You may have encountered some people with such an attitude (if not rash or really low spirited enough to say these very words). First let us consider "I Know Everything" or "I know All". Lets begin by analyzing the universe of knowledge in which such a personage is apparently well versed in.
Let us begin with He/She know everything. This is true and concurs with the first statement.
He/She knows that he/she knows everything. The aforementioned behaviour indicates the veracity of the same.
He/She knows what all he/she does not know!! Here comes the paradox! If the person knows what (s)he doesn't know, it means that the person doesn't know something. But if the same person knows not what (s)he doesn't know, that is the very thing he doesn't know! Hence he doesn't know all!
Similar line of logic applies on the other proposition - I know nothing. By saying so, a person confesses to know "nothing", which indicates he has knowledge of something!
So after all, one can never have knowledge of everything! So all you intelligent guys out there, show some modesty the next time your opportunity to dazzle comes :)
Let us begin with He/She know everything. This is true and concurs with the first statement.
He/She knows that he/she knows everything. The aforementioned behaviour indicates the veracity of the same.
He/She knows what all he/she does not know!! Here comes the paradox! If the person knows what (s)he doesn't know, it means that the person doesn't know something. But if the same person knows not what (s)he doesn't know, that is the very thing he doesn't know! Hence he doesn't know all!
Similar line of logic applies on the other proposition - I know nothing. By saying so, a person confesses to know "nothing", which indicates he has knowledge of something!
So after all, one can never have knowledge of everything! So all you intelligent guys out there, show some modesty the next time your opportunity to dazzle comes :)
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ReplyDeletelets assume there exists a set Z = { X / where X is a set that is not subset of itself}
ReplyDeleteWhat are the members of this set ?
Will this set contain Z itself?
There cannot exist a set which is not a subset of itself, nor is the null set included thereby (i am assuming you are not restricting the same to a proper subset). So it has no members. Hence Z is a null set and hence it will not contain anything (even itself).
DeleteI guess the paradox you are referring to is the Russell's paradox: "A set (R) of all sets that do not 'contain' themselves"
In this case if our set R if it does not contain itself, it should contain itself. On the other hand if it contains itself, it cannot do so :)