An Abstract of "A New Theory of Content I: Basic Content"
Philosophers of science, for instance, Carnap and Popper, take the (logical) content of a proposition to be given by its consequence class. This notion of content is inappropriate for many of the formal needs of philosophers of science. The basic problem is that given this notion of content any arbitrary a and b share common content, namely (a v b). This notion of content has disastrous effects on, for instance, Carnap's attempts to explicate the notion of confirmation in terms of probabilistic favorable relevance, and Popper's attempts to define verisimilitude. For instance, as concerns the case of confirmation, if any (contingent) consequence of a given proposition is part of the content of that proposition, then for any evidence e and theory T, e conclusively confirms part of the content of T, namely T v e, and e conclusively disconfirms part of the content of T, namely T v ~e. As concerns the case of verisimilitude, if any consequence of a proposition counts as part of its content then, under Popper's standard definition of verisimilitude, where the atomic sentence Fa is true it has no more verisimilitude than its negation since, where 'Gb' is an unrelated true atomic sentence, the false ~Fa contains the true content part '~Fa v Gb' which is not part of the truth content of Fa. After reviewing some of the problems of the traditional notion of content I present an alternative notion of (basic) content which better fits our intuitions about content and better serves the formal needs of philosophers of science. Both a semantic and syntactic characterization of content are given for a number of generic propositional languages. Various formal properties are demonstrated, including completeness and transitivity of content, and a mechanical decision procedure for determining content parts is displayed.