I don’t recall where it is said that such an object is necessary for a Kuhnian revolution to have occurred. There was a crisis, in the Kuhnian sense, when the old understanding of limit (perhaps labeling it as limit1 will be clearer) could not explain the existence of e.g., continuous functions without derivatives anywhere, or counterexamples to the Dirichlet principle. Then Weierstrass developed limit2 with deltas and epsilons. Limit1 was then abandoned in favor of limit2.
I don’t recall where it is said that such an object is necessary for a Kuhnian revolution to have occurred. There was a crisis, in the Kuhnian sense, when the old understanding of limit (perhaps labeling it as limit1 will be clearer) could not explain the existence of e.g., continuous functions without derivatives anywhere, or counterexamples to the Dirichlet principle. Then Weierstrass developed limit2 with deltas and epsilons. Limit1 was then abandoned in favor of limit2.