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Q&A Why does “unless” mean “if not”?

2 answers  ·  posted 4y ago by PSTH‭  ·  edited 3y ago by Peter Taylor‭

Question logic
#2: Post edited by user avatar Peter Taylor‭ · 2021-08-05T07:27:43Z (over 3 years ago)
A proposed edit tried to improve the typography with nbsp; this is a better fix
  • Harry Gensler. [*Introduction to Logic*](https://www.amazon.com/Introduction-Logic-Harry-J-Gensler/dp/1138910597) (2017 3 ed). p 169.
  • >“Unless” is also equivalent to “if not”; so we also could use “(∼B ⊃ D) (“If you
  • don’t breathe, then you’ll die”).”
  • Nicholas JJ Smith, [*Logic: The Laws of Truth*](https://www.amazon.com/Logic-Truth-Nicholas-J-J-Smith/dp/0691151636) (2012). p 115.
  • >The statement “P unless Q” means that if Q is not true, P is true—so we
  • translate it as $¬ \, Q→P$.
  • Using solely the original meaning of "unless" below, please expound why? How does definition 1 below ≡ if not? I know that definition 1 is obsolete, but I'm interested in the etymology. [*OED* Third Edition, June 2017](http://www.oed.com/view/Entry/215075). [Screenshot](https://i.stack.imgur.com/iZLrR.jpg).
  • > †**A.** adv. Only in conjunctional phrases followed by _than_ or _that_.
  • >
  • >1. Forming a conjunctional phrase introducing a case in which an exception to a preceding negative statement (expressed or implied) will or may exist: (not) on a less or lower condition, requirement, etc., _than_ (what is specified). _Obsolete_.
  • Harry Gensler. [*Introduction to Logic*](https://www.amazon.com/Introduction-Logic-Harry-J-Gensler/dp/1138910597) (2017 3 ed). p 169.
  • >“Unless” is also equivalent to “if not”; so we also could use “$({\sim}B \supset D)$ (“If you
  • don’t breathe, then you’ll die”).”
  • Nicholas JJ Smith, [*Logic: The Laws of Truth*](https://www.amazon.com/Logic-Truth-Nicholas-J-J-Smith/dp/0691151636) (2012). p 115.
  • >The statement “P unless Q” means that if Q is not true, P is true—so we
  • translate it as $¬ \, Q→P$.
  • Using solely the original meaning of "unless" below, please expound why? How does definition 1 below ≡ if not? I know that definition 1 is obsolete, but I'm interested in the etymology. [*OED* Third Edition, June 2017](http://www.oed.com/view/Entry/215075). [Screenshot](https://i.stack.imgur.com/iZLrR.jpg).
  • > †**A.** adv. Only in conjunctional phrases followed by _than_ or _that_.
  • >
  • >1. Forming a conjunctional phrase introducing a case in which an exception to a preceding negative statement (expressed or implied) will or may exist: (not) on a less or lower condition, requirement, etc., _than_ (what is specified). _Obsolete_.
#1: Initial revision by user avatar PSTH‭ · 2020-11-10T07:30:40Z (almost 4 years ago)
Why does “unless” mean “if not”? 
Harry Gensler. [*Introduction to Logic*](https://www.amazon.com/Introduction-Logic-Harry-J-Gensler/dp/1138910597) (2017 3 ed). p 169. 

>“Unless” is also equivalent to “if not”; so we also could use “(∼B ⊃ D) (“If you
don’t breathe, then you’ll die”).”


Nicholas JJ Smith, [*Logic: The Laws of Truth*](https://www.amazon.com/Logic-Truth-Nicholas-J-J-Smith/dp/0691151636) (2012). p 115.

>The statement “P unless Q” means that if Q is not true, P is true—so we
translate it as $¬ \, Q→P$.


Using solely the original meaning of "unless" below, please expound why? How does definition 1 below ≡ if not? I know that definition 1 is obsolete, but I'm interested in the etymology. [*OED* Third Edition, June 2017](http://www.oed.com/view/Entry/215075). [Screenshot](https://i.stack.imgur.com/iZLrR.jpg).



>  †**A.** adv. Only in conjunctional phrases followed by _than_ or _that_.
> 
>1. Forming a conjunctional phrase introducing a case in which an exception to a preceding negative statement (expressed or implied) will or may exist: (not) on a less or lower condition, requirement, etc., _than_ (what is specified). _Obsolete_.