The chapter talks about Shel Silverstein's The Giving Tree, which is a favorite of many children, adults, and teachers. The story of a relationship between a boy and a tree is charming for, despite the vicissitudes of the relationship, the two end up together at the end, with the boy — now an old man — sitting contentedly on the tree — itself reduced to a mere stump. The book raises an important issue in the field (...) of environmental ethics. It asks us to recognize that between childhood and old age, people operating within the Western tradition of ethics are not mindful of the value that the non‐human beings in their environment have for them as well as for future generations. Harkening to such warnings, environmental ethicists have attempted to raise important issues about our relationship with the other beings that make up our world. (shrink)

In this paper, we investigate a new model theoretical tree property (TP), called the antichain tree property (ATP). We develop combinatorial techniques for ATP. First, we show that ATP is always witnessed by a formula in a single free variable, and for formulas, not having ATP is closed under disjunction. Second, we show the equivalence of ATP and [Formula: see text]-ATP, and provide a criterion for theories to have not ATP (being NATP). Using these combinatorial observations, we find (...) algebraic examples of ATP and NATP, including pure groups, pure fields and valued fields. More precisely, we prove Mekler’s construction for groups, Chatzidakis’ style criterion for pseudo-algebraically closed (PAC) fields, and the AKE-style principle for valued fields preserving NATP. We give a construction of an antichain tree in the Skolem arithmetic and atomless Boolean algebras. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Buddhist-Christian Studies 20 (2000) 151-165 [Access article in PDF] Santayana and Buddhism: The Choice between the Cross and the Bo Tree Paul Grimley KuntzEmory UniversitySantayana honors Gotama Buddha as a profound religious genius as well as an original philosopher. Gotama's way is genuine spiritual wisdom, and constantly compared with Christian mysticism as a way of enlightenment. It is therefore understandable that a Spaniard, who learned his catechism in (...) Ávila, and who was educated in the New England of Emerson and other Transcendentalists who honored Oriental wisdom, should have so much to say about the Buddha and Buddhism.The effort of this paper is to gather many of the isolated passages to give a coherent picture of Santayana and Buddhism. One difficulty to be overcome is that the philosopher rarely quotes his sources (the exception is a single quotation from Dasgupta). Although Santayana has numerous opinions, he does not reveal on which translations he has relied. Nor does he contrast different traditions of Buddhists. To overcome the vagueness of scholarship, I have used the volumes found in Widener Library: the sorts of books known to Santayana's dissertation director, Josiah Royce, and those of a sympathetic sort that had led Santayana as early as the writing of his dissertation on Rudolf Hermann Lotze to reject the latter's defiantly Christian and Western contempt for oriental "superstition." The sympathy can be expressed as similar to that of Schopenhauer in reading the Upanishads or Wilhelm von Humboldt in studying the Bhagavadgita. Santayana's study makes him aware of his Catholicism but he is unlike the Jesuit Dahlmann who attacks Buddhism as Nihilism. Santayana is more like his contemporaries who worked in psychology and philosophy of religion. Although Friedrich Heiler's work 1 and writings of James Bissett Pratt 2 were a bit too late to have influenced Santayana, comparison serves to illuminate and strengthen Santayana's conclusions. Perhaps Heiler is even more appropriate because Buddhistic insights remind him of those of St. Theresa. Santayana would support Pratt's view that Nirvana is not the annihilation of all desire but the extinguishing of evil passions. What Santayana finds congenial in Christian Neo-Platonism and in Spinoza, as well as in Buddhism, is the achievement of freedom of the spirit. 3 It has become a commonplace of world history that the two greatest founders of religion whose ways of salvation triumphed in Europe and in Asia respectively are the Christ and the Buddha. Philosophers of religion like Heiler accept both as saviors with a universal message, one, Jesus "the master of prayer" ("der Meister des Gebets"), the [End Page 151] other, Gotama "the master of contemplation" ("der Meister der Versenking"). Santayana is not concerned with the fact of the success of their missions, for there are indeed other triumphs such as Mohammed's Islam, and if it be classified as a religion, Marx's Communism. Santayana is hardly offering his services as a philosophic mediator, as Whitehead tries to do in Religion in the Making, to bring the two communities of faith to a closer approximation of a truly universal religion. 4Santayana reveals great personal depth as he ponders the contrast between the Gospel and the Fourfold Noble Truth. What is the appeal of Christ on the Cross dying "to save us?" What is the appeal of "the serene Buddha, lifting the finger of meditation and profound counsel?" 5 These questions are asked in a meditation in Soliloquies in England in the sympathetic way of those American philosophers who like Pratt have the option of remaining Christian or converting to Buddhism. William James might well have patted Santayana on the back for struggling with the alternatives, for wrestling with a live option. Probably because of Buddha's message of truth, Santayana has shifted from religion as poetry, which James considered "rotten," to how "a general truth about existence and experience" is symbolized poetically, which James would consider healthy.In answering the question "What does the cross signify?" Santayana strips away the "various analogies, legal, sentimental, or chivalrous," and he... (shrink)

Let S2S [WS2S] espectively be the storn [weak] monadic second order theory of the binary tree T in the language of two successor functions. An S2S-formula whose free variables are just individual variables defines a relation on T (rather than on the power set of T). We show that S2S and WS2S define the same relations on T, and we give a simple characterization of these relations.

The journal continues to publish translations of individual chapters of the book by the famous phenomenologist Michael Marder “The Philosopher’s Plant. An Inteellectual Herbarium”. Of the twelve stories, the fourth, “Augustine’s Pears”, and sixth “Maimonides Palm Tree” are selected. In the chapter “Augustine’s Pears” the first avowal in the Confessions of St. Augustine concerns the episode with the theft of pears, which he committed in the company of teenage friends. Today, most of us will perceive this theft as a (...) relatively innocent teenage prank. However, for Augustine, this act is symbolic, since, according to him, he did not crave pears, but forbidden fruit and the thrill of breaking the law. Whether these events actually took place is irrelevant. To demand to separate the real from the imaginary is to ignore the main message of Augustine and his method. The world for him is a matter of interpretation, an intermediate step towards the God. Everything empirically real pales in comparison with the “fictions” of faith, hope and love that pave the road to heaven. The separation of plant processes from plants themselves, life from continuous growth, and physiological activity from the mortal organism prevents their vitality. The fruit that does not rot in the guise of a good deed, and the memory that is eternally stored in God are theological and metaphysical fantasies that destroy the essence of the metaphor that carries them in itself. If the characteristic philosophical gestures of Augustine are spiritualization, interiorization and the use of allegories, then his ethics, although seeking legitimization in the discourse of natural law, is based on the obvious deprivation of life of its natural properties. By suppressing the plant within himself, Augustine excludes real plants from the sphere of moral significance. Although the fruits of the earth allegorically represent works of mercy, a merciful approach to plants is considered inappropriate. It is not surprising that Augustine shows almost no interest in the plants themselves, treating them as translucent screens through which the divine order shines through. If we want Augustine’s philosophy to remain relevant today, it is necessary to extract the ethical core from the shell of its theological denial of the world. Now that the transcendent absolute is no longer immune from questions, the certainty that the world exists for the sake of something external inevitably collapses. In the process of mourning the loss of the absolutes, one should remember the meaning of Augustine’s modified motto: Mundo frui! Enjoy the world! The chapter “Maimonides’ Palm Tree” is dedicated to Rabbi Moses Ben Maimon –Maimonides – presented a unified worldview based on the theories of his predecessors, and systematized religious laws in a code of fourteen volumes – “Repetition of the Torah”. Maimonides pays attention to everyday details, for example, what is allowed and what is forbidden to those who observe Sabbath; describes in detail the rules governing the sale, gifts and the right to use property. He demands that the stump with two shoots be left untouched from the olive tree. But palm trees can be uprooted because they do not give shoots – that is, these trees can be subjected to unlimited violence. The author calls the palm arbor sacra, thus referring to the concept of homo sacer introduced by J. Agamben. The statement of Maimonides – “man has an erroneous idea of himself and believes that the whole world exists only for his sake” – could well serve as a unifying slogan in today’s struggle against the domination of man over nature. “The Guide for the Perplexed”, the main philosophical work of Maimonides, contains clear and strict information about plants. Maimonides prefers to combine plants with inorganic substances rather than grouping plants together with animals. His “The Book of Cleanness” praises the cleansing properties of the soil, or, more precisely, the attachment of the plant to the soil. Regardless of the contamination of the seeds, their sprouts are purified as soon as they take root, reviving their original connection with the divine origin of existence. But the growth of plants threatens the very integrity of the Law. In order to control the excess of plant raw materials, Maimonides defends the purity of species. Plants are trivial and therefore unworthy of divine interest. A chain reaction occurs: plants are neglected, left to themselves, and subsequently they become more and more mysterious. Their freedom is still more radical than that inherent in the free will of man. (shrink)

In this paper, we give a flavour of how, against the odds, Reggio-Emilia-inspired pedagogical documentation can work in reconceptualizing environmental education, reconfiguring child subjectivity and provoking an ontological shift from autopoiesis to sympoiesis in teacher education. Working posthuman(e)ly and transdisciplinarily across three foundation phase teacher education courses at a university in South Africa, we situate our teaching within current environmental precarities. We show how we stirred up trouble in and outside our university classroom and provoked our students to “make kin” (...) with children, each other, other animals, and the more-than-human, but also to stay with the trouble, that is, to learn to be truly present in colonized spaces. (shrink)

Imagine a model of the universe that, if true and known to be true, would solve the following philosophical problems: the direction and flow of time, an ontology for laws of nature, the interpretation of quantum mechanics, the interpretation of probability, a semantics for counterfactuals, trans-world and trans-temporal identity, essentialism and natural kinds, and free will and responsibility. The successful solution to these problems would convince most of us that we should, at the very least, give this model serious consideration. (...) This is the argument of Storrs McCall's A Model of the Universe: Space-Time, Probability, and Decision. Assume that the branched-tree model of the universe is true, and all these problems are solved. Thus, the branched-tree model should at least be a plausible candidate for the true model of the universe. (shrink)

A wide Aronszajn tree is a tree of size and height $\omega _{1}$ with no uncountable branches. We prove that under $MA$ there is no wide Aronszajn tree which is universal under weak embeddings. This solves an open question of Mekler and Väänänen from 1994. We also prove that under $MA$, every wide Aronszajn tree weakly embeds in an Aronszajn tree, which combined with a result of Todorčević from 2007, gives that under $MA$ every wide (...) Aronszajn tree embeds into a Lipschitz tree or a coherent tree. We also prove that under $MA$ there is no wide Aronszajn tree which weakly embeds all Aronszajn trees, improving the result in the first paragraph as well as a result of Todorčević from 2007 who proved that under $MA$ there are no universal Aronszajn trees. (shrink)

A main thesis of Fred Sommers' type theory, is that an isomorphism exists between any natural language and the categories discriminated by that language. Here the author gives an explanation of what this claim comes to. And then it is argued that, so understood, the claim is incompatible with Zermelo-Fraenkel set theory. Finally, it is argued against trying to salvage the isomorphism thesis by appealing to some other set theory.

In an online, participatory class, we interpreted 'The Dream of Geese Nesting in Trees' knowing nothing of the dreamer beyond age and gender, and having none of the dreamer’s associations. Our interpretation included predictions about the dreamer. When it was complete, we asked the bringer of the dream (who had until then been mostly silent and who also gave no visual feedback to our discussion) to give us more information about the dreamer. Our main predictions were confirmed. Goslings are falling (...) on the dreamer’s head. This record is another iteration of an experiment that will be described more fully in the paper, 'The Dream of the Six-Legged Dog: An Experimental System that Tests Meaning,' soon to be published. This iteration repeats and confirms the evidence given in that paper. AUDIO RECORD OF COMPLETE CLASS: link is at top of paper you can download from this page. (shrink)

This article puts into conversation Friedrich Nietzsche’s perspectivism and a particular expression of “African animism,” drawn from my ethnographic fieldwork in Ghana. Nietzsche’s perspectivism extends interpretation beyond the human species into natural processes. Like perspectivism, African animism troubles the binaries—body/soul, nature/culture—that permeate anthropocentric thinking. Human-nonhuman relations are refigured as socio-ecological relations: the earth may be regarded as life-generating ancestors; baobab trees may approach humans as kin. These two images of the world intersect, but they do not mesh together. Nietzsche adopts (...) perspectivism as active intersections between dynamic processes, within an open universe that has not been predesigned for humans. Animism tends toward a world of personalized relationships that would reach harmony if we would only lighten our ecological footprint. I draw upon such resonances to advance a new ethic of experiential environmentalism that treats ecological threats as lived risks and shared experiences with a lively and communicating “environment.”. (shrink)

For [Formula: see text], the coarse similarity class of A, denoted by [Formula: see text], is the set of all [Formula: see text] such that the symmetric difference of A and B has asymptotic density 0. There is a natural metric [Formula: see text] on the space [Formula: see text] of coarse similarity classes defined by letting [Formula: see text] be the upper density of the symmetric difference of A and B. We study the metric space of coarse similarity classes (...) under this metric, and show in particular that between any two distinct points in this space there are continuum many geodesic paths. We also study subspaces of the form [Formula: see text] where [Formula: see text] is closed under Turing equivalence, and show that there is a tight connection between topological properties of such a space and computability-theoretic properties of [Formula: see text]. We then define a distance between Turing degrees based on Hausdorff distance in the metric space [Formula: see text]. We adapt a proof of Monin to show that the Hausdorff distances between Turing degrees that occur are exactly 0, [Formula: see text], and 1, and study which of these values occur most frequently in the senses of Lebesgue measure and Baire category. We define a degree a to be attractive if the class of all degrees at distance [Formula: see text] from a has measure 1, and dispersive otherwise. In particular, we study the distribution of attractive and dispersive degrees. We also study some properties of the metric space of Turing degrees under this Hausdorff distance, in particular the question of which countable metric spaces are isometrically embeddable in it, giving a graph-theoretic sufficient condition for embeddability. Motivated by a couple of issues arising in the above work, we also study the computability-theoretic and reverse-mathematical aspects of a Ramsey-theoretic theorem due to Mycielski, which in particular implies that there is a perfect set whose elements are mutually 1-random, as well as a perfect set whose elements are mutually 1-generic. Finally, we study the completeness of [Formula: see text] from the perspectives of computability theory and reverse mathematics. (shrink)

Recall that for any Boolean algebra (BA) A, the cellularity of A is c(A) = sup{|X| : X is a pairwise-disjoint subset of A}. A pseudo-tree is a partially ordered set (T, ≤) such that for every t in T, the set {r ∊ T : r ≤ t} is a linear order. The pseudo-tree algebra on T, denoted Treealg(T), is the subalgebra of ℘(T) generated by the cones {r ∊ T : r ≥ t}, for t in (...) T. We characterize the cellularity of pseudo-tree algebras in terms of cardinal functions on the underlying pseudo-trees. For T a pseudo-tree, c(Treealg(T)) is the maximum of four cardinals c\sbT, ι\sbT, φ\sbT, and μ\sbT : roughly, c\sbT measures the "tallness" of the pseudo-tree T; ι\sbT the "breadth"; φ\sbT the number of "finite branchings"; and μ\sbT the number of places where T "does not branch." We give examples to demonstrate that all four of these cardinals are needed. (shrink)

The method of Socratic proofs (SP-method) simulates the solving of logical problem by pure questioning. An outcome of an application of the SP-method is a sequence of questions, called a Socratic transformation. Our aim is to give a method of translation of Socratic transformations into trees. We address this issue both conceptually and by providing certain algorithms. We show that the trees which correspond to successful Socratic transformations—that is, to Socratic proofs—may be regarded, after a slight modification, as Gentzen-style proofs. (...) Thus proof-search for some Gentzen-style calculi can be performed by means of the SP-method. At the same time the method seems promising as a foundation for automated deduction. (shrink)

With its Vedāntic metaphysics and devotionally rich narratives, the Bhāgavata Purāṇa can provide valuable models for ecological care and preservation. Throughout the Purāṇa, we find narratives that can be harnessed in service of the environment, whether it be Kṛṣṇa battling the serpent Kāliya or Varāha lifting the Earth from the depths of the cosmic ocean. This article, however, will focus on a little-known narrative found in Book Four, namely, the Pracetās’ destruction, and eventual protection, of the Earth’s trees. The Pracetās’ (...) narrative is significant for several reasons: instead of simply venerating nature, the story demonstrates the challenge of balancing human needs and the needs of other life forms; it accords agency to the Earth by giving the forest a voice within the narrative; and it bridges the boundary between human beings and the natural world by building kinship relationships between them. This article will explore the ways in which Vaiṣṇava commentators have interpreted this episode as they attempt to negotiate the question: who has priority—humans or nature? (shrink)

This article is an investigation on how two theologians from the Early Church interpreted the withered fig tree, as narrated by the evangelist Matthew (Mt 21:18–22). The two theologians referred to are Origen of Alexandria, who belongs to the pre-Nicene era and represents the Alexandrian School, and Ps.-Chrysostom who belongs to the post-Nicene era, and represents the School of Antioch. Origen believed that when the fig tree withered, it referred to Israel’s withering. This interpretation of the narrative surrounding (...) the withered fig tree was very common in the Early Church. Ps.-Chrysostom makes it very clear that he cannot agree with this interpretation, which was quite common in the Early Church. He stated that it is wrong to liken the fig tree to the synagogue of the Jews. He argues that Jesus could not curse the synagogue, because he said that ‘The Son of Man did not come to destroy, but to seek and save the lost’ (cf. Lk 9:56). Moreover, if the synagogue withered, fruitful branches such as Paul, Stephen, Aquila and Priscilla could not have sprouted from the roots. These names are proof that God did not entirely reject the Jewish people. Ps.-Chrysostom then offers a different explanation to the question why the fig tree withered: He points out that Adam used the leaves of a fig tree to cover his nakedness. When Jesus caused the fig tree to wither, he wanted to show that he can give Adam a new garment of water and spirit that glistens like snow. Christ gave back to Adam what the serpent had robbed him of, namely ‘the angel-like life, the luxuriance of paradise, the garment of incorruptibility’ (PC. cp. 4). Contribution: The primary goal of this article is to explore the exegetical practices of two ancient theologians who came from two different schools and from two different eras. This study shows how they interpreted the account of the withered fig tree (Mt 21:18–22), based on their respective theological perspectives. (shrink)

The narratives of plants offered by science, history, poetry, mythology and direct personal experience are often thought to contradict one another and are thus held as separate. Like leaves of a tree, however, the posthumous botanical works of nineteenth-century American naturalist and philosopher Henry David Thoreau gather together the diverse stories that give meaning to plants. Drawing from the concept of multiple narrative streams as a method of writing natural history inspired by Thoreau, this article explores many accounts of (...) the flora of the biodiverse Southwest corner of Western Australia. Botanical science, Aboriginal spirituality, nature poetry and colonial histories offer versions that explain the natural histories of Southwest plants using different, though complementary, perspectives. The meandering together of narrative streams ensures the perpetuity of non-scientific stories and the potential for cross-pollination between disciplines and diverse ways of knowing the natural world. (shrink)

Public reason is central to John Rawls’s political liberalism, as a mechanism for citizens to discuss about matters of common interest. Although free and equal, reasonable and rational, citizens of a democratic society disagree on their understanding of truth and right, giving rise to the fact of reasonable pluralism. Thus, Rawls works out an idea of public reason which allows citizens to argue about political matters and yet remaining divided in their comprehensive doctrines. On the other hand, African culture (...) has developed the practice of palaver as way of dealing with social and political questions of the community. Usually held under a tree, scholars believe that the palaver is the African version of deliberative democracy. In this article, I elaborate the two ideas and compare them in order to see whether they are completely opposite or whether they can enrich each other. Thus, the first section focuses on Rawls’s idea of public reason, the second explores the palaver practice and the last section compares them. (shrink)

This paper studies the relation between some extensions of the non-associative Lambek Calculus NL and their interpretation in tree models (free groupoids). We give various examples of sequents that are valid in tree models, but not derivable in NL. We argue why tree models may not be axiomatizable if we add finitely many derivation rules to NL, and proceed to consider labeled calculi instead.We define two labeled categorial calculi, and prove soundness and completeness for interpretations that are (...) almost the intended one, namely for tree models where some branches of some trees may be resp. all branches of all trees must be infinitely extending. Extrapolating from the experiences in our quite simple systems, we briefly discuss some problems involved with the introduction of labels in categorial grammar, and argue that many of the basic questions are not yet understood. (shrink)

Two new modes of thinking have spread through systematics in the twentieth century. Both have deep historical roots, but they have been widely accepted only during this century. Population thinking overtook the field in the early part of the century, culminating in the full development of population systematics in the 1930s and 1940s, and the subsequent growth of the entire field of population biology. Population thinking rejects the idea that each species has a natural type (as the earlier essentialist view (...) had assumed), and instead sees every species as a varying population of interbreeding individuals. Tree thinking has spread through the field since the 1960s with the development of phylogenetic systematics. Tree thinking recognizes that species are not independent replicates within a class (as earlier group thinkers had tended to see them), but are instead interconnected parts of an evolutionary tree. It lays emphasis on the explanation of evolutionary events in the context of a tree, rather than on the states exhibited by collections of species, and it sees evolutionary history as a story of divergence rather than a story of development. Just as population thinking gave rise to the new field of population biology, so tree thinking is giving rise to the new field of phylogenetic biology. (shrink)

We study model theoretic tree properties and their associated cardinal invariants. In particular, we obtain a quantitative refinement of Shelah’s theorem for countable theories, show that [Formula: see text] is always witnessed by a formula in a single variable and that weak [Formula: see text] is equivalent to [Formula: see text]. Besides, we give a characterization of [Formula: see text] via a version of independent amalgamation of types and apply this criterion to verify that some examples in the literature (...) are indeed [Formula: see text]. (shrink)

The dynamics of the "Etang de Berre", a brackish lagoon situated close to the French Mediterranean sea coast, is strongly disturbed by freshwater inputs coming from an hydroelectric power station. The system dynamics has been described as a sequence of daily typical states from a set of physicochemical variables such as temperature, salinity and dissolved oxygen rates collected over three years by an automatic sampling station. Each daily pattern summarizes the evolution, hour by hour of the physicochemical variables. This article (...) presents results of forecasts of the states of the system subjected to the simultaneous effects of meteorological conditions and freshwater releases. We recall the main step of the classification tree method used to build up the predictive model (Classification and Regression Trees, Breiman et al., 1984) and we propose a transfer procedure in order to test the stability of the model. Results obtained on the Etang de Berre data set allow us to describe and predict the effects of the environmental variables on the system dynamics with a margin of error. The transfer procedure applied after the tree building process gives a maximum gain in prediction accuracy of about 15%. (shrink)

In this paper, we study the notion of arborescent ordered sets, a generalizationof the notion of tree-property for cardinals. This notion was already studied previously in the case of directed sets. Our main result gives a geometric condition for an order to be ℵ0-arborescent.

Syntacticians have proposed three-dimensional syntactic structures to account for the peculiarities of coordination. This paper proposes a way of interpreting such structures and gives an account of sentences of the sort 'John bought and Mary sold a total of ten cars' based on a notion of 'implicit' coordination.

We give definitions that distinguish between two notions of indiscernibility for a set {aη∣η∈ω>ω}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\{a_{\eta} \mid \eta \in ^{\omega>}\omega\}}$$\end{document} that saw original use in Shelah [Classification theory and the number of non-isomorphic models. North-Holland, Amsterdam, 1990], which we name s- and str−indiscernibility. Using these definitions and detailed proofs, we prove s- and str-modeling theorems and give applications of these theorems. In particular, we verify a step in the argument that TP is equivalent (...) to TP1 or TP2 that has not seen explication in the literature. In the Appendix, we exposit the proofs of Shelah [Classification theory and the number of non-isomorphic models. North-Holland, Amsterdam, 1990, App. 2.6, 2.7], expanding on the details. (shrink)

We give a sound and complete axiomatization for the full computation tree logic, CTL*, of R-generable models. This solves a long standing open problem in branching time temporal logic.

A dichotomy result of Sevenster (2014) [29] completely classified the quantifier prefixes of regular Independence-Friendly (IF) logic according to the patterns of quantifier dependence they contain. On one hand, prefixes that contain “Henkin” or “signalling” patterns were shown to characterize fragments of IF logic that capture NP-complete problems; all the remaining prefixes were shown instead to be essentially first-order. In the present paper we develop the machinery which is needed in order to extend the results of Sevenster to non-prenex, regular (...) IF sentences. This involves shifting attention from quantifier prefixes to a (rather general) class of syntactical tree prefixes. We partially classify the fragments of regular IF logic that are thus determined by syntactical trees; in particular, a) we identify four classes of tree prefixes that are neither signaling nor Henkin, and yet express NP-complete problems and other second-order concepts; and b) we give more general criteria for checking the first-orderness of an IF sentence. (shrink)

The objects we encounter in ordinary life and scientific practice - cars, trees, people, houses, molecules, galaxies, and the like - have long been a fruitful source of perplexity for metaphysicians. The Structure of Objects gives an original analysis of those material objects to which we take ourselves to be committed in our ordinary, scientifically informed discourse. Koslicki focuses on material objects in particular, or, as metaphysicians like to call them "concrete particulars", i.e., objects which occupy a single region of (...) space-time at each time at which they exist and which have a certain range of properties that go along with space-occupancy, such as weight, shape, color, texture, and temperature. The Structure of Objects focuses in particular on the question of how the parts of such objects, assuming that they have parts, are related to the wholes which they compose. (shrink)

In this paper we introduce a new technique of proving undecidability results. This technique is based on the notion of a Thue tree. We also give examples of applications of this method to term rewriting, Horn implication problem and database dependencies.

Plant succession is a phenomenon ascribed to vegetation dynamics at the scale of the plant community. The study of plant succession implies the analysis of the species involved and their relationships. Depending on the research done, the characteristics of trees have been studied according to either static, dimensional or partial approaches. We have revised the principal theories of succession, the methods of describing structure and development of tree and relationship established between tree species' attributes and their successional status. (...) During studies of succession, we propose that the profile of plant species be completed by including the organizational attributes of their structure as well as their development dynamics. We suggest an approach to the architecture that gives a general overview of the mode of development, revealing, among other things, that a limited number of architectural models may be found in nature. We hypothesize that community dynamics, in succession, may to a certain degree arise from the dynamic nature of plant development. This line of reasoning is in accordance with the current school of thought on process structuralism. (shrink)

We give a new proof of a theorem of Shelah which states that for every family of labeled trees, if the cardinality κ of the family is much larger (in the sense of large cardinals) than the cardinality λ of the set of labels, more precisely if the partition relation holds, then there is a homomorphism from one labeled tree in the family to another. Our proof uses a characterization of such homomorphisms in terms of games.

In this paper, we construct group trees of tame Polish groups of the form, where are countable abelian. Our first example where all are torsion reaches the known upper bound. Next we give examples having height for any, close to the known bound.

In the paper A non-implication between fragments of Martin’s Axiom related to a property which comes from Aronszajn trees , Proposition 2.7 is not true. To avoid this error and correct Proposition 2.7, the definition of the property is changed. In Yorioka [1], all proofs of lemmas and theorems but Lemma 6.9 are valid about this definition without changing the proofs. We give a new statement and a new proof of Lemma 6.9.

We consider the problem of choosing the location of a public facility either (a) on a tree network or (b) in a Euclidean space. (a) (1996) characterize the class of target rules on a tree network by Pareto efficiency and population-monotonicity. Using Vohra's (1999) characterization of rules that satisfy Pareto efficiency and replacement-domination, we give a short proof of the previous characterization and show that it also holds on the domain of symmetric preferences. (b) The result obtained for (...) model (a) proves to be crucial for the analysis of the problem of choosing the location of a public facility in a Euclidean space. Our main result is the characterization of the class of coordinatewise target rules by unanimity, strategy-proofness, and either replacement-domination or population-monotonicity. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Fellini's Crowds and the Remains of ReligionAndrew Mckenna (bio)The fascist parade in Federico Fellini's Amarcord enables us to take the measure of the director's analytic and inteve genius. It begins amid swirls of dust and smoke emanating from the town train station, as if attributing the successful spread of Italian fascism to a failure of perception. The party is, as the saying goes, blowing smoke in our face, producing (...) a cultural climate favorable to murky thinking. The haze connotes the inability to properly envision phenomena with any mental or moral clarity, to distinguish matters clearly, such as the difference that the film suggests in a later scene, with comic irony, between a real military victory and shooting a gramophone out of a bell tower because it is playing the communist Internationale.But we cannot get away with anything like blaming fascism only on the weather, moral or physical. Far more revealing is the next sequence of shots, in which local party officials and members, all in uniform, are shown running a little breathlessly in loose formation, while exchanging remarks that express gleeful admiration of their leader and his party. They hustle up some stairs in the same loose formation and stand facing the camera, medium close-up, in order to acclaim the party slogans booming from loudspeakers. They shout in unison before, we note, the slogans are fully pronounced, so that we are made aware that they are not really listening to what is being said, but only acting in concert. Their acclamation is comically out of sync—with reality, perceptual and, by implication, social. This image of the bersaglieri running in unison is familiar to spectators at political rallies and from newsreels at the time, and to historians since then. But Fellini has moved the camera in closer than it has ever been before, combining two or three characters in a head-shot as they trot up the street. It is a classic gesture of defamiliarization, as the Russian formalists called it when identifying art-work, that makes this phenomenon available to deeper understanding. [End Page 159]We have just viewed a penetrating analysis of group action, a symbolic discourse on crowd behavior as it concerns organized political activity. The running here is not natural to such a group; it must mean something. It isn't dictated to them as orders; it must obey the dictates of the phenomenon that Fellini is revealing to us. This brilliantly orchestrated scene prompts the question: why, when, for what reason does a crowd run? The answers, typically, are two: in fear, in panic, as from fire or flood; or in rage, in fury, as against an abhorred enemy culprit—to the Bastille, or the gallows, or the nearest tree or lamppost that can serve as such. Though it is closer to the second case, Fellini's gang of fascists fits neither of these models precisely, and we have to step back a bit and reflect upon what he is representing to us about crowd behavior and organized political activity of a certain kind, of the kind that can only succeed, perhaps, amid a hazy climate of moral perception. We need to probe further the logic of this phenomenon, to explore the meaning of what appears before our eyes, as the philosophers do when they say they are doing phenomenology. We can do this by further considering alternative models of behavior.In a military parade, we have an organized crowd of a certain specific type, in which a group is massed in rigid formation and everyone moves in lock-step order to the regular beat of the drum or to a repeated count of numbers. Fellini gives us an example of this in the fascist youth athletic exercises performed by uniformed groups of boys and girls who move their rifles and hoops to a steady eight-count beat. So we know the director of Amarcord is thinking about mass movements of all sorts. Moreover, his film also provides us with a crowd phenomenon at the opposite end of the social spectrum. At the beginning of the film, we witness the nightly passagiata, the evening town stroll still very... (shrink)

The aim of this article is to show that what Gaston Bachelard called the “psychology of the imagination” often doubles as moral psychology. In Water and Dreams, for example, Bachelard presents “water’s morality,” which is a morality attained by an imagination of water’s purity. Similarly, in Air and Dreams, he explores the aerial imagination that forms the moral thought in Thus Spoke Zarathustra and calls the will to dynamism in Nietzschean philosophy “an experimental physics of moral life.” In Earth and (...) Reveries of Will, numerous terrestrial images are considered and the moralities they embody are discussed—among them the supreme hardness of the oak tree in Virginia Woolf’s Orlando and the “counsel of solidity” it gives. As Bachelard becomes more inclined to call his endeavor a “phenomenology of the imagination,” concern for morality becomes less pronounced. And yet in two of his later works, The Poetics of Space and The Poetics of Reverie, Bachelard continues to delve into the ways imagination allies with moral life. Sensitively heeding the solicitations from the material world and our responses to them, Bachelard’s psychology of the imagination is a project of self-knowledge of an unusual sort: it uncovers “the autobiography of lost possibilities” and revives confidence in human strength. Finally, a comparison between Bachelard’s moral psychology with the work of Theodor Adorno and of John McDowell shows that its philosophical significance is best viewed as a re-enchantment project—the re-enchantment of nature and our relationship with it. (shrink)

The question is how do Scanning Electron Microscopes (SEMs) give us access to the nano world? The images these instruments produce, I argue, do not allow us to see atoms in the same way that we see trees. To the extent that SEMs and STMs allow us to see the occupants of the nano world it is by way of metaphorical extension of the concept of “seeing”. The more general claim is that changes in scientific instrumentation effect changes in the (...) concepts central to our understanding of scientific results. (shrink)

We show that MRP + MA implies that ITP(λ, ω 2 ) holds for all cardinal λ ≥ ω 2 . This generalizes a result by Weiß who showed that PFA implies that ITP(λ, ω 2 ) holds for all cardinal λ ≥ ω 2 . Consequently any of the known methods to prove MRP + MA consistent relative to some large cardinal hypothesis requires the existence of a strongly compact cardinal. Moreover if one wants to force MRP + MA (...) with a proper forcing, it requires at least a supercompact cardinal. We also study the relationship between MRP and some weak versions of square. We show that MRP implies the failure of □(λ, ω) for all λ ≥ ω 2 and we give a direct proof that MRP + MA implies the failure of □(λ, ω 1 ) for all λ ≥ ω 2. (shrink)

Let κ be a singular cardinal. Karp's notion of a chain model of size κ is defined to be an ordinary model of size κ along with a decomposition of it into an increasing union of length cf. With a notion of satisfaction and -isomorphism such models give an infinitary logic largely mimicking first order logic. In this paper we associate to this logic a notion of a dynamic EF-game which gauges when two chain models are chain-isomorphic. To this game (...) is associated a tree which is a tree of size κ with no κ-branches -branches). The measure of how non-isomorphic the models are is reflected by a certain order on these trees, called reduction. We study the collection of trees of size κ with no κ-branches under this notion and prove that when cf = ω this collection is rather regular; in particular it has universality number exactly κ+. Such trees are then used to develop a descriptive set theory of the space cf κ. The main result of the paper gives in the case of κ strong limit singular an exact connection between the descriptive set-theoretic complexity of the chain isomorphism orbit of a model, the reduction order on the trees and winning strategies in the corresponding dynamic EF games. In particular we obtain a neat analog of the notion of Scott watershed from the Scott analysis of countable models. (shrink)

We give a short proof of a lemma which generalizes both the main lemma from the original construction in the author’s thesis of a model with no ω2-Aronszajn trees, and also the “Key Lemma” in Hamkins’ gap forcing theorems. The new lemma directly yields Hamkins’ newer lemma stating that certain forcing notions have the approximation property.

Using the concept of progress measure, we give a new proof of Rabin's fundamental result that the languages defined by tree automata are closed under complementation. To do this we show that for certain infinite games based on tree automata, an immediate determinacy property holds for the player who is trying to win according to a Rabin acceptance condition. Immediate determinancy is stronger than the forgetful determinacy of Gurevich and Harrington, which depends on more information about the past, (...) but applies to another class of games. Next, we show a graph theoretic duality theorem for winning conditions. Finally, we present an extended version of Safra's determinization construction. Together, these ingredients and the determinacy of Borel games yield a straightforward recipe for complementing tree automata. Our construction is almost optimal, i.e. the state space blow-up is essentially exponential- thus roughly the same as for automata on finite or infinite words. To our knowledge, no prior constructions have been better than double exponential. (shrink)

We construct a collection of new topological Ramsey spaces of trees. It is based on the Halpern-Läuchli theorem, but different from the Milliken space of strong subtrees. We give an example of its application by proving a partition theorem for profinite graphs.

In lieu of an abstract, here is a brief excerpt of the content:The Buddha through Christian EyesElizabeth J. HarrisIt was in Sri Lanka in 1984 that I had my first ‘encounter’ with the Buddha. When at the ancient city of Anuradhapura, I stole away from the group I was with to return for a few minutes to the shrine room adjacent to the sacred bo tree, the one believed to have grown from a cutting of the original tree (...) under which the Buddha gained enlightenment. Devotees dressed in white were sitting or prostrating silently. I joined them and looked toward the image, which showed the Buddha sitting in meditation against a painted scene of pale blue sky, white clouds, and mountains. Suddenly the image became more than mere plaster. All I can say is that it communicated. It beckoned. Against the blue of the sky, the serene head became suffused with cosmic significance. I know that there was unfinished business between me and the Buddha.The moment was prophetic. Two years later, I returned to Sri Lanka to study Buddhism and stayed over seven years. ‘Study’ is not quite the right word because, together with the academic, I also sought to immerse myself in Buddhism with the wish to see it through the eyes of Buddhists. I practiced meditation under Buddhist teachers, participated in temple devotion, and joined pilgrimages. It was a process that meant temporarily letting go of much that was dear to me as a Christian. But the rewards were inestimable. Never again has the image at Anuradhapura ‘spoken’ to me. In fact, on return visits it has appeared artistically poor, certainly no match for the older stone images, open to the air, in other parts of the city. But then, around and inside that very shrine room in May 1985, Tamil guerrillas gunned down 146 innocent devotees, rupturing centuries of devotion with pools of blood.My seven and a half years in Sri Lanka make it almost impossible for me to write about the Buddha as a complete outsider. I remain a Christian, but the Buddha has become part of me. An exquisitely carved wooden image of the Buddha in meditation is now part of my home. The peace that emanates from it gives me strength. In complete honesty, I can say that I revere the Buddha.But what Buddha do I revere? Do I revere the Buddha in the same way as Buddhists? To reflect on how my appreciation of the Buddha may be different from that [End Page 101] of Buddhists is not easy, for Buddhism contains within itself so many faces of the Buddha. There is the historical Buddha of the earlier parts of the Pali canon, the Buddha of the later hagiographic biographies, the Buddha of popular devotion, Mahayana Buddhism’s vision of multiple Buddhas and cosmic buddhahood, the Buddha of what has been termed Protestant Buddhism. Yet I sense that there is a common thread within all of these faces—namely, the Lord Buddha as the supreme embodiment of compassion and wisdom, the one who has seen into the nature of reality and the human predicament and has taught the path of liberation.All that I know of Buddhism tells me that the person of the Buddha is central. The devotion shown to the image is more than would be given to a human teacher and more than would be given to a god. Acchariya manussa is one phrase used in the Pali texts—“wonderful man.” He is human, yet more than human in that he was enlightened and worked toward this enlightenment without outside aid through countless lives of self-sacrifice and virtue. This I believe all Buddhists would agree to, and such a being is supremely worthy of reverence.How does my appreciation tally with this? It is the Theravada tradition that has nurtured my own understanding, and it has done so in three ways. First, there has been my reading of the Sutta Pitaka of the Pali canon. In the first two years of my time in Sri Lanka, I read through most of the nikaya of the Sutta Pitaka, albeit in translation, and I found myself encountering again and again a teacher I could respect and revere. “How... (shrink)

The author has previously shown that for a certain class of structures $\mathcal {I}$, $\mathcal {I}$-indexed indiscernible sets have the modeling property just in case the age of $\mathcal {I}$ is a Ramsey class. We expand this known class of structures from ordered structures in a finite relational language to ordered, locally finite structures which isolate quantifier-free types by way of quantifier-free formulas. This result is applied to give new proofs that certain classes of trees are Ramsey. To aid this (...) project we develop the logic of EM-types. (shrink)

We show that both Rado's Conjecture and strong Chang's Conjecture imply that there are no special ℵ2-Aronszajn trees if the Continuum Hypothesis fails. We give similar result for trees of higher heights and we also investigate the influence of Rado's Conjecture on square sequences.

We present a variation of the forcing S max as presented in Woodin [4]. Our forcing is a P max -style construction where each model condition selects one Souslin tree. In the extension there is a Souslin tree T G which is the direct limit of the selected Souslin trees in the models of the generic. In some sense, the generic extension is a maximal model of "there exists a minimal Souslin tree," with T G being this (...) minimal tree. In particular, in the extension this Souslin tree has the property that forcing with it gives a model of Souslin's Hypothesis. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:"A Mark ofthe Growing Mind is Veneration of Objects" (Ludwig Wittgenstein) Fay Horton Sawyier Introduction In book 1 of the Treatise,1 Hume directs his attention to two sets of concepts; one of these sets is what I think of as the "basic epistemological set" and the other as the "basic metaphysical or ontological set." Except for the idea of personal identity, the First Inquiry2 addresses the same arrays of (...) concerns. Within the "epistemological set" we find discussions ofknowledge, belief, origin of ideas, etc.; within the "metaphysical set"are seen space, time, identity, cause and effect, uniformity ofnature, external objects and so on.3 For the first (epistemological) set, Hume constructs a mode of analysis which depends crucially on the provenance of an idea or concept. Thatis, asit does forarthistorians today, authenticityortruth depends on how the thingin question came intoyour possession. Hume announces not only that every simple idea depends on and comes from its simple impression, but that the full understandingofa complexidea requires first factoring it into its simple components and then tracing them back to their impressions. Understanding is, so to speak, like displaying the family tree. It turns out that all of the members of the "metaphysical" set have dubious parentage. Even if one grants the accuracy and adequacy of Hume's factoring, we are left facing his demonstrations that for each metaphysical concept there are at least some elements with no clear ancestry from single impressions. In this wayHume directs our attention tohis questforhow suchideas(or such elements withinideas) are ever come by. Why do we attribute identity? Howcanwe assume thereisanecessary connection and apower? What can possibly bring us to imagine, even, that anything can be independent ofour perceptions? And so on. All ofthis is not only at the heart ofthe Humean enterprise inbook 1 ofthe Treatise ami theFirstInquiry butis well-known to anyone even modestly familiar with Hume's writings. The result of his powerful analyses is that these mysterious, illegitimate elements in the metaphysical concepts are generated within subjects exposed to repeated instances of, for example, pairings in time or place, similar sightings after temporal lapses and so on. The processes by which we Volume XVIII Number 2 315 FAY HORTON SAWYIER construct our categories as well as the elements out ofwhich we make them areimportantandin these cases were shown tobe developmental or time-dependent.4 Furthermore, since these processes and these resultant conceptshavebeen shown tohave been generated by us, they are uniquely quaUfied to demonstrate the nature of human nature, which was, after all, the subject ofthe Treatise? Having reminded ourselves ofthese extremely general features of Hume's exposition, I want now to isolate and to highlight some particular and peculiar features. 1.The subject upon whose mind or sensibilities paired and repeated events are presumed to impinge and by whose consequent conditioning these otherwise inexplicable concepts can be understood is always an adult male.6 2.The presentingsituation which is presumed to arise and repeatfor this adult male is always hypothetical and never observed. 3.Thisman'sconstructionofanyoneofthese concepts (like necessary connection) is always as his solution to a logical problem, his way-out ofa mental awkwardness or unease. 4.These adult male concept generators and logical problem solvers neverseem to doanything but sitstill and look around themselves.7 The fundamental character ofmy inquiry can be understood as a search for the (presumably deleterious) consequences of the four particular features noted above. Since the lives and experiences of young children are neglected and since acquisition of the basic metaphysical set is always initiated in early childhood, one may well hypothesize that Hume's results will be damaged or skewed. Intuitively, this would seem to be an obvious inference, but proof is needed that in some cases Hume did indeed misconstrue certain basic concepts and that the central factor in his shortfall was his neglect of the child's experience of concept development and acquisition. By contrast, his contemporary, Thomas Reid, remarked, "Could we obtain a distinct and full history of all that hath passed in the mind ofa child from thebeginning ofUfe and sensation, till it grows to the use ofreason... this would be a treasury of natural history, which would probably give... (shrink)

The principle of proportionality is seen as the highest peak of structural, logical thinking that enables balancing between constitutional principles and their interferences. So far, Alexy's weight formula has been the most advanced approach in structured balancing of proportionality stricto sensu, while this paper shows it as still too subjective. Despite judicial tests—or different, manifestly inappropriate reasonableness tests—proportionality stricto sensu hides some form of the jumping-to-conclusions bias, because the inference is made through a subjective lens. The paper presents structured legal (...) balancing (and hence reasoning) based on Bayes’ theorem. This paper, based on the connection between probability and hypothetical legal norms, transfers the four-part structure of proportionality into the relevant four-part structure of the Bayes tree. This transfer shows the first as flawed due to its failing to consider means that can have the same effects as the considered ones. Only by inclusion of the latter can the total probability of a considered case be established. Numerical proportionality à la Bayes can be further improved through the use of public-value weights that are obtained from surveys or online communities of people giving weights in the real time (collective wisdom). The Bayesian approach can also be used in adjudication as a control in assessing judicial standards in use. (shrink)

A unary algebra is an algebraic system A = , where ƒ 0 ,…,ƒ n are unary operations on A and n ∈ ω. In the paper we develop the theory of effective unary algebras. We investigate well-known questions of constructive model theory with respect to the class of unary algebras. In the paper we construct unary algebras with a finite number of recursive isomorphism types. We give the notions of program, uniform, and algebraic dimensions of models, and then we (...) investigate these notions on unary algebras. We find connections between algebraic and effective properties of r.e. representable unary algebras. We also deal with finitely generated r.e. unary algebras. We show the connections between trees and unary algebras. Our interests also concern recursive automorphisms groups, r.e. subalgebra and congruence lattices of effective unary algebras. (shrink)