Fabrice Correia

Standard possible world semantics for propositional modal languages ignore truth-value gaps. However, simple considerations suggest that it should not be so. In Section 1, I identify what I take to be a correct truth-clause for necessity under the assumption that some possible worlds are incomplete (i.e., "at" which some propositions lack a truth-value). In Section 2, I build a world semantics, the semantics of TV-models, for standard modal propositional languages, which agrees with the truth-clause for necessity previously identified. Sections 3–5 are devoted to systematic concerns. In particular, in Section 4, Prior’s system Q (propositional version) is given a TV-models semantics and proved adequate (i.e., sound and complete) with respect to it.

Say that two sentences are factually equivalent when they describe the same facts or situations, understood as worldly items, i.e. as bits of reality rather than as representations of reality. The notion of factual equivalence is certainly of central interest to philosophical semantics, but it plays a role in a much wider range of philosophical areas. What is the logic of factual equivalence? This paper attempts to give a partial answer to this question, by providing an answer the following, more specific question: Given a standard propositional language with negation, conjunction and disjunction as primitive operators, which sentences of the language should be taken to be factually equivalent by virtue of their logical form? The system for factual equivalence advocated in this paper is a proper fragment of the first-degree system for the logic of analytic equivalence put forward in the late seventies by R. B. Angell. I provide the system with two semantics, both formulated in terms of the notion of a situation’s being fittingly described by a linguistic item. In the final part of the paper I argue, contra a view I defended in my “Grounding and Truth-Functions”, that the logic for factual equivalence I advocate here should be preferred to Angell’s logic if one wishes to follow the general conception of the relationships between factual equivalence and the notion of grounding put forward in the 2010 paper

In the third of his Logical Investigations, Husserl draws an important distinction between two kinds of parts: the dependent parts like the redness of a visual datum or the squareness of a given picture, and the independent parts like the head of a horse or a brick in a wall. On his view, the distinction is to be understood in terms of a more fundamental notion, the notion of foundation. This paper is an attempt at clarifying that notion. Such attempts have already been undertaken by Peter Simons and Kit Fine, and the paper also contains elements of comparison of our three sets of views