‘Unsettledness’ in a bivalent language: a modest, non-epistemic idea

In this paper, I suggest a novel, non-epistemic approach towards accommodating the appearance of ‘unsettledness’ or—in some sense—gaps in a bivalent language. While the suggestion is modest, I think it to be quite plausible. My aim is simply to lay out the proposal, as concisely as possible, and briefly consider a few objections. Accordingly, §2 sets out some terminology. (I should warn that §2 simply marches through some definitions without pause. Readers might prefer to first read §3 and, in turn, return to §2.) §3 sketches the main issue, namely, accommodating the appearance of (some sort of) ‘gaps’ or ‘unsettledness’ in our otherwise bivalent language. §4 and §5 present the main proposal. §6 briefly considers a few objections, and §7 offers a brief review and closing remarks.