Matti Eklund

Jaakko Hintikka has argued that ordinary first-order logic should be replaced byindependence-friendly first-order logic, where essentially branching quantificationcan be represented. One recurring criticism of Hintikka has been that Hintikka'ssupposedly new logic is equivalent to a system of second-order logic, and henceis neither novel nor first-order. A standard reply to this criticism by Hintikka andhis defenders has been to show that given game-theoretic semantics, Hintikka'sbranching quantifiers receive the exact same treatment as the regular first-orderones. We develop a different reply, based around considerations concerning thenature of logic. In particular, we argue that Hintikka's logic is the logic that bestrepresents the language fragment standard first-order logic is meantto represent. Therefore it earns its keep, and is also properly regarded as first-order.

Supervaluationism, traditionally conceived, is the conjunction of three theses: Vagueness in a language gives rise to there being a multitude of acceptable assignments of semantic values to some expressions of the language, These assignments correspond to possible completions of the meanings of vague expressions, Truth is truth under all acceptable assignments, and falsity is falsity under all acceptable assignments. Supervaluationism has three chief virtues. It preserves classical logic. It provides an account of what vagueness is . And it extends nicely to the vagueness of singular terms. I argue, however, that the existence of vagueifiers ‐ expressions like‘roughly’– pose problems for thesis of Supervaluationism, and that the supervaluationist can get around these problems only at a serious cost. Toward the end of the paper, I present an alternative analysis of vagueness, which preserves the main virtues of Supervaluationism, but which identifies vagueness as semantic Overdetermination, rather than as semantic underdetermination