How many larmas were eaten?

Our four Scribes - Plato, Socrates, Diogenes and Aristotle - were enjoying an argument and, mindful of what happened when they let the drink run too freely, wisely chose to refresh themselves with larma fruit instead. They had thirteen larma fruit between them on a plate and they helped themselves as they went along, too busy to pay very close attention as to whether each man received his fair share. After a while, all the larmas were eaten, and the following discussion ensued:

Plato: Did you eat more larmas than I did, Socrates?
Socrates: I don't know. Did you eat more larmas than I did, Diogenes?
Diogenes: I don't know.
Aristotle: Aha!

Aristotle now knew how many larmas everyone had eaten - and, of course, knowing that Aristotle knew, the other three were able to make the same deduction. Given that:

• All four Scribes were extremely intelligent, flawlessly logical, and knew that their fellows were too
• Prior to the discussion, each of the Scribes knew only that everyone had eaten at least one larma
• Each Scribe knew how many larmas he himself had eaten
• No Scribe would dream of asking a question to which he already knew the answer

How many larmas did everyone eat?