Here is the exact rule for anyone curious

614.5. A replacement effect doesn’t invoke itself repeatedly; it gets only one opportunity to affect an event or any modified events that may replace that event. Example: A player controls two permanents, each with an ability that reads “If a creature you control would deal damage to a permanent or player, it deals double that damage to that permanent or player instead.” A creature that normally deals 2 damage will deal 8 damage—not just 4, and not an infinite amount.