finite or aggregative structure

1 فلسفه:: ساختار متناهی _ تراکمی

The proof for a beginning (and Creator) of past time has been the source of considerable debate since its formulation by the Kalam philosophers, a school of medieval Arabic philosophers who promoted natural theism and advocated for the impossibility of an " actual infinite" being applied to a finite or aggregative structure.1 The Kalam proof against the infinity of past time was not accepted in the Western medieval world because Saint Thomas Aquinas followed Aristotle in allowing for the possibility of infinite temporal regression.2 temporary definitions of time are subject to Hilbert's prohibition of actual infinities in finite or aggregative structures. that a very probative version of this proof can be formulated if two theoreti- cal developments are taken into serious consideration: (1) an ontological ex- planation of time as " a continuous succession of non-contemporaneous dis- tension intrinsic to changeable reality" (which means time must be a real aggregative structure), and (2) the mathematical distinction between an ac- tual and potential infinity (and the prohibition of actual infinities to finite or aggregative structures). This ontological explanation of time is important for applying the Hilbertian prohibition of actual infinities to past time, for as will be seen, Hilberts prohibition of actual infinities applies to any finite or aggregative structure. We may now proceed to an explanation of Hilberts distinction be- tween potential and actual infinities and the prohibition of the application of actual infinities to finite or aggregative structures.

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