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Axioms of Infinity as the Starting Point for Rigorous Mathematics.

A more than sufficient starting point for the development of all currently accepted rigorous mathematics is provided by a pair of assumptions about how many individuals there are: the relative assertion that there are as many of them as there are small classes of them, and the absolute assertion tha...

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Published in:Annals of the Japan Association for the Philosophy of Science Vol. 20; no. 1; pp. 17 - 29
Main Author: Burgess, John P.
Format: Article
Published: Sasaki Printing & Publishing Co., Ltd. 2012
Subjects:
Axioms
Infinity (Mathematics)
Mathematics
Assertions (Logic)
Heuristic
Euclidean algorithm
Online Access:View this record in EBSCOhost
Summary:A more than sufficient starting point for the development of all currently accepted rigorous mathematics is provided by a pair of assumptions about how many individuals there are: the relative assertion that there are as many of them as there are small classes of them, and the absolute assertion that there are indescribably many of them. But explaining what the foregoing assertion means is more work than establishing that it is true.