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Cardinality and acceptable abstraction. (English) Zbl 1436.03029

Summary: It is widely thought that the acceptability of an abstraction principle is a feature of the cardinalities at which it is satisfiable. This view is called into question by a recent observation by Richard Heck. We show that a fix proposed by Heck fails but we analyze the interesting idea on which it is based, namely that an acceptable abstraction has to “generate” the objects that it requires. We also correct and complete the classification of proposed criteria for acceptable abstraction.

MSC:

03A05 Philosophical and critical aspects of logic and foundations
00A30 Philosophy of mathematics
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References:

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