# Enumerable#all? and empty arrays **URL:** \ **Category:** Ruby\ **Created:** [August 9, 2006, 6:44pm UTC](https://www.ruby-forum.com/t/enumerable-all-and-empty-arrays/64518 "2006-08-09T18:44:09Z")\ **Posts on this page:** 8\ **Page:** 1
**Author:** ![reflex](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/r/f05b48/32.png) [@reflex](https://www.ruby-forum.com/u/reflex)\ **Post date:** [August 9, 2006, 6:44pm UTC](https://www.ruby-forum.com/t/enumerable-all-and-empty-arrays/64518/1 "2006-08-09T18:44:09Z")
Hello I found this to be somewhat amusing: > > a = [] > > =\> [] > > > a.all? > > =\> true > > > a.all? { |i| i == 10 } > > =\> true Is there any reasoning for Enumerable#all? to always return true for empty arrays? Best regards, Andre ---
**Author:** ![reflex](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/r/f05b48/32.png) [@reflex](https://www.ruby-forum.com/u/reflex)\ **Post date:** [August 9, 2006, 7:35pm UTC](https://www.ruby-forum.com/t/enumerable-all-and-empty-arrays/64518/2 "2006-08-09T19:35:14Z")
On Thu, 10 Aug 2006, Andre N. wrote: > Is there any reasoning for Enumerable#all? to always return true for > empty arrays? > > Best regards, > Andre well - it’s either that or false. we’d need maybe for it to really make sense. consider [].all?{|x| x.nil?} # true or false?? either is arbitrary -a ---
**Author:** ![reflex](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/r/f05b48/32.png) [@reflex](https://www.ruby-forum.com/u/reflex)\ **Post date:** [August 9, 2006, 7:50pm UTC](https://www.ruby-forum.com/t/enumerable-all-and-empty-arrays/64518/3 "2006-08-09T19:50:15Z")
Andre N. wrote: > =\> true > > > > a.all? { |i| i == 10 } > > =\> true > > Is there any reasoning for Enumerable#all? to always return true for > empty arrays? It’s what modern logic says… or something like it. > **[Square of opposition](https://en.wikipedia.org/wiki/Square_of_opposition#The_problems_of_existential_import)** > > In term logic (a branch of philosophical logic), the square of opposition is a diagram representing the relations between the four basic categorical propositions. > The origin of the square can be traced back to Aristotle's tractate On Interpretation and its distinction between two oppositions: contradiction and contrariety. > However, Aristotle did not draw any diagram; this was done several centuries later by Apuleius and Boethius. > In traditional logic, a proposition (Latin: propositio) is a spoke... ---
**Author:** ![reflex](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/r/f05b48/32.png) [@reflex](https://www.ruby-forum.com/u/reflex)\ **Post date:** [August 9, 2006, 7:59pm UTC](https://www.ruby-forum.com/t/enumerable-all-and-empty-arrays/64518/4 "2006-08-09T19:59:16Z")
Andre N. wrote: > =\> true > > Is there any reasoning for Enumerable#all? to always return true for > empty arrays? I think they are modeled after universal and existential quantifiers in predicate calculus: a.all?(&b) is true iff for all x in a b[x]. This leads to a.all? being true. a.any?(&b) is true iff there exists an x in a for which b[x]. This leads to a.any? being false. ---
**Author:** ![reflex](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/r/f05b48/32.png) [@reflex](https://www.ruby-forum.com/u/reflex)\ **Post date:** [August 9, 2006, 8:05pm UTC](https://www.ruby-forum.com/t/enumerable-all-and-empty-arrays/64518/5 "2006-08-09T20:05:16Z")
On Thu, Aug 10, 2006 at 01:41:48AM +0900, Andre N. wrote: > Is there any reasoning for Enumerable#all? to always return true for > empty arrays? a.all?{ … } == true can be read as “All elements in a satisfy { … }”, which we can interpret as “there is no element in a such that { … } is not satisfied”, which is obviously true if a is empty. ---
**Author:** ![reflex](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/r/f05b48/32.png) [@reflex](https://www.ruby-forum.com/u/reflex)\ **Post date:** [August 9, 2006, 8:29pm UTC](https://www.ruby-forum.com/t/enumerable-all-and-empty-arrays/64518/6 "2006-08-09T20:29:18Z")
On Thu, 2006-08-10 at 03:03 +0900, Mauricio F. wrote: > can be read as “All elements in a satisfy { … }”, which we can interpret as > “there is no element in a such that { … } is not satisfied”, which is > obviously true if a is empty. OK, thank you all for the explanations 🙂 Andre ---
**Author:** ![reflex](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/r/f05b48/32.png) [@reflex](https://www.ruby-forum.com/u/reflex)\ **Post date:** [August 23, 2006, 2:34am UTC](https://www.ruby-forum.com/t/enumerable-all-and-empty-arrays/64518/7 "2006-08-23T02:34:17Z")
On Thu, Aug 10, 2006 at 08:55:12AM +0900, Just Another Victim of the Ambient M. wrote: > > =\> true > > say the condition is true… > > unless mathematician.is\_an :intuitionist # (pretty rare) Sorry I couldn’t resist -Jürgen ---
**Author:** ![reflex](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/r/f05b48/32.png) [@reflex](https://www.ruby-forum.com/u/reflex)\ **Post date:** [August 10, 2006, 1:56am UTC](https://www.ruby-forum.com/t/enumerable-all-and-empty-arrays/64518/8 "2006-08-10T01:56:42Z")
“Andre N.” [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) wrote in message news:removed\_email\_address@domain.invalid… > Is there any reasoning for Enumerable#all? to always return true for > empty arrays? ``` It's mathematically consistent. You may be surprised to hear this but mathematicians are generally ``` optimists. Thus, if a condition is “vacuously satisfied,” then we generally say the condition is true…