Tarski asked whether the arithmetic identities taught in high school are complete for showing all arithmetic equations valid for the natural numbers. The answer to this question for the language of arithmetic expressions using a constant for the number one and the operations of product and exponentiation is affirmative, and the complete equational theory also characterises isomorphism in the typed lambda calculus, where the constant for one and the operations of product and exponentiation respectively correspond to the unit type and (...) the product and arrow type constructors. This paper studies isomorphisms in typed lambda calculi with empty and sum types from this viewpoint. Our main contribution is to show that a family of so-called Wilkie–Gurevič identities, that plays a pivotal role in the study of Tarski’s high school algebra problem, arises from type-theoretic isomorphisms. We thus close an open problem by establishing that the theory of type isomorphisms in the presence of product, arrow, and sum types is not finitely axiomatisable. Further, we observe that for type theories with arrow, empty and sum types the correspondence between isomorphism and arithmetic equality generally breaks down, but that it still holds in some particular cases including that of type isomorphism with the empty type and equality with zero. (shrink)

An old and well-known objection to non-classical logics is that they are too weak; in particular, they cannot prove a number of important mathematical results. A promising strategy to deal with this objection consists in proving so-called recapture results. Roughly, these results show that classical logic can be used in mathematics and other unproblematic contexts. However, the strategy faces some potential problems. First, typical recapture results are formulated in a purely logical language, and do not generalize nicely to languages containing (...) the kind of vocabulary that usually motivates non-classical theories—for example, a language containing a naïve truth predicate. Second, proofs of recapture results typically employ classical principles that are not valid in the targeted non-classical system; hence, non-classical theorists do not seem entitled to those results. In this paper, we analyze these problems and provide solutions on behalf of non-classical theorists. To address the first problem, we provide a novel kind of recapture result, which generalizes nicely to a truth-theoretic language. As for the second problem, we argue that it relies on an ambiguity and that, once the ambiguity is removed, there are no reasons to think that non-classical logicians are not entitled to their recapture results. (shrink)

The infinitary function of the truth predicate consists in its ability to express infinite conjunctions and disjunctions. A transparency principle for truth states the equivalence between a sentence and its truth predication; it requires an introduction principle—which allows the inference from “snow is white” to “the sentence ‘snow is white’ is true”—and an elimination principle—which allows the inference from “the sentence ‘snow is white’ is true” to “snow is white”. It is commonly assumed that a theory of truth needs to (...) satisfy a transparency principle to fulfil the infinitary function. Picollo and Schindler (Erkenntnis 83:899–928, 2017) argue against this idea. They prove that, given certain assumptions, an elimination principle is sufficient for the purpose. Then, they pose a challenge: to show why we should incorporate introduction principles to our theory of truth. In this essay I take on the challenge. I show that, given the authors’ assumptions, an introduction principle is also sufficient to perform the infinitary function. (shrink)

The main aim of this paper is to introduce the logics of evidence and truth $$LET_{K}^+$$ and $$LET_{F}^+$$ together with sound, complete, and decidable six-valued deterministic semantics for them. These logics extend the logics $$LET_{K}$$ and $$LET_{F}^-$$ with rules of propagation of classicality, which are inferences that express how the classicality operator $${\circ }$$ is transmitted from less complex to more complex sentences, and vice-versa. The six-valued semantics here proposed extends the 4 values of Belnap-Dunn logic with 2 more values (...) that intend to represent (positive and negative) reliable information. A six-valued non-deterministic semantics for $$LET_{K}$$ is obtained by means of Nmatrices based on swap structures, and the six-valued semantics for $$LET_{K}^+$$ is then obtained by imposing restrictions on the semantics of $$LET_{K}$$. These restrictions correspond exactly to the rules of propagation of classicality that extend $$LET_{K}$$. The logic $$LET_{F}^+$$ is obtained as the implication-free fragment of $$LET_{K}^+$$. We also show that the 6 values of $$LET_{K}^+$$ and $$LET_{F}^+$$ define a lattice structure that extends the lattice L4 defined by the Belnap-Dunn four-valued logic with the 2 additional values mentioned above, intuitively interpreted as positive and negative reliable information. Finally, we also show that $$LET_{K}^+$$ is Blok-Pigozzi algebraizable and that its implication-free fragment $$LET_{F}^+$$ coincides with the degree-preserving logic of the involutive Stone algebras. (shrink)

We introduce a methodology whereby an arbitrary logic system L can be enriched with temporal features to create a new system T(L). The new system is constructed by combining L with a pure propositional temporal logic T (such as linear temporal logic with Since and Until) in a special way. We refer to this method as adding a temporal dimension to L or just temporalising L. We show that the logic system T(L) preserves several properties of the original temporal logic (...) like soundness, completeness, decidability, conservativeness and separation over linear flows of time. We then focus on the temporalisation of first-order logic, and a comparison is make with other first-order approaches to the handling of time. (shrink)

The present work looks at what we call “the multiverse of quantification”, where visible and invisible numbers permeate all aspects and venues of life. We review the contributions of different authors who focus on the roles of quantification in society, with the aim of capturing different and sometimes separate voices. Several scholars, including economists, jurists, philosophers, sociologists, communication and data scientists, express concerns or identify critical areas of our relationship with new technologies of ‘numericization’. While mindful of the important specificities (...) of the different families of quantification, we use our broad and holistic canvas to explore possible spaces for a more systematic investigation of incumbent and novel quantifications, as to increase communication among disciplinary communities, and among these and society, in the pursuit a democratic agency and self-defence. (shrink)

Presents spiritual reflections, thoughts, stories, and ideas intended to inspire readers to realize the immeasurable value of every moment of life, and to encourage them to conduct their lives accordingly.

This article details the variety of critical strategies in Mary Wollstonecraft’s A Vindication of the Rights of Woman, finding strong connections with her writing as a reviewer for the Analytical Review, the literary review published by the reformer and Dissenter Joseph Johnson. In Rights of Woman, Wollstonecraft employed textual analyses and an evolving set of theoretical positions that had been introduced in the course of her career at the Analytical Review. By elucidating the importance of the reviews and the specificity (...) of Wollstonecraft’s procedures, this article contributes to a growing consensus that Rights of Woman initiated feminist literary criticism. (shrink)

No cinema brasileiro recente, o diálogo entre o documentário e a ficção tem merecido destaque, com produções de baixo orçamento e ideias originais. É o caso de Santiago (João Moreira Salles, 2007) e Viajo Porque Preciso, Volto Porque Te Amo (Marcelo Gomes, Karim Aïnouz, 2009), filmes que trabalham esse diálogo de forma sutil e diegética, ressignificando imagens de um arquivo próprio, pessoal.

A pandemia da Covid-19 transformou realidades e exigiu comportamentos sociais jamais experienciados que, na dimensão eclesial, vêm revelando compreensões e posturas inadequadas à mistagogia evangélica, mas que também podem provocar um discipulado missionário ad extra, na concepção de Igreja Povo de Deus. Portanto, o presente artigo objetivou, a partir de uma hermenêutica de Mc 4,35-41, refletir sobre o protagonismo laical em tempos de pandemia, sua autocompreensão eclesial e seu posicionamento diante da crise sanitária. Para tanto, estruturou-se em três pontos: teceu (...) uma compreensão da perícope marcana à luz da pandemia; refletiu sobre a postura do laicato em meio a crise sanitária e, por fim, teceu pistas para um agir missionário coerente ao discipulado, concluindo que mesmo em meio a posturas inadequadas o laicato é fortemente chamado ao protagonismo eclesial contribuindo para a superação da crise sanitária provocada pelo novo coronavírus. (shrink)

We provide a model in which students must choose whether or not to cheat on a course exam. By assuming that the moral cost of acting dishonestly decreases as the number of other people who behave in the same way increases, our model explains one important channel by which unethical behavior of other individuals can influence observers’ behavior. Through the use of the Global Games approach of equilibrium selection, we build a framework that provides the micro-foundations of peer effects on (...) academic dishonesty and shows how better student technology of cheating and higher disutility of effort make the cheating equilibrium more likely to be selected. By extending the model, we find that the peer effect strength is not affected by the level of homogeneity of the cohort, but decreases in the size of the class. Our approach may be seen as an important step towards reduced-form models of peer effects on dishonest behavior. (shrink)

But never let it be doubted that depression, in its extreme form, is madness. (Styron, 1990, p. 62)There is nothing wrong with our biology or our intelligence; sometimes we are just stuck. (Cvetkov...

The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous aproaches to quantified LFIs presented in the literature. The case of QmbC, (...) the simpler quantified LFI expanding classical logic, will be analyzed in detail. An axiomatic extension of QmbC called QLFI1o is also studied, which is equivalent to the quantified version of da Costa and D'Ottaviano 3-valued logic J3. The semantical structures for this logic turn out to be Tarkian structures based on twist structures. The expansion of QmbC and QLFI1o with a standard equality predicate is also considered. (shrink)

From the early to mid-1970s, Michel Foucault posited that power consists of a relation rather than a substance and that this relation is comprised of unequal forces engaged in a warlike struggle against each other, resulting invariably in the domination of some forces over others. This understanding of power, which he retrospectively dubbed `Nietzsche's hypothesis' and `the model of war', underpinned his well-known analyses of disciplinary power. Yet, Foucault in his Collège de France course from the academic year 1975-6, `Society (...) Must Be Defended', suddenly began to call into question this understanding and his doubts about it did not abate well into the late 1970s. In this article, we suggest that his militant politics in the early 1970s sustained his adherence to the war model and that his more cautious political attitude later in the decade underpinned his suspicions about this model. Key Words: biopolitics • Henri de Boulainvilliers • Michel Foucault • Thomas Hobbes • militancy • F. W. Nietzsche • politics • power • race • war. (shrink)

In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally a (...) non-deterministic matrix. The aim of this paper is to obtain a swap structures semantics for some Ivlev-like modal systems proposed in 2015 by M. Coniglio, L. Fariñas del Cerro and N. Peron. Completeness results will be stated by means of the notion of Lindenbaum–Tarski swap structures, which constitute a natural generalization to multialgebras of the concept of Lindenbaum–Tarski algebras. (shrink)

In 1986, Mikenberg et al. introduced the semantic notion of quasi-truth defined by means of partial structures. In such structures, the predicates are seen as triples of pairwise disjoint sets: the set of tuples which satisfies, does not satisfy and can satisfy or not the predicate, respectively. The syntactical counterpart of the logic of partial truth is a rather complicated first-order modal logic. In the present article, the notion of predicates as triples is recursively extended, in a natural way, to (...) any complex formula of the first-order object language. From this, a new definition of quasi-truth is obtained. The proof-theoretic counterpart of the new semantics is a first-order paraconsistent logic whose propositional base is a 3-valued logic belonging to hierarchy of paraconsistent logics known as Logics of Formal Inconsistency, which was proposed by Carnielli and Marcos in 2002. (shrink)

Recently, it has been proposed to understand a logic as containing not only a validity canon for inferences but also a validity canon for metainferences of any finite level. Then, it has been shown that it is possible to construct infinite hierarchies of "increasingly classical" logics—that is, logics that are classical at the level of inferences and of increasingly higher metainferences—all of which admit a transparent truth predicate. In this paper, we extend this line of investigation by taking a somehow (...) different route. We explore logics that are different from classical logic at the level of inferences, but recover some important aspects of classical logic at every metainferential level. We dub such systems meta-classical non-classical logics. We argue that the systems presented deserve to be regarded as logics in their own right and, moreover, are potentially useful for the non-classical logician. (shrink)

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)

The volume will implement the research efforts of both Machiavelli scholars and those in related general and specific fields.

A ideia de uma crise do rádio consolidou-se no imaginário coletivo nas últimas décadas, a despeito de não haver ancoragem na realidade. Se muitas rádios tradicionais AM e FM saem do ar, vendidas a igrejas eletrônicas ou novos grupos empresariais, multiplica-se a oferta de conteúdos no contexto de um rádio expandido, que transborda para novas plataformas e é consumido nos mais diversos dispositivos. O rádio vai bem, obrigado, embora algumas emissoras de rádio em ondas hertzianas estejam mal das pernas, lamentando-se (...) da concorrência com serviços on-line e da erosão dos habituais índices de audiência, antes medidos em centenas de milhares de ouvintes por minuto. (shrink)

Despite being fairly powerful, finite non-deterministic matrices are unable to characterize some logics of formal inconsistency, such as those found between mbCcl and Cila. In order to overcome this limitation, we propose here restricted non-deterministic matrices (in short, RNmatrices), which are non-deterministic algebras together with a subset of the set of valuations. This allows us to characterize not only mbCcl and Cila (which is equivalent, up to language, to da Costa's logic C_1) but the whole hierarchy of da Costa's calculi (...) C_n. This produces a novel decision procedure for these logics. Moreover, we show that the RNmatrix semantics proposed here induces naturally a labelled tableau system for each C_n, which constitutes another decision procedure for these logics. This new semantics allows us to conceive da Costa's hierarchy of C-systems as a family of (non deterministically) (n+2)-valued logics, where n is the number of "inconsistently true" truth-values and 2 is the number of "classical" or "consistent" truth-values, for every C_n. (shrink)

Kant, los sábados por la tarde -- ¿Andaría en algo Sócrates? -- El álef de "El Aleph" -- La angustia ya no se lleva -- El tango de la muerte -- Los ilotas y la juventud maravillosa -- Los jóvenes en Flores -- El filósofo y la princesa.

Se indagó sobre el desarrollo de la Investigación Acción Participativa en Psicología. Se observó que en América y Europa, esta metodología se utiliza en una variedad de áreas disciplinares, principalmente en la Psicología Comunitaria. Aborda fundamentalmente problemáticas sociales, comunitarias y ps..

ExcerptAt its core, the concept of biopolitics refers to the constitution of the life of a population as the object and objective of politics. Of course, Michel Foucault pioneered this concept in his analyses from the late 1970s, first in his Collège de France course from the academic year 1975–76, “Society Must Be Defended”, and subsequently in the first volume of The History of Sexuality, published in the fall of 1976.1 Taking as his cue the analysis in the latter publication, (...) Giorgio Agamben, in a few highly schematic but rich and provocative passages from the introduction to his now seminal…. (shrink)

Entrevista com o professor Mauro Rêgo Sá Costa para o dossiê Rádio nas Bordas.