It all depends on what view of science you're taking. For example, take quantum mechanics.

Assuming the timeframe is linear and no precognition is available, then the nose can exist in both a normal and extended state until it is observed. The standing state is an ungrown nose, the growth is only triggered when statement != truth. Therefore to say "My nose is about to grow" is inaccurate, which will trigger a nasal surface area increase. At the time the statement was made, the nose was not about to grow. As we have already accepted the timeframe is a mono-directional forward linear progression, the latter reaction cannot affect the earlier statement. As the nose grows, it will become visible to Pinocchio, thereby setting the state as one of growth. Given it is the act of Pinocchio seeing his own nose that sets the quantum state of the nose, the follow-up question should be "Given the previous followed procedures, what would happen if Pinocchio has his eyes shut?"

Another follow-up question is "Why isn't he down the local brothel declaring he's Superman?"