In Thin objects: an abstractionist account (Oxford University Press, 2018), Øystein Linnebo claims that ‘mathematical objects are thin in the sense that very little is required for their existence’. Linnebo articulates his view in an abstractionist manner: according to Linnebo, the truth of the right‐hand side of a Fregean abstraction principle, which states that two items stand in a given equivalence relation, is sufficient for the truth of its left‐hand side, which states that the same abstract object is associated to (...) both items. This special issue contains nine articles discussing different aspects of Linnebo's book. In this introduction, we provide an opinionated introduction to the Special Issue and an overview of the contributions. (shrink)

Husserl’s philosophy of mathematics, his metatheory, and his transcendental phenomenology have a sophisticated and systematic interrelation that remains relevant for questions of ontology today. It is well established that Husserl anticipated many aspects of model theory. I focus on this aspect of Husserl’s philosophy in order to argue that Thomasson’s recent pleonastic reconstruction of Husserl’s approach to essences is incompatible with Husserl’s philosophy as a whole. According to the pleonastic approach, Husserl can appeal to essences in the absence of a (...) positive metaphysical account of their nature. I show, using central results from recent model theory, that the pleonastic approach undermines Husserl’s approach to formalization and categoricity, an effect that will ripple out from Husserl’s philosophy of mathematics into Husserl’s metatheory and transcendental phenomenology. The result is that Husserl cannot appeal to formal essences without metaphysical commitments. However, the very observations Thomasson makes about the nature of eidetic intuition in Husserl lead to a general strategy for responding to the problem. The article thus illustrates that the pleonastic and the model-theoretic routes for making Husserl relevant to present-day ontology are competing approaches, but I conclude that Husserl scholars seeking to set Husserl’s present-day relevance into sharp relief could do worse than to emphasize the model-theoretic nature of Husserl’s enterprise. (shrink)

Realisms Interlinked is a sublime work. It reanimates theoretical philosophy with a distinctive synthesis of ideas and methods drawn from the common-sense metap.