It is argued that the so‐called principles of “strong centering” and “weak centering” central to the traditional Lewis‐Stalnaker semantics for counterfactuals are both fallacious. A foundation for an alternative semantics without these prinsciples is outlined. The core idea is that the statistically normal worlds – rather than those worlds most qualitatively similar to the actual world – should serve as the semantical fulcrum.

Thirteen meanings of 'implication' are described and compared. Among them are relations that have been called: logical implication, material implication,deductive implication, formal implication, enthymemic implication, and factual implication. In a given context, implication is the homogeneous two-place relation expressed by the relation verb 'implies'. For heuristic and expository reasons this article skirts many crucial issues including use-mention, the nature of the entities that imply and are implied, and the processes by which knowledge of these relations are achieved. This paper is (...) better thought of as an early stage of a dialogue than as a definitive treatise. (shrink)