  Unfortunately, Basic Law V implies a contradiction, and this was pointed out to Frege by Bertrand Russell just as the second volume of the Grundgesetze was going to press. Russell recognized that some extensions are elements of themselves and some are not; the extension of the concept extension is an element of itself, since that concept would map its own extension to The True. The extension of the concept spoon is not an element of itself, because that concept would map its own extension to The False (since extensions aren’t spoons). But now what about the concept extension which is not an element of itself?  Let \(E\) represent this concept and let \(e\) name the extension of \(E\). Is \(e\) an element of itself? Well, \(e\) is an element of itself if and only if \(E\) maps \(e\) to The True (by the definition of ‘element of’ given at the end of the previous paragraph, where \(e\) is the extension of the concept \(E\)). But \(E\) maps \(e\) to The True if and only if \(e\) is an extension which is not an element of itself, i.e., if and only if \(e\) is not an element of itself. We have thus reasoned that \(e\) is an element of itself if and only if it is not, showing the incoherency in Frege’s conception of an extension.