This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
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.” • It’s 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? • Russell’s solution to the paradox: (132) “…classes…are incomplete symbols…you 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.” •...
View Full Document
- Spring '08
- Logic, Bertrand Russell, external world, incomplete symbols