Formal reconstructions of St. Anselm’s ontological argument

Eder, Günther; Ramharter, Esther

doi:10.1007/s11229-015-0682-8

Cited by 13 publications

(7 citation statements)

References 17 publications

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“…• It follows Eder and Ramharter's criteria (Eder & Ramharter, 2015) for the formal reconstruction of Anselm's ontological argument very closely.…”

Section: Simplifications Of the Proofmentioning

confidence: 56%

Kurt Gödel's reception of Charles Hartshorne's ontological proof

Kanckos¹,

Lethen²

2021

Preprint

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In 1962 Charles Hartshorne published a modal logic proof formalizing Anselm of Canterbury's ontological argument for the necessary existence of God. This article presents Kurt Gödel's notes on this proof which have now been discovered in his Nachlass among other theological material, and discusses possible influences on the development of Gödel's own ontological proof. To complete the picture, strong connections between Anselm of Canterbury's and Gödel's conceptions of God and his positive properties are pointed out.

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“…• It follows Eder and Ramharter's criteria (Eder & Ramharter, 2015) for the formal reconstruction of Anselm's ontological argument very closely.…”

Section: Simplifications Of the Proofmentioning

confidence: 56%

Kurt Gödel's reception of Charles Hartshorne's ontological proof

Kanckos¹,

Lethen²

2021

Preprint

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“…All our embeddings have so far implicitly assumed that all possible worlds are accessible from each other. This is an oversimplification 4 that we correct in the following section.…”

Section: Pvs Proofmentioning

confidence: 89%

PVS Embeddings of Propositional and Quantified Modal Logic

Rushby¹

2022

Preprint

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Modal logics allow reasoning about various modes of truth: for example, what it means for something to be possibly true, or to know that something is true as opposed to merely believing it. This report describes embeddings of propositional and quantified modal logic in the PVS verification system. The resources of PVS allow this to be done in an attractive way that supports much of the standard syntax of modal logic, while providing effective automation.The report introduces and formally specifies and verifies several standard topics in modal logic such as relationships between the standard modal axioms and properties of the accessibility relation, and attributes of the Barcan Formula and its converse in both constant and varying domains.

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“…Cf. also Eder and Ramharter (2015), where the authors state that the T-system would "seem to be mandatory on any modal conception of conceivability which can claim to be faithful to Anselm's reasoning" (p. 2814). structure [α, X].…”

Section: The Structure and Relevance Of The Modal Ontological Argumentmentioning

confidence: 99%

“…Taking into account this assumption, we will omit systems possessing a different set of primitive rules, such as D+and T+(with the so called MacIntosh rule), which are sometimes also considered in MOArelated literature (seeChellas and Segerberg 1994).10 The operators M and L can also be understood as formal counterparts of Anselm's "it is conceivable that" and "it is not conceivable that not", respectively (seeEder and Ramharter 2015, p. 2814). In turn, for the constant g, the following interpretation is sometimes proposed: "There is a necessarily existent being that has all perfections essentially"(van Inwagen 2012(van Inwagen , p. 158, 2018.…”

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confidence: 99%

The correctness and relevance of the modal ontological argument

Biłat

2020

Synthese

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This paper deals with some metaphilosophical aspects of the modal ontological argument originating from Charles Hartshorne. One of the specific premises of the argument expresses the idea that the existence of God is not contingent. Several well-known versions of the argument have been formulated that appeal to different ways of clarifying the latter. A question arises: which of the formally correct and relevant versions is proper or basic? The paper points to some criteria of formal correctness, and distinguishes two types of relevance for these versions: strong and weak. Its aim is to furnish a strictly worked out answer to the question, taking into account each of these types. As a result, a very simple, formally correct and (weakly) relevant version of the modal ontological argument is formulated. The results obtained are also used to criticize a popular belief about the relations in which the main versions of the modal ontological argument stand to one another.

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Formal reconstructions of St. Anselm’s ontological argument

Cited by 13 publications

References 17 publications

Kurt Gödel's reception of Charles Hartshorne's ontological proof

Kurt Gödel's reception of Charles Hartshorne's ontological proof

PVS Embeddings of Propositional and Quantified Modal Logic

The correctness and relevance of the modal ontological argument

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