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Maimonides here and elsewhere echoes Avicenna's idea of God as "necessary being"—literally, "The Necessary of Existence" (wājib al-wujūd)—whose essential nature it is to exist, and who, as such, does not rely on another for His existence.
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A second principle is the Aristotelian "impossibility of an ordered, actual infinity" which, with the first principle, guarantees that "there cannot be an infinite number of levels of being and that there must be one being whose existence is necessary in itself Avicenna's 'Necessary of Existence' (wajib al-wujud)", the Light of Lights (Walbridge 2000: 24 5; PI, 87.1 89.8).
Like Aristotle (Categories 5, 2b5 6), Alyngton can therefore affirm that primary substances are the necessary condition of existence for any other items of the world: nothing could exist, if primary substances stopped existing (In Cat., cap. de substantia, p. 286).
The British anthropologist A.R. Radcliffe-Brown explored the theoretical implications of functionalism as a relationship between a social institution and the "necessary conditions of existence" of a social system.
Figure 11 Illustration of the necessary condition of existence of an order-2 limit cycle.
Based on symbolic dynamics, the paper provides a satisfactory and necessary condition of existence for consecutive periodic orbits of the Lorenz maps.
Therefore, for the necessary condition of existence of an order-2 limit cycle we only need to focus on cases (SC11) and (SC2), which will be addressed later.
Based on the necessary condition of existence of an order-2 limit cycle, we can prove case (ii) in Lemma 8.1.
In the previous sections we have shown that a threshold of viral replication is necessary for existence of the latent reservoir and that the decay rate of the reservoir is rapidly maximized with decreasing replication.
Undeniably, Avicenna offers here a description of the status of necessary existence and a deduction of its properties.
The existence of God is necessary for the existence of intelligible being; but intelligible being certainly exists; the existence of God is therefore necessary.
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