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**naive (intuitive) definition of "set"**

I happened upon a book by a Joseph Landin, once head of the math department at University of Chicago and subsequently Ohio State University, in which he gives this as a definition of a set and states this property:

Shortly thereafter, he writes,A set is a collection of objects; the nature of the objects is immaterial. The essential characteristic of a set is this: Given an object and a set, then exactly one of the following two statements is true.

a) The given object is a member of the given set.

b) The given object is not a member of the given set.

Would you please explain why his second statement is so? I cannot fathom why this is not a perfectly consistent and constructible set.It might be tempting to speak of "the set of people who will visit the city of Chicago during 2050." But, clearly, such a collection cannot qualify as a set according to our understanding of this term.