In evolutionary biology, niche construction is sometimes described as a genuine evolutionary process whereby organisms, through their activities and regulatory mechanisms, modify their environment such as to steer their own evolutionary trajectory, and that of other species. There is ongoing debate, however, on the extent to which niche construction ought to be considered a bona fide evolutionary force, on a par with natural selection. Recent formulations of the variational free-energy principle as applied to the life sciences describe the properties of (...) living systems, and their selection in evolution, in terms of variational inference. We argue that niche construction can be described using a variational approach. We propose new arguments to support the niche construction perspective, and to extend the variational approach to niche construction to current perspectives in various scientific fields. (shrink)

One important question in emotion science is determining what emotions there are. To answer this question, researchers have assumed either that folk emotion concepts are unsuitable for scientific inquiry, or that they are constitutive or explanatorily significant for emotion research. Either option faces a challenge from the cultural variability of folk emotion concepts, prompting debate on the universality of emotions. I contend that cultural variation in emotion should be construed as variations in components rather than entire emotional repertoires. To (...) do this, I distinguish between hypotheses concerning emotional repertoires and those focused on specific emotional features within various cultural contexts. I hold that decisions regarding emotional repertoire hypotheses call for either revising current classification systems or maintaining them, but that, given underdetermination by evidence, this entails a preference for maintaining emotion taxonomies. This, in turn, leaves empirical hypotheses on specific emotional features as the most viable avenue for scientific inquiry. (shrink)

I use an old challenge to motivate a new view. The old challenge is due to variation in our perceptions of secondary qualities. The challenge is to say whose perceptions are accurate. The new view is about how we manage to perceive secondary qualities, and thus manage to perceive them accurately or inaccurately. I call it perceptual structuralism. I first introduce the challenge and point out drawbacks with traditional responses. I spend the rest of the paper motivating and defending (...) a structuralist response. While I focus on color, both the challenge and the view generalize to the other secondary qualities. (shrink)

The Universal Variational Paradigm (UVP) defines reality as a self-consistent variational process of distinctions. All physical laws, stable structures, and temporal evolution arise from a single informational functional — the Fisher information measure. From three irreducible axioms — difference, stationarity, and non-closure — UVP derives quantum mechanics, general relativity, and the arrow of time as expressions of the same universal law. The theory unifies physics, biology, and consciousness under one variational geometry where being is the stable evolution of difference.

According to Smell Objectivism, the smells we perceive in olfactory experience are objective and independent of perceivers, their experiences, and their perceptual systems. Variations in how things smell to different perceivers or in different contexts raise a challenge to this view. In this paper, I offer an objectivist account of non-illusory contextual variation: cases where the same thing smells different in different contexts of perception and there is no good reason to appeal to misperception. My central example is that (...) of dihydromyrcenol, a substance that can smell both woody and citrusy depending on what other odourants one has recently been exposed to. I first argue that the subjects’ apparently conflicting reports about the way dihydromyrcenol smells are best understood as comparative characterisations of a smell. Given this understanding, different reports can be correctly made in response to perceiving the very same smell. I then argue that the phenomenal difference between the experiences subjects have across contexts can be explained compatibly with Smell Objectivism. On the account proposed, subjects perceive the very same smell but different qualities, notes, or aspects of it are salient to them, depending on the context of perception. I then consider how the proposed defence of Smell Objectivism can be adapted to other cases where the same thing is reported as smelling different in different contexts. (shrink)

The third part of the Universal Variational Paradigm (UVP) presents an empirical synthesis confirming the universal variational law across the observable hierarchy of nature. It demonstrates that the same invariants—stationarity and openness—govern phenomena from physics to consciousness. -/- Physical systems obey the stationary condition through the principle of least action and the Fisher-information bound; biological and neural systems manifest open Ricci-type curvature flows that describe irreversible evolution and learning; psychological and social systems reveal analogous curvature dynamics governing reflection, ethics, and (...) cultural adaptation. -/- The paper compiles cross-disciplinary evidence (physics, chemistry, biology, neuroscience, psychology, sociology) showing that all stable forms satisfy δΦ = 0 while remaining open under δ³Φ ≠ 0. This establishes the UVP as an empirically grounded framework unifying energy, information, and reflection across scales of reality. (shrink)

In this paper, I argue that the ‘social meanings’ associated with sociolinguistic variation put pressure on the standard philosophical conception of language, according to which the foremost thing we do with words is exchange information. Drawing on parallels with the explanatory challenge posed by slurs and pejoratives, I argue that the best way to understand social meanings is to think of them in speech act theoretic terms. I develop a distinctive form of pluralism about the performances realized by means (...) of sociolinguistic variants, and I claim that engagement with such performances is an utterly pervasive feature of our linguistic activity. (shrink)

There is variation in how people perceive colors and other secondary qualities. The challenge of perceptual variation is to say whose perceptions are accurate. According to Sextus, Protagoras’ response is that all of our perceptions might be accurate. As this response is traditionally developed, it is difficult to explain color illusion and color constancy. This difficulty is due to a widespread assumption called perceptual atomism. This chapter argues that, if we want to develop Protagoras’ response, we need to (...) give up perceptual atomism. It ends with a brief sketch of an alternative called perceptual structuralism. (shrink)

VBRC treats the low-energy regime atlas as a summary-interface atlas rather than a single master equation replacing classical, quantum, and relativistic laws. Under the Internal Invisibility Principle, those familiar laws appear as gate-dependent readouts of one Part-I-compatible representative and its reduced Schur operator, not as independent primitives. Following the Part I order—an admissible state/comparison arena C, a comparison language E, protocol-induced partial readout and IIP, the summary-entry discipline F = ΣH,P (unread content), with F = DI II only after a (...) first-order representative has been declared, admitting only F on the retained side, the core density ecore read on the retainedeffective pair (IR, F), and only then gate-dependent regimes—this paper does not attempt to unify familiar classical, quantum, and relativistic laws by collapsing them into one final equation. Instead, Part XV declares a low-energy geometric representative of ecore, studies the reduced Schur operator Seff obtained under the admissible summary-reduction gate, and applies the three series readings R1, R2, R3 to the resulting retained law: the stationary reading δEXV/δqA = 0, the dissipative reading ΓAq˙ A + δEXV/δqA = 0, and the conservative (time-completed) reading MAq¨ A + δEXV/δqA = 0. The conservative–dissipative equation that contains both inertial and frictional terms is used in this Part only as a transition completion containing the R2 and R3 limits in one notation; it is not a fourth primitive reading and does not replace the declared comparison representative. No claim of absolute uniqueness of EXV is made beyond the declared first-order representative scope. Accordingly, Part XV should not be read as opening a fresh representative branch of the theory: it declares a low-energy geometric realization FXV = DI II of the Part I summary channel and studies the gate atlas carried by the corresponding retained law, with classical, quantum, and relativistic equations treated as conditional comparison readouts rather than as new primitives or as a new master equation. The recovery of familiar laws is conditional: each named law appears only as a gate-dependent effective regime of that common structure, with explicit validity conditions and transition thresholds. Breakdown is therefore read not as inconsistency but as passage into a neighboring regime. The characteristic matter terms of the effective laws are likewise not inserted by hand: effective mass/gap terms arise through summary reduction of the already licensed summary channel in Schur-type form on the R3 (conservative) field branch, while effective stress-energy terms arise through metric variation of the same geometric representative in its R1 metric branch. Its main contribution is therefore not a new local law but a single low-energy atlas of emergence, validity windows, and transition behavior for the declared representative, with the principal formal reductions recorded in the appendices. A common-source theorem internal to this Part shows, after admissible summary reduction, that the three readings on the retained branch are controlled by one and the same reduced Schur operator Seff that is derived (not inherited as a primitive) from the declared representative and gate: stationary softening, dissipative growth/decay, and conservative dispersion are then three reading-dependent interpretations of the sign-changes of one common reduced symbol. The threshold quantities fixed here are also the low-energy starting point of the later late-gate trilogy: the mixed-gate discriminant and the upper-gate critical scale are different gate-specific realizations of the same transition grammar rather than disconnected additions. (shrink)

This work re-examines Penrose’s 1965 singularity theorem from a variational standpoint. The analysis shows that the theorem relies on a fixed set of structural assumptions—such as geodesic completeness, energy conditions, and a pre-defined spacetime ontology—that are not derived from a closed dynamical principle. -/- When reformulated within a self-contained variational framework, these assumptions are no longer required, and the configurations associated with singular behavior are replaced by regular, coherence-limited states. In this setting, neither curvature divergence nor geodesic incompleteness arises as (...) a necessary feature. -/- The result suggests that the original theorem should be understood as a statement about the internal consistency of a specific formal structure, rather than as a universal prediction about physical reality. -/- More generally, the analysis highlights the importance of distinguishing between mathematical consistency within a chosen framework and genuine physical necessity when assessing foundational results. (shrink)

This paper develops a mode-based reformulation of variational calculus, differential geometry, and analytical structures, in which convergence is treated not as a fixed background notion but as a parameterized class of operational procedures. -/- The central idea is that analytical objects—derivatives, admissible variations, metrics, and measures—should be defined through stability with respect to classes of convergence modes encoding discretization, ordering, and regularization. -/- Within this perspective: - variational principles become mode-dependent, - tangent structures generalize to mode-dependent cones, - differential structures (...) depend on admissible directions of convergence, - solution spaces admit a categorical organization over mode classes. -/- The paper shows that this dependence is not merely formal: mode-dependent functionals, gradients, and gradient flows may exhibit behavior that differs essentially from their classical counterparts. In particular, different mode classes may induce different minimizers, different gradients, and different asymptotic dynamics. -/- The mode differential is further interpreted as a restriction of the classical differential to admissible tangent cones, providing a geometric link between mode-based and classical analysis. -/- The results suggest a shift from fixed analytical structures to families of structures determined by operational stability, offering a unified framework connecting analysis, geometry, and dynamics. (shrink)

Human cognition operates under severe resource limitations while simultaneously managing subjective phenomenological states such as thermal discomfort, tactical pressure, or cognitive overload. Here we introduce **Lagrangian Processing**, a normative framework that treats the mind as a resource-rational optimizer solving constrained variational problems in which inequality constraints encode phenomenological boundaries. By applying Lagrange multipliers (and their Karush–Kuhn–Tucker generalization) to multi-dimensional cognitive variables, the model yields explicit shadow prices (λ) that quantify the phenomenal “cost” or “pressure” imposed by each binding constraint. We (...) demonstrate the framework in two domains: heat tolerance under physiological stress and line memorization plus tactical calculation in chess. (shrink)

This paper fixes non-variation within a non-modal structural system. -/- Non-variation is fixed. Variation is not introduced and not constituted. Change is not introduced and not constituted. -/- No variation of difference is introduced. -/- Non-variation is fixed as non-constitution of variation. -/- No modality is introduced. No possibility or necessity is introduced. -/- This paper does not establish what it operates on. It is not accessible from within this text.

Under the Internal Invisibility Principle (IIP), the retained law does not read the unread sector pointwise. It reads only the licensed summary F = ΣH,P (unread content). Part VI takes this summary entry as given and asks the dual question to Part V: what closed-summary response operator is produced when the retained/open variation is eliminated from the same two-sector Hessian generated by the fixed core density? The active closed-side variable of this Part is not the raw unread coordinate II (...) . It is the licensed summary variation around a declared background summary F ⋆ , v = δF ∈ S⋆ F , S ⋆ F := TF ⋆ Ran ΣH,P . When the summary representative is linear, we suppress the star and write SF = Ran ΣH,P ; in the first-order representative F = DI II , this becomes SF = Ran(DI ). Starting from e (P) core = β 2 ∥DRIR∥ 2 P + α 2 ∥F∥ 2 P + η⟨IR, F⟩P , F = ΣH,P (unread content), written as a functional E g⋆ VI[IR, F] of the retained-summary pair (IR, F), we linearize around an upstream-selected background representative (g⋆, I⋆ R, F⋆ ). The resulting quadratic form in open/closed-summary variations (u, v) is Schur-reduced by eliminating the open variation u, giving Lcl,eff = C − B ∗A −1B. In the canonical Laplace-type representative, Lcl,eff = αI − η 2PRan(βD∗ RDR + M⋆ R) −1PRan. Thus the unread/closed-summary channel is not inserted as an arbitrary dark component; it receives a calculable resolvent-shaped response produced by the same variational core. Source-like, background-like, DM-like, and DE-like language appears only after additional downstream readout gates are declared. Before such gates, the generic output of Part VI is one mixed closed-summary response operator. The source/background split is a readout decomposition of this operator, not an ontological splitting into independent fluids, and Part VI does not claim a completed dark-sector phenomenology, a unique halo profile, or a unique equation of state. (shrink)

Darwin's ideas on variation, heredity, and development differ significantly from twentieth-century views. First, Darwin held that environmental changes, acting either on the reproductive organs or the body, were necessary to generate variation. Second, heredity was a developmental, not a transmissional, process; variation was a change in the developmental process of change. An analysis of Darwin's elaboration and modification of these two positions from his early notebooks (1836-1844) to the last edition of the /Variation of Animals and (...) Plants Under Domestication/ (1875) complements previous Darwin scholarship on these issues. Included in this analysis is a description of the way Darwin employed the distinction between transmission and development, as well as the conceptual relationship he saw between heredity and variation. This paper is part of a larger project comparing commitments regarding variation during the latter half of the nineteenth century. (shrink)

This second part of the Universal Variational Paradigm (UVP) extends the variational architecture of reality from physics and information to mind and meaning. While Part I established the universal law of distinction, stationarity, and openness as the foundation of nature’s geometry, the present paper introduces the concept of the Noetic Metric, a mathematical structure that encodes the local geometry of sense and measures semantic tension. Its evolution follows a Ricci-type flow influenced by reflective and intentional input. -/- The Noetic Geometry (...) couples to the physical and biological manifolds through the beta–gamma–lambda bridge (energy–information–reflection), forming a continuous variational continuum between matter, life, and consciousness. Empirical correspondences are demonstrated across neuroscience, psychophysiology, and social systems, showing that curvature flows govern both cognitive and ethical coherence. -/- Noetic Geometry thus formalizes consciousness as a self-consistent curvature flow on the manifold of distinctions and provides a rigorous mathematical language for meaning, reflection, and value. (shrink)

VBRC treats mass-like gaps as summary-interface footprints rather than primitive coefficients. Part V computes the Schur-reduced retained operator generated by the fixed core density e (P) core = β 2 ∥DRIR∥ 2 P + α 2 ∥F∥ 2 P + η⟨IR, F⟩P , F = ΣV (unread content). The calculation is performed on the retained-effective variables (IR, F); the unread coordinate II appears only through the representative pullback F = D (V ) I II . At an R2-selected effective background (...) q ⋆ eff = (g, I⋆ R, F⋆ ), the quadratic expansion and Schur elimination of v ∈ SV := TF ⋆ Ran(ΣV ) give Leff(q ⋆ ) = βD∗ RDR + V ′′ ⋆ − η 2 α PSV . In the first-order representative, PSV = PRan(DI ) . The Schur term is an order-0, projectorvalued spectral footprint, not itself a positive scalar mass coefficient. The mass/gap datum is m2 gap(q ⋆ ) = λ + min Leff(q ⋆ ) Hphys R  . R3 provides only the dispersion check c −2 ∂ 2 t u + Leffu = 0, ω2 j = c 2λj . Thus Part V is a calculation of a summary-mediated spectral gap, not a theory of primitive mass insertion or a unique hidden-sector ontology. (shrink)

People speak in different ways within and across contexts; and utterances that are equivalent in their essential content and force can differ in their social significance in virtue of differing phonologically, morphologically, syntactically, and lexically. These dimensions of linguistic variation have not received sustained philosophical attention. We argue that meaningful form contributes significantly to the speech acts that agents perform with their utterances. Speakers communicate social information by navigating fine-grained differences in how they speak, and hearers systematically pick up (...) on and use this information. Moreover, these fine-grained differences performatively alter the conversational context. We review three options for handling these aspects of speech within the philosophy of language—exclusionism, informationalism, and performativism—and sketch prospects and challenges for a theory of sociolinguistic variation going forward. (shrink)

Part XVI studies the mixed gate: the readout regime in which a retained law inherited through the Part XV reduced representative is propagated conservatively while the background against which it propagates is itself still being formed by dissipation. The central correction made explicit here is structural. Conservation (R3) and dissipation (R2) are not two readings simultaneously leading on one and the same retained mode; they occupy different layers. Dissipation is the compression of unread content into the licensed summary F = (...) ΣH,P (unread content), represented as F = DI II only after a first-order carrier has been declared, and this compression forms and evolves the background. Conservation acts on the retained sector IR on top of that already-summarized background. The mixed gate is therefore not a fourth primitive evolution law: it is the regime in which the background is not yet frozen, so the conservative retained propagation acquires an apparent friction. By the Internal Invisibility Principle, unread content does not enter the retained equation as raw data. It enters only through the licensed summary channel F = DI II , here carried by a summary-response kernel RΣ (not a hidden physical field). The decisive consequence is that the friction is derived, not primitive: the retained mixed equation closes as MR∂ 2 t u + h MR µ˙ µ + η 2DR1D∗ i | {z } ΓR ∂tu + -/- LR − η 2DR0D∗
| {z } Leff u = 0, where R0 = R RΣ(s) ds and R1 = R s RΣ(s) ds are the zeroth and first moments of the summary response, and µ(t) is the (possibly time-dependent) background measure produced by the dissipative layer. The friction is thus the additive footprint of a non-frozen R2 background: a kinematic part ΓB = MRµ/µ ˙ from an evolving background measure, and a dynamical part ΓA = η 2DR1D∗ from a finite summary-response lag. The restoring operator Leff = LR − η 2DR0D∗ and the finite-lag friction ΓA = η 2DR1D∗ are two moments of the same licensed summary response: the zeroth moment R0 gives the restoring Schur footprint, the first moment R1 the dynamical memory friction. The kinematic part ΓB = MRµ/µ ˙ has a different origin — the footprint of an evolving background measure — so the friction is additive, ΓR = ΓA + ΓB, but only ΓA is the first-moment partner of the restoring footprint. The operator Leff is thus the zeroth-moment mixed representative of the common reduced Schur operator of Part XV; in the quasistatic/static-resolvent limit R0 → L −1 I it reduces to LR − η 2DL−1 I D∗ = Seff, so Part XVI introduces no new restoring operator, only the non-frozen, time-completed reading of the same Schur reduction. Given the declared summary-response kernel and background measure, none of these terms is an independently fitted retained damping parameter. The principal retained readouts are the modewise dispersion MRω 2 + iΓRω − Ω 2 eff(k) = 0, Ω 2 eff(k) = β|k| 2 + m2 eff − η 2σΣ(k), and the mixed discriminant ∆mix(k) = 4MR Ω 2 eff(k) − Γ 2 R, which classifies underdamped, critical, overdamped, and unstable windows within one retained equation. The associated energy law d dtEmix(t) = −⟨∂tu, ΓR∂tu⟩ holds as a strict monotone law on frozen-coefficient branches (time-independent Leff, ΓR); on a genuinely time-dependent background it carries the extra term + 1 2 ⟨u,L˙ effu⟩ and is a ledger-transfer law rather than a strict Lyapunov law. In either case it is read not as a primitive sink loss but as a ledger migration: retained energy is transferred either into the summary fiber (finite-lag layer) or to the evolving background (background-measure layer, as in redshift), the conservative content of IR being preserved upstream of the compression. Two limits of the same equation realize two historically separate phenomena: a static background with a finite-lag kernel (ΓR = η 2DR1D∗ ) gives Caldeira–Leggett / Mori–Zwanzig damping, decoherence onset, and near-horizon irreversible readout; an evolving background with an instantaneous kernel (ΓR = MRµ/µ ˙ , i.e. damping rate µ/µ ˙ = 3H in FRW) gives cosmological redshift / Hubble friction. The principal contribution of this Part is therefore not a new formula but the identification of the mixed gate as conservative R3 propagation on a nonfrozen R2 background, with ΓR a derived additive footprint and ∆mix(k) its licensed classifier. The VBRC-internal origin of the background evolution µ(t) (cosmic expansion as an R2 background flow) and non-Markovian higher-moment corrections are flagged as open. (shrink)

VBRC treats the upper gate (Planck-label) as a gate-scoped R3 time completion of the protocol-licensed summary-side quotient, not as a direct opening of raw unread interior data and not as a numerical claim about physical Planck-scale ontology. Under the Internal Invisibility Principle of Part I, raw II never enters retained laws; what the upper gate declares is an independent conservative completion of the summary FXVII = ΣHXVII,PXVII (unread content) = DXVIIII , equivalently of its summary-side quotient QXVII I = C (...) (PXVII) I / ker DXVII, in parallel with the R3 completion of IR already permitted by Part I. Quartic dispersion, branch splitting, and critical thresholds are readouts of that licensed quotient-level completion at the retained-effective level, not of a directly observable hidden sector. This Part studies an upper-gate/UV opening—called here the upper gate (Planck-label)— within the atlas fixed in Part XV. It should be read not as a literal numerical claim about the physical Planck scale, and not as a new structural law-space, but as the gate-scoped reading in which the conservative R3 completion is applied simultaneously to the retained channel IR and to a representative of the summary-side quotient QXVII I inherited from Part I, so that the licensed summary is read on a fully time-completed window rather than a quasistatic one (as in Part XV) or a memory-frequency-dependent one (as in Part XVI). The central point is not a small correction to a single low-energy branch, and not an ontological access to a hidden sector, but an exact retained-effective closure on the inherited branch that yields quartic dispersion, genuine branch splitting, and a threshold instability of the licensed summary-quotient completion. The representative-branch conventions, the licensed summary-instance discipline, the admissible backbone class EXV, and the common reduced Schur operator Seff are inherited from Part XV and are not restated here in full. Starting from a minimal coupled action built on the inherited branch, we derive the exact representative-level coupled equations of motion and eliminate the time-completed summaryquotient representative to obtain a nonlocal effective retained-channel closure. The resulting effective restoring operator is the same common reduced Schur operator Seff of Part XV, evaluated on the upper-gate-completed unread-side window LII → □α = ∂ 2 t + αD∗D; the present Part attaches second-order time evolution to IR and to a gauge-fixed representative of the summary-side quotient QXVII I simultaneously, and reads the result. Plane-wave analysis yields the quartic dispersion relation ω 4 − (α + β)|k| 2ω 2 + αβ|k| 4 − η 2 |k| 2 = 0, with branch splitting and the critical wave number kc = η √ αβ . These are the central upper-gate outputs of the paper. Unlike representative Hořava-type linearized tensor-mode comparisons, where higher-spatial-derivative corrections are often read as deformations of a single propagating branch, the present quartic law is derived from the upper-gate summary-quotient two-channel opening (R3 simultaneously on IR and on a gauge-fixed representative of QXVII I ) and yields a genuine two-branch spectral structure. At the mode level, the instability is equivalently the loss of positive definiteness of the representative-level coupled stiffness matrix on the nonzero window 0 < |k| < kc, and the lower branch selects a unique fastest-growing scale |k| 2 max = η 2 √ αβ ( √ α + √ β) 2 . Within the present symbolic linearized analysis, the lower-branch instability is interpreted as the signal that the licensed summary-quotient completion cannot persist as the stable readable low-energy regime and must reorganize toward a reduced phase in which the summary is again read on a quasistatic window. The threshold η 2 − αβ|k| 2 continues, one gate higher, the same threshold grammar that organized Part XV’s low-energy threshold ∆c and Part XVI’s mixed discriminant ∆mix. In the post-instability frozen/static exact-channel reduction considered below, the upper gate fixes the magnitude of the exact-channel Schur residue m2 res := η 2 α , so that, in general, kc η = m2 resrα β , which simplifies to kc η = m2 res only at the symmetric point α = β. The quantity m2 res = η 2/α is not a universal mass term; it is a channel-selective retained residue, restricted to the exact channel and absent on the coexact and harmonic channels. The sign at which η 2/α enters the direct linear frozen calculation is the negative shift − η 2/α on the exact channel, which is itself a linearized Schur signature of the lower-branch instability; its positive mass/gap interpretation belongs to the stable reduced branch selected after the gate-handoff mechanism. Mass is therefore not the primary content of the gate but the residue of the reduced stable phase reached through gate handoff. The passage from instability to reduced stability is conditional on a supercritical saturation scenario and on a frozen-handoff condition; the linear analysis alone establishes the instability of the upper-gate completion of the summary-side quotient, while the stable reduced phase is the admissible post-instability reading considered here. (shrink)

According to the traditional Bayesian view of credence, its structure is that of precise probability, its objects are descriptive propositions about the empirical world, and its dynamics are given by conditionalization. Each of the three essays that make up this thesis deals with a different variation on this traditional picture. The first variation replaces precise probability with sets of probabilities. The resulting imprecise Bayesianism is sometimes motivated on the grounds that our beliefs should not be more precise than (...) the evidence calls for. One known problem for this evidentially motivated imprecise view is that in certain cases, our imprecise credence in a particular proposition will remain the same no matter how much evidence we receive. In the first essay I argue that the problem is much more general than has been appreciated so far, and that it’s difficult to avoid without compromising the initial evidentialist motivation. The second variation replaces descriptive claims with moral claims as the objects of credence. I consider three standard arguments for probabilism with respect to descriptive uncertainty—representation theorem arguments, Dutch book arguments, and accuracy arguments—in order to examine whether such arguments can also be used to establish probabilism with respect to moral uncertainty. In the second essay, I argue that by and large they can, with some caveats. First, I don’t examine whether these arguments can be given sound non-cognitivist readings, and any conclusions therefore only hold conditional on cognitivism. Second, decision-theoretic representation theorems are found to be less convincing in the moral case, because there they implausibly commit us to thinking that intertheoretic comparisons of value are always possible. Third and finally, certain considerations may lead one to think that imprecise probabilism provides a more plausible model of moral epistemology. The third variation considers whether, in addition to conditionalization, agents may also change their minds by becoming aware of propositions they had not previously entertained, and therefore not previously assigned any probability. More specifically, I argue that if we wish to make room for reflective equilibrium in a probabilistic moral epistemology, we must allow for awareness growth. In the third essay, I sketch the outline of such a Bayesian account of reflective equilibrium. Given that this account gives a central place to awareness growth, and that the rationality constraints on belief change by awareness growth are much weaker than those on belief change by conditionalization, it follows that the rationality constraints on the credences of agents who are seeking reflective equilibrium are correspondingly weaker. (shrink)

This work develops the mathematical foundations of a quartic variational framework in which no geometric, dynamical, or ontological structures are assumed a priori. The only primitive object is a real quartic functional defined over a measurable domain, with the configuration space minimally determined by the polynomial order of the integrand. Through a complete structural analysis, we show that admissible field configurations arise exclusively as stationary points of the functional, which acts as a global admissibility operator. A systematic construction of the (...) space of quartic invariants is provided, proving that the class of allowed integrands is finite-dimensional and that the functional used here occupies a distinguished position in this class. The linearized dynamics around stationary configurations is shown to induce an emergent second-order evolution equation derived from the Hessian of the functional. Finally, a decisional operator is introduced to resolve residual degeneracy inside the admissible set, completing the structural programme. The resulting framework is proved to be unique, universal, and necessary under minimal assumptions. (shrink)

The purpose of this paper is to contribute to the ongoing analyses that aim to confront the problem of marked variation. Negatively marked differences are those natural variations that are used to cleave human beings into different categories (e.g., of disablement, of medicalized pathology, of subnormalcy, or of deviance). The problem of marked variation is: Why are some rather than other variations marked as epistemically or culturally significant or as a diagnostic of pathology, and What is the epistemic (...) background that makes these—rather than other variations—marked as subnormal? For Wilson (2018a), critical examination of the problem of marked variation is central to understanding the epistemology of medicalized pathology that made the history of eugenics possible. My aim is to explore the role marked variation plays in eugenic and other problematic classifications and the inferences they appear to license. I pay particular attention to the normative valuations of marked variations, how these valuations affect the inferences that are made by others about those possessing the variation, and how those possessing the variation perceive themselves. In the final sections, I illustrate this by critically discussing three putative kinship conceptions of race. I rely on these to extend the scope of the puzzle of marked variation from the context of historic and current markings of an individual’s variation as disability in the eugenics movement to historic and current markings for assigning putative racial ascriptions to individuals and groups. Lastly, I suggest that the problem of marked variation is a problem that looms over any epistemic account that is dependent upon sorting or classifying. (shrink)

VBRC treats Part IV as the observability layer of an already licensed retained summary, not as a new footprint-generation layer. Under the Internal Invisibility Principle, unread content is never exported as raw data; Part IV studies the pushforward, disintegration, event, entropy, and record structures by which an already licensed retained summary becomes observable. Part I fixes the constitutional framework under the Internal Invisibility Principle (IIP): unread interior content does not enter observable physics as pointwise data, but only through a declared (...) hidden-to-retained summary channel F = ΣH,P (unread content), realized in the scoped operator class as F = DI II . Parts II–III then generate admissible laws under that fixed backbone and its declared readings. The present Part IV does not produce new laws. It studies how those already generated retained laws become observable, namely how a declared observation protocol reads, weights, updates, and records the retained summary channel. The minimal protocol is Inst0 = (Π, µ), refined as a representation protocol P δ = (Πδ obs, µδ ,U δ ). The central result is a deterministic-vs-probabilistic dichotomy: if the retained deterministic update T : X → X factors through the readout, the observed update is deterministic; if it does not, then on a positive-measure set of readouts the conditional law of the next output is non-Dirac, equivalently assigning positive kernel weight to at least two disjoint measurable output sets. Probability is therefore forced by the disintegration of µ along Π, rather than added as an independent axiom; it is the protocol-level form of partial observation under IIP. From pushforward and disintegration, the following protocol outputs are obtained at the Representation Layer: (i) probability as the pushforward ν = Π#µ; (ii) observational entropy as fiber weight, S δ obs(y) = kB log Wδ(y), with the point-fiber form kB log µ(Π−1 (y)) used only in finite or atomic instances; and (iii) update and event as conditionalization/disintegration along a declared gate, with record-entropy monotonicity for accumulated records recovered via the Shannon chain rule, while DPI is used only for post-processing/garbling comparisons. Observational equivalence x ∼Π x ′ ⇔ Π(x) = Π(x ′ ) defines the operational quotient Xδ phys = X/∼Π; any fiber-preserving Φ with Π◦Φ = Π acts as a channel-specific operational symmetry. Concrete sector statements are recorded only as later implementations of the same observation-fiber/protocol structure, not as core derivations of Part IV. Part IV therefore stops at the general protocol calculus: pushforward probability, fiber-weight entropy, conditional update, event structure, record accumulation, and operational quotient/gauge. The fixed comparison language, the background-parametrized core density, and the readings R1–R3 are inherited from the law-generation papers; no metric or geometric background is varied in this Part. (shrink)

Part I formulates a variational interface for physical laws under protocol-limited readout. The variational backbone E is treated as a comparison language on configuration space: differences, gradients, and orderings of E carry the operative content, whereas the absolute level of E does not. The word “fixed,” applied to E throughout the series, therefore means that the same comparison rule is used across stationarity, gradient operation, and time-completion readings; it does not mean that the numerical value of E is conserved. An (...) admissible readout protocol is partial, situated, and selective; finite readout is treated separately under the finite-capacity status (FC/RF), not as a consequence of the IIP alone. This partiality is encoded by the Internal Invisibility Principle (IIP): a protocol-bound readout induces a retained/unread split, and the unread complement may affect the retained law only through protocol-licensed summaries, never as raw data. The IIP-operational primitive is the licensed summary rule F = ΣH,P (unread content). Within the declared first-derivative two-sector local representative scope adopted in Part I, this summary rule is realized by a first-order carrier as F = DI II , and the minimal retained/unread interface is the bilinear pairing ⟨IR, F⟩. Unread components in ker DI carry no retained comparison content and are treated as quotient/gauge data. The results established here are structural: quotient descent under summary-only unread dependence, principal-class invariance under admissible equivalence moves, and compatibility of the three readings R1/R2/R3 of one fixed comparison structure. Realization and closure claims are deferred to later Parts under their declared protocol instances and validity gates. (shrink)

The Principle of Maximal Freedom (PMF) has served as the central dynamical orientation of Temporal Rate Ontology (TRO), directing DAG continuation growth toward configurations of higher continuation multiplicity. In its existing formulation, however, PMF functions as a meta-principle rather than a precise variational law: it orders admissible extensions but does not specify what quantity is extremized, over what trajectory class, or under what constraints. This paper upgrades PMF to a genuine variational principle. We introduce a finite-horizon constrained structural freedom functional, (...) in which continuation multiplicity gain is balanced against a synchronization cost penalizing temporal-rate disparity across the active frontier. The probabilistic selection rule defines an exponential family distribution over admissible extensions, with continuation multiplicity and synchronization cost as sufficient statistics. The result is a falsifiable dynamical law with three explicit parameters: foresight depth H, synchronization strength gamma, and selection sharpness beta. We derive three nontrivial observables: a frontier segregation effect with an explicit Boltzmann-Gibbs selection ratio, a characteristic interface width between regions of differing temporal rate (qualitative prediction, with quantitative scaling deferred to the local-gradient refinement), and a three-regime relaxation law for localized frontier perturbations. A simulation design protocol is provided, specifying DAG generator, lambda initialization, and measurement of all three observables, making the paper directly reproducible. We identify the global-variance cost as the tractable first formulation and the local-gradient form as the target of a subsequent paper. (shrink)

Part II computes the R1 and R2 laws generated by applying the Part I readings to the core density e (P) core = β 2 ∥DRIR∥ 2 P + α 2 ∥F∥ 2 P + η ⟨IR, F⟩P , F = ΣH,P (unread content), α, β > 0. Following the constitutional setting of Part I, the primary variables are (IR, F) on the retained-effective state space C (H,P) eff = C (P) R × Ran ΣH,P ; the first-order expression F (...) = DI II is a representative pullback, and equations involving II are representative lifts of the effective laws, not primary dynamics of an unread interior. The norms in e (P) core use the protocol pairing ⟨·, ·⟩P ; a metric/L 2 representative realizes them as | · |g integrated against dvolg, and F = DI II holds only after the representative carrier is declared. The primary R1 output is the effective stationarity system β D∗ RDRIR + η F = 0, Z M ⟨αF + ηIR, δF⟩ dvol = 0 ∀ δF ∈ TF Ran Σ. When the summary range is the full retained section space, the constrained condition reduces to the algebraic relation αF + ηIR = 0; Schur elimination then gives the retained law βD∗ RDRIR − (η 2/α)IR = 0. In the first-order representative F = DI II , the constrained condition becomes D∗ I (αF + ηIR) = 0, and a closed-range projector PI = DI (D∗ IDI ) −1D∗ I yields the projected Schur form βD∗ RDRIR − (η 2/α)PI IR = 0. The primary R2 output is the unread-summary compression flow, not a physical damping law for the retained sector. The summary map unread content 7→ F = ΣH,P (unread content) is many-to-one and erases representative-dependent unread information; only the licensed summary F survives in the retained law. In compression time τ the retained variable IR is held fixed as the readable source against which the unread summary relaxes: ∂τ IR = 0, ∂τF = −MF (α F + η IR), where MF is the declared positive summary mobility on Ran Σ (in the first-order representative MF = DID∗ I ). This flow settles F to F∗ with MF (αF∗ + ηIR) = 0; substituting F∗ into the retained R1 equation βD∗ RDRIR + ηF∗ = 0 reproduces the Schur law without ever damping IR. The conditional functional Ecomp[F | IR] = R M( α 2 |F| 2 + η⟨IR, F⟩) dvol has F-Hessian α Id ≻ 0, so it is bounded below and decreases monotonically along the flow; a settled background is therefore a compression-residue readout, not primitive data of ecore. A full (IR, F)-gradient flow may still be written as an auxiliary variational relaxation, but it is 1 not the primary physical reading; the conservative physical-time reading of IR belongs to R3 and is closed in Part III. The unread side enters the retained law through summary-footprint channels: the licensed summary F, the constrained summary-side condition, and the Schur-effective operator (algebraic −η 2/α in the range-saturated regime, or projected −(η 2/α)PI in the first-order representative when the range is a proper subspace). Metric, Einstein–Hilbert, and Ricci-type structures are not new law-spaces opened by gates; they are restricted branch-readouts of this already generated R1/R2 law-space. The metric branch is treated only as a restricted readout: with DI = ∂/g and a representative witness ψ0 for the settled summary F∗ = ∂/gψ0, the term α 2 |F| 2 carries the Lichnerowicz footprint R|ψ0| 2 , which becomes an EH term only under constant-density locking |ψ0| 2 = ρ0; the metric is thereby a derived readout of the compressed summary, not external data, with induced coupling γ = αρ0/4 an output rather than an input. (shrink)

VBRC treats Schur duality as an invariant test of the same summary interface. Under the Internal Invisibility Principle (IIP), neither elimination route is a new ontology; both are admissible Schur reductions of one retained-effective block Hessian built on the Part I state space, and Part VII identifies which determinants, indices, criticalities, and stability diagnostics survive the change of route. Part VII asks what remains invariant when both Schur elimination routes are allowed for the same two-sector structure generated from the fixed (...) core density e (P) core(IR, F) = β 2 ∥DRIR∥ 2 P + α 2 ∥F∥ 2 P + η⟨ΓIR, F⟩P , F = ΣH,P (unread content), where the structurally fixed datum is the licensed summary-entry grammar F = ΣH,P (unread content), with F = DI II a declared first-order representative realization, and Γ is a declared representative-level typed interface with fixed normalization. The block Hessian is taken on the retained-effective tangent variables u = δIR, v = δF ∈ TF Ran ΣH,P , rather than on raw unread variations δII . Stationary linearization gives H =  A B∗ B C  . Elimination of the summary coordinate v gives the retained-side Schur operator Sop(H) = A − B∗C −1B, while elimination of the retained coordinate u gives the summary-side dualSchur operator Scl(H) = C − BA−1B∗ . These reduced operators need not coincide and need not act on the same space. Thus the two Schur routes compare reductions of one retained-effective Hessian, not two ontologies of the unread side. The structural claim is narrower. The retained-side route preserves the retained Laplace principal class, while the dual route imports the corresponding A−1 -controlled |k| −2 response kernel into the summary-side readout. The shared global spectral package consists of criticality and determinant/index data: 0 ∈ spec(Sop(H)) ⇐⇒ 0 ∈ spec(Scl(H)) ⇐⇒ 0 ∈ spec(H), and, on a noncritical branch or in a declared relative/regularized convention, LogDet(H) = LogDet(C) + LogDet(Sop(H)) = LogDet(A) + LogDet(Scl(H)), together with the Schur inertia/index identity. The quantity κ = η/√ αβ is treated separately as a dimensionless classification ratio of the normalized two-sector quadratic representative, not as a new primitive coupling. Thus the Part V retained-side mass/gap diagnostic and the Part VI summary-side response diagnostic are two Schur reductions of the same ecore-induced retained-effective block-Hessian geometry, not independent constructions. (shrink)

VBRC treats conservative time-completed dynamics as a retained-law interface rather than as a primitive textbook equation. Under the Internal Invisibility Principle, the unread sector cannot be assigned direct retained status; in this Part it contributes to R3 only through the licensed summary footprint F = ΣH,P (unread content) (represented in the Part III first-order branch by F = DI II ), producing a standard-like retained law with a licensed unread-summary entry. This paper computes the R3 retained law generated directly by (...) the Part I core density e (P) core = β 2 ∥DRIR∥ 2 P + α 2 ∥F∥ 2 P + η ⟨IR, F⟩P , F = ΣH,P (unread content). In the Part III first-order representative, F = DI II . R3 time-completion is imposed only on the retained variable IR; the unread variable II is not assigned an independent kinetic term. The retained first variation is δEcore δIR = βD∗ RDRIR + ηF, and the resulting R3 Euler–Lagrange law is a ∂2 t IR + βD∗ RDRIR + ηF = 0. Thus the unread sector affects the retained R3 law only through the licensed summary F; conservation is a further regime statement depending on the chosen F-gate. The generic VBRC retained law is therefore not a textbook equation: it is a standard-like retained backbone together with a licensed unread-summary footprint. This footprint is the structural signature of the Internal Invisibility Principle (IIP) inside the retained law, not an error term added after the fact. The summary channel is then treated by explicit F-gates. Two core-admissible summarychannel treatments are used in Part III. Under (GF 1), F = FP (t, x) is a protocol-given load. Under (GF 2), instantaneous summary-stationarity gives F = − η α PF IR, PF = PRan(DI ) , so that the retained law becomes a ∂2 t IR + βD∗ RDRIR − η 2 α PF IR = 0. Unread-side time-completion with an independent term ν 2 ∥∂tII ∥ 2 is recorded only as the non-core extension gate (GF 3). The Klein–Gordon, Schrödinger, and Hamilton–Jacobi equations are not starting points of this Part and are not the generic output of the retained R3 calculation. They are downstream, gate-restricted readouts obtained only after the licensed summary footprint is represented, localized, stabilized, or re-expressed as effective lower-order data; only in special degenerate branches does the footprint vanish. Thus the footprint remains part of the R3-generated law-space rather than being erased to recover a textbook equation. The R2/R3 hierarchy is fixed: R2 selects or stabilizes the background representative, while Part III studies R3 retained oscillations on that selected M0/R2-frozen branch. (shrink)

Part X formulates metric gravity as a metric-language readout of the effective Hessian generated by the Part I VBRC core density. The starting datum is not a primitive Lorentzian manifold (M, g), not a metric background placed underneath the theory, and not a functional whose first input is an independent gravitational field. The starting datum is the retainedeffective pair qeff = (IR, FX), FX = ΣX(unread content) ∈ Ran ΣX, together with the Part I core comparison density, written before metric (...) language as ecore = β 2 QR(IR) + α 2 BF (FX, FX) + η Bint(IR, FX). The objects QR,BF ,Bint are effective comparison data, not yet contractions or differential operators supplied by a pre-given metric. In a first-order retained representative one may later realize QR by BR(D (X) R IR, D(X) R IR), but D (X) R is not ∇gX until the metric-readout gate has produced gX. The R2 reading selects, when the relevant stability gate holds, an effective background q ⋆ eff = (I ⋆ R, F⋆ X). The effective Hessian H⋆ X = D2Ecore(q ⋆ eff) then carries the principal-symbol and cone data from which the Part X metric representative is read: [gX] = Rmet σprin(H⋆ X)
. Only after this metric-readout gate has been passed do expressions such as dvolgX , ∇gX , ∂/gX , R(gX), and Gµν(gX) become available. Thus geometry is not the primitive stage on which ecore is written; it is the readable representative extracted from the stabilized comparison structure generated by ecore. After the metric representative is licensed, the same core-generated structure is first displayed in metric language on the retained-effective pair by Emet X [gX, IR, FX], with FX ∈ Ran ΣX. Only after a Lichnerowicz representative has been declared may one choose representative data ψ0 in a summary fiber and write FX = D (X) I ψ0 = ∂/gX ψ0. The residual equation KX µν = 0 is therefore not a primitive variation of a pre-existing metric object. It is the metric-representative form of the core-generated stationarity/readout. The Lichnerowicz, retained-Schur, and summary-side dual-Schur constructions are then treated as readout views of the same Hessian, not as independent source sectors; the legacy label VclSch denotes this summary-side dual-Schur readout, not a physical closed sector. Under the locked density subcase |ψ0| 2 = ρ0, the Lichnerowicz readout yields the Einstein– Hilbert principal display with induced coefficient γE = αρ0/4. The Einstein-form expression γE Gµν(gX) = T eff,(v) µν + R E,(v) µν is a GR-locked comparison display of the metric representative, not the starting law of the Part. The paper therefore makes no claim that VBRC begins with a metric background, no claim that an Einstein equation is inserted as an independent axiom, and no claim that unread-sector content appears as raw matter. Unread content affects the metric display only through protocol-licensed summaries and their derived Lichnerowicz/Schur/readout footprints. (shrink)

Frege famously claimed that variations in the sense of a proper name can sometimes be ‘tolerated’. In this paper, we offer a novel explanation of this puzzling claim. Frege, we argue, follows Trendelenburg in holding that we think in language—sometimes individually and sometimes together. Variations in sense can be tolerated in just those cases where we are using language to coordinate our actions but are not engaged in thinking together about an issue.

This work addresses the question of physical existence at a logically prior level to dynamics, spacetime structure, and empirical modeling. Physical existence is not assumed as a primitive notion, nor identified with empirical detectability, but is derived from a variational criterion of admissibility. A configuration is said to exist physically if and only if it corresponds to a stable stationary solution of a closed variational functional. -/- Within this framework, existence is identified with variational stability rather than with causal efficacy, (...) observation, or phenomenological persistence. The analysis establishes a strict separation between mathematical possibility, physical admissibility, and empirical manifestation. Physical entities, laws, and scales do not pre-exist the variational criterion; they emerge exclusively as invariants of admissible stationary configurations selected by variational closure. -/- The resulting picture inverts the standard epistemic hierarchy of physics. Dynamics, interactions, and measurement presuppose existence and cannot define it. Experiments do not determine what exists, but operate within the space of configurations already admitted by the variational criterion. Apparent experimental contradictions therefore signal a mismatch between experimental interpretation and admissible structure, not a failure of the underlying framework. -/- The variational origin of existence presented here yields a non-arbitrary, self-consistent criterion that eliminates the need for phenomenological patches, external ontological assumptions, or ad hoc selection principles. Physical reality is identified with the set of variationally stable configurations, while non-admissible configurations are excluded by construction. In this sense, the framework provides a foundational account of physical existence as a consequence of stability, rather than as a postulate of theory or observation. (shrink)

VBRC treats time as a synchronization/readout interface rather than a primitive universally readable variable. Under the Internal Invisibility Principle, unread content supplies no transparent clock, and no inverse summary map, to the retained law. The IIP is therefore not used here as a direct generator of time or of the arrow of time; its role is a no-reversal obstruction: a retained-level reversal that requires reconstructing the raw unread sector from a summary is not licensed unless an additional recovery gate is (...) declared. Part VIII therefore studies a time-readout instance declared on the principal cone of an R3 retained law generated from the fixed core comparison density. The Part I inheritance used here is the licensed-summary discipline, not a universal first-order operator: F8 = Σ8(unread content), Σ8 := ΣH8,P8 . When the first-order Laplace-principal representative is activated, F8 = D (8) I I (8) I , but D (8) I is representative data of the declared Part VIII instance, not a structural primitive. By the retained-direction computation and R3 completion imported from Part III, the background-evaluated retained law has the schematic form aB∂ 2 t IR + β(DB R ) ∗DB R IR + ηFB = 0, FB = ΣB 8 (I (8) I ). Under the single-cone Laplace-principal gate, FB is a lower-order or non-principal footprint, so the primary characteristic cone is read from PB(ω, ξ) = aBω 2 − β|ξ| 2 B. Thus Part VIII takes as input the R2-selected background BR2 and the Part III R3 retained law, reads the principal cone of that law, and declares the time readout Πtime on the resulting cone. SR/QM/HJ time formulas are recorded only as compatibility readouts of this declared synchronization instance. (shrink)

The basis of perception is the processing and categorization of perceptual stimuli from the environment. Much progress has been made in the science of perceptual categorization. Yet there is still no consensus on how the brain generates sensory individuals, from sensory input and perceptual categories in memory. This chapter argues that perceptual categorization is highly variable across perceivers due to their use of different perceptual strategies for solving perceptual problems they encounter, and that the perceptual system structurally adjusts to the (...) strategies that are most successful. Despite this variability, the different sensory individuals that result when different perceivers rely on different strategies nonetheless correspond to actual external world objects/features. This view is called 'perceptual pluralism'. (shrink)

The block universe interpretation of relativity secures the ontological equality of past, present, and future, yet it remains structurally silent regarding the modal topology of spacetime. Three options have dominated the literature: the pure block universe, which suppresses modal structure entirely; branching approaches, which multiply realized histories; and modal realism, which posits a plurality of wholly distinct possible worlds. This paper proposes a fourth option: Arborescent Eternalism. Spacetime is modeled as the base manifold of a smooth fiber bundle whose fibers (...) encode the space of locally admissible field configurations at each event — the geometry of global compatibility rather than a multiplicity of worlds. Possibilities are not real elsewhere; they are configurations that fail to achieve global coherence. The realized history is not selected by branching or random draw: it is the unique stationary solution of a global variational functional J defined over the space of admissible sections. The fiber bundle structure is shown to be a structural necessity for three independent reasons, including the precise identification of the fibers with the local solution spaces of the governing field equations — a standard object in the geometric theory of differential equations. The canonical decomposition of J follows from three physically mandatory constraints. The modal domain is shown to be indispensable in a sense that differs in kind from abstract mathematical entities: it is physically indexed to spacetime events, dynamically constrained by the governing field equations, and constitutive of the variational principles themselves. Arborescent Eternalism offers a structural completion of the block universe: modal structure is not a metaphysical addition to physics, but the geometry that physical law already presupposes. (shrink)

VBRC treats classical mechanics as a residual-controlled interface readout of the R3 law-space. Under the Internal Invisibility Principle, protocol-relative unread content appears in the Hamilton–Jacobi and trajectory language only through licensed summary residuals, so classical mechanics is recovered as a gated readable regime rather than assumed as a primitive law. This paper reformulates classical mechanics as a residual-controlled R3 readout of the fixed VBRC core density e (P) core(IR, F) = β 2 ∥DRIR∥ 2 P + α 2 ∥F∥ 2 (...) P + η ⟨IR, F⟩P , F = ΣH,P (unread content), inherited unchanged from Part I; the norms use the constitutional protocol pairing ⟨·, ·⟩P , realized as | · |g in a metric/L 2 representative. Part III already generated the conservative R3 law-space from this core. Part IX does not rederive that law-space. It asks the question one step downstream: when does an already-derived R3 law admit a Hamilton–Jacobi/trajectory readout? The resulting law is not, in general, standard classical mechanics. On a single-phase, non-nodal, residual-controlled regime one obtains ∂tS + H(x, ∇S, t) = RS, ∂t(A 2 ) + div(A 2 v) = RA, where RS and RA are the only licensed classical-channel images of unread, virtual-boundary content relative to the declared classical protocol. For a mechanical Hamiltonian H = |p| 2/(2m) + V this gives the residual-Newtonian law mx¨(t) = −∇V (x(t), t) + ∇RS(x(t), t). Thus standard Hamilton–Jacobi/Newton mechanics is not the generic output of Part IX. It is the residual-free or residual-suppressed comparison gate RS ≈ 0, RA ≈ 0, ∥∇RS∥ ≪ ∥∇V ∥ of the more general VBRC–CM law. The generic law carries an explicit licensed unreadsummary residual. The paper identifies the gates under which this residual classical readout is licensed at fixed ℏ, and records the exit conditions at which the trajectory narrative must be replaced by another admissible representation. In the Schrödinger anchor, RS = −Qℏ, so the Bohm– Madelung quantum potential is read here as the phase residual of the declared anchor. Within a fixed R3 anchor and gate, Schrödinger, WKB, Hamilton–Jacobi, and Newtonian mechanics are readout levels of one retained R3 law, not independent laws. No additional external force, source, or fitting term is added at the classical-readout step. (shrink)

VBRC treats the dark residual source as a metric footprint of unread content, not as an independently inserted dark-matter Lagrangian or bare dark-energy term. This Part is not a cosmological data-fitting rail and does not re-derive gravity: the Part X metric gate is inherited. Its task is the source-entry side of the theory, namely to show how licensed unread summaries can become mass-like, gravitational-source-like, DM-like, DE-like, and Λ-like readouts without inserting primitive dark fluids or a bare dark-energy term. Starting from (...) the Part I comparison-density chain, the closed/unread sector is allowed to enter the retained metric law only through a licensed full summary Ffull = ΣXVIII(unread content), Ffull = DXVIII I II on the canonical first-order branch, and through the shifted displacement f = Ffull − F⋆ relative to a chosen background summary F⋆. For fixed metric g, the open variable is relaxed to u∗(g, f), giving a background-normalized residual energy Ered dark[g, f]. In the shifted representative, E red dark[g, 0] = 0, T dark µν [f] = − 2 p |g| δEred dark[g, f] δgµν . The central construction is that the mass readout is the open-Schur gap SR = A − BC−1B ∗ , whereas the dark gravitational source is generated by the opposite dual-Schur residual SI = C − B ∗A −1B. Thus mass and the dark source are not independent additions, but opposite reductions of one comparison-representative Hessian. A cosmological spectral gate then splits the shifted summary into infrared and inhomogeneous components. The inhomogeneous stress is DM-like only when its averaged density is positive, pressure-suppressed, and clustering on the readout cell; the infrared stress is DE-like only when it is approximately metric-proportional and slowly varying. The cosmological-constant term is identified with the metric-proportional infrared projection of the same reduced stress, not with a raw zero-point vacuum sum. The main structural output is a non-independence theorem: admissible DM-like and DE-like readouts must lift to one dual-Schur residual source and one hidden-summary closure 1 load. At the same quadratic level, SR and SI satisfy a determinant/index duality. In the scalar active-channel representative, their relative conversion has the normalized Lorentzian shape Kconv(k)/Kconv(0) = (1 + ℓ 2 dark|k| 2 ) −1 , ℓdark = p β/mA, which is independent of the coupling amplitude η in that representative, even though the dark response S −1 I , the source amplitude, and the critical scale retain η-dependence through κ 2 = η 2/(αβ). These are structural constraints, not a numerical fit of ΩDM, ΩDE, or w. (shrink)

In this manuscript we study individual variation in the interpretation of conditionals by establishing individual profiles of the participants based on their behavioral responses and reflective attitudes. To investigate the participants’ reflective attitudes we introduce a new experimental paradigm called the Scorekeeping Task, and a Bayesian mixture model tailored to analyze the data. The goal is thereby to identify the participants who follow the Suppositional Theory of conditionals and Inferentialism and to investigate their performance on the uncertain and-to-if inference (...) task. (shrink)

Objectives: Machine learning (ML) has the potential to facilitate “continual learning” in medicine, in which an ML system continues to evolve in response to exposure to new data over time, even after being deployed in a clinical setting. In this article, we provide a tutorial on the range of ethical issues raised by the use of such “adaptive” ML systems in medicine that have, thus far, been neglected in the literature. -/- Target audience: The target audiences for this tutorial are (...) the developers of ML AI systems, healthcare regulators, the broader medical informatics community, and practicing clinicians. -/- Scope: Discussions of adaptive ML systems to date have overlooked the distinction between 2 sorts of variance that such systems may exhibit—diachronic evolution (change over time) and synchronic variation (difference between cotemporaneous instantiations of the algorithm at different sites)—and underestimated the significance of the latter. We highlight the challenges that diachronic evolution and synchronic variation present for the quality of patient care, informed consent, and equity, and discuss the complex ethical trade-offs involved in the design of such systems. (shrink)

We provide a corridor-level closure of the R3 (conservative / time-completed) reading at the level of principal symbols under the density-fixed rule. (The geometric/dissipative metric closure is established in Part II.) This paper does not derive the full coupled theory from E[g, IR, II ]; it classifies the Laplace-backbone-compatible conservative completions and correspondence gates that force the KG→Sch→HJ corridor. Concretely, (i) any local linear second-order time completion preserving the Laplace backbone yields a Klein–Gordon-type principal part; (ii) a rest-mass phase rotation (...) gives an exact KG→Sch identity with explicit relativistic correction; (iii) under a quantitative slowenvelope gate ε = ℏω/(mc2 ) ≪ 1 on a fixed time window, the identity reduces to Schrödinger dynamics; (iv) in the local-potential presentation, WKB yields exact continuity/phase equations and formally reduces to Hamilton–Jacobi as ℏ → 0. As a design constraint in the series, within a fixed linear scalar, local, second-order Laplace-type Schrödinger class (up to lower-order perturbations, possibly order-0 operators), the semiclassical kinetic term is locked to be quadratic; “HJ-only modification” is excluded unless the operator class is changed. (shrink)

Synthetic biology offers a powerful method to design and construct biological devices for human purposes. Two prominent design methodologies are currently used. Rational design adapts the design methodology of traditional engineering sciences, such as mechanical engineering. Directed evolution, in contrast, models its design principles after natural evolution, as it attempts to design and improve systems by guiding them to evolve in a certain direction. Previous work has argued that the primary difference between these two is the way they treat (...) class='Hi'>variation: rational design attempts to suppress it, whilst direct evolution utilizes variation. I argue that this contrast is too simplistic, as it fails to distinguish different types of variation and different phases of design in synthetic biology. I outline three types of variation and show how they influence the construction of synthetic biological systems during the design process. Viewing the two design approaches with these more fine-grained distinctions provides a better understanding of the methodological differences and respective benefits of rational design and directed evolution, and clarifies the constraints and choices that the different design approaches must deal with. (shrink)

The free energy principle holds that any system persisting across a statistical boundary can be described as though it minimizes a single quantity, the variational free energy, and it has been offered as a unifying account of mind and life. Its status is contested: critics have questioned whether the Markov blanket construction is well defined and whether the principle explains anything or merely redescribes it. This paper brings a different kind of test to that debate. Because the variational free energy (...) is built from probabilities it is dimensionless, and dimensional analysis supplies a unit-independent, theory-neutral criterion for physical content: a quantity that genuinely couples to the world must appear as a function of the physical dimensionless groups of the system, whereas a quantity whose value can be changed without moving any such group is not tracking the physics. Applied in a concrete, physically bounded system, bacterial concentration sensing, whose Markov blanket is an actual membrane, the criterion shows that the variational free energy partitions into three parts: a leading term equal to a known physical quantity, the Berg-Purcell measurement number; a dominant correction that is independent of every physical group and can be moved at will by the agent's priors; and a subleading term that does couple to the physics but vanishes as sensing improves. In this system the principle is a bookkeeping device laid over a coupling law that dimensional analysis exhibits directly. The test generalizes: any postulated coupling quantity can be asked whether its dimensional content collapses onto a physical group or floats free of them all. (shrink)

In our daily lives, we often make claims about what is possible or necessary, prompting the question of how we come to acquire these modal claims. In this paper we examine what Vaidya and Wallner have called the "problem of modal epistemic friction." According to this problem, some accounts of modal knowledge presuppose essentialist theses, thereby making the epistemology of modality a special case of the epistemology of essences. Vaidya advances an essence-based account centered on the method of “variation (...) in imagination” (VIM), wherein the essential properties of an object are those that remain constant across imaginative variations over time. However, since this method is closed under logical consequence, it identifies what—in Finean terms—constitutes consequential rather than constitutive essences. In this paper, we aim to refine Vaidya's proposal by offering a way to capture constitutive essences, starting from a consequential perspective. To do so, we will draw on the notion of web consequence (WC), as developed by Schnieder, which helps distinguish constitutive essences from those which are merely consequential. (shrink)

In this brief reply I respond to criticisms of my book, The referential mechanism of proper names, from Michael Devitt and Nicolo D'Agruma. I focus on the question of whether the perspectivism advocated in the book explains the empirical results there detailed.

Individuals tend to judge bad side effects as more intentional than good side effects (the Knobe or side- effect effect). Here, we assessed how widespread these findings are by testing eleven adult cohorts of eight highly contrasted cultures on their attributions of intentional action as well as ratings of blame and praise. We found limited generalizability of the original side-effect effect, and even a reversal of the effect in two rural, traditional cultures (Samoa and Vanuatu) where participants were more likely (...) to judge the good side effect as intentional. Three follow-up experiments indicate that this reversal of the side-effect effect is not due to semantics and may be linked to the perception of the status of the protagonist. These results highlight the importance of factoring cultural context in our understanding of moral cognition. (shrink)

It is illegitimate to read any ontology about "race" off of biological theory or data. Indeed, the technical meaning of "genetic variation" is fluid, and there is no single theoretical agreed-upon criterion for defining and distinguishing populations (or groups or clusters) given a particular set of genetic variation data. Thus, by analyzing three formal senses of "genetic variation"—diversity, differentiation, and heterozygosity—we argue that the use of biological theory for making epistemic claims about "race" can only seem plausible (...) when it relies on the user’s own assumptions about race; the move from biological measures to claims about “race” inevitably amounts to a pernicious reification. We also excavate assumptions in the history of the technical discourse over the concept of "race" (e.g., Livingstone's and Dobzhansky's 1962 exchange, Edwards' 2003 response to Lewontin 1972, as well as contemporary discussions of cladistic "race", and "races" as clusters). We show that claims about the existence (or non-existence) of "race" are underdetermined by biological facts, methods, and theories. Biological theory does not force the concept of "race" upon us; our social discourse, social ontology, and social expectations do. We become prisoners of our abstractions at our own hands, and at our own expense. (shrink)

Finite systems do not operate under complete information, unlimited processing capacity, or stably pre-given decision spaces. They face open possibility spaces in which several continuations are conceivable, without any one of them being fully determined, probabilistically calculable, or formally derivable. This paper develops the concept of contingency mechanics for this situation: the dynamic operational logic through which finite systems transform open possibility into viable continuation. -/- The guiding idea is simple: finite systems must not only choose among possible continuations; they (...) must also stabilize one of them strongly enough to act, think, model, coordinate, or revise, without closing the field of possibility too early. Contingency mechanics therefore describes how possible continuations emerge, how they are compared, how one of them becomes provisionally stable, how successful stabilizations recede into the background, and how they can later become problematic again under changed conditions. -/- The core of the model is: variation → e-profile → e₀-proximate stabilization → immanentization → latent e → actualization → friction/reorganization. e-profiles designate the system-relative stabilization tensions of an order. These tensions include the effort required to generate, maintain, integrate, defend, revise, or reorganize an order. e₀ designates the range in which ordering gain, stabilization costs, revisability, and processing form enter into a viable relation. The paper distinguishes generative, selective, latent, and actualized e and thereby describes stabilization as a life-cycle phenomenon: an order emerges, competes with alternatives, recedes into the background, and can later become processable again through focus, context, or friction. -/- Contingency mechanics is not an ontology of the world in itself. Its claim to generality rests on the fact that every world accessible to a finite system appears as a reconstructed and stabilized order. Within such orders, e is quasi-real: not as a world-absolute substance, but as real stabilization tension within the operative order of a finite system. The paper demonstrates the four states of e through a historically oriented model shift, distinguishes contingency mechanics from Active Inference, free-energy approaches, and Peirce’s abduction, identifies conditions of falsification, and sketches a path of operationalization for LLM systems. (shrink)

Explains Aristotle's views on the possibility of continuous variation between biological species. While the Porphyrean/Linnean classification of species by a tree suggests species are distributed discretely, Aristotle admitted continuous variation between species among lower life forms.

Patrick Grim advances arguments meant to show that the doctrine of divine omniscience—the classical doctrine according to which God knows all truths—is false. In particular, we here have in mind to focus on two such arguments: the set theoretic argument and the semantic argument. These arguments due to Grim run parallel to, respectively, familiar paradoxes in set theory and naive truth theory. It is beyond the purview of this article to adjudicate whether or not these are successful arguments against the (...) classical doctrine of omniscience. What we are here interested in is a way in which these arguments can be generalized. In particular, we show how generalizations of those arguments can target, explicitly, alternatives to the classical doctrine of omniscience, including what we here call 'restricted omniscience' and 'open future open theism'. As a corollary, considerations of Grim-style arguments do not support these alternatives to the classical doctrine of omniscience over the classical doctrine. We conclude that what is paradoxical is not the classical doctrine of omniscience just as such; rather, what is paradoxical is a core commitment shared by the classical doctrine and its more modest alternatives, namely, the thesis that God is a perfectly logical reasoner. (shrink)

Significant variations in the way objects appear across different viewing conditions pose a challenge to the view that they have some true, determinate color. This view would seem to require that we break the symmetry between multiple appearances in favor of a single variant. A wide range of philosophical and non-philosophical writers have held that the symmetry can be broken by appealing to daylight viewing conditions—that the appearances of objects in daylight have a stronger, and perhaps unique, claim to reveal (...) their true colors. In this note we argue that, whatever else its merits, this appeal to daylight is not a satisfactory answer to the problem posed by perceptual variation. (shrink)