Flooring Tile - Installing ceramic tile floor

I want to have a contractor install a ceramic tile floor in a large kitchen and breakfast room.....The floor has a vinyl floor presently....and I know it has to be removed. There is Plywood underneath......and my house is built over a crawl space.....House is very well built and about 25 years old.....My question is : Can the floor be made sturdy enough to disallow movement so there will not be cracking in the grout joints ?.....And If so, can this be done with the cement backer board ?

Backers are only a bonding surface. Crawl down below with the slithery residents of the crawl space and post back with the size of the joists, the unsupported span ans spacing of the joists. How thick is your subfloor? Do you have a vapor barrier on the ground. Are you in an extreme freeze thaw area?