Ori Simchen

The Barcan formula (BF) is commonly paraphrased as the schematic conditional that if it is possible that there be a phi then something or other is possibly a phi. It is validated by the most straightforward systems of quantified modal logic. It is also widely considered to pose a threat to the commonsensical metaphysical view that there are no non-actual (or ‘merely possible’) things. I show how BF can be cleared of such a charge by construing it as a bridge principle connecting modality de dicto and modality de re while retaining a Russellian robust sense of reality in modal matters.

Lewis Carroll’s well-known parable ”What the Tortoise Said to Achilles” gives rise to a recalcitrant and general form of normative skepticism. I argue that the skeptical position inspired by the story is indeed a distinct form of skepticism, engendered by refusal to recognize that any rule reflected upon may possibly retaining its action-guiding force. I show that the skeptic’s attitude builds upon the familiar fact that our reflection upon sources of psychological influence on us may loosen their grip by affording us reflective distance. I conclude by showing how the equally familiar phenomenon that reflection upon a rule does not automatically drain it of its force can be exploited in a satisfactory response to the skeptic.