On the Maximality of Positive Properties and Modal Collapse in Variants of Gödel’s Ontological Proof for the Existence of God

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Gödel’s ontological proof for the existence of God – as an inference from the level of rational, logical structure to the level of being – was strongly influenced by Leibniz’s monadology, which is based on the Ur-Monade – God – conceived as absolutely infinite. Gödel defines God as the maximum of positive properties and he characterizes this maximum (of being) with his postulates implicitly as an ultrafilter structure. Using maximality as criterion we have compared the set of positive properties in Scott’s version of Gödel’s theistic theory with modified variants of it to see whether a maximum is still achieved, or not, and what effect this has on modal collapse. The motivation for these, typically weakened, variants of Gödel’s theistic theory has been to avoid modal collapse and the limited determinism associated with it, and to show that the necessary existence of God can still be proved with less strong axioms. A weakening of the maximality criterion of the ultrafilter structure imposed by Gödel’s (and Scott’s) postulates have thus been applied to the set of positive properties in order to allow for alternative models in which modal collapse does not hold. In these alternative models, however, the maximality criterion for the basic quantity of positive properties is abandoned, so that in them God as a “maximum” is not reached. We argue that this is contrary to Gödel’s intention, and that for his conception of God, maximality and absolute infinity are non-negotiable. What Gödel had in mind, as we argue here, was a holistic – absolutely infinite – view of the world, i.e. with modal collapse, but without limited determinism.

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This article examines Baruch Benedictus Spinoza conceptual understanding of the proofs for the existence of God. It traces the evolution of this theme pursuant to the metaphysical studies of Moderns Philosophy. Тhe concept of God the philosophy of Spinoza is considered by exploring the nature of the relations between the transcendent sphere of God and the spiritual world of the human person. Spinoza argues from the possibility of God's existence to God's necessary existence. God is an absolutely infinite substance, necessarily exists, qua Natura Naturans is immutable. God or Nature. The universe is an expression of God's nature, qua Natura Naturata - God is its immanent cause. Spinoza's God is synonymous with Nature. Substance is defined as in itself. Spinoza understands a substance to be something that is self-caused and self-explained. The transcendence is understood as an ontological category, being discussed connection with the key themes of Christian philosophy (Anry Bergson, Moris Blondel and Wladimir Soloviev), such as time and eternity, person and history, creation and God etc. Spinoza's concept of God is referring to the God of the monotheistic religions, God as One Substance, pertains to a concept of the oneness of God, is transcendent and therefore unknowable. Spinoza's definition of God found on the first page of the Ethics: Being absolutely infinite. From the point of view of historiography, the role of the book Ehtics by Spinoza is highlighted.

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4 - What Is God?
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The Conceivability of God
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In the continuing dialogue between Western philosophy and the Christian religion, the central issue has generally been the existence of God. There has however been a discernible shift in the focus of the discussion in recent years. Rather than the existence of God, the issue now seems to be the concept of God. It is increasingly argued by philosophers critical of religion that the concept of God is basically incoherent, and that therefore the question of God's existence or non-existence does not even arise. What cannot be conceived is not even a possible object of faith.

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