![]() ![]() But Aristotle dominates this first period, as well as most subsequent periods, with respect to quantitative infinity. 987a 15 –19), "thought that finitude and infinity were not attributes of certain other things, e.g., of fire or earth or anything else of this kind, but that infinity itself and unity itself were the substance of the things of which they are predicated." Under their influence plato also made infinity one of the constitutive factors of reality: "All things that are ever said to be consist of a one and a many, and have in their nature a conjunction of Limit and Unlimitedness" ( Philebus 16C also see 23C). The Pythagoreans, as Aristotle reports ( Meta. 3), and, most likely, is some basic natural body that is unlimited because quantitatively inexhaustible. 2), "deathless and indestructible" ( Frag. 610 –546 b.c.), who affirmed that "the first principle of existing things is the unlimited" ( Fragment 1). The first period begins in ancient Greece with Anaximander of Miletus ( c. The following account treats the first two periods as representative of Greek and Neoplatonic thought, and the last three as representative of Christian and modern thought. This article traces the history of the concept of infinity, which falls into five main sections: (1) that of the ancient Greeks, (2) Neoplatonism, (3) that of the Fathers of the Church, (4) medieval scholasticism, and (5) the period since 1600. On the other hand, when applied to matter, infinity signifies a state of indigence, since it manifests that matter of itself lacks form and act these are perfective factors that matter must receive if it is to exist within the real universe, and is to be even indirectly intelligible and describable. This is so because it reveals the absence in God of matter and of other intrinsic factors suggesting mere potency, as well as the absence of extrinsic limits such as time, place, or comprehension by a created intellect -all of which can be linked with imperfection and none of which is proper to God. For example, when predicated of God, infinity denotes perfection. The condition it signifies in these can connote either perfection or imperfection, depending upon whether the termination, which is thereby stated to be absent, is itself a perfection and whether the entity in question should possess it. It is predicated both of extramental, actually existing things (such as God, the visible universe, and matter) and of intramental entities (such as logical concepts and mathematical constructs). In general, the word signifies the state or condition arising from an entity's not having some sort of end, limit, termination, or determining factor. Infinity is derived etymologically from the Latin, infinitas, which is a combination of in (meaning not) and finis (meaning end, boundary, limit, termination, etc.). ![]()
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