Apple Logic

I like to think about logic (and apples).

A man was walking along the road and saw an apple tree with beautiful red apples on it.

There were three fences between him and the apple tree.

He went to the owner of the first fence and asked if he could cross the fence to get some apples. The owner of the first fence said yes, but only if you give me half of all your apples and one half of another apple before you cross back over my fence.

The man said okay.

He went to the owner of the second fence and asked if he could cross the fence to get some apples. The owner of the second fence said yes, but only if you give me half of all your apples and one half of another apple before you cross back over my fence.

The man said okay.

He went to the owner of the third fence and asked if he could cross the fence to get some apples.

The owner of the third fence owned the apple tree.

The owner of the third fence said yes, but only if you give me half of all the apples you pick and one half of another apple before you cross back over my fence.

The man said okay.

So, the man crossed the fences, picked as man apples as he could, and paid all the owners the correct number of apples and half apples.

When the man got back to the road, he had three full apples (uncut). How many apples did he pick from the apple tree?

(HINT:  The man only had to cut apples in half, never quarters, eighths, etc.)