Twelve-year-old Kalman Gabriel wrote to hundreds of famous -- and infamous -- people to find out what kind of advice for life they would impart upon him. The response was overwhelming. Over two hundred people, from Mother Teresa to Mr. Rogers: from Ray Bradbury and Scott Turow to Naomi Judd and Drew Barrymore, responded to Kalman's letters. Leona Helmsley told Kalman, "Presevere," while Elie Weisel advised, "Study. Read. Share." Kalman's files are compulsively readable and infinitely quotable.

Conventional wisdom holds that Judaism is indifferent or even suspiciously hostile to the visual arts due to the Second Commandment's prohibition on creating "graven images," the dictates of monotheism, and historical happenstance. This intellectual history of medieval and modern Jewish attitudes toward art and representation overturns the modern assumption of Jewish iconophobia that denies to Jewish culture a visual dimension. Kalman Bland synthesizes evidence from medieval Jewish philosophy, mysticism, poetry, biblical commentaries, travelogues, and law, concluding that premodern Jewish intellectuals held (...) a positive, liberal understanding of the Second Commandment and did, in fact, articulate a certain Jewish aesthetic. He draws on this insight to consider modern ideas of Jewish art, revealing how they are inextricably linked to diverse notions about modern Jewish identity that are themselves entwined with arguments over Zionism, integration, and anti-Semitism. Through its use of the past to illuminate the present and its analysis of how the present informs our readings of the past, this book establishes a new assessment of Jewish aesthetic theory rooted in historical analysis. Authoritative and original in its identification of authentic Jewish traditions of painting, sculpture, and architecture, this volume will ripple the waters of several disciplines, including Jewish studies, art history, medieval and modern history, and philosophy. (shrink)

Condensed detachment is usually regarded as a notation, and defined by example. In this paper it is regarded as a rule of inference, and rigorously defined with the help of the Unification Theorem of J. A. Robinson. Historically, however, the invention of condensed detachment by C. A. Meredith preceded Robinson's studies of unification. It is argued that Meredith's ideas deserve recognition in the history of unification, and the possibility that Meredith was influenced, through ukasiewicz, by ideas of Tarski going back (...) at least to 1939, and possibly to 1930 or earlier, is discussed. It is proved that a term is derivable by substitution and ordinary detachment from given axioms if and only if it is a substitution instance of a term which is derivable from these axioms by condensed detachment, and it is shown how this theorem enables the ideas of ukasiewicz and Tarski mentioned above to be formalized and extended. Finally, it is shown how condensed detachment may be subsumed within the resolution principle of J. A. Robinson, and several computer studies of particular Hilbert-type propositional calculi using programs based on condensed detachment or on resolution are briefly discussed. (shrink)

The paper sets out to offer an alternative to the function/argument approach to the most essential aspects of natural language meanings. That is, we question the assumption that semantic completeness (of, e.g., propositions) or incompleteness (of, e.g., predicates) exactly replicate the corresponding grammatical concepts (of, e.g., sentences and verbs, respectively). We argue that even if one gives up this assumption, it is still possible to keep the compositionality of the semantic interpretation of simple predicate/argument structures. In our opinion, compositionality presupposes (...) that we are able to compare arbitrary meanings in term of information content. This is why our proposal relies on an ‘intrinsically’ type free algebraic semantic theory. The basic entities in our models are neither individuals, nor eventualities, nor their properties, but ‘pieces of evidence’ for believing in the ‘truth’ or ‘existence’ or ‘identity’ of any kind of phenomenon. Our formal language contains a single binary non-associative constructor used for creating structured complex terms representing arbitrary phenomena. We give a finite Hilbert-style axiomatisation and a decision algorithm for the entailment problem of the suggested system. (shrink)

A recurrent theme in contemporary narratives of grieving is that there is a gap between the griever’s more or less consciously chosen expression of, and acting out of, grief and loss and other people’s seeming lack of acceptance. Starting from the view that the social context of feelings and emotions are constitutive in making an emotional experience what it is, this article explores what is done and experienced in acts of grief. A phenomenological perspective is applied to analyze the conditioning (...) of these experiences, and what the acts of grieving may accomplish in relation to various aspects of the self, indeed selves—that is, in relation to the surviving relative as well as the deceased. (shrink)

Historians have recently used the Internet to circulate political statements about law. This paper explores the statements they issued against President Clinton's impeachment and President Bush's inauguration. It pays special attention to impeachment, comparing the position taken by historians with that taken by the law professors. While concluding that such statements can be useful, the author advises historians lacking the expertise to evaluate the positions taken in a statement to proceed carefully in signing it. She suggests that historians sign only (...) such documents whose scholarship they have made a preliminary assessment that they could individually defend publicly. She also urges historians to craft statements that give the public a sense of the methods they use in interpreting the past. (shrink)

In the first part of this paper we indicate how Meredith's condensed detachment may be used to give a new proof of Belnap's theorem that if every axiom x of a calculus S has the two-property that every variable which occurs in x occurs exactly twice in x, then every theorem of S is a substitution instance of a theorem of S which has the two-property. In the remainder of the paper we discuss the use of mechanical theorem-provers, based either (...) on condensed detachment or on the resolution rule of J. A. Robinson, to investigate various calculi whose axioms all have the two-property. Particular attention is given to D-groupoids, i.e. sets of formulae which are closed under condensed detachment. (shrink)

An equivalence between the category of MV-algebras and the category \ is given in Castiglioni et al. :67–92, 2014). An integral residuated lattice with bottom is an MV-algebra if and only if it satisfies the equations \ \vee = 1}\) and \ = a \wedge b}\). An object of \ is a residuated lattice which in particular satisfies some equations which correspond to the previous equations. In this paper we extend the equivalence to the category whose objects are pairs, where (...) A is an MV-algebra and I is an ideal of A. (shrink)

An equivalence between the category of MV-algebras and the category $${{\rm MV^{\bullet}}}$$ MV ∙ is given in Castiglioni et al. :67–92, 2014). An integral residuated lattice with bottom is an MV-algebra if and only if it satisfies the equations $${a = \neg \neg a, \vee = 1}$$ a = ¬ ¬ a, ∨ = 1 and $${a \odot = a \wedge b}$$ a ⊙ = a ∧ b. An object of $${{\rm MV^{\bullet}}}$$ MV ∙ is a residuated lattice which in (...) particular satisfies some equations which correspond to the previous equations. In this paper we extend the equivalence to the category whose objects are pairs, where A is an MV-algebra and I is an ideal of A. (shrink)

Some may be of the opinion that one event can begin before another only by virtue of the existence of some event (a “witness”) which wholly precedes the other and does not wholly precede the one (and similarly for “ends before” and “does not abut”). Those would prefer $\mathbb{F}$ 0 to $\mathbb{F}$ as a model for observers' apprehensions of events. Since G is a functor from $\mathbb{M}$ to $\mathbb{F}$ 0, the current construction (restricted to $\mathbb{F}$ 0) remains applicable.This work (...) supports a claim that the psychologically fundamental temporal relationships are “wholly precedes”, “begins before”, “ends before” and “abuts”. But only in a very weak sense. Any other set of relationships which is interdefinable with this one, using only quantifier-free formulas in the definitions, could be used to define a category $\mathbb{F}$ ′ which is indistinguishable from $\mathbb{F}$ (because the same functions preserve and reflect the new relationships). This work equally supports the claim that those relationships are the psychologically fundamental ones, or the claim that it is just “wholly precedes” which is fundamental, and that we perceive “begins before” just by virtue of witnesses. But it refutes the claim that only “wholly precedes” is fundamental, and that we understand “begins before” only because we understand time as a linear ordering. (shrink)

In this note, we give a representation of distributive Ockham algebras via natural hom-functors. In order to do this, we describe two different structures (one algebraic, and the other order-topological) on the set of subsets of the natural numbers. The topological duality previously obtained by A. Urquhart is used throughout.

Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. Specifically, (...) a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics. (shrink)

In this paper we expand previous results obtained in [2] about the study of categorical equivalence between the category IRL 0 of integral residuated lattices with bottom, which generalize MV-algebras and a category whose objects are called c-differential residuated lattices. The equivalence is given by a functor ${{\mathsf{K}^\bullet}}$ , motivated by an old construction due to J. Kalman, which was studied by Cignoli in [3] in the context of Heyting and Nelson algebras. These results are then specialized to the (...) case of MV-algebras and the corresponding category ${MV^{\bullet}}$ of monadic MV-algebras induced by “Kalman’s functor” ${\mathsf{K}^\bullet}$ . Moreover, we extend the construction to ℓ-groups introducing the new category of monadic ℓ-groups together with a functor ${\Gamma ^\sharp}$ , that is “parallel” to the well known functor ${\Gamma}$ between ℓ and MV-algebras. (shrink)

Alain Badiou’s treatment of objects in Logics of Worlds is both rich and highly technical, though its terminological challenges are softened by his use of illuminating examples. This article takes a twofold approach to the topic. In a first sense, the theory of objects developed in Logics of Worlds by way of an imagined protest at the Place de la République in Paris exhibits two questionable aspects: (1) the notion that the object is a bundle of qualities (found proverbially in (...) Hume, but also in Kant’s “transcendental object=X”), and (2) the ultimately idealist assumption of a possible isomorphy between appearance and reality. But in a second sense, Badiou’s transcendental account of worlds leads him to a fascinating theory of exemplary entities, one that is immune to the critiques of onto-theology made by Heidegger and Derrida. This can be found in his account of the “transcendental functor” in Alexander the Great’s decisive victory over Darius III at the Battle of Gaugamela in 331 B.C.E. (shrink)

Fried and Kollár constructed a fully faithful functor from the category of graphs to the category of fields. We give a new construction of such a functor and use it to resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure${\cal S}$, there exists a countable field${\cal F}$of arbitrary characteristic with the same essential computable-model-theoretic properties as${\cal S}$. Along the way, we develop a new “computable category theory”, and prove that our (...) functor and its partially defined inverse are computable functors. (shrink)

It is often said that a person P knows the meaning of a sentence S if P knows S’ s truth-conditions, in the sense that given any possible world, P knows whether S is true in that world. This idea of sentence-meaning corresponds fairly closely to what Frege, Russell, Carnap, and other philosophers have had in mind in speaking of the senses, propositional contents, or “locutionary” meanings of sentences; and, not unnaturally, it has encouraged semanticists such as David Lewis, Robert (...) Stalnaker and Max Cresswell to suggest that sentence-meanings or propositions simply are functions from the set of possible worlds onto the truth-values. (shrink)

Given some links between Lyndon’s Interpolation Theorem, term distribution, and Sommers and Englebretsen’s logic, in this contribution we attempt to capture a sense of interpolation for Sommers and Englebretsen’s Term Functor Logic. In order to reach this goal we first expound the basics of Term Functor Logic, together with a sense of term distribution, and then we offer a proof of our main contribution.

Several Gentzen-style syntactic type calculi with product are considered. They form a hierarchy in such a way that one calculus results from another by imposing a new condition upon the sequent-forming operation. It turns out that, at some steps of this process, two different functors collapse to a single one. For the remaining stages of the hierarchy, analogues of Wajsbergs's theorem on non-mutual-definability are proved.

The most difficult problem that Leniewski came across in constructing his system of the foundations of mathematics was the problem of defining definitions, as he used to put it. He solved it to his satisfaction only when he had completed the formalization of his protothetic and ontology. By formalization of a deductive system one ought to understand in this context the statement, as precise and unambiguous as possible, of the conditions an expression has to satisfy if it is added to (...) the system as a new thesis. Now, some protothetical theses, and some ontological ones, included in the respective systems, happen to be definitions. In the present essay I employ Leniewski's method of terminological explanations for the purpose of formalizing ukasiewicz's system of implicational calculus of propositions, which system, without having recourse to quantification, I first extended some time ago into a functionally complete system. This I achieved by allowing for a rule of implicational definitions, which enabled me to define any propositionforming functor for any finite number of propositional arguments. (shrink)

Buber proclaims that 'in the beginning was relation'; that man is by his very nature a Homo Dialogus - incapable of realizing himself without communion with man, with the creation and with his Creator.Buber sought to anchor Zionism in what he defined as 'Hebrew Humanism': "the path of holiness" as opposed to "holy egoism".

Interest in the intersection between bilingualism and cognitive control and accessibility to neuroimaging methods have resulted in numerous studies with a variety of interpretations of the bilingual cognitive advantage. Neurocomputational Emergentism (or Neuroemergentism for short) is a new framework for understanding this relationship between bilingualism and cognitive control. This framework considers Emergence, in which two small elements are recombined in an interactive manner, yielding a non-linear effect. Added to this is the notion that Emergence can be captured in neural systems (...) using computationally inspired models. This review poses that bilingualism and cognitive control, as examined through the Neuroemergentist framework, are interwoven through development and involve the non-linear growth of cognitive processing encompassing brain areas that combine and recombine, in symbiotic and parasitic ways, in order to handle more complex types of processing. The models that have sought to explain the neural substrates of bilingual cognitive differences will be discussed with a reinterpretation of the entire bilingual cognitive advantage within a Neuroemergentist framework incorporating its neural bases. It will conclude by discussing how this new Neuroemergentist approach alters our view of the effects of language experience on cognitive control. Avenues to move beyond the simple notion of a bilingual advantage or lack thereof will be proposed. (shrink)

Rosen's modelling relations constitute a conceptual schema for the understanding of the bidirectional process of correspondence between natural systems and formal symbolic systems. The notion of formal systems used in this study refers to information structures constructed as algebraic rings of observable attributes of natural systems, in which the notion of observable signifies a physical attribute that, in principle, can be measured. Due to the fact that modelling relations are bidirectional by construction, they admit a precise categorical formulation in terms (...) of the category-theoretic syntactic language of adjoint functors, representing the inverse processes of information encoding/decoding via adjunctions. As an application, we construct a topological modelling schema of complex systems. The crucial distinguishing requirement between simple and complex systems in this schema is reflected with respect to their rings of observables by the property of global commutativity. The global information structure representing the behaviour of a complex system is modelled functorially in terms of its spectrum functor. An exact modelling relation is obtained by means of a complex encoding/decoding adjunction restricted to an equivalence between the category of complex information structures and the category of sheaves over a base category of partial or local information carriers equipped with an appropriate topology. (shrink)

The Origin of the ‘Paardekraal Vow’ Contrary to common belief that the ‘1880 Vow' was taken at Paardekraal, on the restoration of the Republic on 13 December 1880, the writer has documentary proof that this ‘Vow’ was in existence almost two years before that date. An agreement is said to have been signed by a number of the Boers at Wonderfontein, where they had gathered between 10 and 13 January 1879 to claim the restoration of the Republic. Both these minutes (...) and the Transvaal press ignored this agreement as it was feared that they would lead to premature armed resistance. The Paardekraal Festival Commission became aware of the agreement in 1945 and adopted it as the ‘Vow of 1880' in their 1946 programme. (shrink)