Abstract
I will argue that the most significant role of the logic of first-order quantifiers lies in its power to express functional dependencies and independencies between variables. The dependence of a variable x on another variable y has been standardly expressed by the formal dependence of a quantifier Qx on another quantifier Qy, which, in turn, is expressed by the former being in the syntactical scope of the latter. First-order logic, where scopes are required to be nested, cannot express all the possible patterns of dependence and independence between variables. To overcome this problem, two solutions have been proposed: to allow for more patterns of dependence and independence between quantifiers (Independence- Friendly (IF) logic); to express explicitly dependencies and independencies of variables (Dependence logic, Independence logic, etc). In both approaches the truth of a sentence amounts to the existence of appropriate “witness individuals” (Skolem functions).We have here a connection between the truth-conditions of quantified sentences and the existence of all the functions which produce these witness individuals. Hintikka has repeatedly argued that these functions codify winning strategies in certain (semantical) games and emphasized their connection to Wittgenstein’s language games. In my contribution I will look at the interesting perspective that language games open for the discussion of logic in general. Some of these points have been discussed in Hintikka/Sandu 2007.
