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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification

[axiom to specify new sets]

2 ideas

10887	Specification: Determinate totals of objects always make a set [Zalabardo]
	Full Idea: Principle of Specification: Whenever we can specify a determinate totality of objects, we shall say that there is a set whose elements are precisely the objects that we have specified.
	From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3)
	A reaction: Compare the Axiom of Specification. Zalabardo says we may wish to consider sets of which we cannot specify the members.

10874	Specification: a condition applied to a set will always produce a new set [Clegg]
	Full Idea: Axiom of Specification: For every set and every condition, there corresponds a set whose elements are exactly the same as those elements of the original set for which the condition is true. So the concept 'number is even' produces a set from the integers.
	From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
	A reaction: What if the condition won't apply to the set? 'Number is even' presumably won't produce a set if it is applied to a set of non-numbers.