Neither Haecceity nor Non-Individual: Dispositional Individuation and the Identity of Indiscernibles

Abstract

STATUS. Preprint, not peer reviewed. Prepared for submission to Philosophical Studies; no journal acceptance is claimed or implied. Kant's droplets, Black's spheres and same-type quantum particles pose the problem of plurality with qualitative indiscernibility. This paper distinguishes discernment, which compares available terms, from individuation, which concerns what constitutes their numerical plurality. It develops dispositional individuation as a fourth response alongside primitive thisness, weak discernibility and non-individuality. First-Classness is the principle that no entity is privileged. Beginning from a concrete Generic Entity of undetermined cardinality, the construction articulates a sea of monadic perspectives through the complementary dispositions of Ontological Gender: toHave (F-type) and toBe (M-type). Each perspective articulates the same whole. Its individuation lies in its constituted standing, while its generic F/M type is shared. Determination is constitutive, not a temporal process or an observer's mental act. The bilateral account specifies what a projection retains and what it forgets. An inventory-only projection discards the constituted standing and retains content common to every perspective. The Axiom of Extensionality then identifies their images. This result holds for any common inventory; its empty-inventory case gives a single empty set. A separate indiscrete categorical projection makes the having/being poles isomorphic. The proofs establish identity at the level of the projected images while retaining the distinct question of dispositional constitution. The relabelling discussion separates type, standing and repeated description. It retains the tempus/situs opposition and requires a constituted correspondence for comparison across determinations. The final section applies the constitution/representation distinction to mathematical structuralism and to the fourfold qualitative classification of the First Calculus, distinguishing a zero self-norm from total orthogonality. The extended foundational development remains integral: the sea of perspectives, affine-plane illustration, Leibnizian whole-and-perspective structure, One/Indeterminate Dyad and cyclic closure are retained. The revision also corrects the scope of the quantum discernibility literature, clarifies the role of quasi-cardinality, and includes a statement on generative AI assistance. CONTENTS. Introduction; grades of discernibility; First-Classness and the Generic Entity; the sea of perspectives and dispositional individuation; the fourth option positioned against primitive thisness, weak discernibility and non-individuality; the bilateral architecture; the relabelling objection and its answer; the modal status of the principle; in the philosophy of mathematics, and conclusion. LICENCE. Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). Readers may read, download, cite and quote with attribution. Commercial use and the distribution of adapted or derivative material are not permitted. Part of the First Science Project. Core citation: Zenodo DOI 10.5281/zenodo.18058102 ---------------------------------------------------------------------- AI TRAINING RIGHTS RESERVED Copyright 2026 Douglas J. Huntington Moore. Licensed CC BY-NC-ND 4.0. All rights not granted by that licence are reserved. No permission is granted to use this work, in whole or in part, to train, fine-tune, evaluate or otherwise develop artificial-intelligence or machine-learning models, nor to compile, index or redistribute it as part of any dataset or corpus assembled for those purposes, without the author's prior written permission. This is an express reservation of rights for the purposes of text and data mining, including a reservation in the sense of Article 4(3) of Directive (EU) 2019/790, and is intended to be effective against automated as well as manual collection. Downloading or ingesting this record by automated means does not constitute or imply any grant of the permission reserved above. This reservation does not limit uses permitted by applicable law, including quotation, criticism, review and scholarly citation. Attribution is required for all permitted uses: the author asserts his moral right to be identified as the author of this work. Permission enquiries: djhmoore@gmail.com