these results below.The rest of this section is devoted to an introduction of some basic ideas of a theory of complexity for classification problems, which will help to put our results in perspective. Detailed expositions of this general theory can be found, e.g., in Hjorth [2000], Kechris [1999], [2001]. (shrink)

Fundamental analytic, algebraic, and geometric properties of generalized Hamiltonian (Birkhoffian) theory are compared with the properties of a covering unitary phase-space formulation based on complex variables of the form (p+iq). Technical advantages in the unitary phase-space formulation are illustrated by a detailed discussion of the one-dimensional extended damped harmonic oscillator. One advantage is the ability to fully describe nonconservative constraint forces within a globally conservative system. Another advantage is that wider classes of gauge transformations are available to simplify the construction (...) of smooth solution manifolds. (shrink)

This paper studies the properties and performance of models for estimating local probability distributions which are used as components of larger probabilistic systems — history-based generative parsing models. We report experimental results showing that memory-based learning outperforms many commonly used methods for this task (Witten-Bell, Jelinek-Mercer with fixed weights, decision trees, and log-linear models). However, we can connect these results with the commonly used general class of deleted interpolation models by showing that certain types of memory-based learning, including the (...) kind that performed so well in our experiments, are instances of this class. In addition, we illustrate the divergences between joint and conditional data likelihood and accuracy performance achieved by such models, suggesting that smoothing based on optimizing accuracy directError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMaply might greatly improve performance. (shrink)

Behind the economic turbulence and political transformations of recent decades is the transition from the nationstate phase of world capitalism to a new transnational phase. While many detractors of globalization focus on global trade, the process is driven by the transnationalization of capital ownership, which in turn leads to the rise of a transnational bourgeoisie that sits at the apex of the global order. Parallel to the transatlantic and transpacific integration of capital there has been an integration of Southern capitalists (...) into the emergent system of transnational capital. A transnational hegemony is replacing a declining U. S. hegemony, although supra-national structures are still not capable of providing the economic regulation and political conditions for global capitalism to function smoothly. In this period of extraordinary conflict, upheaval, and uncertainty, the role of popular classes will be crucial. But their struggles must take on a transnational perspective and engage in transnational organizing. (shrink)

With the introduction of zoom and cell group Bible study and fellowship gathering with church members from 6 to 10, congregation members of each Korean church have come to appreciate the diversity within each consistory encompassing multigenerational American born Koreans, foreign expats, diplomats, immigrants from middle class and up from the greater Seoul, South Korea area, political refugees and migrant workers who categorically entered this country with Republic of Korea visa but who originally were able to date back their (...) earlier life from Communist Regimes such as Siberia, China, Vietnam and North Korea (Ibuk chulsin) and other Asian of color looking foreigners and mix-breeds with Korean heritage and other combinations. The focus of their Christian practice has been more passive concept of God’s grace grounded on John Wesley tradition rather than their yoking and making progress in lineal fashion into the future with and by believers out of Christian love. A premium is placed in smooth transitioning from static Confucianism and Christianity embracing education, meritocracy, social harmony and order. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Selected Letters by William, Henry JamesWilliam James EarleWilliam and Henry James. Selected Letters. Edited by Ignas K. Skrupskelis and Elizabeth M. Berkeley. Introduction by John J. McDermott. Charlottesville VA: University Press of Virginia, 1997. Pp. xxxi + 570. $ 39.95.Almost fifty years of letters to and from the very diversely brilliant James brothers: in this volume a generous, and probably ample, selection of 216 from a total of (...) 740 surviving letters or postcards, from an original total, according to the present editors, of twice as many. This volume of correspondence reflects the deep, unquestioned, unshakable familial (and virtually statutory) closeness of William and Henry who happened, as adults, to be seldom in the same place. There is, it must be said, very little explicit philosophy, narrowly or broadly defined, in these letters, but the philosophical reader will—or ought to—find much raw material for philosophical reflection. For example, a reasonable historicist thesis of how brotherhood, or family connection generally, plays itself out is supported by these documents. The nineteenth century is not the same as the twentieth. For example, here is William’s comment on the will of his sister, Alice, who left more to her companion and care-giver, Katherine Loring, a [End Page 479] women of extraordinary virtue and burden, than to her brother Robertson: “I can well sympathize with Alice’s desire to leave her something handsome; but I must say that her own consent (being apparently privy to the will) strikes me as tant soit peu lacking in delicacy. Surely no one of us would like to be in such a position in her family or any other” (271). This would be, in 1998, a rather unenlightened and ungenerous attitude, but is natural enough in 1892, even if not quite inevitable, not being shared by Alice herself. There is, incidentally, much discussion of wills and bequests, for the Jameses were of the genteel class, people with small family money and modest private incomes for whom the wherewithal to maintain homes with servants and to provide themselves with country houses and recuperative European vacations was always a faintly embarrassing, and occasionally a pressing, problem.It is probably also true that the much-discussed question of Henry’s homosexuality has, somehow, to be recast in historically relative terms. Here is an early report—1869—of Henry’s from Oxford: “As I walked along the river I saw hundreds of the mighty lads of England, clad in white flannel & blue, immense, fair-haired, magnificent in their youth, lounging down the stream in their punts or pulling in straining crews & rejoicing in their godlike strength” (41). This could not, the point is, be said by anyone, gay or straight, in 1998. Yet Henry is neither generally naive nor uncritically anglophile. He says of the Warwickshire scenery, which in a way he likes, that it is “too monotonously sweet & smooth—too comfortable, too ovine, too bovine, too English in a word.” And he adds, a little surprisingly: “It seems like a vast show region kept up at the expense of the poor” (41). This is only one of many appealing comments not sparsely scattered, but unpredictably, in letters of more ordinary news. Here’s one I liked occasioned by seeing theater in Paris: “We talk about it & write about it & criticize & dogmatize & analyse to the end of time: but those brave players stand forth & exemplify it & act—create—produce!” (66).Of course the “wit and wisdom” are not the monopoly of Henry. Here is William being wise: “We all learn sooner or later that we must gather ourselves up and more or less arbitrarily concentrate our interests, throw much overboard to save any” (55–56). Again: “It is a sweet world, in the interstices of its bedevilment & brutality” (321). And William being funny: “Boils are surely the most slowly evolving things in nature—Christian doctrine is nothing to them” (393). He is talking about his own boils and was subject, at every period, to ailments and infirmities: “Since writing to you, I have been swimming in deep seas of influenza, gout and Erysipelas of the face” (443). Or as he, in 1900, sums it up: “My... (shrink)

Arts and Humanities in Higher Education, Volume 21, Issue 1, Page 3-20, February 2022. As graduate labour market conditions have become increasingly challenging, higher education institutions have intensified their focus on ‘employability’ via strategies such as work placements. Focusing on work placements in the media and creative industries, this article identifies and analyses three key discourses that animate the pedagogical literature in these sectors: work placements as facilitating a ‘smooth transition’ to the labour market; work placements as a place (...) in which inequalities in the labour market are produced; and work placements as a space for fostering resilience and adaptation to labour market precarity. The article argues that critiques of inequalities based on race, class or gender are marked by a transformative impulse that is largely absent in critiques of those based on worker precarity. This highlights a need to adopt pedagogies that similarly unnaturalise the economic conditions of neoliberal capitalism to discursively construct work in new, more socially just, ways. (shrink)

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that (...) of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible. (shrink)

The main purpose of this paper is to present a formal systemPin which we enjoy a smooth-running technique and which countenances a universe of classes which is symmetrical as between large and small. More exactly,Pis a system which differs from the inconsistent system of [1] only in the introduction of a rather natural new restrictive condition on the defining formulas of the elements. It will be proved that if the weaker system of [2] is consistent, thenPis also consistent.After the (...) discovery of paradoxes, it may be recalled, Russell and Zermelo in the same year proposed two different ways of safeguarding logic against contradictions. Since then various simplifications and refinements of these systems have been made. However, in the resulting systems of Zermelo set theory, generation of classes still tends to be laborious and uncertain; and in the systems of Russell's theory of types, complications in the matter of reduplication of classes and meaningfulness of formulas remain. In [2], Quine introduced a system which seems to be free from all these complications. But later it was found out that in it there appears to be an unavoidable difficulty connected with mathematical induction. Indeed, we encounter the curious situation that although we can prove in it the existence of a class V of all classes, and we can also prove particular existence theorems for each of infinitely many classes, nobody has so far contrived to prove in it that V is an infinite class or that there exists an infinite class at all. (shrink)

This paper revisits one of the first models of analog computation, the General Purpose Analog Computer . In particular, we restrict our attention to the improved model presented in [11] and we show that it can be further refined. With this we prove the following: the previous model can be simplified; it admits extensions having close connections with the class of smooth continuous time dynamical systems. As a consequence, we conclude that some of these extensions achieve Turing universality. (...) Finally, it is shown that if we introduce a new notion of computability for the GPAC, based on ideas from computable analysis, then one can compute transcendentally transcendental functions such as the Gamma function or Riemann's Zeta function. (shrink)

Contrary to many of the standard histories of German Idealism, the most recent research suggests that it did not grow smoothly and seamlessly from Kant's critical philosophy into Hegel's mature system, nor did it proceed without serious challenges launched from a wide variety of alternative philosophical perspectives. Probably the most sustained and trenchant assault upon this tradition came from a group of already well-established philosophers and intellectuals who referred to their project as "metacritique," a critical movement spearheaded by such luminaries (...) as J. G. Hamann, S. Maimon, F. H. Jacobi, and J. G. Herder. Employing approaches and arguments clearly prefiguring much later critiques, like those of ordinary language philosophy, logical positivism, and even cognitive psychology, the metacritics attempted to refute the transcendental pretensions of the German idealists through a rigorous linguistic critique of idealist philosophical discourse. This linguistic challenge and its response from the idealist party also drew into its ambit such important figures of the early Romantic movement as August and Friedrich Schlegel and August Ferdinand Bernhardi. Although this extended discussion between the early idealists and their linguistic metacritics formed an important episode of European intellectual history, neither the crucial texts nor an interpretive discussion of them have to date been available to the English-speaking student. The present work fills this important gap in our understanding of the period by offering an extensive interpretive and critical overview of the metacritical challenge and the responses to it, together with English translations of the key texts, each with its own introduction and commentary. This outstanding collection will be useful for any class on German idealism and for providing an accurate historical context for some of the later philosophical charges leveled against this tradition. (shrink)

In this paper, I use the cases of intuitionistic arithmetic with Church’s thesis, intuitionistic analysis, and smooth infinitesimal analysis to argue for a sort of pluralism or relativism about logic. The thesis is that logic is relative to a structure. There are classical structures, intuitionistic structures, and (possibly) paraconsistent structures. Each such structure is a legitimate branch of mathematics, and there does not seem to be an interesting logic that is common to all of them. One main theme of (...) my ante rem structuralism is that any coherent axiomatization describes a structure, or a class of structures. If one weakens the logic, then more axiomatizations become coherent. (shrink)

We investigate an aspect of defeasibility that has somewhat been overlooked by the non-monotonic reasoning community, namely that of defeasible modes of reasoning. These aim to formalise defeasibility of the traditional notion of necessity in modal logic, in particular of its different readings as action, knowledge and others in specific contexts, rather than defeasibility of conditional forms. Building on an extension of the preferential approach to modal logics, we introduce new modal osperators with which to formalise the notion of defeasible (...) necessity and distinct possibility, and that can be used to represent expected effects, refutable knowledge, and so on. We show how KLM-style conditionals can smoothly be integrated with our richer language. We also propose a tableau calculus which is sound and complete with respect to our modal preferential semantics, and of which the computational complexity remains in the same class as that of the underlying classical modal logic. (shrink)

We show that in 4-spacetime modified at very short distances due to the weakening of classical logic, the higher dimensions emerge. We analyse the case of some smooth topoi, and the case of some class of pointless topoi. The pointless topoi raise the dimensionality due to the forcing adding “string” objects and thus replacing classical points in spacetime. Turning to strings would be something fundamental and connected with set theoretical forcing. The field theory/strings dualities originate at the set (...) theoretical level of the theories. It is argued that this fundamental level can help solving some difficulties of the physical dualities. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Overcoming Violence in Practice1Sarah K. PinnockIn Christian thought, the classic theological response to evil and suffering, known as "theodicy," operates on a metaphysical level. It aims to elucidate questions about God: God's power to prevent evil, God's goodness and justice, and God's purposes in allowing evil. It also examines questions about humanity: Are humans chronically prone to sin and violence? Does suffering serve good purposes? Does God redeem suffering? (...) In recent Christian attempts at theodicy, attention has focused on divine omnipotence and human freedom in attempts to exculpate God for cruelty in allowing the magnitude of suffering visible in such events as the Holocaust, where six million Jews and five million Poles, gypsies, homosexuals, and other noncombatants were killed under Nazi orders. Symmetrical with exploration of the "front end" explanatory questions of why bad things happen in a supposedly good world, theodicies also explore the "back end" justificatory questions of how God can heal the damage, unevenly and unfairly distributed, in this life or the afterlife. Key exemplars of modern theodicy are Leibniz and Hegel, thinkers who have greatly influenced twentieth-century analytic and continental philosophy of religion, respectively. Despite the urgency of responding to evil, theodicy has been criticized for its abstract, global approach to suffering and its programmatic focus on justifying God in the face of violence. My own critique of theodicy has epistemic and moral components. Theodicy rests on epistemological hubris, building precarious intellectual systems in pursuing knowledge of God. Additionally, theodicy is guilty of moral turpitude on account of its single-minded focus on explanation, which smooths over the scandal of suffering and overlooks the prevention and alleviation of violence.2Fortunately, there are more promising alternatives than theodicy in Christian thought. Particularly in the twentieth century, existentialist and Marxian philosophical movements have contributed to practical rather than theoretical emphases in response to theodicy questions. Reflection on the situatedness of the subject has prompted this shift as theology becomes more self-conscious of its cultural assumptions. Especially since the 1960s, contextual varieties of theology have emerged that recognize its socially embedded character. Theology is never purely dislocated conceptual reflection, innocent of ethical consequences, but a discourse with practical origins and effects. To use Marxian vocabulary, all theology is an "ideology" expressing the conscious and unconscious interests of a social group or class. This insight [End Page 73] does not dismiss the truth and power of theology, but forces closer examination of its production and implications. As Marx wrote in his "Theses on Feuerbach," "philosophers [and theologians] have only interpreted the world in various ways; the point, however, is to change it."3 Theology as a discourse must attend to how it functions within society to motivate opposition or acceptance of violence. Also, it must attend to how reliably it exposes and articulates violence within its vocabulary, and what social cases of violence it addresses.I propose that the shift toward practical or contextual Christian anti-theodicy responses to violence resonates with Buddhist attention to practice, rather than speculation, in answer to suffering. To use a well-known image from the Buddha's teaching, all human beings are like persons pierced with poisoned arrows. All suffer grievously because of craving and desire, and desperately long for relief. In such a condition of life, sliding toward death while suffering, what is the most urgent need: to find out how to remove the poisoned arrow and heal the wound, or to find out where the arrow came from and why it was shot?4 Of course, the moral of the story is that the alleviation of suffering is primary and urgent. It would be foolish to searchfor an explanation instead of a cure for the poison. Understanding the cosmic origins of suffering is a distraction, irrelevant to alleviating suffering and detrimental to practice. Preoccupation with metaphysical speculation does not produce wisdom. Such wisdom is the fruit of awareness resulting from meditation training.In presenting my ideas to a forum for Buddhist-Christian dialogue, I am very much aware of the perils of comparative thinking. My understanding of Buddhism reflects the Westernized transmission of Mahayana Zen Buddhist traditions, based on writings intended for an... (shrink)

. The deep structural properties of a quantum information theoretic approach to formal languages and universal computation, as well as those of the topology problem of defining the presentation of the Mapping Class Group of a smooth, compact manifold are shown to be grounded in the common categorical features of the two problems.

Background: Detecting and classifying fish diseases is crucial for maintaining the health and sustainability of aquaculture systems. This study employs deep learning techniques, particularly Convolutional Neural Networks (CNNs), to automate the detection of various fish diseases using image data. Methods: The study utilizes a carefully curated dataset sourced from the Kaggle database, comprising images representing seven distinct types of fish diseases, along with images of healthy fish. Data preprocessing techniques, including resizing, rescaling, denoising, sharpening, and smoothing, are applied to enhance (...) image quality and facilitate accurate disease detection. Data augmentation is employed to increase the model's ability to generalize to unseen data. The CNN architecture is designed with cascading convolutional layers, ReLU activation functions, and pooling operations to extract high-level features associated with fish infections. The model architecture, implemented using the Keras Sequential API, includes convolutional layers, max pooling layers, and densely connected layers for classification. Results: Experimental results demonstrated promising performance across various disease categories, with high accuracy and balanced precision and recall values for most classes. The study also discussed the impact of climate change on fish disease incidence and underscores the importance of effective monitoring and management practices facilitated by technological innovations such as Big Data, IoT, sensors, and robotics in ensuring sustainable fisheries management. (shrink)

The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in (...) which the former may be embedded, satisfying the pertinent cohomological conditions required for the coordinatization of all of the tensorial physical quantities, such that the form of the field equations is preserved. We present in detail the construction of these distribution-like algebra sheaves in terms of residue classes of sequences of smooth functions modulo the information of singular loci encoded in suitable ideals. Finally, we consider the application of these distribution-like solution sheaves in geometrodynamics by modeling topologically-circular boundaries of singular loci in three-dimensional space in terms of topological links. It turns out that the Borromean link represents higher order wormhole solutions. (shrink)

In this paper we show that several classes of partially ordered structures having paraorthomodular reducts, or whose sections may be regarded as paraorthomodular posets, admit a quite natural notion of implication, that admits a suitable notion of adjointness. Within this framework, we propose a smooth generalization of celebrated Greechie’s theorems on amalgams of finite Boolean algebras to the realm of Kleene lattices.

Regarding the relation of Plato’s early and middle period dialogues, scholars have been divided to two opposing groups: unitarists and developmentalists. While developmentalists try to prove that there are some noticeable and even fundamental differences between Plato’s early and middle period dialogues, the unitarists assert that there is no essential difference in there. The main goal of this article is to suggest that some of Plato’s ontological as well as epistemological principles change, both radically and fundamentally, between the early and (...) middle period dialogues. Though this is a kind of strengthening the developmentalistic approach corresponding the relation of the early and middle period dialogues, based on the fact that what is to be proved here is a essential development in Plato’ ontology and his epistemology, by expanding the grounds of development to the ontological and epistemological principles, it hints to a more profound development. The fact that the bipolar and split knowledge and being of the early period dialogues give way to the tripartite and bound knowledge and benig of the middle period dialogues indicates the development of the notions of being and knowledge in Plato’s philosophy before the dialogues of the middle period. -/- Keywords Plato; early dialogues; middle dialogues; being; knowledge; development -/- Introduction The differences between two groups of the early and middle period dialogues have always been a matter of dispute. Whereas the developmentalists like Vlastos, Silverman (2002), Teloh (1981), Dancy (2004) and Rickless (2007) think that from the early to the middle dialogues Plato’s philosophy changes, at least in some essential points, the unitarists like Kahn, Cherniss and Shorey believe that there happens no development and the differences must be taken as natural, ignorable and even pedagogic. In his well-known article, Socrates contra Socrates in PLATO, Vlastos lists ten theses of difference between two groups of dialogues. The first group which includes Plato’s early dialogues he divides to 'elenctic' (Apology, Charmides, Crito, Euthyphro, Gorgias, Hippias Minor, Ion, Laches, Protagoras and Republic I) and 'transitional' (Euthydemus, Hippias Major, Lysis, Menexenus and Meno) dialogues. These transitional come after all the elenctic dialogues and before all the dialogues of the second group which compose Plato’s middle period dialogues, including (with Vlastos' chronological order) Cratylus, Phaedo, Symposium, Republic II-X, Phaedrus, Parmenides and Theaetetus (1991, 46-49). Vlastos asserts strictly that his list of differences are 'so diverse in content and method that they contrast as sharply with one another as with any third philosophy you care to mention, beginning with Aristotole’s' (ibid, 46). Vlastos’ list of differences between two Socrateses is considered a view breaking sharply between the early and the middle dialogues. Besides all ten differences between the two Socrateses in Vlastos’ list that can be supportive for our doctrine here, we intend to focus on some ontological as well as epistemological distinctions that have not completely been discussed hitherto. Contrary to the developmentalist theory of Vlastos, unitarian theory of Charles Kahn wishes to eliminate any substantial difference between the early and the middle dialogues. He distinguishes seven 'pre-middle' or 'threshold' dialogues including Laches, Charmides, Euthyphro, Protagoras, Meno, Lysis and Euthydemus from the other Socratic dialogues which he calls 'earliest group' (1996, 41). The threshold dialogues, Kahn thinks, 'embarke upon a sustained project' that is to reach to its climax in the middle period dialogues, namely Phaedo, Symposium and Republic. Believing in that there is no 'fundamental shift'between the early and middle dialogues (ibid, 40), Kahn thinks the Socratic dialogues are just the 'first stage' with a 'deliberate silence' towards the theories of later periods (ibid, 339). One of the reasons of the surprising fact that Plato gives no hint of the metaphysics and epistemology of the Forms in the early dialogues, he thinks, is the pedagogical advantages of aporia. He thinks that Plato 'obscurely', and mostly because of education, hinted to some doctrines and conceptions in his early dialogues and with the aim of clarifying them only in the later ones (ibid, 66). The seven threshold dialogues, Kahn asserts, 'had been designed from the first' to prepare the pupils and readers for the views expounded in the middle period dialogues (ibid, 59-60). To show that the differences of the two Socrateses of the early and middle period dialogue are in their onto-epistemological grounds and thence cannot be explained by a unitaristic view, we try to draw the ontological and epistemological principles of the early dialogues in the first part below in order to show, in the second part, that those principles have been developed in the middle period dialogues. -/- A. The Onto-Epistemologic Principles of the Early Dialogues Socratic dialogues are paradoxical about knowledge because while being knowledge-oriented always searching for knowledge, they deny it and even never discuss it directly. Three elements of Socrates’ way of searching Knowledge throughout the early dialogues, i.e. Socratic 'what is X?' question, his disavowal of knowledge and his elenctic method combined together produce something like a circle which works, more or less, in the same way in these dialogues. Though this circle is an embaressing inquiry always resulting in ignorance instead of knowledge, its motivation is surprisingly Socrates’ passionate enthusiasm for knowledge, an intensive love of wisdom. The starting point of this circle is Socrates’ confession of having no knowledge which might be explicitly asserted or presupposed, maybe because it was one of the famous characteristics of Socrates; a confession always paradoxically accompanied with his intense longing for knowledge (e.g., Gorgias 505e4-5). Every time Socrates encounters with someone who thinks he knows something (οἴεταί τι εἰδέναι) (Apology 21d5) and tries to examine him. This examination seems to be the simplest one asking just what it is that he knows. Socrates’ elenchus, therefore, is always connected with 'what is X?' (τίς ποτέ ἐστιν) question, a question that most of the early dialogues of Plato are concerned with; 'what is courage?' in the Laches, 'what is piety?' in Euthydemus, 'what is temperance?' in Charmides and 'what is beauty?' in Hippias Major. This question we call here 'Socratic question' and probably is the very question the historical Socrates used to employ, is tightly interrelated with both his disavowal and his elenchus. He disclaims knowledge because he cannot find the answer to the question himself and he rejects others’ since they cannot offer the correct answer too. Every interlocutor can claim he knows X, if and only if he can answer the Socratic question. Otherwise, he is more of an ignorant than of a knower of τί ποτέ ἐστι X. Knowing the answer to this question is, thus, knowledge’s criterion for Socrates. Having found out that he cannot answer what it is which he would claim to know, the interlocutor comes to the point Socrates was there at the beginning. The least advantage of this circle is that he becomes as wise as Socrates does about the subject, becoming aware that he does not know it. At the end of the circle they are both still at the beginning, not knowing what X is. So let us first take a glance at these three elements. Socratic disavowal of knowledge is strictly asserted in some passages. At Apology 21b4-5, Socrates says: -/- I do not know of myself being wise at all (οὔτε μέγα οὔτε σμικρὸν σύνοιδα ἐμαυτῷ σοφὸς ὤν) -/- Moreover, at 21d4-6: -/- None of us knows anything worthwhile (καλὸν κἀγαθὸν εἰδέναι) …. I do not know (οἶδα) neither do I think I know. -/- In Charmides Socrates speaks about a fear about his probable mistake of thinking that he knows (εἰδέναι) something when he does not (166d1-2). The somehow generalization of this disavowal can be seen in Gorgias. After calling his disavowal 'an account that is always the same' (509a4-5), Socrates continues (a5-7): -/- I say that I do not know (οἶδα) how these things are, but no one I have ever met, like now, who can say anything else without being absurd. -/- At the end of Hippias Major (304d7-8), Socrates affirms his disavowal of knowledge of 'what is X?' this time about the fine: -/- I do not know (οἶδα) what that is itself (αὐτὸ τοῦτο ὅτι ποτέ ἐστιν). Some other passages, however, made a number of scholars dubious about Socrates’ disavowal. Vlastos mentions Apology 29b6-7 as an evidence : 'that to do wrong and to disobey one’s master, both god and men, I know (οἶδα) to be evil and shameful'. He thinks that if we give this single text 'its full weight' it can suffice to show that Socrates does claim knowledge of a moral truth (1985, 7). Vlastos’ claim is not admittable since it would be too strange, I think, for a man like Socrates to violate his disavowal claim just after emphasizing it. We can see his claim just before the already mentioned passage: -/- And surely it is the most blameworthy ignorance to believe that one knows what one does not know. It is perhaps on this point and in this respect, gentlemen, that I differ from the majority of men and if I were to claim that I am wiser than anyone in anything it world be in this, that, as I have no adequate knowledge (οὐκ εἰδὼς ἱκανῶς) of things in the underworld, so I do not think I have (οὐκ εἰδέναι) (Apology 29b1-6) Vlastos tries to solve what he calls the 'paradox' of Socrates’ disavowal of knowledge distinguishing the 'certain' knowledge from 'elenctic' knowledge (1985, 11) and thinking that when Socrates avows knowledge, we must perceive it as an elenctic knowledge, a knowledge its content 'must be propositions he thinks elenctically justifiable' (ibid, 18). Irwin’s solution is the distinction of knowledge and belief. He approves that Socrates does not 'explicitly' make such a distinction, but still thinks that Socrates’ 'test for knowledge would make it reasonable for him to recognize true belief without knowledge, and his own claims are easily understood if they are claims to true belief alone' (1977, 40). While I agree with Vlastos up to a point, I strongly disagree with Irwin about the early dialogues. As I will try to show below, we are not permitted to consider any kind of distinction within knowledge in Socratic dialogues because only one category of knowledge is alluded to there and the distinction of knowledge and belief thoroughly belongs to the second Sorcates. Although no kind of distinction can be admittable here, I think Vlastos’ distinction can be accepted only if we regard it as a distinction between knowledge, which is unique and without any, even incomparable, rival, and a semi-idiomatic and ordinary one that is a necessary requirement for any argument, and thus, unavoidable even for someone who does not claim any kind of knowledge. An apparent evidence of this is Gorgias 505e6-506a4: -/- I go through the discussion as I think it is (ὡς ἄν μοι δοκῇ ἔχειν), if any of you do not agree with admissions I am making to myself, you must object and refute me. For I do not say what I say as I know (οὐδὲ γάρ τοι ἔγωγε εἰδὼς λέγω ἃ λέγω) but as searching jointly with you (ζητῶ κοινῇ μεθ᾽ ὑμῶν). -/- The minimal degree of knowledge everyone must have to take part in an argument, conduct it and use the phrase "I know" when it is necessary is what Socrates cannot deny. We can call it elenctic knowledge only if we agree that it is not the kind of knowledge that Socrates has always been searching, the one that can be accepted as the answer of Socratic 'what is X?' question. His disavowal of knowledge is applied only to the knowledge which can truly be the answer of Socratic question and pass the elenctic exam; a knowledge that, I believe, is never claimed by first Socrates. Socrates conducts his method of examining his interlocutors’ knowledge, our second element here, by almost the same method repeated in Socratic dialogues. That whether we are allowed to regard all the examinations of Socrates in the early dialogues as based on the same or not has been a matter of dispute. Vlastos himself (1994, 31) distinguished Euthydemas, Lysis, Menexenns and Hippias Major from the other Socratic dialogues because he thinks Socrates has lost his faith to elenchus in there. Irwin (1977, 38) distinguishes Apology and Crito where Socrates’ own convictions is present. Contrary to some scholars like Benson (2002, 107) who take elenchus in all the Socratic dialogues as a unique method, Michelle Carpenter and Ronald M. Polansky (2002, 89-100) argue pro the variety of methods of elenchus. Thomas C. Brickhouse and Nicholas D. Smith (2002, 145-160) even reject such a thing as Socratic elenchus which can gather all of the Socrates’ various arguments under such a heading. There can be no solution for the problem of elenchus, they think, is due to 'the simple reason that there is no such thing as 'the Socratic elenchos"'(p.147). Though we consider elenchus a somehow determined process and a part of Socratic circle in the early dialogues, all we assume is that whatever differences it might have in different dialogues, it has the same onto-epistemological principles and, thus, we are not going to take it necessarily as a unique method. This method sets out to prove that the interlocutors are as ignorant as Socrates himself is. That whether elenchus is constructive, capable of establishing doctrines as Vlastos (1994) or Brickhouse and Smith (1994, 20-21) believe or not is another issue to which this paper is not to claim anything. What is crucial for our discussion here is that elenchus does not reach to the very knowledge Socrates is looking for. This is strictly against Irwin who thinks that not only elenchus leads to positive results, 'it should even yield knowledge to match Socrates’ conditions'(1977, 68, cf. 48). He does not explain where and how they really yield to that kind of knowledge. He explains his elenctic method in his apology in the court (Apology 21-22), that how he used to examine wise men, politicians, poets and all those who had the highest reputation for their knowledge and every time found that they have no knowledge. If we accept, as I strongly do, that Socrates’ disavowal of his knowledge is not irony, it might seem more reasonable to agree that the process that has that disavowal as its first step cannot be irony as well. The key of the circle which can explain why Socrates disclaims knowledge and how he can reject others’ claim of having any kind of knowledge lies in the third element, Socratic question. In Hippias Major (287c1-2), Socrates asks: 'Is it not by Justice that just people are Just? (ἆρ᾽ οὐ δικαιοσύνῃ δίκαιοί εἰσιν οἱ δίκαιοι). He insists at 294b1 that they were searching for that by which (ᾧ) all beautiful things are beautiful (cf. b4-5, 8). At Euthyphro 6d10-11 it is said that the Socratic question is waiting for 'the form itself (αὐτὸ τὸ εἶδος) by which (ᾧ) all the pious actions are pious; and at 6d11-e1: -/- Through one form (που μιᾷ ἰδέᾳ) impious actions are impious and pious actions pious. -/- Since the X itself is that by which X is X, knowing 'X itself' is the only way of knowing X. It is probably because of this that Socrates makes the distinction between the ousia as a right answer to the question and effect as a wrong one: -/- I am afraid, Euthyphro, that when you were asked what piety is (τὸ ὅσιον ὅτι ποτ᾽ ἐστίν) you did not wish to make clear its nature itself (οὐσίαν … αὐτοῦ) to me, but you said some effect (πάθος) about it. (Euthp. 11a6-9) -/- 1. Knowledge of what X is Now it is time to look for the onto-epistemological principles of Socratic circle and its three elements. It cannot reasonably be expected from the first Socrates to present us explicitly and clearly formulated principles of his onto-epistemology when such explications cannot be found even in the second Socrates who has some obviously positive theoris. Since there must be some principles underlying this first systematic inqury of knowledge, we must seek to them and be satisfied with elicitation of the first Socratas’ principle. What will be drawn out as his principles cannot and must not, thus, be taken as very fix and dogmatic principles. Some very slightest principles and grounds suffice for our purposes here. The first principle that is the prima facie significance of the Socratic question and his implementation of all those elenctic arguments I call the principle of 'Knowledge of What X is' (KWX): -/- KWX To know X, it is required to know what X is. -/- Aristotle (Metaphysics 1078b23-25, 27-29, 987b4-8) takes Plato’s τί ἐστι question as seeking the definition of a thing that is the same as historical Socrates’ search but applying to a different field. That Plato’s 'what is X?' question was a search for definition became the prevailed understanding of this question up to now. I am going neither to discuss the answer of Socratic question nor to challenge taking it as definition. What I am to insist is that knowledge is attached firmly to the answer of the question: Knowledge of X is not anything but the knowledge of what X is. It entails, certainly, the priority of this knowledge to any other kind of knowledge about X but it also has something more fundamental about the relation of knowledge and Socratic question. Socrates’ exclusive focus on the answer of his question can authorize the consideration of such an essential role for KWX in his epistemolgoy. The total rejection of his interlocutors’ knowledge when they are unable to answer the question can be regarded as a strong evidence for it. Socrates’ elenctic method and his rejection of others’ knowledge in the early dialogues, which all end aporetically with no one accepted as knower and nothing as knowledge, prevent us from finding any positive evidence for this. We have to be content, therefore, of negative evidences which, I think, can be found wherever Socrates rejects his interlocutors’ knowledge when they are not able to give an acceptable answer to his 'what is X?' question. 2. Bipolar Epistemology Socrates’ rejection of his interlocutors’ knowledge has another epistemological principle as its basis. Let me call this principle Bipolar Epistemology' (BE): BE There is no third way besides knowledge and Ignorance. -/- BE says that about every object of knowledge there are only two subjective statuses: knowledge and Ignorance. Socrates’ disavowal, however, says nothing but that he is ignorant of knowledge of X because he does not know what X is. This means that BE is presupposed here. Socrates’ elenchus and his rejection of interlocutors’ having any kind of knowledge are the necessary results of the fact that he does not let any third way besides knowledge and ignorance. The first Socrates never let anyone partly know X or have a true opinion about it, as he would not let anyone know anything about X when he did not know what X is. -/- 3. Bipolar Ontology The principle of BE in first Socrates’ epistemology is parallel to another principle in his ontology. Plato’s bipolar distinction between being and not being is as strict and perfect as his distinction between knowledge and ignorance. This principle I shall call the principle of 'Bipolar Ontology' (BO): BO Being is and not being is not. BO is apparently the same with the well-known Parmenidean Principle of being and not being (cf. Diels-Kranz (DK) Fr. 2.2-5). Euthydemus’ statement against the possibility of false knowledge can be good evidence for this principle: -/- The things which are not surely do not exist (τὰ δὲ μὴ ὄντα … ἄλλο τι ἢ οὐκ ἔστιν). (Euthydemus 284b3-4) -/- He continues (b4-5): -/- There is nowhere for not being to be there (οὖν οὐδαμοῦ τά γε μὴ ὄντα ὄντα ἐστίν). -/- That BE does not let true opinion as a third option besides knowledge and ignorance seems to be related to BO’s rejecting a third option besides being and not being, which is itself the basis of the impossibility of false belief. Socrates’ elaborate discussion of the problem of false belief in Theatetus that leads to a more decisive discussion and finally to some solutions in Sophist can make our consideration of BO for the first group of dialogues authentive. -/- 4. &5. Split Knowledge and Split Being The fourth principle I shall call the principle of 'Split Knowledge' (SK): -/- SK Knowledge of X is separated from any other knowledge (of anything else) as if the whole knowledge is split to various parts. -/- This Principle is hinted and criticized as Socrates’ way of treating with knowledge in Hippias Major: -/- But Socrates, you do not contemplate the entireties of things, nor do people you have used to talk with (τὰ μὲν ὅλα τῶν πραγμάτων οὐ σκοπεῖς, οὐδ᾽ ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι). (301b2-4) -/- Contrary to Rankin who regards the passage as 'antilogical, almost eristic in tone rather than presenting a serious philosophy of being' (1983, 54), I think it can be taken as serious. Hippias criticizes Sorcates that he does not contemplate (σκοπεῖς) the entireties of things (ὅλα τῶν πραγμάτων), a critique which Socrates is not its only subject but all those whom Socrates accustomed to talk with (ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι). This last phrase, I think, extends this critic beyond this dialogue to other Socratic dialogues. Hippias’ use of the perfect tense of the verb ἔθω (to be accustomed) is a good evidence of this extension. We can get, thus, these ἐκεῖνοι as Socrates’ interlocutors in his other dialogues that hints that this criticism has the epistemological groundings of the previous dialogues as its subject. What ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι points to is that Hippias does not have in mind Socrates’ way of treating things only in this dialogue, but he is also criticizing Socrates’ way throughout his dialogues. At 301b4-5, Socrates and his interlocutors’ way of beholding things is described as such: -/- You people knock (κρούετε) at the fine and each of the beings (ἕκαστον τῶν ὄντων) by taking each being cut up in pieces (κατατέμνοντες) in words (ἐν τοῖς λόγοις). This leads us to our next principle that is parallel to, and the ontological side of, SK, the principle of 'Split Being'(SB): -/- SB Everything (being) is separated from any other thing as if the whole being is split to many beings. -/- Socrates and his interlocutors and thus, as we saw, the Socratic dialogues are accused to regard everything as it is separated from all other things. This separation is en tois logois that, I think, can reasonably be taken as saying that Socratic dialogues (it refers of course to the dialogues before Hippias Major) cut up all things which have the same name/definition from all other things and try to understand them separately, without considering other things that are not in their logos. They, for example in Hippias Major, are cutting up to kalon and try to understand what it and all others inside this logos are by separating it from all other things. This is directed straightly against Socratic question and the way Socratic dialogues follow to find its answer, every time separating one logos. As Meyer (1995, 85) points out, every question 'presupposes that the X in question in a logos is something' and 'every answer to every question aims at unity' (84). The critique of Hippias Major is, therefore, at the same time a critique of SK and SB. It is also a critique of KWX because it is only based on KWX that Socratic dialogues could search for the answer of 'what is X' question supposing that knowing what X is is enough for the knowledge of X. SK and KWX are absolutely interdependent. What Socrates and all his previous interlocutors have neglected in Socratic dialogues, Hippias says, was 'continuous bodies of being' (διανεκῆ σώματα τῆς οὐσίας) (301b6). Either this theory actually belongs to the historical Hippias as it is being said or not, it is strictly criticizing SB. We have the same phrase with changing sūma to logos some lines later at 301e3-4: διανεκεῖ λόγῳ τῆς οὐσίας. Although this theory that can be observed as both an ontological and an epistemological theory is rejected by Socrates (301cff.), it is still against first Socrates’ onto-epistemological principles and might let us look at what is rejected as Socratic prineple. -/- 6. Knowledge is of Being The sixth principle that I think is presupposed by the first Socrates, is the 'Knowledge of Being' Principle (KB): -/- KB Knowledge is of Being. -/- This principle is obviously the source of the problem of false knowledge, a very important problem throughout Plato’s philosophy. We face this problem maybe for the first time in Euthydemus. In less than 20 Stephanus’ pages, 276-295, we are encountered with different interwoven problems about knowledge , all grounded in the problem of false opinion. Having challenged the obvious possibility of telling lies at 283e, at 284 Euthydemus discusses it saying that the man who speaks is speaking about 'one of those things that are (ἓν μὴν κἀκεῖνό γ᾽ ἐστὶν τῶν ὄντων)' (284a3) and thus speaks what is (λέγων τὸ ὄν) (a5). He must necessarily be saying truth when he is speaking what is because he who speaks what is (τὸ ὄν) and the things that are (τὰ ὄντα) speaks truth (τἀληθῆ λέγει) (a5-6). This is based on Parmenidean principle of the impossibility of being of not being which Euthydemus restates (284b3-4) and we mentioned discussing BO principle above. The things that are not are nowhere (οὐδαμοῦ) and there is no possibility for anyone to do (πράξειεν) anything with them because they must be made as being before anything else can be done, which is impossible (b5-7). The words, then, are of things that exist (εἰσὶν ἑκάστῳ τῶν ὄντων λόγοι) (285e9) and as they are (ὡς ἔστιν) (e10). The result is that no one can speak of things as they are not. It is this impossibility of false speach that is extended to thinking (δοξάζειν) at 286d1 and leads to the impossibility of false opinion (ψευδής … δόξα) (286d4). The general conclusion is asserted at 287a extending this impossibility to actions and making any kind of mistake. Not only knowledge is of being but speech, thought and action are of being simply because of the fact that nothing can be of not being. -/- B. First Socrates’ Principles in the Middle Period Dialogues Out of what were presupposed or criticized mostly in five dialogues, Euthyphro, Euthydemus, Hippias Major, Laches and Charmides, we tried to draw the first Socrates’ principles. Our inquiry here is directed to find out the fate of these principles in the three dialogues of the middle period, Meno, Phaedo and Republic. To do this, first we ought to check the situation of Socratic circle in these dialogues. The Socratic circle that was predominant in the early dialogues, does not look like a circle here anymore though they certainly have some features in common. Meno, Phaedo and Republic II-X are not committed to the principles of the circle and the whole circle in disrupted in them. The difference of the two Socrateses towards acquiring knowledge is obvious. The Socrates of Meno, Phaedo and Republic is evidently more self-confident that he can get to some truths during his arguments as he does. They are in their first appearance, as almost all other dialogues, committed to Socrates’ disavowal. All of them try to keep the shape of the Socratikoi Logoi genre, which is committed to the historical Socrates’ way of discussion; a dramatic personage who is to challenge his interlocutors, ask them and refuse the answers. Nevertheless, the fact is that what we have in common between two groups of dialogues is mostly a dramatic structure. Whereas the first group’s arguments are based on Socrates’ disavowal and lead to no positive results, the second group is decisively going to achieve some positive results. The aim of the first Socrates was to show others that they are ignorant of what they thought they knew. The new Socrates of Meno, on the opposite, makes so much efforts to show that the slave boy has within himself true opinions (ἀληθεῖς δόξαι) about the things that he does not know (οἶδε) (85c6-7). Despite his lack of knowledge, he has true opinions nevertheless. The way from these true opinions to knowledge, as Socrates states, is not so long. These true opinions are now like a dream but 'can become knowledge of the same things not less accurate than anyone’s' (οὐδενὸς ἧττον ἀκριβῶς ἐπιστήσεται περὶ τούτων) (c11-d1), if they be repeated by asking the same questions. The most outstanding text regarding Socrates’ disavowal is Meno 98b where he explicitly claims knowledge: -/- And indeed I also speak as (ὡς) one who does not know (εἰδὼς) but is guessing (εἰκάζων). However, [about the fact] that true opinion and knowledge are different, I do not altogether expect (δοκῶ) myself to be guessing (εἰκάζειν), but if I say about anything that I know (εἰδέναι) -which about few things I say- this is one of the things that I know (οἶδα). (98b1-5) This passage is very significant about Plato’s disavowal of knowledge. There can hardly be found, I think, anywhere else in Plato’s corpus where Socrates speaks about his knowledge of something as such. He says first that he speaks as someone who does not know. This ὡς οὐκ εἰδὼς λέγω comparing with what he used to say in the first group, οὐκ οἶδα, has this added ὡς. Socrates does not claim strongly anymore that he does not know anything but speaks only as someone who does not know. He needs this ὡς not only because he is going to accept that he does know some, though few, things immediately after this sentence, but also because he needs his previous disavowal to be loosened from Meno on. He does not merely say here that he knows something. It is then different from the examples mentioned before which could be taken as idiomatic or at least not emphatic. Socrates’ remarkable emphasis on distinguishing εἰδέναι from εἰκάζειν departs it from all other passages where he says only he knows something. Moreover, he claims definitely that he has knowledge about few (ὀλίγα) things. From the early to the middle dialogues, Socrates’ attitude to knowledge has totally renewed its face. He brings forth a new concept, true opinion, and he does not speak of knowledge as he used to before; the rough, perfect and unachievable knowledge of the first group has turned to something more smooth, realistic and achievable. Comparing with the early dialogues that did not set out from the first to reach positive results, the middle ones are extraordinarily and surprisingly positive and hence destroy the basis of the Socratic circle. The questions and answers are purposely directed to some specific new theories; most of them are not directly related to the topics or the main questions of the dialogues. They are suggested when Socrates draws the attention of the interlocutor away from the main question because of the necessity of another discussion. Even if the main question remains unanswered, we have still many positive theories, prominently of metaphysical type. These theories are so abundant and dominant in these dialogues, especially Phaedo and Republic, that one might think that they may appear to be arbitrarily sandwiched in there. This helps dialogues to keep their original Socratic structure while they are suggesting new theories. Hence, the Socratic question of 'what is X?', though is still used to launch the discussion, is loosened and is forgotten for most part of the dialogues. Meno that has first a differently formulated question, 'can virtue be taught?', leads finally to the Socratic question of 'What is virtue?'. Phaedo is dedicated to the demonstration of the immortality of soul and the life after death without having a central Socratic question. The case of Republic is more complicated. The first book, on the one hand, has all the criteria of a Socratic circle: its 'what is justice?' question, Socrates’ strong disavowal (e.g. 337d-e), his rejection of all answers and coming back to the first point without finding out any answer. This Book, considered alone, is a perfect Socratic dialogue, as many scholars regard it as early and separated from other books. The books II-X are, on the other hand, far from implementing a Socratic circle. They have still the 'what is justice?' question as their incentive leading question, but they are, in most of the positive doctrines and methods that encompass the main parts, ignoring the question. Even these books that, I believe, are the farthest discussions from the Socratic circle are so cautious not to break the Socratic structure of the dialogue as long as it is possible. What is changed is not the structure of the dialogue but the ontological and epistemological grounds based on which new theories are suggested. -/- 1. Knowledge of the Good We can clearly see in the second group of dialogues that the KWX principle loses the place it had before in our first group. It is not, of course, rejected, but still we cannot say that it has the same situation. KWX that was based on Socratic question, as we discussed before, was the leading principle of the first Socrates’ epistemology and of the highest position. Other epistemological principles, SK directly and BE indirectly, were relying on Socratic question and therefore on KWX. Such a position does not belong to KWX from Meno on. What makes it different in the second Socrates is another principle that is needed it not only as its complementary principle but also as what is more fundamental. Plato, then, does not reject KWX in this period, but, it seems, he transcends to another more basic principle; a principle we shall call the principle of 'Knowledge of the Good' (KG): -/- KG Knowledge of X requires knowledge of the Good. -/- Whereas all the dialogues of our first group are free from any discuscon about KG, it bears a very important role in the second group so as becomes the superior principle of knowledge in Republic. Trying to solve the problem of teachability of virtue, Socrates says that it can be teachable only if it is a kind of knowledge because nothing can be taught to human beings but knowledge (ἐπιστήμην) (Meno 87c2). The dilemma will be, then, whether virtue is knowledge or not (c11-12) and since virtue is good, we can change the question to: whether is there anything good separate from knowledge (εἰ μέν τί ἐστιν ἀγαθὸν καὶ ἄλλο χωριζόμενον ἐπιστήμης) (d4-5). Therefore, the conclusion will be that if there is nothing good which knowledge does not encompass, virtue can be nothing but knowledge (d6-8). What let us discuss KG as an epistemological principle for the second Secrates is the relation he tries to establish between knowledge and the Good which, though is alongside with the mentioned thesis and the idea of virtue as knowledge, goes much deeper inside epistemology asking to regard the Good as the basis of knowledge. The effort of Phaedo cannot succeed in establishing the Good as the criterion of explanation and knowledge since, I think, it needs a far more complicated ontology of Republic where Socrates can finally announce KG. What is said in Republic is totally compatible with Phaedo 99d–e and the metaphor of watching an eclipse of the sun. In spite of the fact that we do not have adequate knowledge of the Idea of the Good, it is necessary for every kind of knowledge: 'If we do not know it, even if we know all other things, it is of no benefit to us without it' (505a6-7). The problem of our not having sufficient knowledge of the Idea of Good is tried to be solved by the same method of Phaedo 99d-e, that is to say, by looking at what is like instead of looking at thing itself (506d8-e4). It is this solution that leads to the comparison of the Good with sun in the allegory of Sun (508b12-13). What the Good is in the intelligible realm corresponds to what the sun is in the visible realm; as sun is not sight, but is its cause and is seen by it (b9-10), the Good is so regarding knowledge. It has, then, the same role for knowledge that the sun has for sight. Socrates draws our attention to the function of sun in our seeing. The eyes can see everything only in the light of the day being unable to see the same things in the gloom of night (508c4-6). Without the sun, our eyes are dimmed and blind as if they do not have clear vision any longer (c6-7). That the Good must have the same role about knowledge based on the analogy means that it must be considered as a required condition of any kind of knowledge: -/- The soul, then, thinks (νόει) in the same way: whenever it focuses on what is shined upon by truth and being, understands (ἐνόησέν), knows (ἔγνω) and apparently possesses understanding (νοῦν ἔχειν). (508d4-6) -/- Socrates does not use agathon in this paragraph and substitutes it with both aletheia and to on. He links them with the Idea of the Good when he is to assert the conclusion of the analogy: -/- That which gives truth to the objects of knowledge and the power of knowing to the knower, you must say, is the Idea of the Good: being the cause of knowledge and truth (αἰτίαν δ᾽ ἐπιστήμης οὖσαν καὶ ἀληθείας) so far as it is known (ὡς γιγνωσκομένης μὲν διανοοῦ). (508e1-4) Knowledge and truth are called goodlike (ἀγαθοειδῆ) since they are not the same as the Good but more honoured (508e6-509a5). KG, which had been implicitly contemplated and searched in Phaedo, is now explicitly being asserted in Republic. As what was quoted clearly proves, this principle is the very one which we can observe as the most fundamental principle of the second Socrates in Republic, corresponding to the role KWX had in the first Socrates. The Form of the Good in Republic, of which Santas speaks as 'the centerpiece of the canonical Platonism of the middle dialogues, the centerpiece of Plato’s metaphysics, epistemology, ethics and …' (1983, 256) much more can be said. Plato’s Cave allegory in Book VIII dedicates a similar role to the Idea of the Good. The Idea of the Good is there as the last thing to be seen in the knowable realm, something so important that its seeing equals to understanding the fact that it is the cause of all that is correct and beautiful (517b). Producing both light and its source in visible realm, it controls and provides truth and understanding in the intelligible realm (517c). -/- 2. Tripartite Epistemology BE is thoroughy rejected in the second Socrates and substituted by its opposite, the principle of 'Tripartite Epistemolgy' (TE): -/- TE Opinion is an epistemological status between knowledge and ignorance. BE of the first Socrates was denying any third way besides knowledge and ignorance which was the foundation of Socratic circle without which Socrates could not reject his interlocutors’ possessing any kind of knowledge. We cannot say, however, that the first Socrates had a third epistemological status in mind but rejected it. Such a status was unacceptable for him so that one can say that he would reject any kind of such status if suggested. There were only two possibilities about knowledge: either one knows something or he does not know it. TE, thus, was not the first Socrates’ discovery and, I think it is not the second Socrates’discovery. All we can see in our second group of dialouges is that he uses this principle as an already demonstrated one. Having examined the slave boy in Meno for the prupose of showing the working of recollection, it truns out that he has some opinions in him while he still does not know. Without trying to prove it, Socrates takes this as the distinction between knowledge and opinion: -/- So, he who does not know (οὐκ εἰδότι) about what he does not know (περὶ ὧν ἂν μὴ εἰδῇ) has within himself true opinions (ἀληθεῖς δόξαι) about the same things he did not know (περὶ τούτων ὧν οὐκ οἶδε) (85c6-7). -/- The same distinction is set between ὀρθὴν δόξαν and ἐπιστήμην at 97b5-6 ff. (also cf. 97b1-2: ὀρθῶς μὲν δοξάζων … ἐπιστάμενος). He connects then their difference to the myth of Daedalus, the statue that would run away and escape. So are true opinions, not willing to remain long in mind and thus not worthy until one ties them down by αἰτίας λογισμῷ (98a3-4). Socrates says that this tying down is anamnesis. We face, in Phaedo, the same relation is settled between knowledge as the process of being tied down and getting the capability to give an account, on the one hand, and anamnesis, on the other hand. When a man knows, he must be able to give an account of what he knows (Phaedo 76b5-6) and since not all people are able to give such an account, those who recollect, recollect what once they learned (76c4). Although the distinction between knowledge and opinion is not explicitly used in Phaedo, referring to the parallel link between knowledge plus account and anamnesis in Phaedo and Meno, one can say that those who cannot recollect are not able to give account and, thus, are in a state of opinion. What is said at Phaedo 84a, though not yet a definite distinction between knowledge and opinion, makes a distinction between their objects so as we can agree that it is presupposed. The soul of the philosopher, Socrates says, follows reason, stays with it forever and contemplates the divine, which is not the object of opinoin (ἀδόξαστον) (84a8, cf. Meno 98b2-5). The distinction of knowledge and belief in Republic has a significant difference with what we discussed in Meno and Phaedo since the distinction of Meno was based on anamnesis and thus more an epistemological distinction. Even in Phaedo that we do not have any elaborate discussion about the distinction, the only hint to the matter at 76 is bound to the theory of anamnesis. In addition to the relation of the distinction with this theory, there is another evidence that does not permit us to consider the distinction as an ontological distinction. Let’s see Meno 85c6-7: -/- So, he who does not know about what he does not know has within himself true opinions about the same things he did not know (τῷ οὐκ εἰδότι ἄρα περὶ ὧν ἂν μὴ εἰδῇ ἔνεισιν ἀληθεῖς δόξαι περὶ τούτων ὧν οὐκ οἶδε). (85c6-7) -/- This last sentence persists that the objects of knowledge and true opinion are the same. What Socrates is to say here is that whereas he does not know X he has true opinion about the same X. I think Socrates’ sentence that the slave boy οὐκ εἰδότι ἄρα περὶ ὧν ἂν μὴ εἰδῇ and his restatement of it by saying περὶ τούτων ὧν οὐκ οἶδε is because he wants to emphasize that the slave boy who does not know, has true opinion about the same thing. Socrates could say this just with using τούτων and there would be no necessity to bring περὶ ὧν ἂν μὴ εἰδῇ for οὐκ εἰδότι if he did not want to emphasize. -/- 3. Tripartite Ontology The distinction between knowledge and true opinion in Republic, on other side, has nothing to do with recollection, but is based on an ontological principle, 'Tripartite Ontology' (TO): -/- TO There are things that both are and are not. -/- This principle I confine, among our three dialogues of the second group, to Republic not extended to Meno and Phaedo, is obviously the opposite of BO. Speaking about the lovers of sights and sounds in the fifth book, Socrates distinguishes them from philosophers because their thought is unable to understand the nature of beautiful itself besides beautiful things (476a6-8) and hence they can only have opinions. The philosopher who, on the contrary, believes in beautiful itself and can distinguish it from beautiful things (476c9-d3), has knowledge because he knows, contrasting others who have opinion because they only opine (d5-6). Since those whose knowledge were degraded as opinion will complain about Socrates’ such calling their thought, he provides them the following argument (476e7-477b1): -/- - Does the person who knows, knows (γιγνώσκει) something (τὶ) or nothing (οὐδέν)? - He knows something (τί). - Something that is (ὂν) or is not (οὐκ ὄν)? - Something that is (ὂν) for how could something that is not be known (πῶς γὰρ ἂν μὴ ὄν γέ τι γνωσθείη)? - Then we have an adequate grasp of this: No matter how many ways we examine it, what completely is (παντελῶς ὂν) is completely knowable (παντελῶς γνωστόν) and what is in no way (μὴ ὂν δὲ μηδαμῇ) is in every way unknowable (πάντῃ ἄγνωστον). - A most adequate one. - Good. Now, if anything is such as to be and also not to be (ὡς εἶναί τε καὶ μὴ εἶναι), won’t it be intermediate (μεταξὺ) between what purely is (εἰλικρινῶς ὄντος) and what in no way is (μηδαμῇ ὄντος)? - Yes, it’s intermediate. - Then as knowledge (γνῶσις) is set over what is (τῷ ὄντι), while ignorance (ἀγνωσία) is of necessity set over what is not (μὴ ὄντι) mustn’t we find an intermediate between ignorance (ἀγνοίας) and knowledge (ἐπιστήμης) to be set over the intermediate, if there is such a thing? -/- From the third status of being we must reach to the third status of knowledge. The simple reading of this text can be an existential reading, taking the "is" of the mentioned sentences as existence. The problem is that when it is said that there is something that both is and is not reading "is" existentially, it sounds too bizarre to be acceptable. It cannot easily be understandable to have something as both existent and non-existent at the same time. This problem arose so many debates and led many scholars to reject the existential reading of "is" and suggest some other readings like predicative or veridical readings. I think though Plato’s complicated ontology of Republic cannot be correctly understood by a simple existential reading, this "is" cannot be free from existential sense of being and, thus, cannot be reduced to just a predicative or veridical sense of being. -/- 4. Bound Knowledges In addition to KG, the Good is also the basis of another principle in the second Socrates, namely the principle of 'Bound Knowledge' (BK): -/- BK Knowledge of everything is bound to the knowledge of the Good. -/- We distinguished BK from KG because we want to insist, in BK, on what had not been insisted upon in KG, that is, the binding role that the Good plays in the second Socrates, contrasting the absence of such a role in the first Socrates. Socrates remembers, in Phaedo, his wonderful keen on natural philosophers' wisdom when he was young. The origin of this enthusiasm was Socrates’ hope to know the cause of everything as they used to claim. When he was searching the matters of his interest on their basis, Socrates says, he became convinced he can get no acceptable answer from them and found himself blind even to the things he thought he knew before. One day he hears Anaxagoras’ theory that 'it is Mind that arranges and is the cause of everything (ὡς ἄρα νοῦς ἐστιν ὁ διακοσμῶν τε καὶ πάντων αἴτιος)' (Phd. 97c1-2 cf. DK, Fr.15.8-9, 11-12, 12-14) and thinks that he can finally find what he has always expected, i.e. something which can explain all things. What I intend to show here is that what makes Socrates hopeful is that Anaxagoras’ theory tries 1) to explain all things by one thing and 2) this explanation is understood by Socrates as if it is based on the concept of the Good. That Socrates was searching for one explanation for all things can be proved even from what he has been expecting from natural philosophers. The case is, nonetheless, more clearly asserted when he speaks about Anaxagoras’ theory. In addition to διακοσμῶν τε καὶ πάντων αἴτιος of 97c2 mentioned above, we have τὸ τὸν νοῦν εἶναι πάντων αἴτιον (c3-4) and τόν γε νοῦν κοσμοῦντα πάντα κοσμεῖν (c4-5) all emphasizing on the cause of all things (πάντα) which can clearly prove that one of the reasons which caused Socrates to embrace it delightfully was its claim to provide the cause of all things by one thing. Another reason was that Anaxagoras’ Mind, at least in Socrates’ view, was attempting to explain everything by the concept of the Good. This connection between Mind and Good belongs more to the essential relation they have in Socrates’ thinking than Anaxagoras’ theory because there are almost nothing about such a relation in Anaxagoras. The reason for Socrates’ reading can be that Mind is substantially compatible with Socrates’ idea of the relation between good and knowledge. Both the thesis 'no one does wrong willingly' and the theory of virtue as knowledge we pointed to above are evidences of this essential relation. Nobody who knows that something is bad can choose or do it as bad. The reason, when it is reason, that means when it is as it should be, when it is wise or when it knows, works only based on good-choosing. In this context, when Socrates hears that Mind is considered as the cause of everything, it sounds to him like this: good should be regarded as the basis of the explanation of all things. We see him, thus, passing from the former to the latter without any proof. This is done in the second sentence after introducing Mind: -/- I thought that if this were so, the arranging Mind would arrange all things and put each thing in the way that was Best (ὅπῃ ἂν βέλτιστα ἔχῃ). If one then wished to find the cause of each thing by which it either perishes or exists, one needs to find what is the best way (βέλτιστον αὐτῷ ἐστιν) for it to be, or to be acted upon, or to act. On these premises then it befitted a man to investigate only, about this and other things, what is the most excellent (ἄριστον) and best (βέλτιστον). The same man must inevitably also know what is worse (χεῖρον), for that is part of the same knowledge. (97c4-d5) This passage is a good evidence of Socrates’ leap from Anaxagoras’ Mind to his own concept of the Good that can explain why Socrates found Anaxagoras theory after his own heart (97d7). Mind is welcomed because of its capability for explanation on the basis of good to 'explain why it is so of necessity, saying which is better (ἄμεινον), and that it was better (ἄμεινον) to be so' (97e1-3). What Socrates thought he had found in Anaxagoras can indicate what he had been expecting from natural scientists before. Socrates could not be satisfied with their explanations because they were unable to explain how it is the best for everything to be as it is. It can probably be said, then, that it was the lack of the unifying Good in their explanation that had disappointed him. We must insist that we are discussing what Socrates thought that Anaxagoras’ theory of Mind should have been, not about Anaxagoras’ actual way of using Mind. Phaedo 97c-98b, is not about what Socrates found in Anaxagoras but what he thought he could find in it. On the contrary, it should also be noted that it was not this that was dashed at 98b, but Anaxagoras’ actual way of using Mind. It was Anaxagoras’ fault not to find out how to use such an excellent thesis (98b8-c2, cf. 98e-99b). Socrates gives an example to show how not believing in 'good' as the basis of explanation makes people be wanderers between different unreal explanations of a thing. His words δέον συνδεῖν (binding that binds together) as a description for the Good we chose as the name of BK principle: They do not believe that the truly good and binding binds and holds them together (ὡς ἀληθῶς τὸ ἀγαθὸν καὶ δέον συνδεῖν καὶ συνέχειν οὐδὲν οἴονται). (99c5-6) -/- Having in mind Plato’s well-known analogy of the sun and the Good at Republic 508-509, we can dare to say that his warning of the danger of seeing the truth directly like one watching an eclipse of the sun in Phaedo (99d-e) is more about the difficulty of so-called good-based explanation than its insufficiency, a difficulty which is precisely confirmed in Republic (504e-505a, 506d-e). Moreover, BK is asserted in a more explicit way in the Republic, where the Good is considered not only as a condition for the knowledge of X, as was noted above discussing KG, but also as what binds all the objects of knowledge and also the soul in its knowing them. At Republic VI, 508e1-3, when Socrates says that the Form of the Good 'gives truth to the things known and the power to know to the knower (τοῦτο τοίνυν τὸ τὴν ἀλήθειαν παρέχον τοῖς γιγνωσκομένοις καὶ τῷ γιγνώσκοντι τὴν δύναμιν ἀποδιδὸν)', he wants to set the Good at the highest point of his epistemological structure by which all the elements of this structure are bound. This binding aspect of the Good is by no means a simple binding of all knowledges or all the objects of knowledge, but the most complicated kind of binding as it is expected from the author of the Republic. The kind of unity the Good gives to the different knowledges of different things is comparable with the unity which each Form gives to its participants in Republic: as all the participants of a Form are united by referring to the ideas, all different kinds of knowledge are united by referring to the Good. If we observe Aristotle's assertion that for Plato and the believers of Forms, the causative relation of the One with the Forms is the same as that of the Forms with particulars (e.g. Metaphysics 988a10-11, 988b4), that is to say the One is the essence (e.g., ibid, 988a10-11: τοῦ τί ἐστὶν, 988b4-6: τὸ τί ἢν εἶναί) of the Forms besides his statement that for them One is the Good (e.g., ibid, 988b11-13) the relation between the Good and unity may become more understandable. Since the quiddity of the Good (τί ποτ᾽ ἐστὶ τἀγαθὸν) is more than discussion (506d8-e2), we cannot await Socrates to tell us how this binding role is played. All we can expect is to hear from him an analogy by which this unifying role is envisaged, the sun. The kind of unity that the Good gives to the knowledge and its objects in the intelligible realm is comparable to the unity that the sun gives to the sight and its objects in the visible realm (508b-c). The allegory of Line (Republic VI, 509d-511), like that of the Sun, tries to bind all various kinds of knowledges. The hierarchical model of the Line which encompasses all kinds of knowledge from imagination to understanding can clearly be considered as Plato’s effort to bind all kinds of knowledges by a certain unhypothetical principle. The method of hypothesis starts, in the first subsection of the intelligible realm, with a hypothesis that is not directed firstly to a principle but a conclusion (510b4-6). It proceeds, in the other subsection, to a 'principle which is not a hypothesis' (b7) and is called the 'unhypothetical principle of all things' (ἀνυποθέτου ἐπὶ τὴν τοῦ παντὸς ἀρχὴν) (511b6-7). This παντὸς must refer not only to the objects of the intelligible realm but to the sensible objects as well. Plato does posit, therefore, an epistemological principle for all things, a principle that all things are, epistemologically, bound and, thus, unified by. -/- 5. Bound Beings The ontological aspect of BK we shall call the principle of 'Bound Beings' (BB): -/- BB Being of all things are bound by the Good. -/- We saw in our principle of Split Being (SB) how the first Socrates was criticized because of his approach to split being and separate each thing from other things. The principle of Bound Beings intends to make the things more related, a duty which is done again by the Good. In the allegory of Sun, there are two paragraphs that evidently and deliberately extend the binding role of the Good to the ontological scene: -/- You will say that the sun not only makes the visible things have the ability of being seen but also coming to be, growth and nourishment. (509b2-4) -/- This clearly intends to remind the ontological role the sun plays in bringing to being all the sensible things in order to display how its counterpart has the same role in the intelligible realm (b6-10): -/- Not only the objects of knowledge (γιγνωσκομένοις) owe their being known (γιγνώσκεσθαι) to the Good, but also their existence (τὸ εἶναί) and their being (οὐσίαν) are due to it, though the Good is not being but superior to it in rank and power. That the Good is here represented as responsible for being of things in addition to their being known means, in my opinion, that Plato wants to posit BB in addition to BK. The allegory of Cave at the very beginning of the seventh Book (514aff.) can be taken as another evidence. The role of the Good, one might say, is confined to the intelligible realm because it is asserted that the role the Good plays in this realm is corresponding to that of the sun in the visible realm. The fact that Plato wants to observe the Good also as the ontological cause of the sensible things is obvious from his saying, in the allegory of Cave, that the Form of the Good 'produces light and its source (τὸν τούτου κύριον) [i.e. the sun] in the visible realm' (517c3). We can conclude, then, that the ontological function of the Good is not confined to the intelligible realm in which it is the lord and provides truth and understanding (c3-4) because it is also responsible to produce τὸν κύριον of light. 6. Proportionality of Being and Knowledge Insofaras BE and BO principles of the first Socrates gave way to TE and TO principles of the second Socrates, we cannot expect him to preserve KB in the same way as it was in the first Socrates. The new tripartite ontology and epistemology necessitates some modifications in KB which results in the principle of 'Proportionality of Being and Knowledge' (PBK): -/- PBK To every class of being there is a proportionate category of knowledge. -/- This principle, of course, does not entail the refutation of KB and thus is not kind of rejecting PBK but only a more complicated version of it. Based on PBK, we can still agree that knowledge is of being (KB) but the issue is that since none of the concepts of knowledge and being in the second Socrates are as simple as they were for the first Socrates, we need a more complicated principle for their relation here. Although from Meno 97a where the distinction of knowledge and true opinion is drawn out in the second group of the dialogues, we can expect a new relation, it is articulated in its most complete way in Republic and specifically in the allegory of Line. All the beings are divided there hierarchically to four classes, to each of them belongs a class of knowledge: imagination to images, belief to the sensible things (more correctly: the things of which they[in previous class] were images (ᾧ τοῦτο ἔοικεν)), thought to mathematical objects (?) and understanding to the Forms and the first principle. The degree of clarity that each of the classes of knowledge shares in (σαφηνείας ἡγησάμενος μετέχειν) is proportionate to the degree that its object shares in truth (ἀληθείας μετέχει). (511e2-4) -/- Conclusion From the six onto-epistemilogical principles of the first Socrates, four principles turn to their opposite in the middle period dialogues. While bipolar epistemology and ontology of the early dialogues give place to tripartite epistemology in the middle period dialogues and tripartite ontology in Republic, the split knowledge and being of the first Socrates are inclined to be substituted by bound knowledges and bound beings in the second Socrates and specifically in Republic. Not all our system of principles in this article is necessarily determinative. Either they are rightly formulated or not, our result would not be vulnerable if we accept that 1) making the distinction of knowledge and belief, 2) accepting the being of not being and 3) trying to bind both being and knowledge by the concept of the Good happens only in middle period dialogues, having been absent in the early ones. These are the favourite results all those somehow arbitrary and even oversimplified principles were to illustrate; that there is kind of a development in the epistemological as well as the ontological grounds of Plato’s philosophy. -/- Notes . (shrink)

The quantum mechanical transition probability is symmetric. A probabilistically motivated and more general quantum logical definition of the transition probability was introduced in two preceding papers without postulating its symmetry, but in all the examples considered there it remains symmetric. Here we present a class of binary models where the transition probability is not symmetric, using the extreme points of the unit interval in an order unit space as quantum logic. We show that their state spaces are strictly convex (...) smooth compact convex sets and that each such set _K_ gives rise to a quantum logic of this class with the state space _K_. The transition probabilities are symmetric iff _K_ is the unit ball in a Hilbert space. In this case, the quantum logic becomes identical with the projection lattice in a spin factor which is a special type of formally real Jordan algebra. (shrink)

We extend classical work by Janusz Czelakowski on the closure properties of the class of matrix models of entailment relations—nowadays more commonly called multiple-conclusion logics—to the setting of non-deterministic matrices (Nmatrices), characterizing the Nmatrix models of an arbitrary logic through a generalization of the standard class operators to the non-deterministic setting. We highlight the main differences that appear in this more general setting, in particular: the possibility to obtain Nmatrix quotients using any compatible equivalence relation (not necessarily a (...) congruence); the problem of determining when strict homomorphisms preserve the logic of a given Nmatrix; the fact that the operations of taking images and preimages cannot be swapped, which determines the exact sequence of operators that generates, from any complete semantics, the class of all Nmatrix models of a logic. Many results, on the other hand, generalize smoothly to the non-deterministic setting: we show for instance that a logic is finitely based if and only if both the class of its Nmatrix models and its complement are closed under ultraproducts. We conclude by mentioning possible developments in adapting the Abstract Algebraic Logic approach to logics induced by Nmatrices and the associated equational reasoning over non-deterministic algebras. (shrink)

We propose a novel edge detector in the presence of Gaussian noise with the use of proximal support vector machine (PSVM). The edges of a noisy image are detected using a two-stage architecture: smoothing of image is first performed using regularized anisotropic diffusion, followed by the classification using PSVM, termed as regularized anisotropic diffusion-based PSVM (RAD-PSVM) method. In this process, a feature vector is formed for a pixel using the denoised coefficient’s class and the local orientations to detect edges (...) in all possible directions in images. From the experiments, conducted on both synthetic and benchmark images, it is observed that our RAD-PSVM approach outperforms the other state-of-the-art edge detection approaches, both qualitatively and quantitatively. (shrink)

Alternative non‐B‐DNA conformations formed under physiological conditions by sequences called flipons include left‐handed Z‐DNA, three‐stranded triplexes, and four‐stranded i‐motifs and quadruplexes. These conformations accumulate and release energy to enable the local assembly of cellular machines in a context specific manner. In these transactions, nucleosomes store power, serving like rechargeable batteries, while flipons smooth energy flows from source to sink by acting as capacitors or resistors. Here, I review the known biological roles for flipons. I present recent and unequivocal findings (...) showing how innate immune responses are regulated by Z‐flipons that identify endogenous RNAs as self. Evidence is also presented supporting important roles for other flipon classes. In these examples, the dynamic exchange of energy between flipons and nucleosomes enables rapid switching of genetic programs without altering flipon sequence. The increased phenotypic diversity enabled by flipons drives their natural selection, with adaptations evolving faster than is possible by codon mutation alone. (shrink)

On June 11, 1963, in a dramatic gesture that caught the nation's attention, Governor George Wallace physically blocked the entrance to Foster Auditorium on the University of Alabama's campus. His intent was to defy Attorney General Nicholas Katzenbach, sent on behalf of the Kennedy administration to force Alabama to accept court-ordered desegregation. After a tense confrontation, President Kennedy federalized the Alabama National Guard and Wallace backed down, allowing Vivian Malone and James Hood to become the first African Americans to enroll (...) successfully at their state's flagship university. That night, John F. Kennedy went on television to declare civil rights a "moral issue" and to commit his administration to this cause. That same night, Medgar Evers was shot dead. In The Schoolhouse Door, E. Culpepper Clark provides a riveting account of the events that led to Wallace's historic stand, tracing a tangle of intrigue and resistance that stretched from the 1940s, when the university rejected black applicants outright, to the post-Brown v. Board of Education era. We are there in July 1955 when Thurgood Marshall and lawyers at the NAACP Legal Defense Fund win for Autherine Lucy and "all similarly situated" the right to enroll at the university. We are in the car with Lucy in February 1956 as university officials escort her to class, shielding her from a mob jeering "Lynch the nigger," "Keep 'Bama white," and "hit the nigger whore." Clark exposes the many means, including threats and intimidation, used by university and state officials to discourage black applicants following the Lucy episode. And he explains how University of Alabama president Frank Anthony Rose eventually cooperated with the Kennedy administration to ensure a smooth transition toward desegregation. We also witness Robert Kennedy's remarkable face-to-face plea for Wallace's cooperation and the governor's adamant refusal: "I will never submit voluntarily to any integration in a school system in Alabama." As Clark writes, Wallace's carefully orchestrated surrender would leave the forces of white supremacy free to fight another day. And the Kennedys' public embrace of the civil rights movement would set in motion a political transformation that changed the presidential base of the Democratic party for the next thirty years. In these pages, full of courageous black applicants, fist-shaking demonstrators, and powerful politicians, Clark captures the dramatic confrontations that transformed the University of Alabama into a proving ground for the civil rights movement and gave the nation unforgettable symbols for its struggle to achieve racial justice. (shrink)

Novikov is one of Russia's leading logicians and the appearance of this fine textbook is a good indicator of increasing American interest in Soviet logic. The book contains some new material, including a new independence proof of the rule of complete induction from the remaining axioms of first-order arithmetic. The first third of this work consists in chapters on propositional algebra and the propositional calculus. The first-order predicate calculus comes next under discussion: here a number of important classical results—Gödel's incompleteness (...) theorem, the Compactness theorem, Skolem-Löwenheim theorem—are proved rigorously. The author throughout the book leans fairly heavily on model-theoretic techniques, hence knowledge of some algebra, especially elementary field theory, will be useful. The last two chapters are concerned with first order arithmetic and the elements of proof theory. The only shortcoming is the lack of a bibliography and related scholarly apparatus; the student using this text may have difficulty locating material in other publications relevant to that in the book without outside assistance. The translation is very smooth and clear. Altogether, a first-class job.—P. J. M. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Role of Glass in Interior Architecture:Aesthetics, Community, and PrivacyMatthew Ziff (bio)Design education seeks to infuse students with knowledge, skills, and attitudes, regarding the design of the built environment. In the areas of knowledge and attitude, sophistication and competence are developed through both practice (largely carried out in the design studio environment), and engagement with critical analysis (largely carried out in seminar classes and traditional lecture format class (...) environments). For design students the world of design is both to be known and understood, and to be created, at their own studio desk. In order to both know and create design, students often behave like nocturnal predators, seeking what is necessary in a mode that is often unobserved, and then returning to digest their catch, to produce responsive and synthetic work. One arena in which design students find rich fields of information is that of material characteristics. Materials used in the design and construction of the built environment form a significant portion of the skeleton of a designer's body of knowledge, skills, and attitudes toward design. A current hotbed of material character and application is that of the world of glass. This essay is an exploration of some of the issues that the architectural uses of glass raise from the point of view of design student exploration.Materials evoke physical and psychological responses. Human beings are complex creatures and an individual's response to specific material applications can be unpredictable. Even so, it is reasonable to expect that there are shared attitudes that form the basis for responses to the physical character of the built environment. From delight, to confusion, materials used in the architecture of things large and small, from buildings to fountain pens, contain literal meaning, or expression of method, as well as possible symbolic and cultural meaning. The contemporary use of glass, particularly in interior architecture, presents a vivid arena for emotional and intellectual stimulation and response. [End Page 10]Glass planes that are sheer, opaque, translucent, colorful, brittle, imposing in mass, irregular in surface texture, flawlessly smooth, deformed through casting or by application of pressure and heat, are being used to create spaces that convey ambiguous relationships between private experience and public display. What is an ambiguous relationship? It is one to which a reasonable response is a high degree of uncertainty regarding the course of action one might take, or in the degree of understanding of the context one can develop. To know that the stair in the train station leads to track 4 is a condition that can be created by the use of unambiguous design; a visual connection from where one has to make a choice of paths to follow to the destination, track 4, creates a clear understanding of where track 4 is to be found. If track 4 can be seen from the position at which a choice is required, then certainty, clarity, is possible, if not probable. Visual connection is exactly what clear glass allows, and provides, yet ambiguity results because of the physical, hard barrier, transparency aside. "I can see track 4, but I cannot get there". The clarity provided by being able to see through glass, or even by being able to see light coming through translucent glass, is not sufficient to offset the uncertainty, or the mixed message, of not being able to get there, to touch what we can see.Glass in interiors offers a tactile and sensory titillation; the excitement of knowing that with a single swing of a hammer, or an umbrella handle, the beautiful sheet of curved frosted lemon ice colored tempered glass can be shattered into fragments.Windows have long been the predominant interior and exterior architectural element in which glass has played a major role. The glass used in Windows on the World, the famous restaurant atop the World Trade Center, destroyed during its collapse, and the glass used in a simple double hung window in a one story ranch house each share architectural duties of providing view from inside to outside, light transmission from outside to inside, heat gain, and acoustical isolation. Human eyes are sometimes described as "windows to the soul," which suggests the ability to... (shrink)

The paper follows the track of a previous paper “Natural cybernetics of time” in relation to history in a research of the ways to be mathematized regardless of being a descriptive humanitarian science withal investigating unique events and thus rejecting any repeatability. The pathway of classical experimental science to be mathematized gradually and smoothly by more and more relevant mathematical models seems to be inapplicable. Anyway quantum mechanics suggests another pathway for mathematization; considering the historical reality as dual or “complimentary” (...) to its model. The historical reality by itself can be seen as mathematical if one considers it in Hegel’s manner as a specific interpretation of the totality being in a permanent self-movement due to being just the totality, i.e. by means of the “speculative dialectics” of history, however realized as a theory both mathematical and empirical and thus falsifiable as by logical contradictions within itself as emprical discrepancies to facts. Not less, a Husserlian kind of “historical phenomenology” is possible along with Hegel’s historical dialectics sharing the postulate of the totality (and thus, that of transcendentalism). One would be to suggest the transcendental counterpart: an “eternal”, i.e. atemporal and aspatial history to the usual, descriptive temporal history, and equating the real course of history as with its alternative, actually happened branches of the regions of the world as with only imaginable, counterfactual histories. That universal and transcendental history is properly mathematical by itself, even in a neo-Pythagorean model. It is only represented on the temporal screen of the standard historiography as a discrete series of unique events. An analogy to the readings of the apparatus in quantum mechanics can be useful. Even more, that analogy is considered rigorously and logically as implied by the mathematical transcendental history and sharing with it the same quantity of information as an invariant to all possible alternative or counterfactual histories. One can involve the hypothetical external viewpoint to history (as if outside of history or from “God’s viewpoint to it), to which all alternative or counterfactual histories can be granted as a class of equivalence sharing the same information (i.e. the number choices, but realized in different sequence or adding redundant ones in each branch) being similar and even mathematically isomorphic to Feynman trajectories in quantum mechanics. Particularly, a fundamental law of mathematical history, the law of least choice of the real historical pathway is deducible from the same approach. Its counterpart in physics is the well-known and confirmed law of least action as far as the quantity of action corresponds equivocally to the quantity of information or that of number elementary historical choices. (shrink)

A generalized and unifying viewpoint to both general relativity and quantum mechanics and information is investigated. It may be described as a generaliztion of the concept of reference frame from mechanics to thermodynamics, or from a reference frame linked to an element of a system, and thus, within it, to another reference frame linked to the whole of the system or to any of other similar systems, and thus, out of it. Furthermore, the former is the viewpoint of general relativity, (...) the latter is that of quantum mechanics and information. Ciclicity in the manner of Nicolas Cusanus (Nicolas of Cusa) is complemented as a fundamental and definitive property of any totality, e.g. physically, that of the universe. It has to contain its externality within it somehow being namely the totality. This implies a seemingly paradoxical (in fact, only to common sense rather logically and mathematically) viewpoint for the universe to be repesented within it as each one quant of action according to the fundamental Planck constant. That approach implies the unification of gravity and entanglement correspondiing to the former or latter class of reference frames. An invariance, more general than Einstein's general covariance is to be involved as to both classes of reference frames unifying them. Its essence is the unification of the discrete and cotnitinuous (smooth). That idea underlies implicitly quantum mechanics for Bohr's principle that it study the system of quantum microscopic entities and the macroscopic apparatus desribed uniformly by the smmoth equations of classical physics. (shrink)