André Hampshire

Standard instruction in oscillations and waves often presents sinusoidal solutions, complex exponentials, standing waves, and Fourier decomposition as disconnected mathematical devices. This paper offers a unified pedagogical reconstruction organized around three levels of structure. At the most general level, any exactly periodic dynamics admits a phase coordinate on the closed orbit, because the evolution factors through the quotient ℝ/Tℤ ≅ S¹. At the level of linear harmonic systems, a restoring force proportional to displacement enforces uniform phase advance. The resulting dynamics take the form of a rotation in a two-dimensional state space, and observable motion appears as the projection of this rotation. In this formulation, the complex exponential exp(−iωt) arises naturally as the representation of phase rotation, rather than as a computational device. At the level of spatially distributed linear media, local coupling of oscillatory degrees of freedom with inertia and restoring forces yields the wave equation; its monochromatic solutions are plane waves exp[i(kx − ωt)], standing waves arise through superposition under boundary conditions, and Fourier analysis resolves general solutions into independent phase-translation modes. The framework does not propose new physical laws. It provides a structurally motivated derivation and pedagogical reorganization of standard results around the roles of recurrence, phase, and translation symmetry, aimed at upper-division physics instruction.

Why does morality exist? Under what structural conditions does moral normativity emerge? This paper argues that morality is the regulatory structure governing how agents may act within fragile responsibility couplings. Four conditions are jointly necessary for moral wrongness to be applicable: fragility (at least one party has degradable action-capacity), agency (at least one party has genuine alternatives), modulation (alternatives differ in their effects on the fragile party’s action capacity), and coupling (the parties stand in an epistemically accessible dependence relation). When all four obtain, actions can strengthen or weaken the viability of the coupling, and wrongness becomes structurally well-defined. When any condition fails, losses may still occur, but they are tragic rather than wrong. The paper formalizes this using viability theory, derives a viability condition on couplings that excludes predatory structures, reinterprets loss as the empirical signature of coupling-degradation, and proves that in a hypothetical world without degradable coupling, moral categories do not arise. A structural asymmetry among coupling types emerges as a consequence: predatory couplings are dynamically unstable, maintenance couplings merely preserve slack, and mutual couplings can generate slack over time—a result of the viability condition rather than a teleological explanation of morality.

What makes an action right? This paper develops a structural answer: an action is optimally right if and only if it minimizes aggregate loss among viable options, and permissible if it remains within the best attainable severity class. The framework takes loss—the diminution of action-capacity within responsibility structures—as its foundational primitive, drawing on an independently developed ontology of loss as temporal foreclosure. From this foundation, the paper derives: (1) a three-level verdict structure (optimal, permissible, wrong) grounded in severity thresholds, (2) lexicographic severity aggregation that captures categorical priorities without abandoning outcome-sensitivity, (3) a viability constraint that blocks demandingness objections by treating agency-destruction as catastrophic loss internal to the framework, and (4) a counterfactual structure of wrongness that explains why unavoidable harm is not wrong while easily avoidable harm is worse. The resulting view is a structurally constrained consequentialism that explains why deontological prohibitions have force, why special obligations emerge from relationships, and why predatory structures fail to qualify as moral systems. The framework preserves consequentialist outcome-sensitivity while explaining the categorical priorities emphasized by deontological theories in terms of the structure of loss.

This paper develops structural loss-minimization ethics, a unified moral framework built from a single primitive: loss. The framework provides: (1) a first-order theory of right action (right action minimizes aggregate loss among viable options), (2) a theory of moral character (good character is a robust policy of loss-minimization across situations), (3) a theory of moral appraisal (attribution is inference about character from observed behavior under discriminating conditions), and (4) a deflationary account of moral worth as a dispositional property (policy robustness) whose social function is to support coordination under uncertainty. The framework dissolves traditional puzzles about the relationship between motives and outcomes, explains why moral luck is troubling, grounds the importance of counterfactuals, and unifies questions that the philosophical literature has treated as separate research programs. Unlike classical utilitarianism, the framework operates on loss rather than utility, reads loss off situational structure rather than calculating hedonic sums, and reframes several standard objections by restricting evaluation to viable continuations of agency and by using lexicographic severity aggregation. The resulting view is best understood as a structurally constrained consequentialism with a policy-inference account of moral worth.

This paper advances two claims about philosophical work on moral worth. The primary claim is methodological: when thought experiments are used evidentially to support claims about agents’ motivations or policies, they must satisfy minimal discriminability conditions; many central cases in the literature fail this requirement. The secondary claim is institutional: the systematic neglect of these conditions is structurally sustained by training, publication, and hiring practices. I begin with Kant’s shopkeeper and show that it fails basic discriminability conditions familiar from experimental reasoning: the scenario provides no evidence about the variable it purports to reveal. The same structural flaw pervades contemporary work. Through case studies of Portmore, Arpaly, Isserow, and Fearnley, I diagnose four recurring patterns: unexplained primitives, underdescribed scenarios, convergence-free reflective equilibrium, and neglect of functional grounding. Each author makes genuine contributions; in each case, the contributions are constrained by methods that limit what can be achieved. The formal tools required to address these problems—probability theory, decision theory, game theory, information theory—have existed for decades to centuries. I present the Constraint-Sensitive Moral Appraisal framework as proof of concept: applying standard inferential methods dissolves the apparent difficulties into tractable questions about policy attribution under uncertainty.

Accounts of moral worth—the property that makes an agent praiseworthy for acting rightly—typically proceed by conditional analysis: given some standard of rightness, what further condition distinguishes praiseworthy from non-praiseworthy right action? This paper argues that such accounts face an underidentification problem: without invariance constraints on the bracketed predicate “rightness,” the explanatory target is not well-defined, and downstream claims about moral worth are not stably evaluable for correctness. I develop an alternative account on which moralworth attributions function as compressed signals tracking counterfactual policy reliability under coordination constraints. The framework recovers the phenomena that motivate moral-worth talk while avoiding the underidentification problem. I show that the two approaches generate divergent predictions about praise judgments, and I argue that the constraint-sensitive account better explains cases—including those traditionally favorable to the duty-based view.

This paper develops a formal account of the concepts woman, sex, and gender. I argue that many difficulties in contemporary feminist philosophy arise from conflating three independent dimensions: reproductive type, expressive mode, and the normative process that enforces expectations based on perceived type. Once these are distinguished, the familiar puzzles dissolve. Sex is reproductive type, biologically fixed and defined by developmental organization toward gamete production. Expression is behavioral presentation, individually variable and socially legible. Gender is neither a property nor an identity but a process: the patterned application of normative expectations to persons on the basis of type. The structure of this process is invariant across cultures, though its content varies. I show that the most sophisticated ameliorative account of “woman” (Jenkins 2016) fails for six independent structural reasons, each stemming from a methodological substitution of construction for analysis. In contrast, the framework developed here provides coherent definitions, clarifies the status of trans identity, resolves the pronoun question, and grounds ethical distinctions between type-based and expression-based treatment—without requiring anyone to deny biological reality or disregard lived expression. The result is a clearer conceptual schema within which ongoing social and political debates can proceed more productively.

This paper presents a new mathematical framework for grounding moral obligations in the structural constraints of finite resources. Agents are modeled as multi-dimensional systems whose continued existence requires satisfying fundamental needs—each with its own decay rate and finite buffer. This yields three qualitatively distinct regimes: Sufficiency, where resources exceed combined needs; the Zero-Instantiation Constraint (ZIC), where resources exactly match needs; and Scarcity, where total needs exceed what the environment can supply. Across these regimes, the dynamics of resource flows determines both the limits and the possibilities of moral action. In Sufficiency, obligations are real but bounded, and a non-empty region of supererogatory action becomes available. At ZIC, obligations are uniquely fixed and leave no slack. Below ZIC, dual preservation is impossible, making classical moral theorizing—obligation, fairness, maximizing the good—structurally undefined. The framework distinguishes duty from generosity, sustainable sacrifice from collapse, and informed self-giving from hope under uncertainty. It also introduces non-fungible, person-specific need dimensions that render another’s existence constitutive of one’s own—explaining phenomena such as parental sacrifice, grief-induced functional decline, and rational ultimate self-sacrifice. In shock-prone worlds, the analysis further shows that two-agent systems are structurally brittle: no dyad can maintain redundancy under finite buffers. By contrast, three-agent configurations admit genuine shock-tolerant resilience, establishing a triadic minimum for robust interdependence. The resulting theory does not rely on utility, preference, or idealized norms. Instead, it shows how moral demands emerge from the existential structure of embodied agents operating under real constraints. This offers a new foundation for structural ethics and clarifies where moral reasoning succeeds—and where the world itself makes moral solutions impossible.

Structural ethics is a research program examining moral possibility and obligation under resource constraints. It formalizes the mathematical structure of moral space, showing that classical ethical theories presuppose resource sufficiency and become undefined at or below critical feasibility thresholds. The program unifies three frameworks—feasibility (ZIC), sustainable duty (Enoughness), and measurable affection (Love)—into a single resource-indexed moral ontology. Together they reveal that morality, like physics, has structure: its boundaries, dynamics, and limits can be expressed in formal, testable terms. The result is an empirically grounded metaethics for resource-constrained moral life.

Philosophical treatments of love often oscillate between two extremes: conceiving it as an ineffable emotion resistant to quantification, or reducing it to arbitrary preference orderings. This paper advances a third approach—treating love as measurable through supererogatory patterns of resource allocation within a bounded moral framework. Using basic needs as objective limits—those of the dependent below and those of the self above—I argue that the gap between moral duty and actual allocation yields a quantifiable, behaviorally grounded metric of love. The framework (1) distinguishes love from duty, (2) enables interpersonal comparison of affection, (3) renders love empirically measurable, and (4) explains our intuitions about neglect, adequate care, and loving relationships. I defend this model against major objections and explore its implications for moral psychology, parent–child relationships, and the ethics of care. The resulting “love metric” operates within the bounded interval I elsewhere define as “enoughness,” presupposing the feasibility conditions derived in my work on the phase structure of moral space.

This paper develops a formal account of bounded moral responsibility grounded in a single symmetrical principle. Every moral agent and every dependent being possess basic needs (BN): conditions, biologically determined yet socially elaborated, beneath which existence or flourishing would be impaired. In relations of care, these needs generate both the lower and upper bounds of moral sufficiency. The dependent’s basic needs (BNother) determine the minimum that must be met; the caregiver’s basic needs (BNself ) determine the maximum that can be met without self-violation. The circumstantial limit is thus not an independent moral principle but the application of the same basic-needs constraint to the self: CL = BNself . This symmetry establishes an interval of enoughness within which care remains sustainable and morally adequate. Violating BNself not only constitutes self-cruelty but predictably degrades future capacity to satisfy BNother, producing a temporal interdependence between self- and other-directed obligation. When BNother structurally exceeds BNself , the resulting shortfall necessitates collective rather than individual responsibility. The framework thereby unifies sufficiency, sustainability, and moral consistency under a single structural principle of basic need.

I develop a formal framework for moral theory under resource constraints. Modeling agents with multi-dimensional basic needs competing for finite environmental resources, I prove a trichotomy theorem: the space of viability-preserving allocations is either positive dimensional (Sufficiency), singleton (Zero-Instantiation Constraint), or empty (Scarcity). I show that classical moral theories (Kantian, utilitarian, Singerian, Rawlsian) implicitly assume Sufficiency and become undefined or degenerate at or below the Zero-Instantiation Constraint (ZIC). The framework explains why demanding prescriptions exhibit systematic non-instantiation and formalizes the boundary conditions implicit in “ought implies can.” Applications include development ethics, healthcare resource allocation, and the demandingness debate.