One approach is to direct the conversation back to an investigation of the problem.
Firstly, you should acknowledge that there's a disagreement, and propose to change gears to break the stalemate. You've both made your cases and you still don't agree on what should be done. Defuse the situation by saying something like: You're the boss. Ultimately, what you say goes. But I don't think you want to force every decision we make. Let's see if we can get somewhere by changing perspectives.
(Ideally, he should be the one to lead the discussion this we, but we don't always get the boss we deserve).
The trick is to get away from solutions. When you talk about which solution to choose, you end up arguing, because solutions are mutually exclusive. When you talk about aspects of the problem, you can both be looking out for different aspects of the problems and still have a productive discussion.
For instance, your boss will likely want a cheap and fast solution, whereas you may want one that is maintainable, and works well for the customer. The solution is to map out what these requirements mean in detail and to find a smart way of satisfying all of them. You might, for instance, design an ideal solution, but then add a plan of implementation that allows for the first implementation to be delivered quickly and cheaply, but with a continued development towards a more sustainable solution.
A second point to bear in mind is that once people are convinced of something, reason and logic work against you. The more arguments you throw at them, the more they dig their heels in. The trick is togive up on convincing them of the whole big truth at once, and to find somesmall commitment they can make. Ie. don't try to convince someone that Apple is better than Microsoft, buy them an ipod nano. Break the absolutes. Don't try to turn a staunch Republican into a Democrat, just ask him which Democrat he'd support if he had to. Find one small commitment towards your point of view and ask them to make it (and be prepared to do the same).