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Paradox of the class of all grounded classes

Journal of Symbolic Logic 18 (2):114 (1953)

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Buttresses of the Turing Barrier.Paolo Cotogno - 2015 - Acta Analytica 30 (3):275-282.details The ‘Turing barrier’ is an evocative image for 0′, the degree of the unsolvability of the halting problem for Turing machines—equivalently, of the undecidability of Peano Arithmetic. The ‘barrier’ metaphor conveys the idea that effective computability is impaired by restrictions that could be removed by infinite methods. Assuming that the undecidability of PA is essentially depending on the finite nature of its computational means, decidability would be restored by the ω-rule. Hypercomputation, the hypothetical realization of infinitary machines through relativistic and (...) Download Export citation Bookmark
Relatives of the Russell Paradox.Kees Doets - 1999 - Mathematical Logic Quarterly 45 (1):73-83.details A formula ϕ in the one non-logical symbol ϵ with one free variable x is Russell if the sentence Vχ) is logically valid. This note describes a pattern common to the classical examples of Russell formulas, adds a couple of new ones, and constructs many formulas that are near-Russell. Download Export citation Bookmark 3 citations
A Topological Approach to Yablo's Paradox.Claudio Bernardi - 2009 - Notre Dame Journal of Formal Logic 50 (3):331-338.details Some years ago, Yablo gave a paradox concerning an infinite sequence of sentences: if each sentence of the sequence is 'every subsequent sentence in the sequence is false', a contradiction easily follows. In this paper we suggest a formalization of Yablo's paradox in algebraic and topological terms. Our main theorem states that, under a suitable condition, any continuous function from 2N to 2N has a fixed point. This can be translated in the original framework as follows. Consider an infinite sequence (...) Download Export citation Bookmark 4 citations
‘Qinghua School of Logic’: Mathematical Logic at Qinghua University in Peking, 1926–1945.Jan Vrhovski - 2021 - History and Philosophy of Logic 42 (3):247-261.details Mathematical logic was first introduced to China in early 1920s. Although, the process of introduction was facilitated by the lectures of Bertrand Russel at Peking University in 1921 and continued by China’s most passionate adherents of Russell’s philosophy, the establishment of mathematical logic as an academic discipline occurred only in late 1920s, in the framework of a recently reorganised Qinghua University in Peking. The main aim of this paper is to shed some light on the process of establishment of mathematical (...) Download Export citation Bookmark
Filosofía, matemática y paradojas: el caso de la paradoja Burali-Forti en la argumentación de Descartes sobre la existencia de Dios.Henry Sebastián Rangel-Quiñonez & Javier Orlando Aguirre-Román - 2016 - Cuestiones de Filosofía 2 (19):127-152.details El presente escrito presenta las ventajas y desventajas de la formalización matemática como una herramienta para el análisis de argumentos complejos o difusos en la filosofía. De tal forma, aquí se encuentra un recorrido histórico de algunas consideraciones del papel de las matemáticas en la búsqueda del conocimiento. Posterior a ello, se muestra cómo por medio de la teoría de conjuntos y laabstracción matemática, es posible proponer una reinterpretación de algunos textos filosóficos. Para lograr este objetivo, se presenta, a manera (...) Download Export citation Bookmark
Fixed points and unfounded chains.Claudio Bernardi - 2001 - Annals of Pure and Applied Logic 109 (3):163-178.details By an unfounded chain for a function f:X→X we mean a sequence nω of elements of X s.t. fxn+1=xn for every n. Unfounded chains can be regarded as a generalization of fixed points, but on the other hand are linked with concepts concerning non-well-founded situations, as ungrounded sentences and the hypergame. In this paper, among other things, we prove a lemma in general topology, we exhibit an extensional recursive function from the set of sentences of PA into itself without an (...) Download Export citation Bookmark 3 citations
A Yabloesque paradox in epistemic game theory.Can Başkent - 2018 - Synthese 195 (1):441-464.details The Brandenburger–Keisler paradox is a self-referential paradox in epistemic game theory which can be viewed as a two-person version of Russell’s Paradox. Yablo’s Paradox, according to its author, is a non-self referential paradox, which created a significant impact. This paper gives a Yabloesque, non-self-referential paradox for infinitary players within the context of epistemic game theory. The new paradox advances both the Brandenburger–Keisler and Yablo results. Additionally, the paper constructs a paraconsistent model satisfying the paradoxical statement. Download Export citation Bookmark
Borges: literato y filósofo de las paradojas.Javier Orlando Aguirre Román & Henry Sebastián Rangel Quiñonez - 2019 - Revista Filosofía Uis 18 (1):89-108.details el presente texto es una revisión crítica de parte de la obra del escritor argentino Jorge Luis Borges con el fin de evidenciar el talante filosófico de este autor. Para ello se presta especial atención al uso de la noción de infinito y las paradojas que de él resultan. Nuestra conclusión es que, si se va a considerar a Borges como filósofo, se debe concluir que, ante todo, es un “filósofo de las paradojas”. Sobre esta base se puede entender su (...) idealismo escéptico. (shrink) Download Export citation Bookmark

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