Counterpossibles, Impossible Worlds, and the Notion of Similarity

The subject of this paper is a world-semantic analysis of counterpossibles, i.e., counterfactuals with impossible antecedents. We focus on the notion of similarity between worlds, which determines truth-value of counterfactuals. There are two commonly accepted assumptions about this notion. According to the first one, every possible world is more similar to the actual world than any impossible world. According to the second one, the trivial world (world where everything is true) is the most dissimilar to the actual world. Considering the notion of similarity we argue for a negative thesis and a positive thesis. The negative thesis is that both of these assumptions are false, and as such should not be taken as a “guide” to our understanding of similarity. The positive thesis is an alternative interpretation of the notion of similarity. The interpretation is based on an analogy of the inference to the best explanation and on the assumption that similarity is a ternary relation satisfied by the actual world, a non-actual world and a given factor of similarity. Similarity understood in this manner is a notion which requires an indication of a rule which supports the truth of the antecedent and explains its connection with the consequent.