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Entities Without Identities vs. Temporal Modalities of Choice

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Fig. 1

Notes

  1. Bracketed page citations within the text refer to Mark van Atten’s Brouwer Meets Husserl.

  2. Null and Simons (1981).

  3. Küng (1975, p. 152).

  4. Brouwer shared (p. 33–36) Kant’s view of inner time as isomorphic to the continuum. Incompatible protended choices are neither earlier nor later than each other, so they fail Trichotomy (which was assumed for the transfinites by Cantor and Zermelo and is satisfied by the retended past and present and by the continuum). Van Atten shares Brouwer’s Kantian mistake of assuming future time satisfies Trichotomy, which Gurwitsch preserved for the countable ordinals by deriving them from only present and retended time (vide Null and Simons 1981).

  5. Küng (1975, pp 150–153).

  6. Theorem 16 in Null (2007a, p. 40).

  7. Gurwitsch (1966, pp. 124–140).

  8. Troelstra (1983, p. 201).

  9. Null (2007b). Vide §3, N-Definitions 1, 2, and 3. Both Fig. 1 (for U = 6) and Fig. 1a (for \(\hbox{U} ={\mathbb{N}})\) satisfy (and hence are models of) the seven §3 Intentional Temporality Axioms.

  10. Gurwitsch (1966, pp. 134–138).

  11. Gurwitsch (1966, p. 131).

  12. Null (2007b). See §4. The modal component of the inference system of any logic of intentionality is Brouwerian.

References

  • Gurwitsch, A. (1966). On the intentionality of consciousness. In A. Gurwitsch (Ed.), Studies in phenomenology and psychology. Evanston: Northwestern University Press.

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  • Küng, G. (1975). Das Noema als Reelles Momen.t. In P. J. Bossert (Ed.), Phenomenological perspectives. The Hague: Martinus Nijhoff.

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  • Null, G. T., & Simons, R. A. (1981). Aron Gurwitsch’s ordinal foundation of mathematics and the problem of formalizing ideational abstraction. Journal of the British Society for Phenomenology, 12(2).

  • Null, G. T. (2007a). The ontology of intentionality I: The dependence ontological account of order: Mediate and immediate moments and pieces of dependent and independent objects. Husserl Studies, 23(1), 33–69.

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  • Null, G. T. (2007b). Two-valued logics of intentionality: Temporality, truth, modality, and identity. Husserl Studies, 23(3), 187–228.

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  • Troelstra, A. S. (1983). Analysing choice sequences. Journal of Philosophical Logic, 12, 197–260.

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  1. Department of Philosophy, University of Wisconsin, 1903 Lakeside Place, Green Bay, WI, 54320, USA

    Gilbert Null

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Null, G. Entities Without Identities vs. Temporal Modalities of Choice. Husserl Stud 24, 119–130 (2008). https://doi.org/10.1007/s10743-007-9030-2

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