 Finally, there is of course the general question of how one should handle logically complex statements concerning, at least in part, mereologically indeterminate objects. A natural choice is to rely on a three-valued semantics of some sort, the third value being, strictly speaking, not a truth value but rather a truth-value gap. In this spirit, both Johnsen and Tye endorse the truth-tables of Kleene (1938) while Hyde those of Łukasiewicz (1920). However, it is worth stressing that other choices are available, including non-truth-functional accounts. For example, Akiba (2000) and Morreau (2002) recommend a form of “supervaluationism”. This was originally put forward by Fine (1975) as a theory for dealing with de dicto indeterminacy, the idea being that a statement involving vague expressions should count as true (false) if and only it is true (false) on every “precisification” of those expressions. Still, a friend of de re indeterminacy may exploit the same idea by speaking instead of precisifications of the underlying reality—what Sainsbury (1989) calls “approximants”, Cohn and Gotts (1996) “crispings”, and T. Parsons (2000) “resolutions” of vague objects. As a result, one would be able to explain why, for example, (69) appears to be true and (70) false (assuming that Tibbles's head is definitely part of Tibbles), whereas both conditionals would be equally indeterminate on Kleene's semantics and equally true on Łukasiewicz's: