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1

Remarks on the Gödelian Anti-Mechanist Arguments

100%

Raatikainen P.

Studia Semiotyczne

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2020

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vol. 34

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issue 1

EN

Certain selected issues around the Gödelian anti-mechanist arguments which have received less attention are discussed.

2

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

75%

Bjørdal F. A.

Logic and Logical Philosophy

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2018

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vol. 27

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issue 3

329-350

EN

A metaphysical system engendered by a third order quantified modal logic S5 plus impredicative comprehension principles is used to isolate a third order predicate D, 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 D we in Section 2 derive the thesis (40) that all properties are D 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 D suggests weakened Gaunilo-like 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.

3

Gödel, Wittgenstein and the Sensibility of Platonism

63%

Poręba M.

Eidos. A Journal for Philosophy of Culture

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2021

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vol. 5

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issue 1

108-125

EN

The paper presents an interpretation of Platonism, the seeds of which can be found in the writings of Gödel and Wittgenstein. Although it is widely accepted that Wittgenstein is an anti-Platonist the author points to some striking affinities between Gödel’s and Wittgenstein’s accounts of mathematical concepts and the role of feeling and intuition in mathematics. A version of Platonism emerging from these considerations combines realism with respect to concepts with a view of concepts as accessible to feeling and able to guide our behavior through feeling.

4

Diagonal Anti-Mechanist Arguments

51%

Kashtan D.

Studia Semiotyczne

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2020

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vol. 34

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issue 1

EN

Gödel’s first incompleteness theorem is sometimes said to refute mechanism about the mind. §1 contains a discussion of mechanism. We look into its origins, motivations and commitments, both in general and with regard to the human mind, and ask about the place of modern computers and modern cognitive science within the general mechanistic paradigm. In §2 we give a sharp formulation of a mechanistic thesis about the mind in terms of the mathematical notion of computability. We present the argument from Gödel’s theorem against mechanism in terms of this formulation and raise two objections, one of which is known but is here given a more precise formulation, and the other is new and based on the discussion in §1.

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2 Studia Semiotyczne

1 Eidos. A Journal for Philosophy of Culture

1 Logic and Logical Philosophy

1 Bjørdal F. A.

1 Kashtan D.

1 Poręba M.

1 Raatikainen P.

1 2021

2 2020

1 2018

Remarks on the Gödelian Anti-Mechanist Arguments

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

Gödel, Wittgenstein and the Sensibility of Platonism

Diagonal Anti-Mechanist Arguments