We analyze the degree-structure induced by large reducibilities under the Axiom of Determinacy. This generalizes the analysis of Borel reducibilities given in Alessandro Andretta and Donald A. Martin [1], Luca Motto Ros [6] and Luca Motto Ros. [5] e.g. to the projective levels.

We show that if κ is a weakly compact cardinal then the embeddability relation on trees of size κ is invariantly universal. This means that for every analytic quasi-order R on the generalized Cantor space View the MathML source there is an Lκ+κ-sentence φ such that the embeddability relation on its models of size κ, which are all trees, is Borel bi-reducible to R. In particular, this implies that the relation of embeddability on trees of size κ is complete for (...) analytic quasi-orders on View the MathML source. These facts generalize analogous results for κ=ω obtained in Louveau and Rosendal [17] and Friedman and Motto Ros [6], and it also partially extends a result from Baumgartner [3] concerning the structure of the embeddability relation on linear orders of size κ. (shrink)

We show that if Ƒ is any "well-behaved" subset of the Borei functions and we assume the Axiom of Determinacy then the hierarchy of degrees on $P(^\omega \omega )$ induced by Ƒ turns out to look like the Wadge hierarchy (which is the special case where Ƒ is the set of continuous functions).

In [9] we have considered a wide class of "well-behaved" reducibilities for sets of reals. In this paper we continue with the study of Borel reducibilities by proving a dichotomy theorem for the degree-structures induced by good Borel reducibilities. This extends and improves the results of [9] allowing to deal with a larger class of notions of reduction (including, among others, the Baire class ξ functions).

We study Polish spaces for which a set of possible distances $A \subseteq R^+$ is fixed in advance. We determine, depending on the properties of A, the complexity of the collection of all Polish metric spaces with distances in A, obtaining also example of sets in some Wadge classes where not many natural examples are known. Moreover we describe the properties that A must have in order that all Polish spaces with distances in that set belong to a given class, (...) such as zero-dimensional, locally compact, etc. These results lead us to give a fairly complete description of the complexity, with respect to Borel reducibility and again depending on the properties of A, of the relations of isometry and isometric embeddability between these Polish spaces. (shrink)

Answering one of the main questions of [S.-D. Friedman, T. Hyttinen and V. Kulikov, Generalized descriptive set theory and classification theory, Mem. Amer. Math. Soc. 230 80, Chap. 7], we show that there is a tight connection between the depth of a classifiable shallow theory [Formula: see text] and the Borel rank of the isomorphism relation [Formula: see text] on its models of size [Formula: see text], for [Formula: see text] any cardinal satisfying [Formula: see text]. This is achieved by (...) establishing a link between said rank and the [Formula: see text]-Scott height of the [Formula: see text]-sized models of [Formula: see text], and yields to the following descriptive set-theoretical analog of Shelah’s Main Gap Theorem: Given a countable complete first-order theory [Formula: see text], either [Formula: see text] is Borel with a countable Borel rank, or it is not Borel at all. The dividing line between the two situations is the same as in Shelah’s theorem, namely that of classifiable shallow theories. We also provide a Borel reducibility version of the above theorem, discuss some limitations to the possible complexities of [Formula: see text], and provide a characterization of categoricity of [Formula: see text] in terms of the descriptive set-theoretical complexity of [Formula: see text]. (shrink)

Answering one of the main questions of [S.-D. Friedman, T. Hyttinen and V. Kulikov, Generalized descriptive set theory and classification theory, Mem. Amer. Math. Soc. 230 80, Chap. 7]...

Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This is in strong contrast to the case of the isomorphism relation, which as an equivalence relation on graphs is far from complete.In this article we strengthen the results of [5] by showing that not only does bi-embeddability give rise to analytic equivalence relations which are complete (...) under Borel reducibility, but in fact any analytic equivalence relation is Borel equivalent to such a relation. This result and the techniques introduced answer questions raised in [5] about the comparison between isomorphism and bi-embeddability. Finally, as in [5] our results apply not only to classes of countable structures defined by sentences of ℒω1ω, but also to discrete metric or ultrametric Polish spaces, compact metrizable topological spaces and separable Banach spaces, with various notions of embeddability appropriate for these classes, as well as to actions of Polish monoids. (shrink)

Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This is in strong contrast to the case of the isomorphism relation, which as an equivalence relation on graphs (or on any class of countable structures consisting of the models of a sentence of L ω ₁ ω ) is far from complete (see [5, 2]). In (...) this article we strengthen the results of [5] by showing that not only does bi-embeddability give rise to analytic equivalence relations which are complete under Borel reducibility, but in fact any analytic equivalence relation is Borel equivalent to such a relation. This result and the techniques introduced answer questions raised in [5] about the comparison between isomorphism and bi-embeddability. Finally, as in [5] our results apply not only to classes of countable structures defined by sentences of ω ₁ ω , but also to discrete metric or ultrametric Polish spaces, compact metrizable topological spaces and separable Banach spaces, with various notions of embeddability appropriate for these classes, as well as to actions of Polish monoids. (shrink)

Answering some of the main questions from [L. Motto Ros, The descriptive set-theoretical complexity of the embeddability relation on models of large size, Ann. Pure Appl. Logic164(12) (2013) 1454–1492], we show that whenever κ is a cardinal satisfying κ<κ=κ>ω, then the embeddability relation between κ-sized structures is strongly invariantly universal, and hence complete for (κ-)analytic quasi-orders. We also prove that in the above result we can further restrict our attention to various natural classes of structures, including (generalized) trees, graphs, or (...) groups. This fully generalizes to the uncountable case the main results of [A. Louveau and C. Rosendal, Complete analytic equivalence relations, Trans. Amer. Math. Soc.357(12) (2005) 4839–4866; S.-D. Friedman and L. Motto Ros, Analytic equivalence relations and bi-embeddability, J. Symbolic Logic76(1) (2011) 243–266; J. Williams, Universal countable Borel quasi-orders, J. Symbolic Logic79(3) (2014) 928–954; F. Calderoni and L. Motto Ros, Universality of group embeddability, Proc. Amer. Math. Soc.146 (2018) 1765–1780]. (shrink)

At their best, mottos help us cope by crystallizing attitudes, eliciting resolve, and guiding conduct. Mottos have moral significance when they allude to the virtues and reflect the character of individuals and groups. As such, they function in the moral space between abstract ethical theory and contextual moral judgment. I discuss personal mottos such as those of Isak Dinesen (“I will answer”) and group mottos such as found in social movements (“Think globally, act locally”), professions (“Above all, do no harm”), (...) philosophy (“The personal is political”), and therapeutic groups like Alcoholics Anonymous (“One day at a time”). (shrink)

In this paper, we bring together research on complex problem solving with that on motivational psychology about goal setting. Complex problems require motivational effort because of their inherent difficulties. Goal Setting Theory has shown with simple tasks that high, specific performance goals lead to better performance outcome than do-your-best goals. However, in complex tasks, learning goals have proven more effective than performance goals. Based on the Zurich Resource Model, so-called motto-goals should activate a person’s resources through positive affect. It was (...) found that motto-goals are effective with unpleasant duties. Therefore, we tested the hypothesis that motto-goals outperform learning and performance goals in the case of complex problems. A total of N = 123 subject participated in the experiment. In dependence of their goal condition, subjects developed a personal motto, learning, or performance goal. This goal was adapted for the computer-simulated complex scenario Tailorshop, where subjects worked as managers in a small fictional company. Other than expected, there was no main effect of goal condition for the management performance. An unexpected gender effect revealed better performance for men than women, pointing to a potential stereotype threat. As hypothesized, motto goals led to higher positive and lower negative affect than the other two goal types. Even though positive affect decreased and negative affect increased in all three groups during Tailorshop completion, participants with motto goals reported the lowest rates of negative affect. Exploratory analyses investigated the role of affect in complex problem solving via mediational analyses and the influence of goal type on perceived goal attainment. (shrink)

Whether in slogans, catchphrases, adages or proverbs, we encounter mottos every day, but we rarely take time to reflect on them. In Of Mottos and Morals: Simple Words for Complex Virtues, Martin explores the possibility that mottos themselves are worthy of serious thought, examining how they contribute to moral guidance and help us grapple with complexity.

Ausgangspunkt dieses Artikels ist die Einsicht, die auch von Wittgenstein und der "schweigenden Mehrheit" geteilt wird, daß die meisten sogenannten fundamentalen Begriffe und Probleme der Philosophie erkenntnistheoretisch unrentabel sind, insbesondere der Begriff der Gültigkeit (von Beweis- und Rechenregeln) und seine traditionelle Problematik. Im Gegensatz zu Wittgenstein wird diese Einsicht aber nicht auf "Sinnlosigkeit", d.h. Präzisionsunfähigkeitjener Problematik, sondern auf ihre Oberflächl d.h. unangemessene Allgemeinheit, zurückgeführt.

Ausgangspunkt dieses Artikels ist die Einsicht, die auch von Wittgenstein und der "schweigenden Mehrheit" geteilt wird, daß die meisten sogenannten fundamentalen Begriffe und Probleme der Philosophie erkenntnistheoretisch unrentabel sind, insbesondere der Begriff der Gültigkeit (von Beweis- und Rechenregeln) und seine traditionelle Problematik. Im Gegensatz zu Wittgenstein wird diese Einsicht aber nicht auf "Sinnlosigkeit", d.h. Präzisionsunfähigkeitjener Problematik, sondern auf ihre Oberflächl d.h. unangemessene Allgemeinheit, zurückgeführt.

The present article aims to examine whether this Platonic dialogue can be regarded as polemical and competing with the similar educational proposals put forward by Xenophon and Antisthenes for the young Alcibiades aspiring to power in the city of Athens. The present article has been divided into two major parts. In the first one, I propose to unify the two opposing points of view that are reflected in the interpretations of the motto: the one that takes it to be a (...) solitary dialogue of a soul talking to itself and the one that takes it to be an intersubjective dialogue. In the second part, I try to highlight a few points of contact and conflict between Plato, Xenophon and Antisthenes, arguing that it is the latter two that may be alluded to in the dialogue, albeit indirectly, as competing and polemical targets. (shrink)

This paper attempts to delve into the heart of Zen Buddhism by discussing the four Zen mottos, which provide the philosophical and spiritual pillars of Zen. The four Zen mottos, “special transmission outside doctrine,” “not to establish language,” “direct point to the mind,” and “seeing into one’s nature and attaining the Buddhahood,” address the fundamental questions about language in its role of the expression and transmission of the spirituality. The mottos indicate that enlightenment is nothing but breakthroughs in an individual’s (...) searching for meanings and a new level of consciousness in their life practice. The experiences of enlightenment as new horizons of consciousness cannot be fixed in conceptual language and reduced to doctrinal principles. Enlightenment, as concrete experiences in the “flux” of the mind, can be most directly expressed and effectively transmitted in poetic language. Poetry can metaphorically capture, articulate, and evoke the spiritual experiences that are often viewed as mystical or ineffable in an abstract paradigm. Poetry can capture the living experiences of life without making judgments and fixation based on doctrines and conceptual frameworks; therefore it is “a special transmission outside the doctrine.” Poetry can deliver spiritual messages without directly asserting and delimiting them; therefore, it “does not establish language.” Poetry can “directly point to the mind” by freeing the speaker from any fixed positions, frameworks, and logical rules, so it can directly appeal to people’s minds and respond to concrete situations. The poetics of Zen renders a contrast to the traditional approach to Buddhism that seeks the abstract representation of enlightenment based on exegeses and interpretations of the established words given by the founders and predecessors. (shrink)

There is only one occurrence of the word ‘progress’ in the Philosophical Investigations. It is located in the sentence that serves as the book’s epigraph. The book, however, does not explicit prese...

“Only connect …,” the epigraph of Forster's Howards End, offers itself as a model of moral diplomacy. The efficacy of genuine human connection—whether it takes the form of creative action or of decent human relations—in containing and civilizing force is an idea that informs the novel's conception of what constitutes and ensures civilized life. Forster regarded propriety and convention as expressions of force and so applauded any assault on conventional feeling as an act of moral heroism. This essay introduces the (...) third installment of the Common Knowledge symposium “Peace by Other Means”: it explores and indeed extols the moral efficacy of connection in containing force and resolving conflicts, but it also contemplates the obstacles to connection, which Forster dramatizes with his characteristic honesty. (shrink)

O presente artigo tem por objectivo fazer uma reflexão sobre o motto, o prólogo e a introdução a O conceito de Angústia (1844) de Søren Kierkegaard. Longe de serem meros preâmbulos, estes textos constituent importantes chaves de leitura para a obra que encabeçam. Na verdade, a distinção socrática entre o que se sabe e o que não se sabe do motto de O conceito de angústia transforma-se no argumento propriamente dito da obra. A partir desta distinção, Kierkegaard desenvolve a sua (...) crítica contra a confusão moderna das ciências, ao mesmo tempo que propõe uma nova divisão em ordem a poder situar legitimamente a questão do pecado. Em vez de conceber o pecado de maneira especulativa, a psicologia da angústia é apresentada como a única disciplina em que propriamente se pode tratar o problema do pecado e, ao mesmo tempo, ser consciente da sua incompreensibilidade. /// The objective of this article is to think about the motto, preface and introduction to Kierkegaard's The Concept of Anxiety (1844). Far from being mere preambles, these texts constitute the reading key for the book they lead. As a matter of fact, the Socratic distinction between what we understand and what we do not understand from The concept of Anxiety's motto becomes the philosophical argument of the work. From this distinction, Kierkegaard carries out a critique against the modern confusion of sciences and at the same time proposes a new arrangement in which to place legitimately the problem of sin. Instead of conceiving sin in a speculative way, the psychology of anxiety shows itself to be the only discipline able to deal properly with the question of sin and to be conscious of its mysterious dimension. (shrink)

Motto-goals describe a desired mind-set and provide a person with a guiding principle of how to approach a personal goal or obligation. We propose that motto-goals can be conceptionalized as individually created metaphors and that the figurative, metaphorical language and the characteristics of the formation process make them effective in changing the perception of unpleasant personal obligations as more inherently enjoyable and raise vitality levels. To test whether a newly devised minimalistic motto-goal intervention can make goal striving more attractive and (...) energize goal-oriented action in relation to an unpleasant obligation, two experimental studies were conducted. In Study 1 the motto-goal condition led to stronger anticipation of activity related incentives and vitality compared to a distraction task. The effect on vitality was partially mediated by a change in feelings of autonomy. Study 2 replicated the effects compared to a placebo intervention and further found motto-goals to be specifically effective in increasing the anticipation of activity related incentives as opposed to outcome related incentives. The results support that applying motto-goals built with a newly developed minimalist motto-goal intervention can influence the subjective experience of individuals faced with a previously unpleasant obligation. (shrink)

Social epistemology balances neoclassic and nonclassic, normative and descriptive, and veritistic and constructionist approaches. Among these approaches exist two terminologically different though (in fact) similar proposals: naturalization and socialization. Both proposals lead to a kind of interdisciplinary imperialism reducing epistemology to a ?positive science? like sociology of knowledge, social history of science, and science and technology studies. I call this attitude the ?strong version? of naturalism. How, then, can we save epistemology without indulging in purely transcendental contemplations while simultaneously securing (...) its connections to the empirical sciences that analyze knowledge in a social context? Can social epistemology be reduced to any one or to a set of special approaches to knowledge as a completely naturalizing program? If not, is social epistemology a kind of philosophical epistemology and what is its differencia specifica? And how is the social epistemology related to special approaches to knowledge? In proposing a ?weak version? of naturalism?an idea of the social epistemology based on interdisciplinary interaction?a reimagining of the concepts of ?interdisciplinarity? and ?context? is required. (shrink)