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References in:
Gödel's "slingshot" argument and his onto-theological system
In Kordula Świętorzecka (ed.), Gödel's Ontological Argument: History, Modifications, and Controversies. Semper. pp. 123-162 (2015)
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After introductory reminder of and comments on Gödel’s ontological proof, we discuss the collapse of modalities, which is provable in Gödel’s ontological system GO. We argue that Gödel’s texts confirm modal collapse as intended consequence of his ontological system. Further, we aim to show that modal collapse properly fits into Gödel’s philosophical views, especially into his ontology of separation and union of force and fact, as well as into his cosmological theory of the nonobjectivity of the lapse of time. As (...) |
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According to the standard opinions in the literature, blocking the unacceptable consequences of the notorious slingshot argument requires imposing constraints on the metaphysics of facts or on theories of definite descriptions (or class abstracts). This paper argues that both of these well-known strategies to rebut the slingshot overshoot the mark. The slingshot, first and foremost, raises the question as to the adequate logical formalization of statements about facts, i.e. of factual contexts. It will be shown that a rigorous application of (...) |
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Kurt Gödel’s version of the ontological argument was shown by J. Howard Sobel to be defective, but some plausible modifications in the argument result in a version which is immune to Sobel’s objection. A definition is suggested which permits the proof of some of Godel’s axioms. |
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The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, (...) |
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By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) |
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This book is an original examination of attempts to dislodge a cornerstone of modern philosophy: the idea that our thoughts and utterances are representations ... |
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We describe a KB Gödelian ontological system, and some other weak systems, in a fully formal way using theory of types and natural deduction, and present a completeness proof in its main and specific parts. We technically and philosophically analyze and comment on the systems (mainly with respect to the relativism of values) and include a sketch of some connected aspects of Gödel's relation to Kant. |
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Gödel's philosophical views were to a significant extent influenced by the study not only of Leibniz or Husserl, but also of Kant. Both Gödel and Kant aimed at the secure foundation of philosophy, the certainty of knowledge and the solvability of all meaningful problems in philosophy. In this paper, parallelisms between the foundational crisis of metaphysics in Kant's view and the foundational crisis of mathematics in Gödel's view are elaborated, especially regarding the problem of finding the “secure path of a (...) |
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Quantified modal logic has reputation for complexity. Completeness results for the various systems appear piecemeal. Different tactics are used for different systems, and success of a given method seems sensitive to many factors, including the specific combination of choices made for the quantifiers, terms, identity, and the strength of the underlying propositional modal logic. The lack of a unified framework in which to view QMLs and their completeness properties puts pressure on those who develop, apply, and teach QML to work (...) |
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This is a wide-ranging 2004 book about arguments for and against beliefs in God. The arguments for the belief are analysed in the first six chapters and include ontological arguments from Anselm to Gödel, the cosmological arguments of Aquinas and Leibniz, and arguments from evidence for design and miracles. The next two chapters consider arguments against belief. The last chapter examines Pascalian arguments for and against belief in God. There are discussions of Cantorian problems for omniscience, of challenges to divine (...) |
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Kurt Gödel argues in “Russell’s Mathematical Logic” that on the assumption that, contrary to Russell, definite descriptions are terms, it follows given only several “apparently obvious axioms” that “all true sentences have the same signification .” Stephen Neale has written that this argument, and others by Church, Davidson, and Quine to similar conclusions, are of considerable philosophical interest. Graham Oppy, responding to this opinion, says they are of minimal interest. Falling between these is my opinion that implications of these arguments (...) |
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