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On Overspill Principles and Axiom Schemes for Bounded FormulasMathematical Logic Quarterly 42 (1): 341-348. 2006.We study the theories I∇n, L∇n and overspill principles for ∇n formulas. We show that IEn ⇒ L∇n ⇒ I∇n, but we do not know if I∇n L∇n. We introduce a new scheme, the growth scheme Crγ, and we prove that L∇n ⇒ Cr∇n⇒ I∇n. Also, we analyse the utility of bounded collection axioms for the study of the above theories. Mathematics Subject Classification: 03F30, 03H15.
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Maximum Schemes in ArithmeticMathematical Logic Quarterly 40 (3): 425-430. 2006.In this paper we deal with some new axiom schemes for Peano's Arithmetic that can substitute the classical induction, least‐element, collection and strong collection schemes in the description of PA. Mathematics Subject Classification: 03F30, 03H15.
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871The Ontological Commitments of Logical TheoriesEuropean Review of Philosophy 4 157-182. 1999.This paper is partly inspired by a well-known debate between Ruth Barcan Marcus, Terence Parsons and W. V. 0. Quine in the sixties> concerning the extent to which Quantified Modal Logic is committed to Essentialism; the issue nevertheless goes back to the origins of "analytic philosophy'', to the reflections of Frege, Russell, and the earlier Wittgenstein on the nature of logic. By elaborating on a suggestion by Quine, we purport to show that there is a relevant and interesting way to look at th…Read more
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99In situanalysis of the tensile deformation mechanisms in extruded Mg–1Mn–1NdPhilosophical Magazine 93 (6): 598-617. 2013.
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Verificaciones y contactosEl Catoblepas: Revista Crítica Del Presente. forthcoming.Se analiza la estructura gnoseológica y política de las comisiones de expertos internacionales en sus tratos con la ETA.
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19“Thinking alone hurts”. A Systemization of the Experience of the International Group of Doctoral Students working on and from Central AmericaÍSTMICA Revista de la Facultad de Filosofía y Letras 1 (36). 2025.El Grupo Internacional de Doctorandxs sobre y desde Centroamérica (DOCAX) surgió en el 2022 con el propósito de crear un espacio de acompañamiento y diálogo para estudiantes de diversos doctorados que hacemos investigación en esta zona. Al respecto, el trabajo tiene como objetivo sistematizar la experiencia que hemos tenido como grupo; para lo cual utilizaremos materiales como notas, fotografías, encuentros virtuales y presenciales, ponencias en varios eventos y un cuestionario aplicado a sus mi…Read more
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14Recent Computability Models Inspired from BiologyTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 18 (1): 71-84. 2003.We briefly present two areas of natural computing, vividly investigated in the recent years: DNA computing and membrane computing. Both of them have the roots in cellular biology and are rather developedat the theoretical level (new concepts, models, paradigms of computer science, with mathematical and epistemological significance have been considered in this framework), but both areas are still looking for implementations of a practical interest.
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7In this paper we will try to provide a solid form of intrinsic set theoretical optimism. In other words, we will try to vindicate Gödel’s views on phenomenology as a method for arriving at new axioms of ZFC in order to decide independent statements such as CH.
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8P.A. Michelis. An aesthetic aproach to Byzantine Art. Foreword by sir Herbert Read. B. T. Batsford Ltd. 1955. 284 págsRevista de filosofía (Chile) 5 (3): 140-143. 2017.
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7Rudolf Arnheim. Art and Visual Perception.Apsychology of the creative eye. Faber y Faber Limited. 24 Russel Square, London. 1956. 408 páginas (review)Revista de filosofía (Chile) 5 (3): 143-145. 2017.
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39Technological Surveillance Study on the Development of Beekeeping TechnologiesEvolutionary Studies in Imaginative Culture 1565-1576. forthcoming.This study employed a technology surveillance process in the beekeeping sector with the objective of identifying emerging technologies that are relevant to small beekeepers in emerging economies. The analysis of patents classified under A01K 47/00 revealed the emergence of pivotal innovations in domains such as hive design, automated honey extraction, and the integration of sensors for hive monitoring. The surveillance process facilitated the collection and analysis of data on the most patented …Read more
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9In this brief note we will continue with the exploration of Gödel's phenomenological program. We intend to provide a positive account of such program by means of an intentional reading of the context principle.
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Jorge J.E. Gracia, Metaphysics and its Task. The Search for the Categorical Foundation of Knowledge (review)Acta Philosophica 12 (2). 2003.
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S. L. Brock, Action and Conduct. Thomas Aquinas and the Theory of Action (review)Acta Philosophica 8 (1). 1999.
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28Jiménez Cataño, Rafael, Semántica y racionalidad en Frege. Un estudio desde las operaciones mentales (review)Acta Philosophica 1 (2). 1992.
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108Libertad individual frente a determinación socialRevista de Filosofía (Madrid) 4 (1): 161-198. 1990.The paper explores different possibilities in order of maintaining a compatibilism between free will, in a strong sense, and determinism. The notion of determinism is analyzed in deep. It is defended a general conception of free will as a certain kind of mental causation in absence of fatalism. Also, it is argued that other compatibilist possibilities would be possible inside that general conception of free will, being some of them more radical than other ones
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149La razón de lo pretendidamente ilógico. Un posible puente entre Lógica y PsicologíaRevista de Filosofía (Madrid) 20 (1): 77. 1998.Pese a su origen y desarrollo filosófico, Lógica y Psicología, históricamente, han tendido no sólo a la disociación sino, más allá, al enfrentamiento. Durante décadas, excepción hecha de la llamada lógica intuicionista. la peor acusación que se le pudo hacer a un lógico fue la de psicologista. Sin embargo, lógica y psicología. tal y como pretende sena larse en este trabajo, no sólo están mucho más cercanas de lo que pudie ra parecer sino que. también, viven en una relación complementaria
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13In this brief paper we wish to summarize the core points of what we have called `Gödel's phenomenological program'. We claim that some of these require the same amount of attention as those other aspects from Gödel's program that have been exhaustively treated in the contemporary discussions around the status of CH. Finally, from this phenomenological standpoint, we make some remarks regarding concrete proposals for achieving the so-called `dream solution' of CH.
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59Programas moleculares y sistemas lógico-formalesKairos 5 77-89. 2012.info:eu-repo/semantics/publishedVersion.
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28In this paper we analyze object-talk, some of its uses and misuses, more closely. Our main claim is that object-talk should be understood in the context of faith instead of that of rational argumentation. Hence, object-talk is compared with God-talk and the way of understanding the so-called 'abstract entities' from logic and mathematics turns out to be essentially linked with how the contact with the Divine is conceived. Moreover, we discuss the particular case of the independence phenomenon an…Read more
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11The purpose of the present dialogue is threefold: (a) Refining our previous interpretation of Wittgenstein's philosophy of mathematics through the 'Phenomenology' chapter of the 'Big Typescript'; (b) Examining the role of phenomenological and historical analysis in the contemporary debate surrounding the axioms of set theory; (c) Providing a brief interpretation of Kant's Architectonic as a general framework for such debate. The conclusion of the article, which add certain theological connotatio…Read more
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8Putnam and Finkelstein can be read as providing an answer to Kripke's skeptical argument by appealing to the way mathematics is commonly pursued. Nowadays, the debate surrounding pluralism has questioned the postulation of a unique way of developing mathematical activity. In this paper, we wish to reformulate Kripke's argument as a challenge for the conjunction of 'ifthenism' and a reasonable form of pluralism and, at the same time, propose a reading of some passages of the 'Philosophical Invest…Read more
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77Cascading Failures Analysis Considering Extreme Virus Propagation of Cyber-Physical Systems in Smart GridsComplexity 2019 1-15. 2019.