Husserl, Model Theory, and Formal Essences

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.

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Notes

  1. 1.

    Cf. Husserl’s letter to Weyl dated 5 June 1920 (Van Dalen 1984, p. 5).

  2. 2.

    Eidetic and categorial intuition are distinct, but the precise differences will not concern us at this juncture. Since my concern is with formal essences, I will be concerned in the latter part of the article with categorial intuition. As it becomes relevant, I’ll differentiate more clearly between these two.

  3. 3.

    The differences discussed here between sensory intuition and eidetic intuition carry over to a large degree also to the differences between sensory and categorial intuition. However, there will in turn be crucial differences between eidetic intuition and categorial intuition that figure centrally into the reasons for the failure of Thomasson’s approach in the case of formal essences. Thomasson’s comments apply primarily to eidetic intuition, but later in this paper, in concert with my attempt to pass from the consideration of material to formal essences, we’ll be more concerned with categorial intuition.

  4. 4.

    Husserl says: “The essence (eidos) is an object of a new kind. Just as the given in the individual or experiential intuition is an individual object, so the given in the intuition of the essence is a pure essence” (2014,§3, p. 12).

  5. 5.

    Cf. Awodey and Reck (2002), Howard (1996), Majer (1997).

  6. 6.

    Indeed, the problem reverberates beyond Husserl’s philosophy of mathematics, into his metatheory and ultimately into transcendental phenomenology. Categoricity came to serve the purpose of clarifying the very nature of theories and informed his developing approach to the philosophical foundations of semantics.

  7. 7.

    Button and Walsh mention McGee (1997, p. 36), Balaguer (1998a, p. 73, b, p. 84), MacBride (2005, p. 581), Hodes (1984, p. 139).

  8. 8.

    See also Husserl (1973, §9).

  9. 9.

    See Tieszen (2005, p. 29).

  10. 10.

    Cf. Kusch (1989, Part II).

  11. 11.

    As cited and translated in Kusch (1989, p. 20).

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Banick, K. Husserl, Model Theory, and Formal Essences. Husserl Stud (2020). https://doi.org/10.1007/s10743-020-09281-8

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