Full Idea
Free logics say 1) singular terms are allowed that do not designate anything that exists; sometimes 2) is added: the domain of discourse is allowed to be empty. Logics with both conditions are called 'universally free logics'.
Gist of Idea
Free logics has terms that do not designate real things, and even empty domains
Source
C. Anthony Anderson (Identity and Existence in Logic [2014], 2.3)
Book Reference
'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.67
A Reaction
I really like the sound of this, and aim to investigate it. Karel Lambert's writings are the starting point. Maybe the domain of logic is our concepts, rather than things in the world, in which case free logic sounds fine.
Related Idea
Idea 18768 We cannot pick out a thing and deny its existence, but we can say a concept doesn't correspond [Anderson,CA]