Most sets would not be members of themselves eg., a set of motor-cycles is not a motor cycle etc. Such sets say are called 'run-of-the-mill' sets.
Some other kinds of sets are 'self-swallowing' , eg., the set of all things except motor cycles, would rather logically have to contain itself (since this set is NOT a motor cycle)
Now, what if we were to define a set of "All run-of-the-mill sets". Af first glance, this seems to be another of those run-of-the-mill sets till you ask yourself if the 'set of all run-of-the-mill sets' is itself a run-of-the-mill set or a self-swallowing one ? If the 'set of all run-of-the-mill sets' is a run-of-the-mill set, then it should be a part of the 'set of all run-of-the-mill sets' else if it is self-swallowing in ... then again, the 'set of all run-of-the-mill sets' should contain itself in which case it would cease to be the 'set of all run-of-the-mill sets' !!!
The problem in the above paradox is one of self-reference. To take another example :
The following statement is false
The preceeding statement is true
In isloation, both of these are harmless, but seen together and the way they reference each other ... we have a very "Strange loop" indeed !!! an unsolvable paradox
Russell's paradox
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