Since his argument is that performance is affected by OOP, I think you should start by showing that he's wrong. It will not be too difficult to do a benchmark to show that the performance is the same or nearly the same when using OOP compared to procedural approach.
Also, the last part of the argument makes me think that your boss doesn't know too much about development in general. Since he's not a programmer himself and does not have a solid background in development, it would be easy to convince him that the things he learned from some unknown websites or some conferences he assisted in 1998 are plain false or not true anymore. Sometimes, it may even be a good idea to invent some fancy arguments, like:
We really must move to OOP quickly, since in PHP 6, it will be impossible to use procedural programming any longer.
Of course, you should use such fancy arguments at your own risk and only when your boss doesn't know anything about the subject and if his own arguments are not proven as well.
Is there a guideline in your company which forces you to never use OOP in PHP?
- If yes, well, it's too bad. It's often hard to discuss about guidelines, especially when the opponent says that in first place, we must not discuss them because they are here to ensure the uniformity of the codebase. You may still try to convince at least your coworkers to start violating the guideline, or trying to do all you can to see this guideline removed.
- If no, then I don't see what's the problem. You write code, you decide to use OOP, you use it. If your colleague wants to rewrite thousands of lines of code to remove OOP, he's free to do it.
Showing world examples (large projects written by professional developers where OOP is actually used) may also be helpful to convince your boss.
Finally, if the boss doesn't listen to any of your technical arguments, there is the last one:
I've done the estimate of the change you requested the last Friday. It will give us four weeks to do it, since the actual code is a mess and it's nearly impossible to find where to put what. Ah, FYI, if the source code was refactored correctly and if we used OOP from the beginning, it would take us only three days.