Open research questions in Philosophy and Theoretical Science

What the literature leaves open

• Applies the reflective register and the imprint test to specific mathematical objects and open questions. Rebuttal: the verdict is discrete and three-state with trinary terminality, fractional truth undefined; convergence operates on the topological sign, never on scalar entries; and no consensus term enters, W_social = 0.

  Condensed TRISDUCTION: A Linguistically, Topologically, and Mathematically Sealed Verification Architecture: Triaxial Orthogonality, Twelve-Gate Closure, the Quaternionic Completion · A Condensed Codex of the Trisduction with Apex Harvest, the Sealed Defense, and the Non-Gödelian Verdicts · 2026 · DOI

• That does not mean that a similar approach that does do away with causal set elements cannot be developed, and this would be an interesting avenue for further research into developing a better structuralist framework for CST.

  Structuralism and the Individuation of Causal Set Elements in Causal Set Theory · 2026 · DOI

• Starting point: Not an additional postulate, but a result The short equation i = E and the empirical studies from physics, cosmology, quantum information, biology, neurobiology and social theory listed below lead to a common structural conclusion:The future is not completely determined, but arises continuously from information-based selection, feedback and stability processes.

  Nothingness – Dimension 0 and the permanent presence of possibility · 2026 · DOI

• ONE AXIOM The paper closes its three Poles and the Realizability-Oracle layer. Five forward directions remain open and are recorded below; each is stated as a dispatch (a named follow-up obligation), not a claimed result. F1 — W2O feedback loop. Prediction P1C,12 (reception W2O-Inversion signature) defines a post-publication audit; F1 closes the loop by formalising how the audited reception fraction feeds back into the Anti-Absorption Protocol as a self-correcting diagnostic (4B Prediction-Watch integration over N ∈ {3, 5} years). F2 — Dual-Track failure modes. Every result here carries the mandatory [O ∩ F R] Dual-Track. F2 is a systematic catalogue of the ways the two tracks can diverge (ontological-without-epistemological and vice versa), i.e. a failuremode taxonomy for the Dual-Track discipline itself. F3 — 1A v5.0 Hilbert-finitism interface. The cost-blindness of WOP-5 (§16) touches the finitist programme. F3 dispatches a 1A v5.0 update relating the δα-quantised cost ledger to Hilbert finitism, with the ♥IVCF Hilbert-space realisation (0A) as the anchor. F4 — 0M v2.0 Three-Gate consolidation. The Three-Gate Architecture (§7), a proven theorem in 1C (Theorem 7.1, its three-way partition forced by the Axiom-M σ-structure on both Dual-Track legs), is a meta-pattern shared by all three Poles and by 8C R83. F4 promotes GateX to a foundational primitive in 0M v2.0, so that any future ALFA-coupling diagnostic theorem (9C Social PSP, 4B v7.0+) inherits the Gate-existence + componentstatus + verdict-firing template directly. F5 — empirical face of the ε∗=1/96 bridge defect (open research direction). The bridge Ψ carries a proven structural defect ε∗ = 2δα = 1/96 (Corollary D.2.1, R1C,21c) — a category-theoretic, proof-checkable quantity, not an empirical claim. F5 records the genuinely open question of whether a faithful operational bridge δα (cid:55)→ ˆδ can be constructed, mapping the framework’s coding-tolerance defect δα to a measurable calibration quantity ˆδ (an expected-calibration-error-type score on verified-vs-claimed cohorts). We make no prediction here: absent such a bridge there is no falsifiable empirical content, which is precisely why ε∗=1/96 is deliberately not registered among P1C,1–P1C,17 (§9, Remark 9.1). We leave it instead as an invitation: should a future reader — inside ONE AXIOM or beyond it — construct the δα (cid:55)→ ˆδ map rigorously, the proven structural constant 1/96 would acquire a sharp, testable empirical face. We would be glad to see that discovery made. The single open Pole-A item is the strict-containment witness selection: WOP-5 establishes existence (§4), but a canonical, cost-blind-robust choice of witness among the §5.5 candidates is left to 1C-A. All other Pole-A, Pole-B and Pole-C obligations are closed in v1.0.

  ONE AXIOM : All Secure · 2026 · DOI

• The formal ontological analysis employs essential dependence relations (E-RIG and E-GEN) and hyperintensional machinery from Fine, Lowe, and Correia, but does not formally derive or test whether these dependence structures can be computationally or algorithmically instantiated to predict or classify natural kinds based on property clusters without prior ontological commitment.

  Natural kind fundamentalism · 2026 · DOI

• The paper adopts a framework that remains deliberately open on whether to adopt a sparse or less sparse view of which kinds are genuinely fundamental, leaving unresolved the specific criteria that would determine the cardinality and boundaries of the fundamental natural kinds category—no decision procedure is provided for controversial cases at disciplinary boundaries.

  Natural kind fundamentalism · 2026 · DOI

• The distinction between metaphysically necessary laws flowing from essential natures of fundamental kinds versus weaker contingent regularities depending on property distributions and structural arrangements is theoretically articulated, but lacks formal empirical procedures to identify which actual scientific laws fall into each category based on observable data or theoretical structure.

  Natural kind fundamentalism · 2026 · DOI

• The framework claims that the modal status of natural kind instantiation—whether fundamental kinds have metaphysically necessary instantiation versus contingent instantiation—should be determined through interplay between metaphysical theorizing and empirical investigation, but provides no concrete methodology or empirical criteria for making this determination in specific cases (e.g., for muons, quarks, or composite kinds).

  Natural kind fundamentalism · 2026 · DOI

• The paper establishes that natural kinds depend rigidly on specific essential properties (e.g., electron depends on unit negative charge, specific mass, and spin), but does not empirically investigate or formally specify which physical properties across different scientific domains qualify as rigid versus generic dependence relations. A systematic taxonomy is needed that maps natural kind categories in physics, chemistry, and biology to their precise essential property profiles.

  Natural kind fundamentalism · 2026 · DOI

• There is no agreement even on so basic a matter as where he falls in the standard scheme of classifying such theories: to Copleston, he is a resemblance-nominalist; to Armstrong, a ‘concept nominalist’; to Edwards and Spade, ‘almost as strong a realist as Duns Scotus’; to Gracia, Pannier, and Sullivan, neither realist nor nominalist; to Hamlyn, the Middle Ages ’ ‘prime exponent of realism, ’ although his theory adds elements of nominalism and ‘conceptualism’; to Wolterstorff, just inconsistent.

  Aquinas on the Problem of Universals · 2015 · DOI

• Quantifier VarianceIn philosophy, we often find ourselves confronted with multiple inconsistent answers to some question, each of which can be embedded into an internally coherent body of theory, and such that there is no agreement about how any new observations we could make would bear on the issue.

  Quantifier Variance and the Collapse Theorems · 2014 · DOI

• Standards Are Prevalent in Everyday LifeHumans routinely use judgment in determining what to accept and what to reject; this is impossible without standards or criteria.

  Critical Thinking: Intellectual Standards Essential to Reasoning Well within Every Domain of Human Thought, Part Two. · 2013

• Recent attempts
\nspawned from logic-based information retrieval theory have formalized properties characterizing “aboutness”,
\nbut no consensus has yet been reached.

  Aboutness from a commonsense perspective · 2000 · DOI

• 22 FUNCTIONALISM AND NEO-FUNCTIONALISM the older literature should be studied, including the "evolutionists"; and the revised attitude towards the historical study of the past. " It appears, then, that the criticism of the classical "evolutionists" was, to some extent, due to insufficient knowledge of their works.

  FUNCTIONALISM AND NEO‐FUNCTIONALISM · 1946 · DOI

• I argue that among these underexplored consequences is a striking variety of neutral monism, construed as the thesis that all entities share the same fundamental modal base.

  The Rationalist’s Road to Neutral Monism · 2026 · DOI

• I argue that a similar problem (or perhaps different problems with similar underlying reasons) befalls other realist accounts and show why various extant solutions are insufficient.

  Counterfactuals, Modal Knowledge, and Understanding · 2025 · DOI

• In this article, I propose the pretence theory of understanding nonsense to explain the riddle of understanding nonsense, and discuss alternative frameworks that are insufficient to solve it.

  The Riddle of Understanding Nonsense · 2023 · DOI

• Third, I contend that it takes more than conversational interchangeability for two sentences to be equivalent and that genuine equivalence has not been established for non-numerical versions of Frege’s biconditionals.

  Properties Ain’t No Puzzle · 2017

• While for Cohen concrete subjectivity remains an open issue, without a proper philosophical account, Natorp manages to put forward a theory of concrete subjectivity within the very limits imposed by the transcendental method.

  Cohen and Natorp on Transcendental and Concrete Subjectivity · 2017 · DOI

• 1)2 The lack of consensus in these debates, as well as the sheer range of interpretations on offer, makes the proper understanding of Aquinas’s views about universals all the more pressing.

  Aquinas on the Problem of Universals · 2015 · DOI

• Finally, the author presents his own objection which appeals to the fact that the Russellian analysis does not account for an intuitive inferential property of attributive assertions.

  The Attributive Use and Russell’s Paradigm · 2013

• While not discussing in detail the former one, I point out that the adequacy of perdurantism is an open question: in particular, reasons appealing to problems of material constitution, given by perdurantists, are unsatisfactory.

  Ingardenowska ontologia czasu i procesu a prezentyzm · 2013

• I find this view fit well with Carnap’s argumentative strategy against substantial character of metaphysical debates, since he stresses the lack of evidences in favour of or against metaphysical claims as the main reason for his deflationism in ontology.

  Późny Carnap a współczesne spory ontologiczne. Cz. II. Czy Carnap był zwolennikiem epistemizmu · 2012

• If one asks what difference is made to our knowledge claims if we accept the existence of an extra-conceptual world, the answer is the following: such recognition undermines the diffused anthropocentric stance which identifies reality with our limited knowledge of it.

  A Limited View of Realism · 2012 · DOI

• The essay argues that, on their usual metalinguistic reconstructions, the open question argument and Frege's puzzle are variants of the same argument.

  Open Questions and the Manifest Image · 2004 · DOI

Most-cited papers in Philosophy and Theoretical Science

• <i>Cosmopraxis</i>: Relational methods for a pluriversal IR · Review of International Studies · 2021 · 59 citations
• Modality, Sparsity, and Essence · The Philosophical Quarterly · 2013 · 56 citations
• Three legs of the missing heritability problem · Studies in History and Philosophy of Science Part A · 2022 · 52 citations
• Reconsidering the Dispositional Essentialist Canon · Philosophical Studies · 2021 · 31 citations
• Theory and ontology in behavioural science · Nature Human Behaviour · 2020 · 27 citations
• Function essentialism about artifacts · Philosophical Studies · 2021 · 25 citations
• Downplaying the change of subject objection to conceptual engineering · Inquiry · 2021 · 24 citations
• Ground and Grain · Philosophy and Phenomenological Research · 2021 · 23 citations
• How Can Theories Represent Social Phenomena? · Sociological Theory · 2022 · 23 citations
• Aboutness from a commonsense perspective · Journal of the American Society for Information Science · 2000 · 22 citations

Most recent work

• ONE AXIOM : All Secure · Zenodo (CERN European Organization for Nuclear Research) · 2026
• The illusion of rigor: Why analytical sophistication cannot substitute for inferential coherence · Theory and Society · 2026
• Deterministic Theories · Philosophy and Phenomenological Research · 2026
• Zhu-Liang Theorem on Truth as Recursive Meta-Nested Function ——Based on Category-Theoretic Construction from Root Consensus of Causality and Self-Consistency (Complete Version) · Zenodo (CERN European Organization for Nuclear Research) · 2026
• THE MODAL DISCIPLINE OF RELATIONAL COHERENCE: a critical–propositional analysis of the article A Modal Dialogue between the Projective Dynamic Logo (PDL) and the Theory of Objectivity (TO), by C. Laubscher, in confrontation with the Theory of Objectivity · Zenodo (CERN European Organization for Nuclear Research) · 2026
• THE MODAL DISCIPLINE OF ONTOLOGICAL FUNDAMENTALITY: a critical–propositional analysis of On Modal Discipline and Ontological Fundamentality: Admissibility, Articulation, and the Scope of the Theory of Objectivity (V 1.0), by Carlos van Hamme, in confrontation with the Theory of Objectivity · Zenodo (CERN European Organization for Nuclear Research) · 2026
• Natural kind fundamentalism · Philosophical Studies · 2026
• THE MODAL DISCIPLINE OF THE INVERSE TRANSFORMATION OF RINDLER SPACETIME: A critical–propositional analysis of Inverse-transformation of 4-dimensional Rindler spacetime, by Sangwha-Yi, in confrontation with the Theory of Objectivity · Zenodo (CERN European Organization for Nuclear Research) · 2026
• Diving for pearls: conceptual abandonment, conceptual engineering, and the limits of thought and language · Philosophical Studies · 2026
• SINGULAR DUALITY AND THE MODAL DISCIPLINE OF OBJECTIVITY A critical–propositional reading of the manuscript A Singular Duality: A Unified Framework Proving Our Mathematical Universe, by C. Mike "WildFacts" Rubendall, in confrontation with the Theory of Objectivity · Zenodo (CERN European Organization for Nuclear Research) · 2026

Related topics in Psychology