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doi: 10.1111/phpr.13036
handle: 10852/107756
AbstractThe 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.
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 5 | |
popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Top 10% | |
influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Top 10% |