Kasparov or Carlsen?

Who is the greatest of all time?

Here’s a thought that popped into my mind yesterday:

Kasparov needed Karpov to become Kasparov, but Carlsen didn’t need anyone to become Carlsen.

I don’t mean that Carlsen hasn’t had any help along the way. He - like Kasparov - has had coaches, a great support system, assistants and so on. The idea is instead that he was able to achieve his level of greatness without the persistent push of an extraordinary, almost equally great rival. It is possible that Kasparov would have become the player he was, at his peak, without having to overcome his “eternal rival”, but I’m inclined to doubt it, and I think Kasparov has acknowledged his indebtedness to Karpov as well.

Similarly, I think Karpov was so dominant from 1975 until Kasparov faced him for the title that he stagnated, and he only reached his greatest level because Kasparov pushed him to the utmost. But Carlsen has been dominant for well over a decade and became the highest-rated player ever - by a substantial margin - despite having no close rivals the entire time. Imagine what he might have been if he had his own “Karpov” to overcome - maybe he would have broken 2900. I think this is also, in part, why he gave up the World Championship, and was only willing to consider it if Firouzja had won the 2022 Candidates. Firouzja represented something new and powerful. A potential challenge, maybe even a potential rival.

Suppose then that we state that Kasparov’s and Carlsen’s achievements and strength are roughly on a par, just for the sake of argument. If we award “GOAT” (“Greatest of all time”, for those unfamiliar with the now-standard - really, overused - acronym) status based on the thought expressed at the start of the post, do we give it to Kasparov for having overcome Karpov, or to Carlsen for blowing past the rest of the world without needing that sort of external motivation?