References of "Archive of Formal Proofs"
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See detailAxiom Systems for Category Theory in Free Logic
Benzmüller, Christoph UL; Scott, Dana S.

in Archive of Formal Proofs (2018)

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See detailFormalisation and Evaluation of Alan Gewirth's Proof for the Principle of Generic Consistency in Isabelle/HOL
Fuenmayor, David; Benzmüller, Christoph UL

in Archive of Formal Proofs (2018)

An ambitious ethical theory ---Alan Gewirth's "Principle of Generic Consistency"--- is encoded and analysed in Isabelle/HOL. Gewirth's theory has stirred much attention in philosophy and ethics and has ... [more ▼]

An ambitious ethical theory ---Alan Gewirth's "Principle of Generic Consistency"--- is encoded and analysed in Isabelle/HOL. Gewirth's theory has stirred much attention in philosophy and ethics and has been proposed as a potential means to bound the impact of artificial general intelligence. [less ▲]

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See detailComputer-assisted Reconstruction and Assessment of E. J. Lowe's Modal Ontological Argument
Benzmüller, Christoph UL; Fuenmayor, David

in Archive of Formal Proofs (2017)

Computers may help us to understand --not just verify-- philosophical arguments. By utilizing modern proof assistants in an iterative interpretive process, we can reconstruct and assess an argument by ... [more ▼]

Computers may help us to understand --not just verify-- philosophical arguments. By utilizing modern proof assistants in an iterative interpretive process, we can reconstruct and assess an argument by fully formal means. Through the mechanization of a variant of St. Anselm's ontological argument by E. J. Lowe, which is a paradigmatic example of a natural-language argument with strong ties to metaphysics and religion, we offer an ideal showcase for our computer-assisted interpretive method. [less ▲]

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See detailTypes, Tableaus and Gödel's God in Isabelle/HOL
Fuenmayor, David; Benzmüller, Christoph UL

in Archive of Formal Proofs (2017)

A computer-formalisation of the essential parts of Fitting's textbook "Types, Tableaus and Gödel's God" in Isabelle/HOL is presented. In particular, Fitting's (and Anderson's) variant of the ontological ... [more ▼]

A computer-formalisation of the essential parts of Fitting's textbook "Types, Tableaus and Gödel's God" in Isabelle/HOL is presented. In particular, Fitting's (and Anderson's) variant of the ontological argument is verified and confirmed. This variant avoids the modal collapse, which has been criticised as an undesirable side-effect of Kurt Gödel's (and Dana Scott's) versions of the ontological argument. Fitting's work is employing an intensional higher-order modal logic, which we shallowly embed here in classical higher-order logic. We then utilize the embedded logic for the formalisation of Fitting's argument. (See also the earlier AFP entry ``Gödel's God in Isabelle/HOL''.) [less ▲]

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