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  1. Computer-Assisted Analysis of the Anderson-Hájek Controversy.Benzmüller Christoph, Weber Leon & Woltzenlogel Paleo Bruno - 2017 - Logica Universalis 11 (1):139-151.
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  • Mechanized analysis of Anselm’s modal ontological argument.John Rushby - forthcoming - International Journal for Philosophy of Religion:1-18.
    We use a mechanized verification system, PVS, to examine the argument from Anselm’s Proslogion Chapter III, the so-called “Modal Ontological Argument.” We consider several published formalizations for the argument and show they are all essentially similar. Furthermore, we show that the argument is trivial once the modal axioms are taken into account. This work is an illustration of Computational Philiosophy and, in addition, shows how these methods can help detect and rectify errors in modal reasoning.
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  • Computer Science and Metaphysics: A Cross-Fertilization.Edward N. Zalta, Christoph Benzmüller & Daniel Kirchner - 2019 - Open Philosophy 2 (1):230-251.
    Computational philosophy is the use of mechanized computational techniques to unearth philosophical insights that are either difficult or impossible to find using traditional philosophical methods. Computational metaphysics is computational philosophy with a focus on metaphysics. In this paper, we develop results in modal metaphysics whose discovery was computer assisted, and conclude that these results work not only to the obvious benefit of philosophy but also, less obviously, to the benefit of computer science, since the new computational techniques that led to (...)
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  • A Computationally Assisted Reconstruction of an Ontological Argument in Spinoza’s The Ethics.Jack K. Horner - 2019 - Open Philosophy 2 (1):211-229.
    The comments accompanying Proposition 11 in Part I of Spinoza’s The Ethics contain sketches of what appear to be at least three more or less distinct ontological arguments. The first of these is problematic even on its own terms. More is true: even the proposition “God exists”, a consequence of Prop. 11, cannot be derived from the definitions and axioms of Part I of The Ethics; thus, Prop. 11 cannot be derived from the DAPI, either. To prove these claims, I (...)
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  • On the PROVER9 Ontological Argument.T. Parent - 2015 - Philosophia 43 (2):475-483.
    Oppenheimer & Zalta have re-formulated their non-modal version of the ontological argument, with the help of PROVER9, an automated reasoning engine. The authors end up rejecting the new argument; however, the theist has a rejoinder worth considering. But after presenting the rejoinder, I highlight that the conceivability of the being does not imply its possibility. One lesson is that even non-modal ontological arguments must engage modal matters concerning God. Another lesson is that if PROVER9 is able to derive a conclusion (...)
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  • Gödel’s Second Theorem and the Provability of God’s Existence.Meir Buzaglo - 2019 - Logica Universalis 13 (4):541-549.
    According to a common view, belief in God cannot be proved and is an issue that must be left to faith. Kant went even further and argued that he can prove this unprovability. But any argument implying that a certain sentence is not provable is challenged by Gödel’s second theorem. Indeed, one trivial consequence of GST is that for any formal system F that satisfies certain conditions and for every sentence K that is formulated in F it is impossible to (...)
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  • The Totality of Predicates and the Possibility of the Most Real Being.Srećko Kovač - 2018 - Journal of Applied Logics - The IfCoLog Journal of Logics and Their Applications 5 (7):1523-1552.
    We claim that Kant's doctrine of the "transcendental ideal of pure reason" contains, in an anticipatory sense, a second-order theory of reality (as a second-order property) and of the highest being. Such a theory, as reconstructed in this paper, is a transformation of Kant's metatheoretical regulative and heuristic presuppositions of empirical theories into a hypothetical ontotheology. We show that this metaphysical theory, in distinction to Descartes' and Leibniz's ontotheology, in many aspects resembles Gödel's theoretical conception of the possibility of a (...)
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  • Saint Anselm.Thomas Williams - 2008 - Stanford Encyclopedia of Philosophy.
    Saint Anselm of Canterbury (1033-1109) was the outstanding Christian philosopher and theologian of the eleventh century. He is best known for the celebrated “ontological argument” for the existence of God in chapter two of the Proslogion, but his contributions to philosophical theology (and indeed to philosophy more generally) go well beyond the ontological argument. In what follows I examine Anselm's theistic proofs, his conception of the divine nature, and his account of human freedom, sin, and redemption.
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  • Incomplete Symbols — Definite Descriptions Revisited.Norbert Gratzl - 2015 - Journal of Philosophical Logic 44 (5):489-506.
    We investigate incomplete symbols, i.e. definite descriptions with scope-operators. Russell famously introduced definite descriptions by contextual definitions; in this article definite descriptions are introduced by rules in a specific calculus that is very well suited for proof-theoretic investigations. That is to say, the phrase ‘incomplete symbols’ is formally interpreted as to the existence of an elimination procedure. The last section offers semantical tools for interpreting the phrase ‘no meaning in isolation’ in a formal way.
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  • Can Computers Help to Sharpen Our Understanding of Ontological Arguments?Christoph Benzmüller & David Fuenmayor - 2018 - In Mathematics and Reality, Proceedings of the 11th All India Students' Conference on Science Spiritual Quest, 6-7 October, 2018, IIT Bhubaneswar, Bhubaneswar, India. India: The Bhaktivedanta Institute. pp. 195226.
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  • Recent Developments in Computing and Philosophy.Anthony F. Beavers - 2011 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 42 (2):385-397.
    Because the label "computing and philosophy" can seem like an ad hoc attempt to tie computing to philosophy, it is important to explain why it is not, what it studies (or does) and how it differs from research in, say, "computing and history," or "computing and biology". The American Association for History and Computing is "dedicated to the reasonable and productive marriage of history and computer technology for teaching, researching and representing history through scholarship and public history" (http://theaahc.org). More pervasive, (...)
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  • A Case Study on Computational Hermeneutics: E. J. Lowe’s Modal Ontological Argument.David Fuenmayor & Christoph Benzmueller - manuscript
    Computers may help us to better understand (not just verify) arguments. In this article we defend this claim by showcasing the application of a new, computer-assisted interpretive method to an exemplary natural-language ar- gument with strong ties to metaphysics and religion: E. J. Lowe’s modern variant of St. Anselm’s ontological argument for the existence of God. Our new method, which we call computational hermeneutics, has been particularly conceived for use in interactive-automated proof assistants. It aims at shedding light on the (...)
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  • Computer-Assisted Analysis of the Anderson–Hájek Ontological Controversy.C. Benzmüller, L. Weber & B. Woltzenlogel Paleo - 2017 - Logica Universalis 11 (1):139-151.
    A universal reasoning approach based on shallow semantical embeddings of higher-order modal logics into classical higher-order logic is exemplarily employed to analyze several modern variants of the ontological argument on the computer. Several novel findings are reported which contribute to the clarification of a long-standing dispute between Anderson and Hájek. The technology employed in this work, which to some degree realizes Leibniz’s dream of a characteristica universalis and a calculus ratiocinator for solving philosophical controversies, is ready to be fruitfully adopted (...)
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  • Variants of Gödel’s Ontological Proof in a Natural Deduction Calculus.B. Woltzenlogel Paleo & Annika Kanckos - 2017 - Studia Logica 105 (3):553-586.
    This paper presents detailed formalizations of ontological arguments in a simple modal natural deduction calculus. The first formal proof closely follows the hints in Scott’s manuscript about Gödel’s argument and fills in the gaps, thus verifying its correctness. The second formal proof improves the first one, by relying on the weaker modal logic KB instead of S5 and by avoiding the equality relation. The second proof is also technically shorter than the first one, because it eliminates unnecessary detours and uses (...)
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  • Anselm's God in Isabelle/HOL.Ben Blumson - 2017 - Archive of Formal Proofs:9.
    Paul Oppenheimer and Edward Zalta's formalisation of Anselm's ontological argument for the existence of God is automated by embedding a free logic for definite descriptions within Isabelle/HOL.
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  • Prover9's Simplification Explained Away.Paweł Garbacz - 2012 - Australasian Journal of Philosophy 90 (3):585 - 592.
    This note discusses P. Oppenheimer and E. Zalta's ?A Computationally-Discovered Simplification of the Ontological Argument? [this journal, 2011]. I try to explain why the simplification presented there was successful and comment on the technical aspects of the method they applied.
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  • Automating Emendations of the Ontological Argument in Intensional Higher-Order Modal Logic.Fuenmayor David & Benzmüller Christoph - 2017 - In KI 2017: Advances in Artificial Intelligence 40th Annual German Conference on AI. Cham, Switzerland: Springer International Publishing.
    A shallow semantic embedding of an intensional higher-order modal logic in Isabelle/HOL is presented. IHOML draws on Montague/Gallin intensional logics and has been introduced by Melvin Fitting in his textbook Types, Tableaus and Gödel’s God in order to discuss his emendation of Gödel’s ontological argument for the existence of God. Utilizing IHOML, the most interesting parts of Fitting’s textbook are formalized, automated and verified in the Isabelle/HOL proof assistant. A particular focus thereby is on three variants of the ontological argument (...)
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  • Ontological Arguments.Graham Oppy - 2014 - Stanford Encyclopedia of Philosophy.
    Latest version of my SEP entry on ontological arguments, which first appeared in 1996. General discussion of ontological arguments. Includes a brief historical overview, a taxonomy of different kinds of ontological arguments, a brief survey of objections to the different kinds of ontological arguments identified in the taxonomy, and more extended discussions of Anselm's ontological argument (Proslogion 2), Godel's ontological argument, and Plantinga's ontological argument.
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