Weird - I posted the following earlier but it has disappeared.
Invoking Homer as proof of tool-free cognition is flawed. It's been awhile since Humanities 101 for me, but I learned that the repetitive epithets, stock scenes, and metrical formulas of the Iliad and Odyssey were precisely the tools that allowed Homer (and the oral tradition that predated him by centuries) to knit those works together. Oral poetry was itself a cognitive technology. Homer's Illiad and Odyssey were works of oral engineering, not free form artistry. You are a humanities professor -- you should know this. The “tools of thinking” have always included external scaffolds, whether carved in stone, written on parchment, or spoken in hexameter.
Not sure what this adds to or detracts from my position (besides the unwarranted invective). You said exactly what I said. Homer's tools are interior, belonging to the mind itself - although you had some newspeak like cognitive technology and oral engineering. And his poetry was passed on orally for generations, which means that people had to memorize it - which is the point of the mental tools you mentioned: tropes, repetitions, rhymers, epithets, etc. I argue that these mental tools are of the sort that should be learned and sharpened, so to speak (and in hindsight, I forgot to mention imagination), because they are proper to thinking.
Note that Socrates went further than I ever would in the Phaedrus and argued that writing itself is deleterious to thinking on the grounds that it destroys memory - and also interestingly enough on the grounds that the inventors of a technology are the last people who can truly judge its benefit. That is, he argues that writing technology replaces the individual's thought with their parroting a thought that they poorly understand. I understand his point, but do not share his concern, which Plato also clearly did not share.
So to me, the real question isn’t whether students should think without tools—that’s never been the human condition. It’s whether they learn to think with their tools, instead of letting the tools do the thinking for them.
As a professor, I can say that students are definitely letting the tools do the thinking. But that is not secret knowledge.
My complaint though was that the parallel with the saw is the issue. Saws saw, but LLMs do not think (I need not repeat this issue). Students who use them do not think through LLMs. LLMs are a black box wish-fulfillment machine. They are not used to record thoughts, but rather to generate output that students confuse with thought. And, pace Socrates, that is the greatest threat to thought.