I was curious, so I checked. Wikipedia has a totally different geographical definition of "Middle East" than you do. And Webster's dictionary agrees with the Wikipedia definition.
So I guess learned people can differ here.
http://en.wikipedia.org/wiki/The_middle_east
Israel is by definition the Near East. That is all of the shemitic nations actually.
Middle East is between the Far East (China, etc.) and the Near East.
Wikipedia is a leftist joke.
All of my dictionaries say that the Persian and Hindi nations are the Middle East.