In German, the functionals for conditionals, embedded questions and disjunctions are distinct: wenn, ob and oder, respectively. In many other languages, however, the three functionals partially converge: als/of/of (abb) in Dutch, si/si/ou (aab) in French, eger/mi/mi (abb) in Turkish, εί/ηέ/ηέ (abb) in Homeric Greek, kung/kung/og (aab) in Tagalog, if/if/or (aab) in English.
Elaborating on these patterns, I will argue that the wide-spread partial convergence is far from accidental. The triple wenn/ob/oder covers the full space for binary non-veridical sentential operators. The functionals establish an essential triangle, reminiscent to the triangle of quantification Danny Jaspers constructed, with ob as the pivot and thus the non-veridical counterpart to Aristole’s affirmative indefinite in the domain of quantification The triangle links the entailment sets of a proposition p, of its negation not-p and of its question ?-p. The functional triple constructs the triangle in such manner that aba languages are unlikely to exist: the conditional and the disjunction diverge in all relevant algebraic aspects. By conjecture, this calculus of non-veridicality is native, as the essential algebras of meaningful language are bound to reflect human semantic capacity.