Dear Cruncher,
I agree with Mr. Khadir's suggestion. It doesn't make any sense to let your boss know of your awareness about his on-going search for your replacement. Rather, you can approach him with your own suggestions regarding sorting out any visible hurdles or issues in the path of company’s growth. No matter you two have different business philosophies, but don’t forget that both of you are working for the same organization with common goals, i.e. its growth & betterment. Also, take the fact of “different business philosophies between you two” positively in a way that combining both of your philosophies together, you can bring a completely new philosophy which will be more meaningful, helpful & powerful for your company’s business. Also, both of you can't oversee the fact that regardless of your style of working; you have to work as per your company's laid standard policies, processes and systems.
And then, you can’t expect your boss to adapt with your ways, rather, you have to adapt with his ways.
Regards,
RR.