If your basement isn't finished, go downstairs and measure the floor joists under your kitchen. Measure how long they are between supports, how high each one is and how far they are apart (center-to-center). If the house was built in 1956, it will almost certainly have fir 2X? floor joists.
The problem won't be that your floor won't be strong enough to support the tiling, the problem may be that the floor won't be strong enough not to bend when you walk on the floor, and there-in lies the problem. If the floor bends when you walk on it, then the bending of the floor may be enough to cause the grout joints to crack in a ceramic tiled floor. A floor will bend slightly when you walk on it, and it's the amount of bending that's at issue. Ceramic tiling and grout simply don't have hardly any elasticity at all to accomodate any bending of the floor. And, of course, the stronger the floor, the less bending you'll have.
So, Glenn is correct in saying that the floor is strong enough to support ceramic tiles. But, that really shouldn't be the question. The correct question is whether the floor is strong enough to be SUITABLE for ceramic tiles.