Actually, most of the radicals existed long before the Shuōwén Jiězì, as recurring graphic elements[1].

They might not have been called 'radicals', or been used to look up dictionaries, but they certainly existed.

[1] Wilkinson, Endymion (2013), Chinese History: A New Manual, Harvard-Yenching Institute Monograph Series, Cambridge, MA: Harvard University Asia Center, ISBN 978-0-674-06715-8

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