Why does “unless” mean “if not”?
Harry Gensler. Introduction to Logic (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 (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 I know that definition 1 is obsolete, but I'm interested in the etymology.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. Screenshot.
†A. adv. Only in conjunctional phrases followed by than or that.
- 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.