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In the article There’s more to mathematics than rigour and proofs, there is a term "judicious extrapolation":

It is of course vitally important that you know how to think rigorously, as this gives you the discipline to avoid many common errors and purge many misconceptions. Unfortunately, this has the unintended consequence that “fuzzier” or “intuitive” thinking (such as heuristic reasoning, judicious extrapolation from examples, or analogies with other contexts such as physics) gets deprecated as “non-rigorous”.

A Google search for "judicious extrapolation" yields several results, suggesting that "judicious extrapolation" is a term. Some examples are:

Wikipedia doesn't mention anything about this.

Is this a term? If yes, what does it mean?

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    $\begingroup$ This is an informal usage... much like "careful extrapolation." Don't read anything deeper into it. $\endgroup$ Apr 7, 2021 at 16:51
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    $\begingroup$ I don't think it's a technical term, just an English phrase. $\endgroup$
    – saulspatz
    Apr 7, 2021 at 16:52
  • $\begingroup$ By interesting terminological coincidence, one of my favorite teaching modes is to present examples of an apparent pattern, and suggest they might be telling us something: "If there's any justice, we should have [such-and-such]." I recall once when a student immediately asked, "But is there any justice?", to which I responded, "In this case, no." and went on to explain how the pattern failed. ... Anyway, I think the author and I are getting at the same notion: extrapolation isn't a guarantee, but it can drive discussion and exploration, so developing an intuition for it isn't a bad thing. $\endgroup$
    – Blue
    Apr 7, 2021 at 17:19

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The term judicious simply means "with good judgement/sense", so judicious extrapolation is extrapolation that's performed in a scientifically or mathematically reasonable manner. It's not really a set phrase, as the term judicious can be applied to any activity to indicate that it is a reasonable thing to do. It's just an adjective + noun pair, and the meaning of either word individually is unchanged when putting them together.

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It's not a technical term.

Extrapolate (Merriam-Webster meaning #1(b)): to project, extend, or expand (known data or experience) into an area not known or experienced so as to arrive at a usually conjectural knowledge of the unknown area.

Judicious: having, exercising, or characterized by sound judgment.

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  • $\begingroup$ would it be any different if I use "sound extrapolation"? $\endgroup$
    – Ooker
    Apr 7, 2021 at 17:32

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