Attempts to solve the logical problems that seem to accompany trinitarian belief are many and varied. But the problem at the heart of it all is the problem of the three and the one (how can God be three persons yet only one God?)
I must confess to being undecided which way to jump yet I do have something of a soft spot for Michael Rae's approach. Here is a fabulous dictionary article by Mike Rae on the issue. He outlines the philosophical problem and overviews a range of attempts to solve it (showing the problems of each), before presenting his own approach.
Of the views on offer Mike's is the one I find myself coming back to most often. He is a very brainy guy!