Purpose is an intention over the long-term to have an effect on the world that is both meaningful to oneself and to others. What are schools doing to help students use the knowledge and skills they learn in school in their own lives and aspirations? This is the first study that compares adolescent purposes and life satisfaction in Singaporean and Israeli schools. Findings showed four purpose clusters for Singaporean adolescents: No Orientation, Self-focused, Other-focused, and both Self- and Other-focused. Israeli adolescents (...) were in three purpose clusters: Self-focused, Other-focused, and Self- and Other-focused. The purpose groups differed on average life satisfaction in both countries: Self- and Other-focused were highest, followed by Self-focused and Other-focused. The No Orientation group in Singapore was lowest. Notably, beyond these differences between the groups, Israeli adolescents reported significantly higher life satisfaction in each purpose group. We discuss implications for schools and education policymakers. (shrink)
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In the global context, the economic-technological powers are also the political-cultural powers, which have the capacity to obtain the maximising benefits from the global flow of information. Meanwhile, the countries which are inferior in economics, technology, etc. feel unable to enjoy the fruits of the information society; they have to struggle for their right to communicate.
Bi-intuitionistic logic is the result of adding the dual of intuitionistic implication to intuitionistic logic. In this note, we characterize the expressive power of this logic by showing that the ﬁrst order formulas equivalent to translations of bi-intuitionistic propositional formulas are exactly those preserved under bi-intuitionistic directed bisimulations. The proof technique is originally due to Lindstrom and, in contrast to the most common proofs of this kind of result, it does not use the machinery of neither saturated models nor elementary (...) chains. (shrink)
Louveau and Rosendal  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  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  about the comparison between isomorphism and bi-embeddability. Finally, as in  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)
This study accounts for the observed patterns of variation and ambiguity in the expression and interpretation of aspect in bare habitual statements in Polish in the framework of Bouma’s ( 2008 ) recent version of stratified bi-directional Optimality Theory (OT).
We consider a “polarized” version of bi-intuitionistic logic [5, 2, 6, 4] as a logic of assertions and hypotheses and show that it supports a “rich proof theory” and an interesting categorical interpretation, unlike the standard approach of C. Rauszer’s Heyting-Brouwer logic [28, 29], whose categorical models are all partial orders by Crolard’s theorem . We show that P.A. Melliès notion of chirality [21, 22] appears as the right mathematical representation of the mirror symmetry between the intuitionistic and co-intuitionistc sides (...) of polarized bi-intuitionism. Philosophically, we extend Dalla Pozza and Garola’s pragmatic interpretation of intuitionism as a logic of assertions  to bi-intuitionism as a logic of assertions and hypotheses. We focus on the logical role of illocutionary forces and justification conditions in order to provide “intended interpretations” of logical systems that classify inferential uses in natural language and remain acceptable from an intuitionistic point of view. Although Dalla Pozza and Garola originally provide a constructive interpretation of intuitionism in a classical setting, we claim that some conceptual refinements suffice to make their “pragmatic interpretation” a bona fide representation of intuitionism. We sketch a meaning-asuse interpretation of co-intuitionism that seems to fulfil the requirements of Dummett and Prawitz’s justificationist approach. We extend the Brouwer-Heyting-Kolmogorov interpretation to bi-intuitionism by regarding co-intuitionistic formulas as types of the evidence for them: if conclusive evidence is needed to justify assertions, only a scintilla of evidence suffices to justify hypotheses. (shrink)
A bi-level account of trust is developed and defended, one with relevance in ethics as well as epistemology. The proposed account of trust—on which trusting is modelled within a virtue-theoretic framework as a performance-type with an aim—distinguishes between two distinct levels of trust, apt and convictive, that take us beyond previous assessments of its nature, value, and relationship to risk assessment. While Ernest Sosa (2009; 2015; 2017), in particular, has shown how a performance normativity model may be fruitfully applied to (...) belief, my objective is to apply this kind of model in a novel and principled way to trust. I conclude by outlining some of the key advantages of the performance-theoretic bi-level account of trust defended over more traditional univocal proposals. (shrink)
In this paper, bi-intuitionistic multilattice logic, which is a combination of multilattice logic and the bi-intuitionistic logic also known as Heyting–Brouwer logic, is introduced as a Gentzen-type sequent calculus. A Kripke semantics is developed for this logic, and the completeness theorem with respect to this semantics is proved via theorems for embedding this logic into bi-intuitionistic logic. The logic proposed is an extension of first-degree entailment logic and can be regarded as a bi-intuitionistic variant of the original classical multilattice logic (...) determined by the algebraic structure of multilattices. Similar completeness and embedding results are also shown for another logic called bi-intuitionistic connexive multilattice logic, obtained by replacing the connectives of intuitionistic implication and co-implication with their connexive variants. (shrink)
WANG Bi 王弼 develops a metaphysic of Dao 道 in his Commentary on Laozi and “The Structure of Laozi’s Subtle Pointers.” I summarize this metaphysic as the following thesis: Dao is featureless and is the ultimate reason why the myriad things exist and are the ways they are. I develop a systematic account of this thesis: I provide an interpretation of the featurelessness of Dao and show how Dao’s featurelessness relates to its fundamental explanatory role as the ontological ground for (...) the myriad things. (shrink)
We prove that certain natural sequent systems for bi-intuitionistic logic have the analytic cut property. In the process we show that the (global) subformula property implies the (local) analytic cut property, thereby demonstrating their equivalence. Applying a version of Maehara technique modified in several ways, we prove that bi-intuitionistic logic enjoys the classical Craig interpolation property and Maximova variable separation property; its Halldén completeness follows.
In their recent paper Bi-facial truth: a case for generalized truth values Zaitsev and Shramko  distinguish between an ontological and an epistemic interpretation of classical truth values. By taking the Cartesian product of the two disjoint sets of values thus obtained, they arrive at four generalized truth values and consider two “semi-classical negations” on them. The resulting semantics is used to define three novel logics which are closely related to Belnap’s well-known four valued logic. A syntactic characterization of these (...) logics is left for further work. In this paper, based on our previous work on a functionally complete extension of Belnap’s logic, we present a sound and complete tableau calculus for these logics. It crucially exploits the Cartesian nature of the four values, which is reflected in the fact that each proof consists of two tableaux. The bi-facial notion of truth of Z&S is thus augmented with a bi-facial notion of proof. We also provide translations between the logics for semi-classical negation and classical logic and show that an argument is valid in a logic for semi-classical negation just in case its translation is valid in classical logic. (shrink)
The aim of this paper is to introduce a new approach to the modal operators of necessity and possibility. This approach is based on the existence of two negations in certain lattices that we call bi-Heyting algebras. Modal operators are obtained by iterating certain combinations of these negations and going to the limit. Examples of these operators are given by means of graphs.