Why is the Trinity a Trinity?

It's well established and accepted by most Christians that God is triune, consisting of the Father, Son, and Holy Spirit. However, while talking with a friend earlier about Wisdom (from Proverbs), I mentioned that Wisdom could almost be considered a fourth Person. This suddenly made me wonder why there are exactly three Persons. Is there any Biblical evidence as to why God "decided" to be a Trinity, as opposed to a Duinity or a Quardrinity? Barring that, what about a doctrine that even touches on this? Though I now call myself non-denominational, I grew up Wesleyan, so I'd prefer Protestant viewpoints, but a Catholic or Orthodox perspective is acceptable.