Finitely Generated Magari Algebras and Arithmetic

Hendriks, A.; Jongh, Dick de

doi:10.1201/9780203748671-6

Cited by 3 publications

(4 citation statements)

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“…In [16,17] Hájek improves upon an, as it turns out, just slightly insufficient model theoretic argument by Magari in [21] to the effect that Gödel's AG1, AG2 and AG3 already suffice for the derivation of the theistic main theorem. Magari's idea is confirmed as applied to Anderson's argument for Hájek shows that Anderson's AA3 and AA4 are superfluous in the presence of full second order modal comprehension with the underlying logic.…”

Section: Pinpoints and Diagnosesmentioning

confidence: 99%

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All Properties are Divine or God Exists - The Sacred Thesis and its Ontological Argument

Bjørdal

2017

LLP

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Abstract. A metaphysical system engendered by a third order quantified modal logic S5 plus impredicative comprehension principles is used to isolate a third order predicate , and by being able to impredicatively take a second order predicate G to hold of an individual just if the individual necessarily has all second order properties which are we in Section 2 derive the thesis (40) that all properties are or some individual is G. In Section 3 theorems 1 to 3 suggest a sufficient kinship to Gödelian ontological arguments so as to think of thesis (40) in terms of divine property and Godly being; divine replaces positive with Gödel and others. Thesis (40), the sacred thesis, supports the ontological argument that God exists because some property is not divine. In Section 4 a fixed point analysis is used as diagnosis so that atheists may settle for the minimal fixed point. Theorem 3 shows it consistent to postulate theistic fixed points, and a monotheistic result follows if one assumes theism and that it is divine to be identical with a deity. Theorem 4 (the Monotheorem) states that if Gg and it is divine to be identical with g, then necessarily all objects which are G are identical with g. The impredicative origin of suggests weakened Gaunilolike objections that offer related theses for other second order properties and their associated diverse presumptive individual bearers. Nevertheless, in the last section we finesse these Gaunilo-like objections by adopting what we call an apathiatheistic opinion which suggest that the best concepts 'God' allow thorough indifference as to whether God exists or not.

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Section: Pinpoints and Diagnosesmentioning

confidence: 99%

“…We mention that Hájek in [16,17] uses moderate cautious comprehension whereas Sobel appeals to full comprehension in the criticism of Gödel, and also Anderson uses full second order comprehension in his rectification of Gödel's proof. Also Hájek's "vorsichtige Komprehension" is impredicative.…”

Section: Higher Order Modal Logicsmentioning

confidence: 99%

All Properties are Divine or God Exists - The Sacred Thesis and its Ontological Argument

Bjørdal

2017

LLP

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“…Hájek (Hájek, 1996) claimed that Anderson's emendation makes Axioms 4 and 5 derivable from the other axioms and definitions. Discussions about the redundancy of these two axioms started with an earlier (and wrong) claim by Magari (Magari, 1988) w.r.t.…”

Section: ∃Xg(x)mentioning

confidence: 99%

“…Neither Gödel's manuscript nor Scott's manuscript reveal whether they use constant or varying domains, and this is also the case for many variants (e.g. Hájek 1996). Nevertheless, some authors of variants of Gödel's ontological argument do explicitly state a preference for varying domains (Anderson, 1990, footnotes 11 and 14).…”

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confidence: 99%

Variants of Gödel’s Ontological Proof in a Natural Deduction Calculus

Kanckos

Paleo

2017

Stud Logica

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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 Axiom 1 for the positivity of properties only once. The third and fourth proofs formalize, respectively, Anderson's and Bjørdal's variants of the ontological argument, which are known to be immune to modal collapse.

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Doing logic by computer: interpolation in fragments of intuitionistic propositional logic

Hendriks

2000

Annals of Pure and Applied Logic

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Finitely Generated Magari Algebras and Arithmetic

Cited by 3 publications

References 1 publication

All Properties are Divine or God Exists - The Sacred Thesis and its Ontological Argument

All Properties are Divine or God Exists - The Sacred Thesis and its Ontological Argument

Variants of Gödel’s Ontological Proof in a Natural Deduction Calculus

Doing logic by computer: interpolation in fragments of intuitionistic propositional logic

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