Husserl, Model Theory, and Formal Essences
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Husserl, Model Theory, and Formal Essences Kyle Banick1 Accepted: 28 September 2020 © Springer Nature B.V. 2020
Abstract 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.
1 Introduction Husserl’s philosophy of mathematics, his metatheory, and his transcendental phenomenology have a sophisticated systematic interrelation that remains relevant for questions of ontology today. At the center of this systematicity is Husserl’s conception of formal essences. Early on, Husserl was vexed by metaphysical and epistemological issues in the developing mathematics of his day. It is widely known that Husserl argued unequivocally against psychologism, but his relationship with Hilbert-style formalism is more nuanced. He was impressed with the level * Kyle Banick [email protected] 1
Philosophy Department, California State University, Long Beach, Long Beach, CA, USA
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of formalization achieved in mathematics, but he also refused to accept deflationary views of mathematical concepts according to which such concepts are solely determined by formal axioms. Husserl sought to enrich our understanding of formal essences with semantic, meaningful content grounded in intuition. A result of this mission is that Husserl’s treatment of formal essences includes an innovative appeal to categoricity. Today, Husserl’s ideas live on in model theory. The importance of categoricity for the philosopher of mathematics is that categoricity undergirds determinacy in mathematical discourse. But this notion resonates further out for Husserl: it undergirds in many ways his entire approach to philos
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