As much as your question may seem like reductio ad absurdum, it highlights the question of whether an automaton is capable of inventing and what it means to invent, just like the question of whether AI is actually "intelligent" and what AGI even means.
My opinion is that living beings like humans can invent; anything else (from simple calculator to sophisticated AI) is merely a tool that living beings can employ in their quest to invent.
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As much as your question may seem like reductio ad absurdum, it highlights the question of whether an automaton is capable of inventing and what it means to invent, just like the question of whether AI is actually "intelligent" and what AGI even means.
My opinion is that living beings like humans can invent; anything else (from simple calculator to sophisticated AI) is merely a tool that living beings can employ in their quest to invent.