|Infinity, infinite, philosophy: infinity is a result of a not stopping procedure, e.g. counting or dividing, or e.g. the continued description of a circular motion. In life-related contexts, infinitely continuous processes, e.g. infinite repetition, or never ending waiting are at least logically not contradictory. A construction rule does not have to exist to give an infinite continuation, such as e.g. in the development of the decimal places of real numbers. See also boundaries, infinity axiom, repetition, finitism, numbers, complex/complexity._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
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Finite/infinite/Leibniz: the set of possible objects of experience must be assumed to be infinite, because otherwise there ought to be a cause for reason why these should not be infinite, and there can be no such thing.
Language/infinite/finite/statement/fact/Leibniz: so there must be an infinite set of facts and correspondingly an infinite set of statements! (Factual truths). A finite mind, however, is incapable of reducing it to a finite set of identical sentences.
One never possesses a (full) proof, although there is always a reason for the truth! This reason can be fully understood by God alone.
Holz I 73/74
Infinity/construction/Leibniz: Leibniz makes the general connexion in an infinite set construible for the finite mind as the mathematically infinite, as a boundary concept in an infinitesimal method of construction.
Border/Leibniz/Holz: every finite mind has only the knowledge of a limited section, but also the realization that a boundary exists, and with it a world which extends beyond this limit.
Holz: the ability to exceed is an a priori determination of "boundaries". (Holz I 155 Helmuth Plessner: "Material a priori": the boundary is a material determinant moment of every finite being.)_____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
G. W. Leibniz
Philosophical Texts (Oxford Philosophical Texts) Oxford 1998
H. H. Holz
Leibniz Frankfurt 1992