 How then do things stand for the strict actualist with respect to the first element of the possibilist’s two-fold challenge? The answer of course depends entirely on what one takes to be a “systematically and philosophically satisfying” account of the truth conditions for modal assertions like  (2).  Possibilists (and their haecceitist and eliminitivist counterparts) clearly consider preservation of Tarski-style compositionality (formalized in an appropriate notion of an intended interpretation) to be essential for meeting this element of the challenge: one must ultimately be able to ground the truth of complex modal statements in the modal properties of (perhaps nonactual, perhaps abstract) individuals. But it is not at all clear that the strict actualist must agree. They might well rather simply reject this demand and insist instead that  (2)  and its like stand on their own and do not need the sort of grounding that possibilists insist upon. Since this is simply a consequence of the rejection of possibilia and their actualist proxies, from the strict actualist perspective, it is a philosophically satisfying result. The apparent loss of Tarski-style compositionality is, for the strict actualist, a price worth  paying.[71]  From this perspective, possible world semantics can with some justification be seen as nothing more than a useful but ontologically inert formal instrument, an evocative but ultimately dispensable philosophical  heuristic.[72]  In that case, the only serious challenge that possibilism raises for the strict actualist is the formulation of an actualistically kosher quantified modal deductive system whose basic principles intuitively reflect strict actualist sensibilities. We turn now to two of the best known accounts. (We will follow common practice and refer to a deductive system with or without a corresponding formal model theory as a  logic.[73])