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Unformatted text preview: Chp. 7 (130-131) The sense in which there are classes is a different one from the sense in which there are particulars, because if the senses of the two were exactly the same, a world in which there are three things and therefore eight classes would be a world in which there are at least eleven things. Its possible to discuss classes of things: o Human beings o Teaspoons o Slummy bars But each of these classes is not in turn one of the things in the class. The class of human beings is not a human being. And the class of slummy bars is not a slummy bar. But, there are apparent exceptions. Consider the class of: o Things that are not teaspoons. o The class of all classes. The class of things that are not teaspoons is not a teaspoon. The class of classes is a class. Now, if we ask ourselves, does the class of things that are not teaspoons belong in the class of things that are not teaspoons, the answer seems to be yes. And, if we ask does the class of classes belong in the class of classes, the answer seems to be yes. No contradictions arise from these two answers. But, consider the class of: o Classes that are not members of themselves We can ask, what classes belong here? o The class of classes? (NO) o The class of human beings? (YES) o The class of slummy bars? (YES) o The class of teaspoons? (YES) o The class of things that are not teaspoons? (NO) And we can give a definite answer for all classes, until we come to this class itself: The class of classes that are not members of themselves. Does this class belong in the class of classes that are not members of themselves? What if we say yes? What if we say no? Russells solution to the paradox: (132) classesare incomplete symbolsyou are talking nonsense when you ask yourself whether a class is or is not a member of itself, because in any full statement of what is meant by a proposition which seems to be about a class, you will find that the class is not mentioned at all and there is nothing about a class in the statement....
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- Spring '08