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I have a question about my Mathematics Educators Stack Exchange post: Why don't textbook authors simplify their propositions written in natural language?

Apology. I reworded my question. Please reopen? Why close my question as "off-topic" ? Please edit my question for me. Thanks to people who rewrote it below.


One challenge faced by students of propositional logic is to understand the relationship between statements in idiomatic English and more formal language; many students are confused by the fact that the English construction "only if" does not translate naively into logical implication. To make matters worse, some propositions are unnecessarily long, forcing students to speculate on unfamiliar, hypothetical situations and requiring a little more conscious thought to discover the logical relationship at play.

Compare

John will break the world's record for the mile run ONLY IF he runs the mile in under 4 minutes.

to these simpler examples:

You're in New York ONLY IF you're in the USA. (If you're in NY, you're in the USA.)

You can aviate ONLY IF you can see. (If you can aviate, then you can see.)

What is the pedagogical value of presenting statements like the first one, in comparison to the shorter examples having the same logical structure?

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I can't speak for the exact reasons why each of the five people who voted to close did so, nor do I know if everyone voted for the exact same reason or not (see this StackExchange meta post which still shows users lamenting that their close-vote reason was not accurately reflected when it did not align with the majority reason).

The five close-vote reasons in MESE are: Duplicate, Needs Details or Clarity, Needs More Focus, Opinion-Based, and "Community-Specific Reason" -- a combination of off-topic or belongs on another site. When I read this question, it seemed like a few of these reasons could have applied, and had I voted to close, I probably would have picked "needs details or clarity". An edit that eliminates some of the parenthetical commentary and makes the question more specifically about math education might make it a candidate to be re-opened, and your first edit gets the question closer. I have made some other modifications in the edit I just proposed. I tried to encapsulate both the "wordiness" and "hypernym of the hyponym" aspects of your original pre-edit question while separating out the actual logical issue of "only if" being difficult for students to understand. I hope you find these edits acceptable.

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