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Not at all. The set may be defined in a way that makes this impossible. Consider the following set: "The set of all exceptions to Goldbach's Conjecture". It isn't known whether there areany exceptions. If there aren't, the set is empty. If there are exceptions, the set will have some elements - but we simply don't know. Assuming that one day the Goldbach Conjecture will be proved (or disproved), there will still be other conjectures in Number Theory that can never be proved or disproved, and a similar set can be defined for one of those.

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Q: Is it possible to determine the cardinality of any set?
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