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Numbers seem to be invested with significance in Arda, just as we invest them with great meaning. Seven is a number with a lot of symbolism. It is a lucky number, it is also significant in Judaism, Christianity and Islam, it numbers those planets/stars/moons in our own system we can see without a telescope. But I think all numbers have their own particular significance within Arda itself, without any reference to how we view them; Tolkien must have been trying to establish a similar history of symbols and symbolism in his own creation.
There are, as far as I can find, several instances of seven being significant. The oldest seems to be Valacirca, the seven stars, which could be the root of all the following symbolism. Then we have the seven fathers of the Dwarves (and the Dwarves are also given seven rings by Sauron), and the seven sons of Feanor. In terms of places, there are seven gates in Gondolin, the seventh being seven hundred (?) feet high, and Minas Tirith is on seven levels, each adding up to seven hundred feet. There are also seven Palantiri.
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Gordon's alive!
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