In this note, we review paradoxes like Russell’s, the Liar, and Curry’s in the context of intuitionistic logic. One may observe that one cannot blame the underlying logic for the paradoxes, but has to take into account the particular concept formations. For proof-theoretic semantics, however, this comes with the challenge to block some forms of direct axiomatizations of the Liar. A proper answer to this challenge might be given by Schroeder-Heister’s definitional freedom.

Resumo: A inclusão no Ensino Superior é uma premissa de âmbito social, educacional e político. Muitos passos têm sido trilhados para que os discursos sobre equidade e igualdade possam ser proferidos e perspectivados, reconhecendo que o ajustamento dos estudantes com Necessidades Educativas Especiais (NEE) precede-se de inúmeros fatores, entre eles, das políticas educativas. Para possibilitar algumas reflexões, o presente estudo, de natureza qualitativa, objetivou conhecer as percepções de colaboradores (n=85) de Instituições de Ensino Superior portuguesas sobre o papel das políticas (...) educativas em prol da inclusão. Os dados, provenientes de um questionário online, foram tratados sob a técnica de análise de conteúdo, com apoio do software webQDA. Os resultados evidenciaram 60 referências na categoria de potencialidades, refletidas na garantia da efetivação do percurso acadêmico de estudantes com NEE no Ensino Superior e concretização dos seus direitos. Verificou-se que 91,7% dos participantes compreendem que as políticas educativas são importantes para o seu país, pelo que 88,2% dos colaboradores acreditam que estas políticas potenciam a inclusão e a permanência de estudantes com NEE no Ensino Superior, na qual 40,7% verificaram ações de apoio e incentivo, ao nível político, em prol da inclusão em Portugal. Palavras-chave: Políticas Educativas; Inclusão; Ensino Superior; Portugal; Necessidades Educativas Especiais. Educational policies and inclusion in Higher Education: perceptions about the Portuguese context Abstract: Inclusion in Higher Education is a social, educational and political premise. Many steps have been taken so that the discourses on equity and equality can be delivered and envisaged, recognizing that the adjustment of students with Special Educational Needs (SEN) is preceded by numerous factors, among them, educational policies. To enable some reflections, the present study, of a qualitative nature, aimed to know the perceptions of employees (n = 85) of Portuguese Higher Education Institutions about the role of educational policies on behalf of inclusion. The data, from an online survey, were treated using the content analysis technique, with the support of the webQDA software. The results revealed 60 references in the potentialities category, reflected in the guarantee of the effectiveness of the academic path of students with SEN in Higher Education and the realization of their rights. It was found that 91.7% of participants understand that educational policies are important for their country, so 88.2% of employees believe that these policies enhance the inclusion and permanence of students with SEN in Higher Education, in which 40.7% verified support and incentive actions, at the political level, in favor of inclusion in Portugal. Keywords: Educational Policies; Inclusion; Higher Education; Portugal; Special Educational Needs. Políticas educativas e inclusión en la educación superior: percepciones sobre el contexto portugués Resumen: La inclusión en la Educación Superior es una premisa en el marco social, educativo y político. Se han dado muchos pasos para que los discursos sobre equidad e igualdad puedan ser pronunciados y verificados, reconociendo que la adaptación de los estudiantes con Necesidades Educativas Especiales (NEE) está precedida por numerosos factores, entre ellos, las políticas educativas. Para posibilitar algunas reflexiones, el presente estudio, de carácter cualitativo, tuvo como objetivo conocer las percepciones de los colaboradores (n = 85) de las Instituciones de Educación Superior portuguesas sobre la función de las políticas educativas a favor de la inclusión. Los datos, provenientes de una encuesta online, fueron tratados mediante la técnica de análisis de contenido, con el apoyo del software webQDA. Los resultados evidenciaron 60 referencias en la categoría de potencialidades, reflejadas en la garantía de la efectividad de la trayectoria académica de los estudiantes con NEE en la Educación Superior y la realización de sus derechos. Se constató que el 91,7% de los participantes entiende que las políticas educativas son importantes para su país, por lo que el 88,2% de los empleados cree que estas políticas potencian la inclusión y permanencia de los estudiantes con NEE en la Educación Superior, en la que el 40,7% verificó acciones de apoyo e incentivo, a nivel político, a favor de la inclusión en Portugal. Palabras clave: Políticas Educativas; Inclusión; Educación superior; Portugal; Necesidades Educativas Especiales. Data de registro: 16/04/2021 Data de aceite: 01/12/2021. (shrink)

Diagonalization is a transversal theme in Logic. In this work, it is shown that there exists a common origin of several diagonalization phenomena — paradoxes and Löb's Theorem. That common origin comprises a common reasoning and a common logical structure. We analyse the common structure from a philosophical point-of-view and we draw some conclusions.

We study the decidability of k-provability in \—the relation ‘being provable in \ with at most k steps’—and the decidability of the proof-skeleton problem—the problem of deciding if a given formula has a proof that has a given skeleton. The decidability of k-provability for the usual Hilbert-style formalisation of \ is still an open problem, but it is known that the proof-skeleton problem is undecidable for that theory. Using new methods, we present a characterisation of some numbers k for which (...) k-provability is decidable, and we present a characterisation of some proof-skeletons for which one can decide whether a formula has a proof whose skeleton is the considered one. These characterisations are natural and parameterised by unification algorithms. (shrink)

Je me propose d'examiner les paragraphes 18 et 19 de la deuxième partie des Prolégomènes. Bien que ces deux paragraphes ne constituent pas l'intégralité de la déduction transcendantale des Prolégomènes, ils ont une fonction essentielle dans la mesure où ils exposent l’argument entier in nuce. Ces deux sections établissent de façon claire que la doctrine de l'idéalisme critique, présentée dans la première partie des Prolégomènes comme un idéalisme qui ne supprime pas « l'existence de la chose qui apparaît », joue (...) un rôle indispensable dans la déduction transcendantale, qui est présentée dans la deuxième partie à partir de la distinction entre jugement de perception et jugement d'expérience. (shrink)

Kreisel’s conjecture is the statement: if, for all$n\in \mathbb {N}$,$\mathop {\text {PA}} \nolimits \vdash _{k \text { steps}} \varphi (\overline {n})$, then$\mathop {\text {PA}} \nolimits \vdash \forall x.\varphi (x)$. For a theory of arithmeticT, given a recursive functionh,$T \vdash _{\leq h} \varphi $holds if there is a proof of$\varphi $inTwhose code is at most$h(\#\varphi )$. This notion depends on the underlying coding.${P}^h_T(x)$is a predicate for$\vdash _{\leq h}$inT. It is shown that there exist a sentence$\varphi $and a total recursive functionhsuch that$T\vdash (...) _{\leq h}\mathop {\text {Pr}} \nolimits _T(\ulcorner \mathop {\text {Pr}} \nolimits _T(\ulcorner \varphi \urcorner )\rightarrow \varphi \urcorner )$, but, where$\mathop {\text {Pr}} \nolimits _T$stands for the standard provability predicate inT. This statement is related to a conjecture by Montagna. Also variants and weakenings of Kreisel’s conjecture are studied. By the use of reflexion principles, one can obtain a theory$T^h_\Gamma $that extendsTsuch that a version of Kreisel’s conjecture holds: given a recursive functionhand$\varphi (x)$a$\Gamma $-formula (where$\Gamma $is an arbitrarily fixed class of formulas) such that, for all$n\in \mathbb {N}$,$T\vdash _{\leq h} \varphi (\overline {n})$, then$T^h_\Gamma \vdash \forall x.\varphi (x)$. Derivability conditions are studied for a theory to satisfy the following implication: if, then$T\vdash \forall x.\varphi (x)$. This corresponds to an arithmetization of Kreisel’s conjecture. It is shown that, for certain theories, there exists a functionhsuch that$\vdash _{k \text { steps}}\ \subseteq\ \vdash _{\leq h}$. (shrink)