Why are the "first conditional", "second conditional", and "third conditional" so named?

Solution 1:

They're numbered in order, based on how removed they are from reality.

First: "If I have time, I'll go." It's not yet known whether or not I'll have time, but it's possible. So the statement is not at all far from reality.

Second: "If I had time, I would study grammar." I don't have time now, but I may in the future, and I know how I plan to spend it. So it's not immediately realistic, but it may become so.

Third: "If I had had time, I would have answered more questions." I didn't have time, and so I didn't answer more questions. This is strictly contrary to reality.