Does checking for block validity involve checking for the validity of the whole blockchain?

Question

In Ethereum Whitepaper there is a following description of Bitcoin's check for block validity:

The algorithm for checking if a block is valid, expressed in this paradigm, is as follows:

1. Check if the previous block referenced by the block exists and is valid.
2. [...]

Does this mean that in order to check block validity we have to recursively check all previous blocks within the blockchain? It sounds like it because if we would use the same algorithm for checking previous block validity then we would have to check validity of it's previous block as well and so on. Is that right?

Answer 1

The check can be done iteratively once and blocks marked as checked. Then we can check that a newly arrived block refers to a block we have previously checked as OK and we don't need to re-check any old blocks that have already been checked.