HAVE verbs often acquire necessity and/or futurate and future uses (e.g.,~English "have to", French "lir-a" read-HAVE `will read'). Ukrainian, at least from the 16th and up to the early 20th century, featured an unusual development: its HAVE verb "maty" had a possibility meaning in addition to necessity and futurate.
The talk consists of three parts. First, I show that the possibility meaning for Ukr. "maty" was indeed present both in the 16th and the early 20th centuries. One of the crucial arguments for both periods comes from parallel texts. Second, even the three-way ambiguity is not the whole story. A close examination of the 16th century texts shows that "maty" was special among Ukrainian modals in being restricted to "double assertion situations": to contexts where more than one of its three basic meanings would be appropriate. The modal "maty" thus lexically encoded double assertion. Third, I apply the iterative-learning framework to the issue of how such a double-assertion item may be innovated and maintained. Simple analysis shows that signalling of double assertions should be difficult to invent, but easy to preserve. This matches the typological observations: Old Ukrainian "maty" appears to be a typologically rare type for HAVE verbs, but despite that, it was stable for many centuries before dying off presumably due to heavy interference from closely related and politically dominating Russian in the course of the 20th century.