Discussion
Why must the domain of an interpretation be non-empty?
Answer: D
Both reasons apply, but the convention is adopted chiefly so that from a universal statement an existential one may be inferred, which fails in an empty domain. Constants needing denotations is the other half of the same point. Decidability and equality are unaffected. A convention adopted to preserve a desired inference, rather than for any deep reason, is worth recognising as such since free logics that drop it exist and behave differently. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.
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