Comment on the following:
The common paradox I gave you in class:
"This very sentence that I am now uttering is false".
Let the above sentence = X
If X is true, then what it says is the case so X is false.
If X is false, then since it is exactly what is says, it's true.
Bertrand Russell's Paradox about sets.
Sets can be members of other sets. For example a set of all desks in the room is also a set of all objects in the building.
Some sets can be members of themselves. For example the set of all objects on page 57 is an object on page 57.
The set of all sets in a set and so a member of itself.
Some sets are clearly not members of themselves. The set of all people is not a person The set of all desks in the room is not a desk in the room.
NOW
consider the set of all sets that are not members of themselves (x). Is X a member of itself?
If it is a member of itself, then it is one of those things that is not a member of itself, therefore it is not a member of itself.
If it is not a member of itself, it is one of those things that is not a member of itself, so it is a member of itself.
This concept is quite confusing, but abnormally simple at the same time. If one chooses to be an individualist, they are choosing to be a part of an individualistic movement, making themselves not an individualist. Its quite a strange theory.
ReplyDeleteThinking about it now, this makes quite the oxymoron. A group of individualists.
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DeleteYes it is quite a strange theory. I think his point was to prove that all logic isn't always logical.
DeleteYes it is quite a strange theory. I think his point was to prove that all logic isn't always logical.
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