I'm reading Bitcoin paper of Satoshi Nakamoto (https://bitcoin.org/bitcoin.pdf).
Each owner transfers the coin to the next by digitally signing a hash of the previous transaction and the public key of the next owner and adding these to the end of the coin. A payee can verify the signatures to verify the chain of ownership.
And the very next sentence is:
The problem of course is the payee can't verify that one of the owners did not double-spend the coin.
That is, as I understand, after every transaction a new transaction hash is generated. So, first, it is not possible to double-spend a coin because it already has a new previous transaction hash. Second, why it says payee can't verify a double-spend if every transaction a coin has a new previous transaction hash?