I did not realize the Doctor was such an ass

[Iamnotspock]

Why is the father stuck in the bowels of the TARDIS? I didn't even know there was a "basement" there. How do you have a basement in a ship with infinite mass?

While the Doctor at one point says, "There are no measurements in infinity," when referring to the size of the TARDIS, he later jettisons 25% of its mass. I like to think it's potentially infinite, with its size and volume able to be modified, with new rooms being created and old ones being deleted, and no limit to how much this can be done. That might explain why, when Sarah asks how big the ship is, the Doctor replies; "How big are you at the moment?"

 

[Christopher]

I think the "infinite" stuff is just a hyperbolic figure of speech, like "It goes on forever."

 

[RoJoHen]

It's as infinite as it needs to be at any particular time.