By MaiKro, in 'English to Latin Translation', Jan 8, 2019.
Ah, interesting; I wasn't aware of that idiom, but it makes sense.
I wouldn't object to scribo in the sense of "engaging in writing" without specifying what (though it still remains transitive in a way; the object is just not mentioned).
Puto, on the other hand, doesn't commonly* mean "to engage in thinking/reflexion". It means thinking a particular thing, thinking such and such. Even in the event that what the person was thinking wasn't explicitly stated, it would still usually* mean holding a certain opinion or belief, thinking or imagining that something is the case.
*There might be some exception to be found somewhere. You never know. What I know is that puto in the sense of engaging in reflexion isn't common usage.
Perhaps somewhere, but given your near-photographic memory and knowledge of the canon, I think we can safely say that even if it did appear somewhere, it would be viewed by most Roman authors as non-standard and probably wrong.
"Question Everything" was one of the 1st ever phrases that I had translated for me on this forum a while back. MaiKro, if you're interested in options other than exige omnia, then a good alternative translation for it would be what was provided for me, which was in omnia inquire (meaning "Inquire Into Everything").
I also had "Think For Yourself" translated for me on this forum a while back as well. I had that translated for me as ipse cogita, so I third this translation.
Thanks for the extended discussion. I think the OP doesn't so much want "Engage in your own reflections" as much as "Come to your own conclusions / judgments / reckonings." And I wonder if cogitare adequately suggests that latter idea.
I wouldn't find it strange to hear an open-ended motto like "You gotta have hope." Sperandum tibi est. Or "Believe!" as in The Polar Express. Credendum est.
That would be something like ipse iudica.
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