The idea that some objects are metaphysically “cheap” has wide appeal. An influential version of the idea builds on abstractionist views in the philosophy of mathematics, on which numbers and other mathematical objects are abstracted from other phenomena. For example, Hume's Principle states that two collections have the same number just in case they are equinumerous, in the sense that they can be correlated one‐to‐one:. The principal aim of this article is to use the notion of grounding to develop this (...) sort of abstractionism. The appeal to grounding enables a unified response to the two main challenges that confront abstractionism. First, we must explicate the metaphor of metaphysical “cheapness.” Second, we must rebut the “bad company” objection, which rejects abstraction principles like (HP) as tarnished by their similarity to inconsistent principles like Frege's Basic Law V. By enforcing a simple requirement that all abstraction be properly grounded, we propose a unified solution to these two hard, and prima facie unrelated, problems. On our view, grounded abstraction simultaneously ensures “cheap” abstracta and permissible abstraction. (shrink)

Many draw the distinction between truth in, and truth at, a possible world. The latter notion purportedly allows for propositions to be true relative to worlds even if they do not exist relative to those same worlds. Despite its wide application, the distinction is controversial. Some think that the notion of truth at a world is unintelligible. Here, I outline and discuss the most influential argument for the unintelligibility of truth at a world, The Picture Thinking Argument. I outline and (...) defend a neglected strategy to respond to this, arguing that if we take seriously the idea that possible worlds represent total ways the world could be, the distinction can be drawn intelligibly. (shrink)

Provides a comprehensive overview and introduction to the Routledge Handbook of Propositions.