We introduce the notion of positive strong amalgamation property and we investigate some universal forms and properties of this notion. Considering the close relationship between the amalgamation property and the notion of complete theories, we explore the fundamental properties of positively complete theories, and we illustrate the behaviour of this notion by bringing changes to the language of the theory through the groups theory.

Generalizedn-gons are certain geometric structures (incidence geometries) that generalize the concept of projective planes (the nontrivial generalized 3-gons are exactly the projective planes).In a simplified world, every generalizedn-gon of finite Morley rank would be an algebraic one, i.e., one of the three families described in [9] for example. To our horror, John Baldwin [2], using methods discovered by Hrushovski [7], constructed ℵ1-categorical projective planes which are not algebraic. The projective planes that Baldwin constructed fail to be algebraic in a dramatic (...) way.Indeed, every algebraic projective plane over an algebraically closed field is Desarguesian [12]. In particular, an algebraically closed field (isomorphic to the base field) can be interpreted in every one of them. However, in the projective planes that Baldwin constructed, one cannot even interpret an infinite group.In this article we show that the same phenomenon occurs for the generalizedn-gons ifn≥ 3 is an odd integer. For each suchnwe constructmany nonisomorphic generalizedn-gons of finite Morley rank that do not interpret an infinite group. As one may expect, our method is inspired by Hrushovski and Baldwin, and we follow Baldwin's line of approach. Quite often our proofs are a verification of the fact that the proofs of Baldwin [2] forn= 3 carry over to an arbitrary positive odd integern(which is sometimes far from being obvious). As in [2], we begin by defining a certain collection of finite graphsK* and a binary relation ≤ on these graphs. We show that (K*, ≤) satisfies the amalgamation property. (shrink)

The class DA of diagonalizable algebras enjoys the interpolation property . Using LDA-Gentzen System corresponding to DA, we show that it has the strong amalgamation property as well.

In this paper, we introduce the notion of $${\textbf{K}} $$ -rank, where $${\textbf{K}} $$ is a strong amalgamation Fraïssé class. Roughly speaking, the $${\textbf{K}} $$ -rank of a partial type is the number “copies” of $${\textbf{K}} $$ that can be “independently coded” inside of the type. We study $${\textbf{K}} $$ -rank for specific examples of $${\textbf{K}} $$, including linear orders, equivalence relations, and graphs. We discuss the relationship of $${\textbf{K}} $$ -rank to other ranks in model theory, including (...) dp-rank and op-dimension (a notion coined by the first author and C. D. Hill in previous work). (shrink)

Various arguments have been given against positive euthanasia, but little attention has been given to the question of whether these arguments are uniformly effective in all contexts. There appears to be a range of cases, involving non-voluntary killing of irreversibly unconscious patients, in which these arguments do not succeed. Various reasons have been given in support of positive killing in such cases. It can be argued that there is a range of cases for which a policy of allowing (...) positive killing is morally required. However, currently there are legal obstacles to implementing such a policy. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 273 Verene, Donald Phillip. Vico's Science of Imagination. Ithaca, New York: Cornell University Press, 1981, Pp. 227. $19.5o. In Chapter 1 (Introduction: Vico's Originality), Verene announces two principal concerns, a two-fold approach, and the predominant contention of his study.. 1. Principal concerns: "to consider the philosophical truth of Vico's ideas themselves, rather than to examine their historical character" (p. 19); to consider "the importance of Vico's conception (...) of barbarism for understanding present society" (p. 28). 2. Two-fold approach: "to interpret the central theses of Vico's thought" from the inside in the spirit of the whole and, at the same time, "to develop the problems of Vico's philosophy themselves" (pp. 19--21 ). 3. Predominant contention: "that Vico's ideas constitute a philosophy of recollective universals which generates philosophical understanding fronl the image, not the rational category. This approach regards imagination as a method of pfiilosophical thought" (p. 19) and the imaginative universal as "a key to his conception of knowledge" (p. 67). Vico's philosophy is depicted and characterized by Verene as fi)llows. Beginning with the imagination (fantasia) as an original and independent power of mind, Vico builds his philosophy on the image, the imaginative universal, thereby creating a position outside Western philosophy as traditionally understood. His New Science is a process of recollective fantasia, a kind of memory, and the system built constitutes a system of memory for all of human reality. By means of his concept of memory, Vico works his way back to the world of original thought, the mythicopoeticfantasia of the first men. His discovery of the imaginative universal as their way of thinking and their kind of knowledge establishes a new genetic origin for philosophical thought. Recollective fantasia constitutes the subject-matter and form of Vico's science itself', i.e., the term designates a type of nlemory through which the New Science is acconlplished as well as the type of thought from which it must be understood. "The New Science is a metaphysical fable, h creates a vera narratio of the recollectire imagination. The storia ideale eterna is an ideal trnth, but not an a priori or fictional one. As the master image of the recollective mind, it precisely contains all of the human event. Metaphysical truth, achieved through the exercise of.[antasia.., is generated out of the mind itself.., as images that actually contain the providential structure of reality" (p. 125). Vico's per|ornlative science "is man's true production of a knowledge of" his own nature" (p. 133). "The proof of the science is found through the reader making it for himself" (p. 156). What is the "recollective imaginative universal"? (a term coined by Verene) as distinguished from the universale fantastico? Vico identifies the latter quite simply. Poetic imagination, he tells us, was active in the first men who, "not being able to form intelligible class concepts of things, had a natural need to create poetic characters ; that is, imaginative class concepts or universals, to which, as to certain models or ideal portraits, to reduce all the particular species that resembled them." (The New Science of Giambattista Vico, trans. Thomas Goddard Bergin and Max Harold Fisch. Cornell University Press, 1968; orig. pub. 1948, w ) Thus in the theological age, 274 HISTORY OF PHILOSOPHY "Jove was born naturally in poetry as a divine character or imaginative universal, to which everything having to do with the auspices was referred by all the ancient gentile nations, which must therefore all have been poetic by nature" (9 381). In the age of heroes, Achilles embodies the idea of valor common to all strong men and Ulysses the idea of prudence common to all wise men (9 403). The myths, fables, and allegories brought to birth by poetic imagination were true stories for their makers. Imaginative universals or genera, "as the human mind later learned to abstract forms and properties from subjects, passed over into intelligible genera, which prepared the way for philosophers.... " (9 934)- Abstracting, categorizing, and predicating on the basis of properties in common, the philosophers in their intelligible class concepts no hmger think in the same manner as the first men did... (shrink)

This paper explores the topic of meaning and its relation to symbolism through a contrastive reading of Whitehead’s 1927 Barbour-Page Lectures alongside the contemporary anthropologist Roy Wagner’s Symbols that Stand for Themselves. Despite their adoption of different registers of inquiry, a complementary relation may be posited between the two approaches. In particular, Whitehead’s emphasis on the foundational nature of symbolic reference within experience and its extendedness beyond merely human contexts may be grafted productively onto Wagner’s discussion of the “orders of (...) trope’”and “figure-ground reversal” within the formation of meaning in language. The argument is exemplified through reference to two contexts within Western culture where the play of symbol and meaning is strikingly evident—the Christian Eucharist and the contemporary sociological pervasiveness of motifs of screens and screening. (shrink)

Let L be a finite relational language and α=(αR:R ∈ L) a tuple with 0 < αR ≤1 for each R ∈ L. Consider a dimension function $ \delta _\alpha (A) = \left| A \right| - \sum\limits_{R \in L} {\alpha {\mathop{\rm Re}\nolimits} R(A)} $ where each eR(A) is the number of realizations of R in A. Let $K_\alpha $ be the class of finite structures A such that $\delta _\alpha (X) \ge 0$ 0 for any substructure X of A. We (...) show that the theory of the generic model of $K_\alpha $ is AE-axiomatizable for any α. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Barrow and Newton E. W. STRONG As E. A. Buxrr HAS ADDUCED,Isaac Barrow (1630-1677) in his philosophy of space, time, and mathematical method strongly influenced the thinking of Newton: The recent publication of an early paper written by Newton (his De gravitatione et aequipondio fluidorum)2 affords evidence not known to Burtt of Newton's indebtedness in philosophy to Barrow, his teacher. Prior to its publication in 1962, this paper (...) was utilized by Alexandre Koyrd in his essay, "Newton and Descartes," 3 a study based on the third Horblit Lecture in the History of Science which he gave at Harvard University, March 8, 1961. Koyr8 maintains that there is a radical opposition in Newton's Principia not only to Descartes' purely scientific theories but also to the Cartesian philosophy. Yet, as he remarks, "we do not find in the Principia an open criticism of the philosophy of Descartes.... " He attributes this fact principally "to the very structure of the Principia: it is essentially a book on rational mechanics, which provides principles for physics and astronomy. In such a book there is a normal place for the discussion of Cartesian optics, but not of the conception of the relations of mind and body, and other such things." Koyrd asserts, nonetheless, that the criticism is not absent. It lurks in Newton's carefully worded definitions of fundamental concepts--those of space, time, motion, and matter--and becomes more apparent in the Optice of 1706 and in the second odition of the Principia. In support of this argument, he makes much of young Newton's unfini.~hed paper. He holds that this essay is of exceptional value "as it enables us to get some insight into the formation of Newton's thought, and to recognize that preoccupation with philosophic problems was not an external additatmentum but an integral dement of his thinking." 4 As concerns "young Newton's conception of space in its being and in its relation to God and time," Koyrd remarks that we learn from this essay The Metaphysical Foundations of Modern Physical Science (New York, 1927), p. 144. A. Rupert Hall and Marie Boas Hall, Unpublished Scientific Papers of Isaac Newton (Cambridge, 1962), Introduction, pp. 75-88; Latin text, pp. 90-121; English translation, pp. 121156. " Newtonian Studies (Harvard University Press, 1965), pp. 53-114. " Newtonian Studies, pp. 82-83. In his De gravitatione et aequipondio fluidorum, Newton is indeed engrossed with philosophic problems. With regard, however, to the announced purpose of his paper, namely, "to treat of the science of gravity and solid bodies in fluids by two methods," does Newton represent kis metaphysical "explanation of the nature of body" as an element of his science essential to its completeness7 He does not do so. At the end of his explanation he remarks: "I have already digressed enough; let us return to the main theme." He proceeds to set forth fifteen more definitions and then turns to the demonstration of two "Propositions on Non-Elastic Fluids." [155] 156 HISTORY OF PHILOSOPHY "that space is necessary, eternal, immutz~ble, and unmovable, that though we can imagine that there is nothing in space we cannot think space is not.., and that if there is no space, God would be nowhere. We learn also that all points of space are simultaneous and that, therefore, the divine omnipresence does not introduce composition in God.... " What we here learn from Newton about space in confutation of Descartes is to be found in Barrow's tenth mathematical lecture, "'Of Space, and Impenetrability." 5 In this lecture, Barrow opposes both Descartes and Hobbes. He objects, as does Newton, to the position taken by Descartes in his Principia Philosophiae, namely, "it is necessary.forMatter to be infinitely extended." He proceeds, as does Newton, to show how "very much Cartesius's great Subtility has failed him in this Case" to conclude that there is space empty of matter and distinct from magnitude from which an infinity of matter cannot be deduced. The correspondence of arguments tendered by Barrow and Newton indicates that the tenth lecture constituted a source from which Newton gleaned principal objections to Descartes' Principia Philosophiae. Although Koyr~ makes reference to Burtt's... (shrink)

Knee proprioception deficits and neuroplasticity have been indicated following injury to the anterior cruciate ligament. Evidence is, however, scarce regarding brain response to knee proprioception tasks and the impact of ACL injury. This study aimed to identify brain regions associated with the proprioceptive sense of joint position at the knee and whether the related brain response of individuals with ACL reconstruction differed from that of asymptomatic controls. Twenty-one persons with unilateral ACL reconstruction of either the right or left knee, as (...) well as 19 controls matched for sex, age, height, weight and current activity level, performed a knee joint position sense test during simultaneous functional magnetic resonance imaging. Integrated motion capture provided real-time knee kinematics to activate test instructions, as well as accurate knee angles for JPS outcomes. Recruited brain regions during knee angle reproduction included somatosensory cortices, prefrontal cortex and insula. Neither brain response nor JPS errors differed between groups, but across groups significant correlations revealed that greater errors were associated with greater ipsilateral response in the anterior cingulate, supramarginal gyrus and insula. This is the first study to capture brain response using fMRI in relation to quantifiable knee JPS. Activated brain regions have previously been associated with sensorimotor processes, body schema and interoception. Our innovative paradigm can help to guide future research investigating brain response to lower limb proprioception. (shrink)

This essay seeks to characterize one of the leading ideas in Bhaṭṭa Jayanta's Nyāyamañjarī, the fundamental role that the idea of complexity plays in its theory of knowledge. The appeal to the causally complex nature of any event of valid awareness is framed as a repudiation of the lean ontology and epistemology of the Buddhist theorists working in the tradition of Dharmakīrti; for Jayanta, this theoretical minimalism led inevitably to the inadmissible claim of the irreality of the world outside of (...) consciousness. In countering this Buddhist position, Jayanta adopts some of his opponents’ characteristic terminology, most notably in his use of sāmagrī, “causal complex” itself. He resituates this borrowed vocabulary within a strong appeal to the theory of the kārakas or the semantic roles detailed by grammarians since the time of Pāṇini. Possibly borrowing this sāmagrī-kāraka amalgam from the Buddhist grammarian-epistemologist Jinendrabuddhi, Jayanta uses it as a point of departure for a sustained attack on the views of Dharmottara, who Jayanta understood as offering the most advanced and most problematic Buddhist philosophical position available in his time and place. (shrink)

The President’s Council on Bioethics has addressed the moral status of human preembryos in its reports on stem cell research and human therapeutic cloning. Although the Council has been criticized for being hand-picked to favor the right-to-life viewpoint concerning human preembryos, it has embraced the idea that the right-to-life position should be defended in secular terms. This is an important feature of the Council’s work, and it demonstrates a recognition of the need for genuine engagement between opposing sides in the (...) debate over stem cell research. To promote this engagement, the Council has stated in secular terms several arguments for the personhood of human preembryos. This essay presents and critiques those arguments, and it concludes that they are unsuccessful. If the best arguments in support of the personhood of human preembryos have been presented by the Council, then there are no reasonable secular arguments in support of that view. (shrink)

We study the amalgamation property in positive logic, where we shed light on some connections between the amalgamation property, Robinson theories, model-complete theories and the Hausdorff property.

Based on historical comparisons among master-pupil chains and other aspects of social networks among philosophers, some prmciples are suggested regarding long-term intellectual change. The higher the eminence ofphilosophers, the more tightly they are connected to mtergenerational chains of other eminent philosophers, and to horizontal circles of the intellectual community. Intellectual creativity proceeds through the contemporaneous development of rival positions, dividing up the available attention space in the intellectual community. Strong thought-communities, those that have strong external support for their (...) institutional base, subdivide to maximize internal distinctiveness; weakly supported thought-communities disappear or amalgamate by syncretism. External conditions thus affect the content of ideas indirectly by affecting the space available in the mternal field of the intellectual community. The content of philosophies, the degree of abstraction and self-conscious reflection upon intellectual operations, depends on how many generations intellectual networks maintain continuity under conditions of creative rivalry. New positions are produced by competitive appropriation of prior ideas and by negation of preexisting positions along the lines of greatest organizational rivalry. (shrink)

We continue the analysis of foundations of positive model theory as introduced by Ben Yaacov and Poizat. The objects of this analysis are $h$-inductive theories and their models, especially the “positively” existentially closed ones. We analyze topological properties of spaces of types, introduce forms of quantifier elimination, and characterize minimal completions of arbitrary $h$-inductive theories. The main technical tools consist of various forms of amalgamations in special classes of structures.

There is a well-established correspondence between interpolation and amalgamation for algebraizable logics that satisfy certain additional assumptions. In this paper, we introduce the Robinson property of a logic and show that a conditionally algebraizable logic without any additional assumptions has the Robinson property if and only if the corresponding class of Lindenbaum–Tarski algebras has the amalgamation property. Moreover, we give the logical characterization of the strong amalgamation property, solving an open problem of Andréka–Németi–Sain. It is also (...) shown that given the mentioned extra assumptions the Robinson property implies the interpolation property. As conditionally algebraizable logics cover algebraizable logics as well as various quantifier logics such as classical first order logic, our results yield a generalization of some of the results concerning interpolation and amalgamation. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Before Confucius: Studies in the Creation of the Chinese ClassicsJohn S. MajorBefore Confucius: Studies in the Creation of the Chinese Classics. By Edward L.Shaughnessy. Albany: State University of New York Press, 1997. Pp. ix + 262. $19.95.The eight essays in this collection (six of them previously published) show the combination of boldness and erudition that is characteristic of all of Edward Shaughnes-sy's work. The results of his investigations (...) are always interesting and felicitously expressed, and if one sometimes resists following the author quite so far down the evidentiary and interpretive road as he himself is willing to go, the intellectual journey is always a rewarding one.The common thread in these essays is Shaughnessy's belief that the Chinese classics, although admittedly written in their final form at a time well after the era [End Page 314] to which they refer-that is, during the Warring States Period or even the Han—preserve much material that authentically refers to, and was originally written more-or-less contemporaneously with, events of the Western Zhou era. He adduces evidence from bronze inscriptions, archaeologically recovered texts, positional and calendrical astronomy, and other securely datable sources to argue for the authenticity of portions of the classics, notably the Book of Documents, the Book of Poetry, and the Book of Changes.Publication of these essays comes just when the antiquity of the classics is being challenged more vigorously than at any time since the "doubting antiquity" movement of the 1920s. In particular, the evidence presented by Bruce and Taeko Brooks and their associates in meetings of the Amherst-based Warring States Working Group tends to support a view not only that the classics were written down much later than the events they purport to describe (almost everyone agrees about that) but that much of the "historical" material in the classics is closer to legend than to fact, and may well represent later confabulation for purposes of political or philosophical advantage. Shaughnessy's Before Confucius and the Brookses' The Original Analects (New York: Columbia University Press, 1998) strikingly represent two poles of the contemporary disagreement about the nature and authenticity of the Chinese classics.As a charter member of the Warring States Working Group who has consistently dissented from its more radical antiquity-doubting positions, I am perhaps unusually well placed to comment on the questions of dating raised by Shaughnessy's work. It seems to me that the key to the synthesis that I suspect will form over the next decade or so is the nature of the archaeologically recovered texts of the Warring States Period that have emerged from the ground in such profusion in recent decades, and continue to do so. These attest to several unexpected things, including the extent to which texts were possessed, copied, and circulated at the time; the implied high level of literacy among the contemporary ruling class; the degree to which assemblages of texts from individual tombs seem not to represent schools, master-disciple lineages, or clear doctrinal or ideological groupings, but rather to testify to a strong eclectic tendency among the contemporary literate elite; and the degree to which recovered texts anticipate later received texts, but in variant and/or partial form (for example, the Guodian Laozi text, recognizably Laozi but a far cry from the complete, received Daodejing).In view of all this, it seems to me reasonable to say that on the one hand a fair amount of material may well have come down to later ages from the Western Zhou and Spring and Autumn periods (through many vicissitudes of copying, recitation, variation, repairs to broken and misarranged bundles of slips, and so on), to enter wide circulation as texts in the Warring States Period. On the other hand, the late Warring States and Han editors of the textual tradition that had come down to them collated, amalgamated, sorted, augmented, and otherwise shaped the texts to a somewhat larger degree than has sometimes been supposed, and it is extremely unlikely that any of the Chinese classics were in circulation in anything like their received form at the end of the Spring and Autumn periods. Thus, while I... (shrink)

The different “postmodern” philosophies that arose from the 1970s to the 1990s have often been considered as a kind of irrationalist-skeptical-relativist “ideology” or assorted amalgam, which in our time would dangerously take over the philosophical academy and western cultures, with grave risk for universalist or simply rationalist projects. Nevertheless, as the title of this article shows, a closer examination of some trends of postmodern thought would be able to perceive that they not only are uncomfortable with the label “relativist,” “irrationalist” (...) or “skeptical,” but also that they offer substantial arguments against, for example, the main theses of relativism. Naturally, none of these trends has any qualms about abominating universalism as well (the presumed mortal enemy of the relativists). Thus the most sensible conclusion would be that what really seems erroneous to authors such as those we shall approach here is the presumed dilemma (presented as inevitable) between relativism and universalism (it is curious that, at least as far as faith in the existence of such a dichotomy is concerned, these presumed irreconcilable enemies, which both the relativists and the universalists believe themselves to be, are plainly in agreement). Only if they subscribe to such a rejection of this dilemma could it be explained that important thinkers of the heterogeneous postmodern group (such as those whom I propose to have a dialogue with in this article) have scorned, on the one hand, any and all universal project of rationality, but have also strongly disallowed relativist proposals (just as, naturally, they have likewise taken advantage of the issue to deny their presumed adherence to relativism as such). This idea, however, has not been understood by a large part of the scholars involved today in epistemology and practical philosophy (the two philosophical specialties in which one most frequently faces the question of relativism). To approach this understanding, therefore, perhaps it would not be amiss to review the different arguments that some postmodern thinkers use against relativism. Specifically, we shall tale a look at the reasoning in this sense that has come from Gianni Vattimo (1936), Paul K. Feyerabend (1924-1994), and Richard Rorty (1931). All of them have too often had to suffer from the suspicion of being considered as relativists. To absolve philosophers such as these from such an accusation seems to be a sine qua non condition for understanding their true position towards the universalism versus relativism dilemma. (shrink)

This article studies the existence of positive periodic solutions for a class of strongly coupled differential systems. By applying the fixed point theory, several existence results are established. Our main findings generalize and complement those in the literature studies.

In lieu of an abstract, here is a brief excerpt of the content:Response to Lauren Kapalka Richerme, "The Diversity Bargain and the Discourse Dance of Equitable and Best," Philosophy of Music Education Review 27, no. 2 (Fall, 2019)Nasim NiknafsI was asked to write a response to Lauren Richerme's convincing research on why and how one should distinguish between "equitable educational practices"1 and what she calls following Ellen Berry the "diversity bargain" where equity as the second-best option has always taken a (...) hit from the more dashing diversity. If I may metaphorically put this conversation into a romantic comedy, equity is always the wingperson of color to diversity as the main protagonist; by the end of the show it is the main protagonist who survives the hardship and reaches salvation, be it a long-lost love, an oasis of sorts, or making it to the finish line. The rest of the cast have the function of complementing and highlighting the main actor but never substituting for it; or they are as Homi Bhabha would say, "almost the same but not quite."2 For the sake of filling in the blank of let's-add-more-color-into-it, the genuine conversation over the nuances of equitable practices gets undermined and diffused of its poignancy. And this is what Richerme is arguing against: let us not forget that a more significant challenge than a mere technicolor presence is at play. In that, my response to Richerme's essay would [End Page 215] not be so much of a response but a grand nod, a body gesture, an embedded signal of approval between two human beings born and raised in two different parts of planet earth who after years of diverse and perhaps un-equitable educational access ended up in the same room at the same time. Thus, my nod to Richerme also originated from personal experiences and intimate familiarities with unequitable educational access. Yes, people of color can be assets to their institutions and their corresponding fields who add to the diversity of knowledge creation practices, but it is not people of color's project or responsibility to act as the trophy to alleviate the unhappy conscience of educational malpractice or give a helping hand to the main protagonists for whom the scenario has already been written. Undoubtedly, they can take on that role if they want to, but it is only contingent upon where their desires lie not where they should lie.I strongly agree with Richerme's claim that music classrooms and I would add any classroom and learning environment should be a place and space for "sharing stories and insights"3 to not only learn about the content material whatever it may be but to learn to empathize with one another, understand positive and negative human behaviors toward humans and their environment, and act against discriminatory practices, racial, ethnic, religious, and gender prejudices, and to the point of Richerme's essay, unequitable practices that are insistent in today's political climate on a global scale.At this very juncture I diverge not from Richerme's fine thesis and argumentation, but from the larger issue of the premise of her arguments grounded on Thomas Green's educational framework.4 Green argues that the "rank order of political arguments that can be mustered in support of the [educational] system … [is] roughly as follows": (1) the fundamental or compelling interests of the state; (2) the aggregate of individual or parental interests; (3) societal interests; and (4) educational goods for their own sake."5 Following Green's framework Richerme analyzes contemporary music education initiatives in relation to the differing political strengths of each group of stakeholders: the state, parents, society, and educational goods for their own sake.There is a sense of mistrust in the local and national government implied by Green's framework, reminding one of the cumulative mistrust of the elite by U.S. citizens. Years of neglect, condescension, and lack of attention to the real and tangible needs of people amalgamated into what today one sees as white nationalism, plutocracy, and protectionism across borders. Green wrote his book, Predicting the Behavior of the Educational System, in 1980; historically the world order was increasingly metamorphosing and establishing itself... (shrink)

We prove a couple of results on NTP2 theories. First, we prove an amalgamation statement and deduce from it that the Lascar distance over extension bases is bounded by 2. This improves previous work of Ben Yaacov and Chernikov. We propose a line of investigation of NTP2 theories based on S1 ideals with amalgamation and ask some questions. We then define and study a class of groups with generically simple generics, generalizing NIP groups with generically stable generics.

We show that not all epimorphisms are surjective in certain classes of infinite dimensional cylindric algebras, Pinter's substitution algebras and Halmos' quasipolyadic algebras with and without equality. It follows that these classes fail to have the strong amalgamation property. This answers a question in [3] and a question of Pigozzi in his landmark paper on amalgamation [9]. The cylindric case was first proved by Judit Madarasz [7]. The proof presented herein is substantially different. By a result of (...) Németi, our result implies that the Beth-definability Theorem fails for certain expansions of first order logic. (shrink)

Biggar’s excellent book allows examination of the adequacy of Christian just war theory over key events of the last century’s British military and interventionary history. I attempt infiltration of key positions behind a creeping barrage, following the contours of Biggar’s arguments, finally firing corrosive Greek fire into the deep Latinate redoubts of Fortresses Augustine and Aquinas. I shall explain why the audit of Biggar’s ambitious defensive system shows a very mixed balance sheet for just war theory.

We study when classes can have the disjoint amalgamation property for a proper initial segment of cardinals. Theorem A For every natural number k, there is a class $K_k $ defined by a sentence in $L_{\omega 1.\omega } $ that has no models of cardinality greater than $ \supset _{k - 1} $ , but $K_k $ has the disjoint amalgamation property on models of cardinality less than or equal to $\mathfrak{N}_{k - 3} $ and has models of (...) cardinality $\mathfrak{N}_{k - 1} $ . More strongly, we can have disjoint amalgamation up to $\mathfrak{N}_\alpha $ for α > ω, but have a bound on size of models. Theorem B For every countable ordinal a, there is a class $K_\alpha $ defined by a sentence in $L_{\omega 1.\omega } $ that has no models of cardinality greater than $ \supset _{\omega 1} $ , but K does have the disjoint amalgamation property on models of cardinality less than or equal to $\mathfrak{N}_\alpha $ . Finally we show that we can extend the $\mathfrak{N}_\alpha $ to $ \supset _\alpha $ in the second theorem consistently with ZFC and while having $\mathfrak{N}_i \ll \supset _i $ for 0 > i < α. Similar results hold for arbitrary ordinals α with |α|= K and $L_{k + ,\omega } $. (shrink)

We use certain strong Q-reducibilities, and their corresponding strong positive reducibilities, to characterize the hyperimmune sets and the hyperhyperimmune sets: if A is any infinite set then A is hyperimmune (respectively, hyperhyperimmune) if and only if for every infinite subset B of A, one has \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{K}\not\le_{\rm ss} B}$$\end{document} (respectively, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{K}\not\le_{\overline{\rm s}} B}$$\end{document}): here \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} (...) \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\le_{\overline{\rm s}}}$$\end{document} is the finite-branch version of s-reducibility, ≤ss is the computably bounded version of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\le_{\overline{\rm s}}}$$\end{document}, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{K}}$$\end{document} is the complement of the halting set. Restriction to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^0_2}$$\end{document} sets provides a similar characterization of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^0_2}$$\end{document} hyperhyperimmune sets in terms of s-reducibility. We also show that no \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A \geq_{\overline{\rm s}}\overline{K}}$$\end{document} is hyperhyperimmune. As a consequence, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\deg_{\rm s}(\overline{K})}$$\end{document} is hyperhyperimmune-free, showing that the hyperhyperimmune s-degrees are not upwards closed. (shrink)

Animal rights positions face the ‘predator problem’: the suggestion that if the rights of nonhuman animals are to be protected, then we are obliged to interfere in natural ecosystems to protect prey from predators. Generally, rather than embracing this conclusion, animal ethicists have rejected it, basing this objection on a number of different arguments. This paper considers but challenges three such arguments, before defending a fourth possibility. Rejected are Peter Singer’s suggestion that interference will lead to more harm than good, (...) Sue Donaldson and Will Kymlicka’s suggestion that respect for nonhuman sovereignty necessitates non-interference in normal circumstances, and Alasdair Cochrane’s solution based on the claim that predators cannot survive without killing prey. The possibility defended builds upon Tom Regan’s suggestion that predators, as moral patients but not moral agents, cannot violate the rights of their prey, and so the rights of the prey, while they do exist, do not call for intervention. This idea is developed by a consideration of how moral agents can be more or less responsible for a given event, and defended against criticisms offered by thinkers including Alasdair Cochrane and Dale Jamieson. (shrink)

A sufficient condition for an extension of positive logic with strong negation to be characterized by a class of finite trees is given.

We show that there is a restriction, or modification of the finite-variable fragments of First Order Logic in which a weak form of Craig's Interpolation Theorem holds but a strong form of this theorem does not hold. Translating these results into Algebraic Logic we obtain a finitely axiomatizable subvariety of finite dimensional Representable Cylindric Algebras that has the Strong Amalgamation Property but does not have the Superamalgamation Property. This settles a conjecture of Pigozzi [12].

Strong comic immoralism maintains that every time a humorous demonstration (for example, a joke) involves a moral defect, it is enhanced aesthetically in virtue of having this moral defect. I want to show that strong comic immoralism is a coherent position, that it is possible to defend, and that there is, in fact, some reason to defend it. By doing this, my hope is that, moving forward, those who are interested in questions about the relationship between immorality and (...) the aesthetic value of jokes will take more seriously the objections that may be presented against their views by the strong comic immoralist, rather than claiming that “no one on this side of Satan” would be one. (shrink)

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

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

This chapter focuses on the issue of methodological usefulness of a strong versus weak adaptationist position in attempting to gain significant insight and to make scientifically important advances and discoveries in human cognition. Strong adaptationism holds that complex design is best explained by task-specific adaptations to particular ancestral environments; whereas weak adaptationism claims that we should not assume that complex design is the result of such narrowly determined task- or niche-specific evolutionary pressures in the absence of substantial corroborating (...) evidence. It argues that in cases of certain domain-specific cognitive competencies strong adaptationism has proven useful but not necessary to recent progress in the field. In other cases, a weak adaptationist strategy has been arguably most productive in advancing scientific understanding, without precluding that the structures uncovered by other means are actually adaptations. (shrink)

We prove that each ∀1 free amalgamation class K over a finite relational language L admits a countable generic structure M isometrically embedding all countable structuresin K relative to a fixed metric. We expand L by infinitely many binary predicates expressingdistance, and prove that the resulting expansion of K has a model companion axiomatizedby the first-order theory of M. The model companion is non-finitely axiomatizable, evenover a strong form of the axiom scheme of infinity.

Fodor's and Pylyshyn's stand on systematicity in thought and language has been debated and criticized. Van Gelder and Niklasson, among others, have argued that Fodor and Pylyshyn offer no precise definition of systematicity. However, our concern here is with a learning based formulation of that concept. In particular, Hadley has proposed that a network exhibits strong semantic systematicity when, as a result of training, it can assign appropriate meaning representations to novel sentences (both simple and embedded) which contain words (...) in syntactic positions they did not occupy during training. The experience of researchers indicates that strong systematicity in any form is difficult to achieve in connectionist systems.Herein we describe a network which displays strong semantic systematicity in response to Hebbian, connectionist training. During training, two-thirds of all nouns are presented only in a single syntactic position (either as grammatical subject or object). Yet, during testing, the network correctly interprets thousands of sentences containing those nouns in novel positions. In addition, the network generalizes to novel levels of embedding. Successful training requires a, corpus of about 1000 sentences, and network training is quite rapid. The architecture and learning algorithms are purely connectionist, but classical insights are discernible in one respect, viz, that complex semantic representations spatially contain their semantic constituents. However, in other important respects, the architecture is distinctly non-classical. (shrink)

One of the most plausible and widely discussed examples of strong emergence is molecular structure. The only detailed account of it, which has been very influential, is due to Robin Hendry and is formulated in terms of downward causation. This paper explains Hendry’s account of the strong emergence of molecular structure and argues that it is coherent only if one assumes a diachronic reflexive notion of downward causation. However, in the context of this notion of downward causation, the (...) strong emergence of molecular structure faces three challenges that have not been met and which have so far remained unnoticed. First, the putative empirical evidence presented for the strong emergence of molecular structure equally undermines supervenience, which is one of the main tenets of strong emergence. Secondly, it is ambiguous how the assumption of determinate nuclear positions is invoked for the support of strong emergence, as the role of this assumption in Hendry’s argument can be interpreted in more than one way. Lastly, there are understandings of causation which render the postulation of a downward causal relation between a molecule’s structure and its quantum mechanical entities, untenable. (shrink)

In this paper we extend of the notion of algebraically closed given in the case of groups and skew fields to an arbitrary h-inductive theory. The main subject of this paper is the study of the notion of positive algebraic closedness and its relationship with the notion of positive closedness and the amalgamation property.

When someone believes something that is justified for her, what part does the subject play in her state of being justified? I will answer this question by developing a strong internalist account of justification according to which the justification of a believing for a subject consists in her having grounds for her belief, and holding the belief in recognition of those grounds. But the internalist theory I defend incorporates key elements of reliabilism into its account. Using perception as a (...) model for justification, I show how ordinary perceivers would appeal to external factors to support their perceptual beliefs, and normally suppose that their beliefs are reliably connected to the objects their beliefs are about. I find in this feature of our common justificatory practice a sufficient basis for positing an externalist condition on justification—namely that subjects are only justified if their beliefs are reliably connected to their objects. (shrink)

This paper consists of a detailed analysis of how the participants in a debate build their emotional position during the interaction and how such a position is strongly related to the conclusion they defend. In this case study, teenage Mexican, students, arguing about access to drinking water, display extensive discursive work on the emotional tonality given to the issue. Plantin’s methodological tools are adopted to follow two alternative emotional framings produced by disagreeing students, starting from a common, highly negative, thymic (...) tonality. Through the analysis of four parameters we describe how the emotional dimension of schematization is argumentatively relevant. In authentic discourse, it is impossible to separate emotion from reason. The conclusion section discusses the implications for the design of argumentation-based pedagogical activities. (shrink)

There is growing international interest in the choice of socioeconomic indicators for health research. This study used a combination of standard and novel methods to compare three occupation-based measures of social position in terms of their ability to explain variation and measure inequality in self-assessed health. The recently developed National Statistics Socioeconomic Classification (NS-SEC) is compared with its predecessor, the Registrar General64 living in private households in Scotland, logistic regression models are used to compare the classifications' ability to predict self-assessed (...) health. Concentration indices are estimated to compare how well they capture inequality in self-assessed health. The study shows that all three classifications are strongly associated with self-assessed health, though the associations are heavily attenuated by adjustment for one another and for other measures of social position. Despite their differing theoretical bases, the three are closely related. No evidence is found that any of them systematically under- or overstate the extent of inequality in self-assessed health in either men or women, and the extent to which they measure independent dimensions of social inequality is questioned. It is concluded that the availability of the new classifications is unlikely to transform our understanding of the extent or the causes of socioeconomic inequality in health, but provides useful opportunities for sensitivity analysis. (shrink)

We initiate the study of a generalization of Kim-independence, Conant-independence, based on the notion of strong Kim-dividing of Kaplan, Ramsey and Shelah. A version of Conant-independence was originally introduced to prove that all [Formula: see text] theories are [Formula: see text]. We introduce an axiom on stationary independence relations, essentially generalizing the “freedom” axiom in some of the free amalgamation theories of Conant, and show that this axiom provides the correct setting for carrying out arguments of Chernikov, Kaplan (...) and Ramsey on [Formula: see text] theories relative to a stationary independence relation. Generalizing Conant’s results on free amalgamation to the limits of our knowledge of the [Formula: see text] hierarchy, we show using methods from Conant as well as our previous work that any theory where the equivalent conditions of this local variant of [Formula: see text] holds is either [Formula: see text] or [Formula: see text] and is either simple or [Formula: see text]. We observe that these theories give an interesting class of examples of theories where Conant-independence is symmetric. This includes all of Conant’s examples, the small cycle-free random graphs of Shelah, and the (finite-language) [Formula: see text]-categorical Hrushovski constructions of Evans and Wong. We then answer Conant’s question on the existence of non-modular free amalgamation theories. We show that the generic functional structures of Kruckman and Ramsey are examples of non-modular free amalgamation theories. We also show that any free amalgamation theory is [Formula: see text] or [Formula: see text], while an [Formula: see text] free amalgamation theory is simple if and only if it is modular. Finally, we show that every theory where Conant-independence is symmetric is [Formula: see text]. Therefore, symmetry for Conant-independence gives the next known neostability-theoretic dividing line on the [Formula: see text] hierarchy beyond [Formula: see text]. We explain the connection to some established open questions. (shrink)

This research examined how strongly appraisals can differentiate positive emotions and how they differentiate positive emotions. Thirteen positive emotions were examined, namely, amusement, awe, challenge, compassion, contentment, gratitude, hope, interest, joy, pride, relief, romantic love and serenity. Participants from Singapore and the USA recalled an experience of each emotion and thereafter rated their appraisals of the experience. In general, the appraisals accurately classified the positive emotions at rates above chance levels, and the appraisal–emotion relationships conformed to (...) predictions. Also, the appraisals were largely judged by participants as relevant to their positive emotion experiences, and the appraisal–emotion relationships were largely consistent across the two countries. (shrink)

A question of Woodin asks if κ is strongly compact and GCH holds below κ, then must GCH hold everywhere? One variant of this question asks if κ is strongly compact and GCH fails at every regular cardinal δ < κ, then must GCH fail at some regular cardinal δ ≥ κ? Another variant asks if it is possible for GCH to fail at every limit cardinal less than or equal to a strongly compact cardinal κ. We get a negative (...) answer to the first of these questions and positive answers to the second of these questions for a supercompact cardinal κ in the context of the absence of the full Axiom of Choice. (shrink)

The health theories of Nordenfelt and Boorse are compared. Critical attention is focused on Nordenfelt's description of his theory as one of holistic welfare, contrasting with Boorse's analytical and statistical approach. Neither theory is found to give an entirely satisfactory account of ‘health’ in scientific medicine or common usage. Because Nordenfelt attenuates the ontological significance of organs and organ parts and simplifies the role of statistics, his theory is regarded as weakly holistic. Boorse underrates the importance of non-statistical evaluation. A (...) mediating position, termed ‘strong holism’ is suggested as a way of integrating normative and statistical elements in a more adequate health concept. (shrink)

We consider the strongest forms of enumeration reducibility, those that occur between 1- and npm-reducibility inclusive. By defining two new reducibilities which are counterparts to 1- and i-reducibility, respectively, in the same way that nm- and npm-reducibility are counterparts to m- and pm-reducibility, respectively, we bring out the structure of the strong reducibilities. By further restricting n1- and nm-reducibility we are able to define infinite families of reducibilities which isomorphically embed the r. e. Turing degrees. Thus the many well-known (...) results in the theory of the r. e. Turing degrees have counterparts in the theory of strong reducibilities. We are also able to positively answer the question of whether there exist distinct reducibilities ≤y and ≤a between ≤e and ≤m such that there exists a non-trivial ≤y-contiguous ≤z degree. (shrink)

Important positive as well as negative results on interpolation property in fragments of the intuitionistic propositional logic (INT) were obtained by J. I. Zucker in [6]. He proved that the interpolation theorem holds in purely implicational fragment of INT. He also gave an example of a fragment of INT for which interpolation fails. This fragment is determined by the constant falsum (), well known connectives: implication () and conjunction (), and by a ternary connective defined as follows: (p, q, (...) r)= df (pq)(pr).Extending this result of J. I. Zucker, G. R. Renardel de Lavalette proved in [5] that there are continuously many fragments of INT without the interpolation property. (shrink)

In this paper we study the relativized Lascar Galois group of a strong type. The group is a quasi-compact connected topological group, and if in addition the underlying theory T is G-compact, then the group is compact. We apply compact group theory to obtain model theoretic results in this note. -/- For example, we use the divisibility of the Lascar group of a strong type to show that, in a simple theory, such types have a certain model theoretic (...) property that we call divisible amalgamation. -/- The main result of this paper is that if c is a finite tuple algebraic over a tuple a, the Lascar group of stp(ac) is abelian, and the underlying theory is G-compact, then the Lascar groups of stp(ac) and of stp(a) are isomorphic. To show this, we prove a purely compact group-theoretic result that any compact connected abelian group is isomorphic to its quotient by every finite subgroup. -/- Several (counter)examples arising in connection with the theoretical development of this note are presented as well. For example, we show that, in the main result above, neither the assumption that the Lascar group of stp(ac) is abelian, nor the assumption of c being finite can be removed. (shrink)

The psychedelic psilocybin has shown promise both as treatment for psychiatric conditions and as a means of improving well-being in healthy individuals. In some jurisdictions (e.g., Oregon, USA), psilocybin use for both purposes is or will soon be allowed and yet, public attitudes toward this shift are understudied. We asked a nationally representative sample of 795 US Americans to evaluate the moral status of psilocybin use in an appropriately licensed setting for either treatment of a psychiatric condition or well-being enhancement. (...) Showing strong bipartisan support, participants rated the individual’s decision as morally positive in both contexts. These results can inform effective policy-making decisions around supervised psilocybin use, given robust public attitudes as elicited in the context of an innovative regulatory model. We did not explore attitudes to psilocybin use in unsupervised or non-licensed community or social settings. (shrink)