Convection

Convection is the transport of heat, mass, or momentum through a fluid by the coherent motion of the fluid itself, driven by density differences that arise from gradients in temperature or composition and that cause lighter parcels to rise and heavier parcels to sink, organizing the fluid into circulatory cells. The essential commitment is that transport is carried not by molecular random walk (as in diffusion) but by bulk-fluid displacement, and that the displacement is self-organized by buoyancy, not imposed from outside. Every convection claim specifies (1) the fluid medium and its relevant properties (density, viscosity, thermal conductivity), (2) the gradient that creates density contrasts, (3) the buoyancy-drag balance that determines whether motion occurs, and (4) the geometry and scale of the resulting circulation cells. The theoretical foundation is anchored in the <!-- FACT-D11-180 -->[^rayleigh-1916]Rayleigh number Ra = gβΔT·d³/(νκ), which quantifies the ratio of buoyancy driving to viscous-thermal damping<!-- FACT-D11-180 -->[^rayleigh-1916], and the critical Rayleigh number Ra_c ≈ 1708 marks the onset of convective instability.

Flow

Convection is a specialization of flow whose transport is carried by buoyancy-driven bulk motion of the fluid itself.

Convection is a specialization of flow in which the transported quantity, typically heat or mass, is carried by coherent bulk-fluid displacement driven by density contrasts arising from temperature or composition gradients. It inherits the general flow commitment of directional transfer of a conserved quantity through a system with rates, conservation, and a driving gradient, and specializes by fixing the transport mechanism to self-organized buoyant circulation rather than diffusion, pressure-driven channel flow, or advection by an externally imposed velocity field.

Transformation

Convection is a kind of transformation: it maps an input distribution into a restructured output via the rule of buoyancy-driven bulk flow.

Convection transports heat, mass, or momentum by the coherent motion of fluid driven by buoyancy from temperature or composition gradients, restructuring spatial distributions of those quantities into circulatory patterns. That fits the Transformation schema: input distribution mapped to output distribution under a rule, with certain properties preserved (mass, energy) and others altered (spatial profile). Convection specializes transformation by fixing the rule as buoyancy-driven bulk fluid motion organized into cells.

Gradient

Convection presupposes gradient because the buoyancy-driven fluid motion is initiated and sustained by density differences arising from gradients in temperature or composition.

Convection is fluid transport driven by density differences that arise from spatial variation in temperature or composition — that is, from gradients of those scalar fields. Without gradient's machinery — the local rate and direction of steepest increase of a scalar field across space — there would be no density contrast to make lighter fluid parcels rise and heavier parcels sink, and no buoyancy-drag balance to organize the fluid into circulatory cells. The gradient prime supplies the spatial-variation structure that initiates and sustains convective motion.


Convergence

**Convergence is the limit-approach principle: a sequence or process is said to converge when its elements eventually enter and remain within every neighborhood of a target limit, formally captured by the epsilon-N condition for sequences (`∀ε > 0, ∃N : n ≥ N ⟹ d(xₙ, x) < ε`)[^cauchy-1821-conv][^weierstrass-1841] and by analogous conditions for functions, measures, distributions, and operators.** The essential commitment is that convergence is what *makes long-run behavior tractable* — a converged process is summarized by its limit, the finite-step behavior is approximated by the limit with quantifiable error, and iterative methods (Newton's method[^newton-1671], gradient descent, fixed-point iteration, MCMC sampling) become trustworthy because their output approaches a known target — and that the *mode* of convergence (pointwise, uniform, in measure, in distribution, almost surely, in `L^p`) is consequential because different modes preserve different downstream properties. Every convergence articulation specifies (1) the *sequence or process* — the indexed family of states or values being analyzed; (2) the *ambient space and metric or topology* — where the elements live and how closeness is measured (a metric `d`, a norm, a topology, a probability measure); (3) the *limit or limit set* — the target the process approaches (a single point, a set, a distribution); (4) the *mode of convergence* — pointwise, uniform, in measure, almost-surely, in distribution, in `L^p`, weak, strong; (5) the *rate of convergence* — sublinear (`1/n^α`), linear / geometric (`r^n` with `0 < r < 1`), superlinear, quadratic (Newton-style); and (6) the *use* the convergence supports — projection (long-run behavior is the limit), termination criteria (stop iterating when within tolerance), comparison (which method converges faster), or detection (does the observed sequence actually converge or is it diverging / oscillating). **Without all six parts the convergence claim is at risk of being a vague "things eventually settle down" intuition; with them, the diagnostic spans real and complex analysis, numerical methods, optimization and machine learning, probability and statistics, dynamical systems, evolutionary biology, and product-design iteration within one structural skeleton — and the question "does this converge, in what mode, at what rate, to what?" becomes prosecutable rather than rhetorical.**


Cooperation

Agents bear individual costs to produce a shared benefit.

Cooperation is the structural situation in which multiple agents take individually costly actions that benefit the group, producing a jointly superior outcome that none could achieve alone, *despite* a standing individual temptation to defect and free-ride. The defining commitment is the tension between collective optimum and individual incentive: cooperation exists only where the socially best move is not the privately dominant one, so the pattern is always about what sustains contribution against the pull of defection. <!-- FACT-D54-271 -->[^nash-1951] Where the privately optimal choice already coincides with the collectively optimal one, there is no cooperation problem to solve—agents will reach the good outcome unaided. Cooperation as a prime names precisely the gap between those two optima and the question of how it is bridged and held open over time.

Social Dilemma

Cooperation presupposes social dilemma because the cooperation problem only exists where individual rationality conflicts with the collective optimum.

Cooperation presupposes social dilemma because the tension cooperation names — costly contribution sustained against the pull of defection — is constituted by the prior structural pattern of a social dilemma: a setting where each agent's dominant strategy yields a collectively worse outcome than universal contribution would. Without that gap between individually rational and collectively optimal action, there is no cooperation problem to solve; agents would reach the good outcome unaided. Cooperation inherits the social dilemma's structural conflict and names the question of what devices — reciprocity, norms, institutions — stabilize contribution against the standing temptation to defect.


The Cooperative Principle and its four maxims describe the normative structure of conversation: (1) participants in a cooperative exchange are assumed to make their contributions "such as required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange" — the **Cooperative Principle**;<!-- FACT-D23-016 -->[^grice-1975] (2) this principle is specified by four **maxims**: *Quantity* (be as informative as required, no more); *Quality* (do not say what you believe false or lack evidence for); *Relation* (be relevant); *Manner* (be clear: avoid obscurity, ambiguity, be brief and orderly);<!-- FACT-D23-017 -->[^grice-1975] (3) speakers regularly **flout** maxims on purpose — saying less than required, stating false things as irony, changing the topic — and listeners interpret the flout as *conversational implicature* (the intended meaning beyond literal content);<!-- FACT-D23-018 -->[^grice-1975] (4) the whole apparatus explains how hearers **derive meaning that is not literally said** — from what the speaker *chose to say* against the backdrop of the cooperative norm.<!-- FACT-D23-019 -->[^grice-1975]

Cooperative principle and Gricean maxims presupposes cooperation because conversational implicature operates on the assumption participants are jointly working toward purpose.

The Cooperative Principle holds that conversational participants make contributions as required by the accepted purpose of the talk exchange, specified by maxims of quantity, quality, relation, and manner. The entire framework presupposes that interlocutors are jointly contributing to a shared purpose despite individual temptations to deceive, mislead, or free-ride on others' clarity. Cooperation supplies the structural commitment: agents take individually costly actions sustaining a joint outcome where defection is tempting. Conversational maxims specialize cooperation to linguistic exchange, with informativeness and truthfulness as the costly contributions sustained against private temptation.

Social Norms

The Cooperative Principle and Gricean Maxims is the specific shape social norms take in conversational cooperation.

The Cooperative Principle and its maxims govern conversational contributions through shared expectations — be informative, truthful, relevant, clear — that participants assume and against which deviations are noticed and exploited as implicature. That is the structure of Social Norms — group-shared behavioral expectations, enforced by mutual sanction, sustained by joint internalization and enforcement — particularized to the domain of talk exchange. Gricean maxims are the specific shape social norms take when the regulated behavior is communicative cooperation under conversational purpose.


Coordination

Aligning independently controlled actors so their separate actions combine into a coherent collective outcome despite distributed decision-making and incomplete shared information.

Coordination, as Thompson (1967) framed it in his foundational analysis of organizational interdependence, is the active alignment of independently controlled actors or processes so their actions combine into a coherent collective outcome, despite distributed decision-making and incomplete shared information. <!-- FACT-D52-151 -->[^thompson-1967] It is the infrastructure that allows separate agents—people, organizations, systems, organisms—to move in concert without centralized control. A single actor does not need coordination (one musician, one agent); coordination emerges when two or more actors must synchronize action toward a goal none can achieve alone, a structural definition Malone and Crowston (1994) developed in their interdisciplinary theory of coordination. <!-- FACT-D52-152 -->[^malone-crowston-1994] The mechanisms are structural: shared protocols, synchronized timing, role assignment, signal interpretation, and rule-following under uncertainty. Coordination subsumes but is not limited to synchronization (timing alone) or cooperation (motivational willingness); it is the full apparatus of alignment.

Concurrency

Coordination presupposes concurrency because aligning independent actors into coherent collective outcome only arises when multiple processes proceed simultaneously.

Coordination is the active alignment of independently controlled actors so their actions combine into a coherent collective outcome. The problem only arises where multiple loci of execution proceed in time-overlapping fashion — the structural situation that concurrency names. A single actor needs no coordination; coordination becomes necessary when separate processes run concurrently and their interleavings raise questions of ordering, contention, and consistency. Concurrency supplies the multi-process-simultaneity substrate; coordination is the alignment work that addresses the consequent ordering and synchronization problems.

Dependency

Coordination presupposes dependency because alignment of independently controlled actors is only required when their actions are mutually contingent.

Coordination presupposes dependency because the active alignment of independently controlled actors only becomes a problem when one actor's progress, output, or interpretation depends on another's. Without dependency's directed reliance — A cannot proceed unless a condition on B is met — there is nothing to synchronize: independent actors with no coupling can act in parallel without any coordination machinery. Dependency supplies the structural couplings that make coordination necessary; coordination then supplies the protocols, signals, and shared frames that resolve those couplings into coherent collective outcomes.

Task Interdependence

Coordination presupposes task interdependence because the active alignment of actors is only required when their tasks are coupled through inputs, outputs, or shared resources.

Coordination's whole rationale is to align actors whose tasks depend on one another — to manage the couplings through which one task's output is another's input, or both compete for shared resources. Without task interdependence's machinery of workflow coupling, the actors would be performing independent tasks with no need for active alignment, and the coordination infrastructure would have nothing to coordinate. Interdependence supplies the structural condition — coupling between tasks — that creates the requirement coordination addresses.


Coordination Problem and Equilibrium Selection

Multiple stable equilibria require alignment on single outcome.

A coordination problem arises when multiple stable equilibria exist and agents must align on a single one to achieve joint benefit, but no equilibrium is uniquely specified by the decision structure itself, as Schelling (1960) first articulated in his analysis of bargaining and conflict. <!-- FACT-D53-106 -->[^schelling-1960] The problem is not how to motivate cooperation—agents *want* to coordinate—but *which* equilibrium to select when many are equally rational, a class of pure-coordination games systematically catalogued by Cooper (1999). <!-- FACT-D53-107 -->[^cooper-1999] This prime focuses on the multi-equilibrium structure itself: the presence of Schelling focal points, Pareto-ranked alternatives, and the selection mechanism that determines which equilibrium becomes locked in. It is fundamentally about *which stable state the system settles into*, not the act of coordinating toward any state.

The coordination problem presupposes coordination because the selection-among-equilibria difficulty arises only within the active-alignment infrastructure of coordination.

The coordination problem names the specific failure mode in which agents who wish to align on a joint outcome must choose among multiple equally-rational equilibria, which is intelligible only against the background of coordination's active-alignment infrastructure. Without coordination's machinery of shared protocols, synchronization, and joint action toward a goal none can achieve alone, there would be no joint outcome to align on and no selection problem to solve. Coordination supplies the goal-structure that makes equilibrium selection a problem at all.

Equilibrium

The coordination problem presupposes equilibrium because its core difficulty is selecting among multiple stable equilibria that all satisfy the balance condition.

The coordination problem arises precisely when more than one stable equilibrium exists and agents must align on a single one. Without equilibrium's machinery of balance conditions and stability — the structural framework by which a system has rest points at which opposing forces balance — there would be no set of alternatives to select among and no question of which stable state the system settles into. The equilibrium prime supplies the multi-rest-point structure that the coordination problem treats as the selection space.

Path Dependence

Coordination problems typically presuppose path dependence because focal-point and lock-in selection makes the chosen equilibrium history-dependent.

A coordination problem arises when multiple stable equilibria exist and agents must align on one without the decision structure itself uniquely picking one. Which equilibrium gets selected typically depends on history — focal points inherited from prior interactions, lock-in from early adopters, accumulated convention. Path dependence supplies exactly this structural fact: outcomes are determined by the specific trajectory of choices, with early decisions constraining later ones. Coordination selection typically rides on this dynamic, though some coordination problems are resolved by salience alone without historical lock-in, so the presupposition is typical.


Correlation

Systematic co-variation between variables, distinct from causation.

Correlation is the structural pattern in which two or more variables systematically co-vary — values of one tend to track values of another above what statistical independence would predict — *without any implied mechanism, direction, or production relation between them*, a pattern Galton (1888) first quantified when measuring the co-variation of human stature across kin. <!-- FACT-D54-286 -->[^galton-1888] The defining commitment is statistical association as a self-standing fact: knowing the value of one variable updates the probability distribution over the other, yet the association is silent about which (if either) drives which, leaving open common-cause, reverse-cause, mediated, or coincidental explanations. <!-- FACT-D54-287 -->[^casella-berger-2002] Correlation answers a recurring epistemic problem: how can a relationship be real, stable, and exploitable for prediction while remaining wholly uncommitted about the underlying causal architecture that produced it?


Correspondence Principle

The Correspondence Principle is the meta-theoretical constraint that (1) a **new, more general theory** must **reproduce the predictions of the older theory it supersedes** in the regime where the older theory was empirically validated, (2) this reduction typically appears as a **well-defined limit**: ℏ → 0 (classical limit of quantum mechanics), c → ∞ (non-relativistic limit of special relativity), G → 0 or high-gravitational-scale limits recovering Newtonian gravity, n → ∞ (large quantum number → classical orbital behavior in Bohr's original formulation), (3) the principle functions both as a **consistency check** — any candidate successor theory that fails to recover established results in their domain is refuted — and as a **constructive guide**: proposing a new theory means specifying how the classical theory emerges from it, and (4) the reduction is **directional**: the new theory is strictly more general, while the old theory remains valid within its domain as a computationally simpler, approximate description.<!-- FACT-D13-100 -->[^bohr-1920]

Compatibility

Correspondence Principle is a kind of compatibility: a new theory must reproduce the predictions of its predecessor in the latter's validated regime.

The Correspondence Principle requires a new, more general theory to reproduce the predictions of the older theory it supersedes in the regime where the older theory was empirically validated, typically as a well-defined limit (h-bar to 0, c to infinity). That is the relational property of Compatibility: two systems coexist without contradiction across the regime where both apply. Correspondence specializes compatibility to successive scientific theories, with the older theory's empirical domain as the alignment region.

Versioning

The correspondence principle presupposes versioning because it constrains how a successor theory must reproduce the predecessor's predictions in their validated regime.

The correspondence principle presupposes versioning because it treats theories as named successive states of a body of knowledge -- predecessor and successor -- where the successor must reproduce the predecessor's empirically validated predictions as a limit. Without versioning's explicit identification, retention, and difference-computation between artifact states, there is no formal way to specify which predictions the new theory must recover, in which regime the old theory was valid, or what the reduction (hbar to zero, c to infinity) computes. The principle IS a consistency constraint on the version transition.


Cost–Benefit Analysis

(1) **Cost–Benefit Analysis (CBA) is a systematic decision-analytic framework that aggregates all significant consequences of a candidate policy, project, or decision into a common monetary metric, computes the net (benefits minus costs) typically in present-value terms, and uses the result as a basis for evaluation. The method's modern form emerged from the interaction of early-twentieth-century welfare economics — particularly A.C. Pigou's <!-- FACT-D09-001 -->[^pigou-1920] 1920 *The Economics of Welfare*, which established the foundational welfare-measurement framework for policy analysis <!-- FACT-D09-001 -->[^pigou-1920] — with the practical needs of U.S. federal public-works evaluation, particularly the 1936 Flood Control Act's requirement that federal projects be undertaken only if "the benefits to whomsoever they may accrue are in excess of the estimated costs," and the subsequent postwar elaboration by the U.S. Army Corps of Engineers, the Bureau of Reclamation, and academic contributors (Jules Dupuit's 1844 antecedent work on consumer surplus and public-works valuation; Otto Eckstein's *Water-Resource Development*, 1958; Roland McKean's *Efficiency in Government Through Systems Analysis*, 1958; the 1950 U.S. Interagency Committee on Water Resources "Green Book"). CBA subsequently became a standardized tool of federal rule-making (OMB Circular A-94, executive-order requirements for regulatory impact analysis beginning with Reagan's EO 12291 in 1981, continuing through Clinton's EO 12866 in 1993 and extending into contemporary practice), international development-bank project appraisal (World Bank, IDB, ADB), and domestic-policy analysis across infrastructure, environmental regulation, health, and education.** (2) The distinctive focus is on the *systematic monetization and aggregation of heterogeneous consequences* across time, across affected parties, and across consequence categories, producing a single net-present-value summary statistic. The analytical payoff is a structured framework for comparing alternatives that forces explicit treatment of usually-opaque trade-offs: how are avoided fatalities valued against the cost of the safety investment that avoids them? How are long-term benefits traded against short-term costs? How are benefits to one population traded against costs to another? The analytical price of this clarity is substantial: monetization of non-market goods (human life, environmental amenity, cultural heritage, biodiversity) requires contested valuation methods (revealed-preference techniques, stated-preference / contingent-valuation surveys, hedonic pricing, benefit-transfer methods), and the resulting numbers carry the imprint of those valuation choices. (3) The practical analytical pipeline involves: defining the decision and its alternatives (including a "without-project" baseline); identifying affected parties and categories of consequence (direct, indirect, ancillary, distributional); monetizing each consequence using an appropriate valuation method; projecting costs and benefits over the project's time horizon; discounting future cash flows to present value; computing the net present value (and sensitivity to key assumptions); and reporting results with attention to distributional effects, residual uncertainties, and non-monetized considerations. (4) The deeper abstraction is that **Cost–Benefit Analysis provides a disciplined, transparent, and extensible framework for evaluating policy and investment decisions — one that forces explicit articulation of the alternatives, the consequence categories, the valuation methods, the time horizons, and the discount rates, thereby structuring both the analytical work and the subsequent deliberative process. The concept is foundational to public-finance evaluation, regulatory impact analysis, infrastructure project appraisal, environmental policy, and health-technology-assessment (which uses cost-effectiveness variants). Together with its companion techniques — cost-effectiveness analysis, distributional analysis, risk and uncertainty analysis, break-even analysis — CBA constitutes the analytical spine of contemporary applied welfare economics in public-policy practice, even as it faces ongoing critiques from distributional, rights-based, and deliberative-democratic perspectives.**

Decision

Cost-benefit analysis presupposes decision because the framework's purpose is to support selecting one alternative over others under constraint.

Cost-benefit analysis aggregates significant consequences of a candidate policy or project into a common monetary metric and uses the net present value as a basis for evaluation. The framework is constituted around the act of choosing — it exists to discriminate between alternatives and recommend one. Decision supplies the act of selecting one alternative from a set, committing future resources, and closing off other paths; CBA is the analytical machinery that informs and structures that selection, presupposing the decisional act as its purpose and addressee.

Value Commensuration

Cost-benefit analysis is the specific shape value commensuration takes when the common metric is monetized and net present value is the aggregation rule.

Cost-benefit analysis is the specific shape value commensuration takes when the common scale is monetary and the aggregation rule is net present value across all significant consequences. Value commensuration's general anatomy — translating heterogeneous values from different frameworks into a single comparable metric, with characteristic loss and contestation — is structurally particularized into willingness-to-pay valuations, monetized externalities, discounted future flows, and a single net-benefit verdict. The general translation-into-common-metric operation is preserved; the specific shape is its monetized, decision-analytic realization for policy and project evaluation.


Counterfactual Reasoning

what-if reasoning
mental simulation
counterfactual thinking
alternative scenario cognition

Counterfactual reasoning is the COGNITIVE PROCESS by which a reasoner mentally simulates one or more alternative states-of-affairs contrary to the actual situation, holds that simulation as a variant scenario, performs a mental-comparison operation between the actual situation and the counterfactual variant, and uses the output of that comparison to guide judgments about causation, blame, regret, learning, and decision-making. The process comprises four essential components: (1) *the actual situation S* as the baseline reference state, the state that actually obtained or was actually observed; (2) *the counterfactual variant S'* generated by mental simulation — a mentally constructed alternative past or future created by altering one or more antecedent conditions in S while holding other factors mentally fixed; (3) *the mental-comparison operation* between S and S' that highlights what would have been different, what consequences would have followed, and how far S diverges from S'; (4) *the cognitive/affective/judgmental output* — the regret, blame attribution, causal inference, learning signal, or decision adjustment that flows from the comparison. This is fundamentally a process of mental simulation and imagination constrained by background knowledge of regularities, laws, and typical causal pathways; it is distinct from the metaphysical or semantic analysis of counterfactual conditionals (see `counterfactuals.md`, which treats the logical structure of "if A had been true, then B would have been true" as a truth-conditional claim). The cognitive process is empirically tractable — Kahneman and Tversky (1981) documented that mental simulation distance, norm violations, and ease of imagining alternatives predict regret intensity and learning effectiveness. The process operates across regret psychology (ruminating on roads not taken), blame and responsibility attribution (considering alternative actions the agent could have taken), educational learning (productive failure and deliberate reflection on counterfactual solution paths), medical decision-making (mental simulation of alternative treatment scenarios), legal reasoning (but-for counterfactuals grounded in cognitive narrative construction), and AI/ML fairness (generating minimal counterfactual input perturbations that flip model decisions). <!-- FACT-D20-031 -->[^kahneman-tversky-1981]


Counterfactuals

Counterfactual reasoning is the construction and evaluation of claims of the form "if A had been the case, then B would have been (or would likely have been) the case," where A is contrary to actual fact and the reasoning asks what would have followed under that altered condition, often for the sake of identifying causal relationships, evaluating decisions, assigning moral or legal responsibility, or exploring alternative possibilities. The essential commitment is that causal and evaluative claims about the actual world require systematic comparison with what would have happened under relevantly-different antecedent conditions, and that such comparisons have a determinable structure — nearest-possible-world similarity, manipulation semantics, or probabilistic intervention — that can be reasoned about with rigor rather than merely guessed at. Every counterfactual claim specifies (1) *the counterfactual antecedent* — the actual state of affairs plus the contrary-to-fact modification, (2) *the would-be consequent* — the claim about what obtains in the altered scenario, (3) *the similarity-ordering of worlds* — the semantics determining which non-actual worlds count as "nearest," and (4) *the causal-explanatory function* — the work the counterfactual does in causal inference, moral reasoning, or decision evaluation. Lewis (1973) <!-- FACT-D19-060 -->[^lewis-1973] established the foundational *possible-worlds analysis*: a counterfactual "if A had been true, C would follow" is true iff C is true in the nearest possible worlds where A is true, with similarity-ordering fixed by convention or context. Stalnaker (1968) <!-- FACT-D19-061 -->[^stalnaker-1968] provided the *unique-world variant*, requiring a single closest world. Pearl (2009) <!-- FACT-D19-063 -->[^pearl-2009] reframed counterfactuals as *interventions on causal graphs* — the do-operator — operationalizing them for causal inference. The recursion is: (a) an actual world-state, (b) an antecedent specifying a contrary-to-fact modification, (c) a similarity metric selecting non-actual worlds where that modification holds, (d) the truth value of the consequent in those worlds. This structure applies from philosophy of logic through causal inference to legal reasoning and ethics.

Causality

Counterfactuals are a kind of causality: causal claims are evaluated by comparing the actual world with what would have happened had a cause differed.

Counterfactual reasoning constructs claims of the form had A not occurred, B would not have occurred and uses them to identify causal structure, evaluate decisions, and assign responsibility. That is one of the four essential components of Causality itself: modal robustness — the counterfactual claim that fixing the cause would have fixed the effect under a fixed background. Counterfactuals are the specialization of causality that isolates and operationalizes the modal component as its primary inferential machinery.

Modal Reasoning

Counterfactual reasoning is a specialization of modal reasoning that evaluates would-have-been claims under contrary-to-fact antecedents.

Counterfactual reasoning is a specialization of modal reasoning. Specifically, it deploys a modal operator (the counterfactual conditional) that quantifies over a structured space of alternatives -- nearest possible worlds, intervention regimes, or similarity-ordered scenarios -- to evaluate what would have followed under an antecedent contrary to actual fact. The truth of the counterfactual claim rests on the inner proposition holding across the relevant accessible alternatives, exactly the Kripke-style move modal reasoning names; counterfactuals are the subclass anchored to contrary-to-fact antecedents.


Coupling

Coupling is the structural relationship whereby two or more subsystems or variables are dynamically linked such that a change in one produces some change in the others, through a specifiable mechanism of interaction<!-- FACT-D26-136 -->[^perrow-1999]; the strength and character of coupling determine whether the subsystems can be analyzed and acted upon separately or must be treated as an integrated whole. The essential commitment is that coupling is a property of the interaction structure, not of either subsystem alone: it is the channel through which state in one becomes input to another, and its degree — from fully decoupled (independent) through loosely coupled (influence exists but is weak or delayed) to tightly coupled (variables are effectively a single system)<!-- FACT-D26-137 -->[^orton-weick-1990] — governs both analytical tractability and the propagation of change and disturbance. Every coupling claim specifies (1) the subsystems being linked, (2) the variables or quantities through which they interact, (3) the strength and direction of the coupling (one-way, reciprocal, asymmetric)<!-- FACT-D26-138 -->[^weick-1976], and (4) the timescale of the coupling relative to the internal dynamics of the subsystems.


Creative Destruction

Creative destruction is the dynamic process by which new products, production methods, business models, and organizational forms displace older ones — generating long-run growth and welfare improvement through the reallocation of resources from less to more productive uses, while simultaneously imposing adjustment costs, firm exits, occupational obsolescence, and distributional disruptions on those tied to the displaced structures. The essential commitment is that economic progress under competitive capitalism is fundamentally driven not by static allocative efficiency (moving to the production possibility frontier given existing technology) but by the *endogenous generation* of new possibilities through innovation and by the *elimination* of outmoded possibilities through competitive displacement, and that attempts to suspend or reverse destruction (to preserve incumbent firms, jobs, or industries) tend to suspend or reverse creation as well. Every creative-destruction articulation specifies (1) the substrate being transformed — products, production methods, supply chains, firms, industries, occupations, entire economic sectors; (2) the innovation mechanism — new technology, new business model, new organizational form, new market (sometimes called the five types of Schumpeterian innovation); (3) the displacement pathway — entry of new firms that outcompete incumbents, transformation of incumbents, or reallocation of factors from declining to growing sectors; and (4) the time horizon and measurement — firm-level (entry and exit), industry-level (productivity gains), economy-wide (long-run growth). The construct was named by Joseph Schumpeter (1942) in *Capitalism, Socialism and Democracy* <!-- FACT-D09-060 -->[^schumpeter-1942], building on earlier observations by Marx (1848), and operationalized empirically in the modern growth-and-productivity literature by Aghion-Howitt (1992) <!-- FACT-D09-062 -->[^aghion-howitt-1992], Foster-Haltiwanger-Krizan (2001) <!-- FACT-D09-065 -->[^foster-haltiwanger-krizan-2001], and others.

Allocation

Creative destruction presupposes allocation because its reallocation of resources from less to more productive uses requires an underlying assignment of supply across uses.

Creative destruction operates by reallocating capital, labor, and other productive resources from displaced firms and methods to ascendant ones, which presupposes the underlying machinery of assigning limited supply across competing uses. Without allocation as the structural substrate, there would be no assignment to revise: the displacement of incumbents and the rise of new entrants would have no resource-redistribution dimension. The allocation prime supplies the assignment structure on which the destructive-creative reshuffling acts.

Transformation

Creative destruction is the specific shape transformation takes in an economy, where innovation restructures the productive base by displacing the old.

Creative destruction is the structurally-particularized form transformation takes in competitive capitalist economies: the input is an existing configuration of products, methods, and firms; the rule is innovation-driven competitive displacement; the output is a restructured economy in which resources have been reallocated from less to more productive uses. The transformation's invariants are aggregate welfare gain and the continuity of market activity; the degrees of freedom being reshaped are the particular firms, technologies, and occupational structures that get displaced.


Critical Juncture

Moment where small variations produce divergent locked-in paths.

A critical juncture is a moment in time where outcomes depend sensitively on the specific choice made—small variations produce divergent paths that then become difficult or impossible to reverse, as Capoccia and Kelemen (2007) define the concept in historical institutionalism. <!-- FACT-D53-121 -->[^capoccia-kelemen-2007] The decision at the juncture itself is consequential, not because of intrinsic properties of the choice, but because of the path-dependent lock-in that follows. Once a path is chosen at the juncture, subsequent conditions tend to reinforce that choice through increasing returns, network effects, institutional inertia, or adaptive expectations, making it progressively harder to switch course, as Pierson (2004) develops in detail. The critical juncture is therefore not the lock-in itself, but the moment of high sensitivity where small causes produce large and divergent effects. <!-- FACT-D53-122 -->[^pierson-2004]

Path Dependence

A critical juncture presupposes path dependence because its consequence-amplifying role only obtains when subsequent dynamics lock in the chosen path.

A critical juncture presupposes path dependence because its high-stakes status depends entirely on what happens afterward: the moment is consequential only if subsequent increasing returns, network effects, or institutional inertia make reversal difficult. It inherits path dependence's commitment that current state is irreducible to prior state plus current shock — history is constitutive — particularized to the branching-point case where a brief window of sensitivity precedes long lock-in. Without path dependence's downstream amplification, the juncture would not be critical.


Critical Mass

The minimum quantity needed to sustain a self-perpetuating process.

Critical mass is the minimum quantity, density, or participation level of interacting elements above which a process becomes *self-sustaining* — each event triggers, on average, at least one further event, so the process propagates on its own rather than decaying toward zero. <!-- FACT-D54-301 -->[^oliver-marwell-teixeira-1985] The defining commitment is a reproduction-ratio threshold: name the average number of successor events produced by each event the *reproduction ratio* (written R, or in epidemiology R₀ / Rₑ, in fission the neutron multiplication factor k), and the prime asserts that the system's fate hinges on whether this single number sits below or above one. Below the threshold (R < 1, subcritical) activity decays geometrically toward extinction; at the threshold (R = 1, critical) it persists at a steady level; above it (R > 1, supercritical) it grows or sustains without continued external driving. <!-- FACT-D54-302 -->[^diekmann-heesterbeek-metz-1990]

Threshold

Critical mass is a specialization of threshold whose specific input is a reproduction-ratio crossing one and whose response is self-sustaining propagation.

Critical mass is a specialization of threshold in which the input variable is the effective reproduction ratio of a propagating process and the response is the qualitative shift from decay to self-sustained activity at R equals one. It inherits the general threshold commitment of a sharp dividing value separating a sub-response regime from a response regime, and specializes by fixing the input to a reproduction count and the output to extinction-versus-runaway. Below the threshold the chain dies; above it, propagation feeds itself.

Tipping Points (or Phase Transitions)

Critical mass is a specialization of tipping point in which the control parameter is participation density and the threshold sits at a reproduction ratio of one.

Critical mass specializes the tipping-point pattern by fixing the control parameter as quantity, density, or participation level of interacting elements and the threshold as the reproduction-ratio crossing of one. Where tipping points name the general structure of alternative stable states separated by a bifurcation driven by positive feedback, critical mass specifies the bifurcation as the self-sustaining-versus-decaying boundary at R=1 — below it activity decays geometrically, above it activity grows self-sustainingly. The reproduction-ratio framing is the particular shape the bifurcation takes in propagation processes.


Criticality

Regime poised at a phase boundary where response becomes scale-free and correlations diverge.

Criticality is the structural state of a system poised at or near a phase boundary, where qualitatively distinct regimes meet and the system's response to perturbation becomes unbounded across scales. The canonical reference is the second-order phase transition of statistical mechanics, where as a control parameter is tuned to a critical value, the correlation length of fluctuations diverges, the susceptibility to external fields diverges, and event-size distributions become power laws rather than exponentials — a regime first systematically characterized in the modern sense by Stanley's (1971) treatise on critical phenomena. <!-- FACT-D56-391 -->[^stanley-1971] A system at criticality is neither in the ordered regime (where structure dominates and small perturbations decay quickly) nor in the disordered regime (where noise dominates and macroscopic patterns dissolve) but in a *boundary regime* where local interactions propagate across all scales. Near the magnetic Curie point, domains of aligned spin appear at every length scale; near the percolation threshold of a random graph, connected clusters span every size; in the critical-brain hypothesis, neural avalanches in cortical tissue follow power-law size distributions; in self-organized criticality, sandpile avalanches show characteristic power-law statistics across orders of magnitude. The structural signature is invariant across these substrates: there is no characteristic event size (the distribution is scale-free), correlations decay as power laws rather than exponentials (the correlation length is effectively infinite), responses to small perturbations can be arbitrarily large (susceptibility diverges), and superficially different systems can share the same critical exponents (universality), an organizing insight Wilson (1971) crystallized in the renormalization-group framework. <!-- FACT-D56-392 -->[^wilson-1971] Criticality is structurally distinct from the threshold at which the transition occurs (a scalar control-parameter value) and from the transition event itself: criticality is the *regime* in which the system lives at or near that boundary, with its distinctive statistical fingerprints, and it can be sustained indefinitely when endogenous dynamics tune the system toward the boundary, as Bak, Tang, and Wiesenfeld (1987) demonstrated with the sandpile model. <!-- FACT-D56-393 -->[^bak-tang-wiesenfeld-1987]

Nonlinearity

Criticality presupposes nonlinearity because divergent susceptibilities and scale-free fluctuations require failure of superposition.

Criticality is the state of a system at a phase boundary where response to perturbation becomes unbounded across scales, with diverging correlation length, susceptibility, and power-law event-size distributions. This rests on nonlinearity: the structural failure of superposition in which scaling inputs does not scale outputs proportionally and combined inputs produce new phenomena including thresholds, bistability, and pattern formation. The qualitative regime change at a critical point, where the system transitions between ordered and disordered phases, is impossible in a strictly linear system where any perturbation simply decays additively.


Cross-Impact Analysis

(1) **Cross-impact analysis is a structured method for examining how multiple future events, trends, or factors influence each other — assessing, for each pair of factors, how the occurrence or strengthening of one factor raises, lowers, or leaves unchanged the probability or intensity of another — thereby revealing interaction effects that single-factor analysis misses.** (2) The distinctive focus is on pairwise interaction assessment across a systematically-bounded factor set, typically represented as a cross-impact matrix where each cell captures the impact of the row-factor on the column-factor, supported in more-formal variants by mathematical aggregation that computes adjusted probabilities or trajectories accounting for all pairwise interactions — distinct from single-factor trend analysis (which treats factors independently), from scenario narratives (which build integrated stories without explicit pairwise matrices), and from full systems-dynamics simulation (which models continuous-time dynamics rather than discrete pairwise impacts). (3) The method typically involves: identifying a bounded factor set (usually 10-30 factors selected for strategic relevance from STEEP/PESTLE-style scanning or Delphi inputs); eliciting pairwise impact assessments (often through expert workshops or structured questionnaires, with magnitudes and directions specified); constructing the cross-impact matrix; running the mathematical aggregation where applicable (Gordon's EIR method, Godet's MICMAC method, probabilistic variants); and interpreting the results for strategic implications. (4) The deeper abstraction is that **in systems of moderately-interconnected factors, the emergent behavior of the system cannot be inferred from independent analysis of the factors — factors that look unimportant in isolation may become critical when their interactions are considered, and factors that look important in isolation may be offset by opposing interactions. Cross-impact analysis is a pragmatic method for surfacing these interaction effects at a tractable level of analytical rigor between the simplicity of single-factor analysis and the complexity of full dynamic simulation.**

Network

Cross-impact analysis is the specific shape network takes when nodes are future events or factors and edges are pairwise influence relations.

Cross-impact analysis is the specific shape network takes when the entities are future events, trends, or factors within a bounded set and the connections are pairwise influence relations — how the occurrence or strengthening of one factor raises, lowers, or leaves unchanged the probability of another. It is a structurally-particularized instance of studying entities through their connection pattern, with the added commitments that connections are typically encoded in a cross-impact matrix and that the analytical payoff is aggregate trajectory adjustment accounting for all pairwise interactions, surfacing systemic effects single-factor analysis misses.


Cultural Diffusion

Cultural diffusion is the spatial-temporal spread of innovations, beliefs, practices, and values from a source culture or region to recipient cultures or regions through networks of contact, communication, and influence<!-- FACT-D29-121 -->[^rogers-1962]. Rogers's foundational 1962 *Diffusion of Innovations* (expanded to 5th edition 2003) proposed the S-curve adoption pattern: a small number of **innovators** (risk-tolerant, first adopters) try a new idea; if it works, **early adopters** (high status, opinion leaders) adopt it; their adoption signals legitimacy, triggering rapid adoption by the **early majority** and **late majority**; finally, **laggards** (tradition-oriented, skeptical) may adopt or reject<!-- FACT-D29-122 -->[^rogers-2003]. The curve rises slowly (few adopters), then accelerates steeply (network effects, visibility, social proof), then plateaus as the pool of potential adopters shrinks. The critical mechanisms are: (1) *observability* — is the innovation visible, allowing potential adopters to see benefits?; (2) *relative advantage* — does it outperform existing practices in ways that matter to the adopter?; (3) *compatibility* — does it align with existing values, skills, and infrastructure, or require wholesale change?; (4) *complexity* — is it easy to understand and use?; (5) *trialability* — can someone experiment with small adoption before full commitment?<!-- FACT-D29-123 -->[^rogers-2003] Hägerstrand's 1953 *Innovation Diffusion as a Spatial Process* documented that innovations spread geographically in expansion patterns: adoption rates are highest near the source and decline with distance, producing spatial clustering<!-- FACT-D29-124 -->[^hagerstrand-1953]. However, **network-tie diffusion** (Granovetter's "strength of weak ties") can overcome spatial distance: innovations spread faster through weak ties (acquaintances, distant contacts) than through strong ties (family, intimate friends) because weak ties bridge otherwise disconnected communities<!-- FACT-D29-125 -->[^granovetter-1973]. The *contagion-versus-threshold* distinction captures two mechanisms: some ideas spread through simple contact (contagion: my neighbor adopts, I'm slightly more likely to; the effect is local and accumulative), while others spread through threshold effects (I adopt only if a critical mass in my reference group has already adopted; there is a tipping point)<!-- FACT-D29-126 -->[^gladwell-2000]. **Structural similarity** predicts diffusion: innovations spread more readily within groups of similar people (homophily effect) and less readily across structural boundaries (class, education, geography, ethnic lines). Boas's 1896 critique of the comparative method questioned whether cultural similarities across remote societies arise from independent invention or from diffusion, establishing the distinction as foundational<!-- FACT-D29-127 -->[^boas-1896]. Kroeber's 1923 *Anthropology* and Wissler's 1923 *Man and Culture* early anthropological treatments documented both diffusion and independent parallel invention, establishing that the same practices (pottery styles, social structures, rituals) arise in multiple places via distinct paths<!-- FACT-D29-128 -->[^kroeber-1923]. Ryan and Gross's 1943 study of hybrid-seed-corn adoption in Iowa demonstrated the adoption curve empirically: innovation spread from extension agents through opinion leaders, with farmers delaying adoption (average lag: 7 years from first to last farmer in a community)<!-- FACT-D29-129 -->[^ryan-gross-1943]. Bass's 1969 mathematical model formalized the adoption curve, distinguishing the coefficient of *innovation* (external influence: advertising, institutional push) from the coefficient of *imitation* (social influence: seeing others adopt, peer pressure)<!-- FACT-D29-130 -->[^bass-1969]. Centola's 2010 networked-diffusion experiments show that adoption on **clustered networks** (where most people know each other) is slower than on **random networks** (weak ties) for simple contagion, but faster for complex contagion (things requiring social reinforcement from multiple sources), reversing expectations<!-- FACT-D29-131 -->[^centola-2010].

Contagion

Cultural diffusion is a kind of contagion in which innovations and practices spread through networks of contact and adoption.

Cultural diffusion is a specialization of contagion: innovations, beliefs, and practices spread from adopter to connected non-adopter through contact, communication, and influence, with each newly adopting agent becoming a fresh transmission source. It inherits contagion's structural commitments — contact-mediated transmission, reproduction in each new host, threshold dynamics governed by transmission rate and network topology — particularized to the cultural-innovation case where what propagates is a practice or idea and the S-curve adoption pattern is the visible signature.


Cultural Friction

Incompatibilities arise when external artifacts meet cultural norms.

Cultural friction is the structural collision that occurs when an artifact, practice, or value system introduced from outside encounters incompatibilities with existing cultural norms, worldviews, or social structures, as Schein (2010) develops in his treatment of culture as the deep, shared assumptions that resist surface-level intervention. <!-- FACT-D53-136 -->[^schein-2010] The friction generates resistance, adaptation demands, and negotiation about what aspects of the new are adopted, modified, or rejected, a process Berry (1997) formalizes in his framework of acculturation strategies (integration, assimilation, separation, marginalization). <!-- FACT-D53-137 -->[^berry-1997] This is not a failure of communication or persuasion, but a signal that two systems hold conflicting values or operate on incompatible logics.

Compatibility

Cultural friction presupposes compatibility because the resistance encountered by an imported artifact is the misalignment between its norms and the host culture's.

Cultural friction presupposes compatibility because the resistance, adaptation demands, and rejection that arise when a practice or artifact is imported are exactly compatibility's failure mode at the level of norms, worldviews, and social structures. Without compatibility's framing of coexistence-and-interaction as a between-entity relational property, friction has no reference: it names the degree to which the imported and host systems fail to align on shared assumptions. Acculturation strategies map onto how the two systems negotiate toward (or away from) compatibility.


Cultural Hegemony

Cultural Hegemony is Antonio Gramsci's analytic claim that (1) dominant social groups maintain their position not only through **coercion** (force, laws, economic compulsion) but critically through **consent** — by establishing their worldview, values, and assumptions as the **common sense of the society**, so that the existing order appears natural, inevitable, or obviously correct, (2) this hegemonic worldview is produced and circulated through **cultural institutions**: education, media, religion, entertainment, language, family structure, whose everyday operation reproduces dominant framings without overt propaganda, (3) subordinate groups come to **partially accept** the hegemonic framing even when it disadvantages them, making visible opposition feel unreasonable, marginal, or self-evidently wrong, and (4) hegemony is not totalizing — it is **contested, partial, and historically contingent**, and counter-hegemonic movements can emerge through what Gramsci called "war of position," slowly building alternative institutions and ideologies before challenging the dominant order directly.

Legitimacy

Cultural hegemony presupposes legitimacy because it works by securing voluntary consent — making dominance appear rightful rather than coerced.

Cultural hegemony presupposes legitimacy because its distinctive mechanism is the production of consent: dominant groups maintain position not chiefly through coercion but by establishing their worldview as common sense, so the existing order appears natural and rightful. That mechanism only works inside legitimacy's prior structure of voluntary compliance based on recognition of rightness. Hegemony inherits legitimacy's general apparatus of authority-treated-as-rightful and specializes it by identifying the cultural-institutional means — education, media, religion, language — through which that recognition is manufactured, often in ways that disadvantage those who accept the framing.

Social Norms

Cultural hegemony presupposes social norms because it works by installing dominant framings as the taken-for-granted normative expectations of a society.

Cultural hegemony presupposes social norms because its mechanism is the conversion of one group's worldview into the shared normative expectations of the broader society — common sense, the taken-for-granted, what everyone knows is appropriate. That conversion requires the prior structure of social norms: distributed expectations sustained by internalization and sanction, applying to everyone similarly situated. Hegemony inherits this norm-architecture and adds the further commitment that the content of the norms tracks the interests of dominant groups, so that compliance with them — felt as ordinary social membership — also reproduces a particular order of inequality.


Culture Lag

Culture lag is Ogburn's formalization of a recurring structural pattern in which a society's components (technologies, institutions, laws, norms, beliefs, values) change at different rates, creating a temporal maladjustment when faster-changing components outpace slower-changing dependent components<!-- FACT-D29-076 -->[^ogburn-1922]. Ogburn (1922) divided culture into *material* (tools, technologies, buildings, infrastructure) and *non-material* (norms, laws, religious beliefs, family structures, institutions) components, arguing that material components typically adapt faster because their success is immediately tangible (the new plow produces more grain) while non-material components change more slowly through deliberative social processes<!-- FACT-D29-077 -->[^ogburn-1922]. The lag is not a temporary friction but a *structural property* of complex systems: when a leading sector changes (almost always technological, though not exclusively), dependent sectors must adapt, but institutional inertia, normative resistance, coordination costs, and sunk-cost effects produce delays. During the lag period, the slower-changing component fits poorly with the faster-changing one, producing friction, harm, missed opportunity, or social strain<!-- FACT-D29-078 -->[^ogburn-1957]. Eventually, the dependent sector catches up through new norms, new laws, new institutions, or rollback of the leading change; but the catch-up is often partial and path-dependent, leaving residual misfit. Brinkman and Brinkman (1997) formalized this as a *dialectic*: the leading and dependent components pull in opposite directions, and only through tension-resolution do they re-equilibrate, but the re-equilibration itself is rarely a return to the prior state — it is a new configuration that embeds the leading change but constrains it through the catch-up<!-- FACT-D29-079 -->[^brinkman-brinkman-1997]. The lag can run *either direction*: non-material changes (new norms around gender, globalization, human rights) can be the leading sector, with material infrastructure (buildings, organizational design, transportation systems) lagging behind<!-- FACT-D29-080 -->[^brinkman-1997].


Curiosity

Curiosity is <!-- FACT-D17-140 -->[^berlyne-1960] the intrinsically motivating drive to acquire information, explore novelty, or resolve uncertainty when the reasoner perceives a gap between current knowledge and a salient possible state of fuller knowledge. Foundational work by Berlyne (1960) establishes curiosity as a motivational state, while Loewenstein (1994) distinguishes two main forms: epistemic curiosity (desire for knowledge) and diversive curiosity (desire for stimulation). The information-gap theory posits that perceived gaps create an aversive state; closing the gap is inherently rewarding. Intrinsic motivation (Ryan & Deci 2000) anchors curiosity's self-sustaining character: information-seeking is pursued for its own value, not solely for instrumental payoff. Curiosity emerges when the gap occupies *the Goldilocks zone* — neither trivially small (already known) nor overwhelmingly large (inaccessible) — producing <!-- FACT-D17-141 -->[^loewenstein-1994] sustained information-seeking behavior and affective engagement. Distinct from interest (a durable preference), surprise (response to violation), or boredom (absence of stimulation), curiosity is characterized by *the information gap*, *the uncertainty-driven seeking*, and *the gap-closing reward* that persist independent of external incentives.

Attention

Curiosity is a specific kind of attention, biasing selective allocation toward information that closes a salient knowledge gap.

Curiosity is a specialization of attention. The general pattern is the selective allocation of a limited cognitive resource to a subset of available information, gating what gets processed deeply. Curiosity instantiates this with the allocation criterion being a perceived information gap: the reasoner orients selective attention toward stimuli that promise to close the gap between current and possible knowledge, with the gap-resolution itself intrinsically rewarding. Berlyne and Loewenstein's information-gap framing makes curiosity the attentional bias whose targeting rule is gap salience, particularly within the Goldilocks zone of optimal challenge.

Uncertainty

Curiosity presupposes uncertainty because the perceived knowledge gap that motivates information-seeking is itself an uncertainty state.

Curiosity presupposes uncertainty because the information-gap that drives exploration is a specific uncertainty condition: the reasoner perceives an unknown quantity (the missing knowledge), evidence about its possible resolution, and a felt difference between current and possible states of fuller knowing. Without uncertainty's apparatus for distinguishing known from unknown and characterizing the unknown, there is no gap to feel or close. Curiosity is the motivational response to epistemic uncertainty operating in the Goldilocks zone where closure feels both possible and worth the effort.


Damping

Damping is the process or mechanism by which energy is systematically removed from a dynamical system's oscillations or fluctuations, reducing amplitude over time and driving the system toward a lower-energy state (rest, equilibrium, or steady oscillation at a smaller amplitude than an undamped counterpart). The essential commitment is that damping opposes motion in proportion to the motion itself (typically velocity), dissipating mechanical or stored energy into heat, radiation, or other forms that exit the dynamical variables of interest. Every damping claim specifies (1) the oscillation or fluctuation whose amplitude is being reduced, (2) the mechanism of energy removal (viscous drag, radiation, hysteresis loss, policy intervention), (3) the damping coefficient or analog that sets the rate of decay, and (4) the damping regime (underdamped, critically damped, overdamped) that characterizes the qualitative response.


Data Integrity

Data integrity is the property that data remains accurate, consistent with its intended meaning and internal rules, and free from unauthorized, erroneous, or accidental modification throughout its lifecycle — creation, storage, transmission, processing, archival, retrieval — enforced by a combination of technical mechanisms (checksums, error- correcting codes, digital signatures, constraints, transactions) and organizational mechanisms (validation rules, audit, change control, provenance tracking). The essential commitment is that data without explicit integrity protection is progressively corrupted by bit rot, transmission errors, software bugs, operator mistakes, and adversarial manipulation; that detecting corruption requires redundancy or cryptographic verification; and that different threats require different mechanisms<!-- FACT-D30-106 -->[^shannon-1948].

Verification

Data Integrity is a kind of verification: checksums, signatures, and audits confirm conformance to the data's intended specification.

Data integrity is preserved by mechanisms — checksums, error-correcting codes, digital signatures, validation rules, audit, provenance — that check stored or transmitted data against the criteria it must satisfy and produce a verdict of accept or repair. That is the defining structure of Verification: a procedure that checks conformance to specification and yields evidence-backed verdicts. Data integrity specializes verification to the case where the specified object is data and the specification covers accuracy, consistency, and authorized state.

Invariance

Data integrity presupposes invariance because preserving accuracy across the data lifecycle is the preservation of intended content under storage, transmission, and processing operations.

Data integrity presupposes invariance because the integrity guarantee names a feature -- the data's intended content and internal rules -- that must remain unchanged under the family of transformations data undergoes (writes, reads, transmission, archival, processing). Checksums, signatures, and constraints are the mechanisms that verify invariance under each operation. Without invariance's joint commitment to preserved feature and preserving operations, there is no formal sense in which data is or is not corrupt; integrity IS engineered invariance with detection and recovery.


Deadlock

Deadlock occurs when *two or more processes or agents are blocked, each waiting for resources or conditions controlled by others, preventing any from proceeding*. The essential commitment is *circular dependency*: a cycle of waiting relationships such that breaking the cycle requires one of the waiting parties to act, but all are blocked awaiting action from others <!-- FACT-D30-061 -->[^coffman-1971].


Deadweight Loss

Deadweight loss is the reduction in total economic surplus (consumer surplus plus producer surplus, plus any government revenue or externality-internalization benefit) that results when a market intervention, market failure, or other distortion prevents mutually beneficial transactions that would occur at competitive equilibrium — a loss in which *no party* receives the foregone surplus, as distinct from transfers where surplus merely shifts between parties. The essential commitment is that there is an unambiguous welfare benchmark (the competitive-equilibrium allocation with no market failures) against which interventions can be evaluated, and that distortions generating deadweight loss are inefficient in the Kaldor-Hicks sense (the gainers cannot compensate the losers).

Pareto Efficiency

Deadweight loss presupposes Pareto efficiency because the welfare benchmark from which the loss is measured is the no-Pareto-improvement-available allocation.

Deadweight loss is the reduction in total surplus relative to a benchmark welfare allocation that distortions prevent the market from reaching. The benchmark is the competitive-equilibrium allocation with no market failures — precisely the Pareto-efficient frontier where no change can make anyone better off without making someone worse off. Pareto efficiency supplies exactly that benchmark: the set of allocations from which no Pareto improvement is available. Deadweight loss is meaningful only against this benchmark, presupposing Pareto efficiency as the reference point from which welfare losses are measured.

Price Elasticity

Deadweight loss typically presupposes price elasticity because the magnitude of welfare lost from a price distortion depends on demand and supply responsiveness.

Deadweight loss is the reduction in total surplus that results when a market distortion prevents mutually beneficial transactions, measured as the welfare triangle. The size of that triangle is determined by how responsive quantity is to price — the more elastic supply and demand, the larger the deadweight loss for a given tax or price wedge. Price elasticity supplies the responsiveness parameter that calibrates the magnitude. Deadweight loss as a quantified welfare claim typically presupposes elasticity, though qualitative existence-of-distortion arguments can be made without it, hence typical.

Allocation

Deadweight loss is the specific shape allocation takes when distortions prevent mutually beneficial transactions, leaving surplus uncaptured by any party.

Deadweight loss is the inefficiency particularization of allocation: it names the structural shortfall between the realized assignment of resources and the welfare benchmark of competitive equilibrium. Where allocation names the bare assignment of limited supply to competing claims generally, deadweight loss specifies the case where the assignment forecloses mutually beneficial trades, producing a loss in which no party captures the foregone surplus — a particular form of misallocation distinguished from transfers, which merely shift surplus between parties.


Decision

Committing to one alternative from a set under uncertainty and trade-off, collapsing open deliberation into a chosen path and foreclosing the others.

Decision is the act of selecting one alternative from a set under conditions of constraint, uncertainty, or trade-off, thereby committing future resources or actions to that choice and closing off other paths, as Hastie and Dawes (2010) develop in their foundational treatment of rational choice. <!-- FACT-D52-166 -->[^hastie-dawes-2010] A decision names the moment when deliberation collapses into commitment: the transition from keeping options open to locking in a path. It spans decision theory (utility, expected value, Bayesian decision rules), behavioral economics (revealed preference, heuristics and biases), management science (decision rights, governance structures), artificial intelligence (action selection, reinforcement learning), philosophy (agency, free will), and applied domains from medicine (clinical decision-making) to public policy (cost-benefit analysis, regulatory choice), a multidisciplinary scope that Edwards (1954) first surveyed in his canonical review. <!-- FACT-D52-167 -->[^edwards-1954]

Constraint

Decision presupposes constraint because selecting one alternative from a set requires that the admissible set be defined by binding restrictions.

Decision is the act of selecting one alternative from a set under conditions of constraint, uncertainty, or trade-off. The set itself is constituted by constraint — a condition that restricts admissible configurations to those satisfying it, producing the feasible set from which selection draws. Without constraint there is no bounded choice set, no closure of options, and no meaningful selection. Constraint supplies the binding restriction that defines what counts as an admissible alternative; decision then ranges over that set and commits to one element, so it presupposes constraint as the substrate of its choice space.

Reversibility and Irreversibility

A decision presupposes reversibility and irreversibility because every selection carries an implicit commitment to a position on the reversal-cost dimension.

A decision is the moment when deliberation collapses into commitment, and the structure of that commitment is defined by where it sits on the reversibility dimension: whether the chosen path can be unwound, at what cost, and within what window. Without the prior distinction between reversible and irreversible action, a decision would have no commitment dimension — no closing-off of alternatives, no resource locking, no preserved or sacrificed flexibility. The reversibility property is what gives decisions their consequential weight.


Decision Fatigue

Decision fatigue is the claim that the quality of decisions a person makes declines over an extended sequence of choices — as the sequence continues, later decisions show more reliance on defaults, more impulsive or status-quo choices, more reluctance to deliberate, and higher error rates than earlier decisions in the same sequence, even when the later decisions are structurally similar to the earlier ones. The essential commitment is that the capacity for effortful deliberation is a depleting or drifting resource over a decision sequence, and that observable choice patterns differ systematically between early-in-sequence and late-in-sequence decisions in ways not explained by the content of the choices themselves. The canonical theoretical lineage traces to Baumeister, Bratslavsky, Muraven, and Tice's (1998) "ego-depletion" framework — the hypothesis that self-control and goal-directed behavior rely on a limited metabolic resource that becomes depleted through use. <!-- FACT-D18-100 -->[^baumeister-bratslavsky-muraven-tice-1998] Vohs, Baumeister, Schmeichel, Twenge, Nelson, and Tice (2008) operationalized this framework specifically for decision-making, demonstrating that the act of making choices impairs subsequent self-control; canonical ego-depletion lineage for decision-fatigue operationalization. Every decision-fatigue claim specifies (1) the decision sequence and agent, (2) the timecourse or count of decisions over which fatigue accumulates, (3) the specific decline in decision quality (defaults, impulsivity, avoidance, error rates), and (4) the comparison condition that isolates the fatigue effect from alternative explanations (content differences, time-of-day circadian effects, caseload selection).

Bias

Decision Fatigue is a kind of bias: depletion produces a systematic, direction-consistent drift toward defaults and impulsive choices.

Decision fatigue produces a systematic — not random — shift in choice patterns as a sequence progresses: later choices reliably tilt toward defaults, status-quo options, and impulsive selections. The displacement is in a consistent direction and persists across the sequence rather than averaging out across additional acts. That is the defining structure of Bias: a persistent offset of process output from the unbiased target. Decision fatigue specializes bias to sequential decision-making under deliberative-resource depletion.

Cognitive Resource Depletion

Decision fatigue is a specialization of cognitive resource depletion in which the depleting capacity is sustained deliberative choice.

Decision fatigue is a specialization of cognitive resource depletion in which the consumed capacity is specifically that for effortful deliberative choice. It inherits the general depletion pattern of time-dependent performance decay under sustained use, reversible by rest, and distinguishes itself by tying the consumption to extended sequences of decisions and by registering its signature in choice-quality markers: more defaults, more impulsivity, more status-quo bias, more errors late in the sequence than early. The substrate is the same depleting resource; the specialization fixes its expenditure to decision-making.

Decision

Decision Fatigue presupposes Decision: the phenomenon is a degradation pattern across a sequence of choice acts.

Decision fatigue is the empirical claim that the quality of choices in a sequence declines as the sequence continues, with later acts showing more default-reliance, impulsivity, and error. The phenomenon is defined over a sequence of Decision events: there must be repeated acts of selecting one alternative from a set before any degradation pattern can be observed or named. Decision fatigue therefore presupposes Decision as the unit it counts and the act whose quality degrades.


Decomposition

Breaking a whole into parts that can be analyzed independently and recombined to reconstitute the whole, making complexity tractable through divide-and-conquer.

Breaking a whole into constituent parts such that the parts, when properly combined, reconstitute the whole; an operation that is reversible and structure-preserving, enabling independent analysis of pieces and their recombination into meaningful wholes, an arrangement Simon (1962) identified as the architecture of nearly all complex systems. <!-- FACT-D52-181 -->[^simon-1962] Decomposition assumes that a complex entity can be understood more easily by separating it into simpler sub-entities, analyzing each sub-entity, and then reassembling. This assumption—that the whole can be reduced to parts without loss of information—is powerful and ubiquitous but not universally true; some systems exhibit emergent properties that vanish when decomposed.


Deductive Reasoning

Deductive reasoning is the pattern of inference in which a conclusion is derived from one or more premises by a rule of inference whose application guarantees that if the premises are true, the conclusion must be true — the inference is truth-preserving, and the conclusion's content is already implicit in the premises rather than extending beyond them. The essential commitment is formal: what makes a deductive inference valid is the structure of the argument, not the subject matter; the same schema (modus ponens<!-- FACT-D20-001 -->[^aristotle-prior-analytics], universal instantiation, transitivity) licenses the move in mathematics, law, or everyday reasoning. Every deductive-reasoning claim specifies four essential components: (1) **the premises and their logical form**, which are taken as given — typically articulated as propositions with identifiable logical structure (universal quantification, conditional, conjunction, disjunction, negation); (2) **the rule of inference or proof schema**, a specifiable mechanism (syllogism, modus ponens, modus tollens, substitution, resolution, mathematical induction applied as proof technique, or formal manipulation under an axiom system) that maps premises to conclusion; (3) **the conclusion and its status as necessarily following — validity** — the entailment that in every possible world where the premises are true, the conclusion is necessarily true; and (4) **the distinct question of soundness**, which separates validity (structure alone) from truth-establishment (validity plus true premises), determining whether the conclusion is established rather than merely hypothetical.


Deep Time

Deep Time is the cognitive and analytic frame in which: (1) **timescales of millions to billions of years** — vastly beyond human biographical, historical, or civilizational horizons — are treated as the relevant frame for understanding certain processes (geological, cosmological, evolutionary, nuclear, climatic); (2) processes that are **imperceptibly slow on human timescales** become dominant forces on deep-time scales (continental drift, biological evolution, stellar nucleosynthesis, radioactive decay of long-lived isotopes); (3) adopting the deep-time frame is a **cognitive discipline** — human intuition systematically underestimates deep-time durations; explicit modeling, analogies, and log-scale representations are needed to reason accurately; (4) the frame has **ethical and planning consequences** in domains where decisions produce effects at deep-time scales (nuclear waste storage, climate commitments, species-extinction decisions), which human planning horizons are poorly adapted to address.

Time

Deep time presupposes time because its content is the cognitive frame adopted for timescales of millions to billions of years.

Deep time presupposes time because its content is a re-framing of the temporal dimension at scales vastly beyond biographical or historical horizons — geological, evolutionary, cosmological. It inherits time's structural commitment to ordered succession with measurable duration and irreversible direction, particularized to the very-long-timescale regime where processes invisible on human timescales become dominant and human intuition systematically underestimates duration. Deep time is time read at log-scale.


Degrees of Freedom

Degrees of freedom quantifies the number of independent parameters required to specify a system's complete state — the number of independent coordinates in mechanics, independent quantities in statistics (after constraints), or independent motions in mechanism design. The construct captures system complexity as a single integer (or effective fractional value) reflecting the dimensionality of state space after constraints are imposed.

Constraint

Degrees of freedom presupposes constraint because counting independent parameters only becomes meaningful once binding restrictions on configurations are specified.

Degrees of freedom counts the independent parameters needed to specify a system's state after constraints are imposed — formally, unconstrained parameters minus constraints. The count is meaningful only against a specified set of binding restrictions that prune the feasible set: holonomic constraints in mechanics, statistical constraints after estimation, kinematic constraints in mechanism design. Without constraints as a first-class structural object defining the admissible subset, the dimensionality reduction that degrees of freedom measures would have nothing to subtract from and no operational content.

Decomposition

Degrees of freedom presupposes decomposition because the count of independent parameters is read off the system's decomposition into independent coordinates after constraints.

Degrees of freedom quantifies the number of independent parameters required to specify a system's complete state, computed as unconstrained parameters minus constraints. This presupposes decomposition: breaking a whole into constituent parts whose independent analysis and recombination reconstitute it. The state is decomposed into a set of independent coordinates (mechanical generalized coordinates, statistical sample components, mechanism joints), each contributing one dimension to state space; constraints reduce the effective count. Without decomposition's structure-preserving partition into independent pieces, there is no notion of independent parameters to count.


Deixis

Deixis is the property of certain linguistic expressions whose reference is fixed only by the *context of utterance*: (1) the reference depends on **who is speaking** (personal deixis: *I*, *you*, *we*), **where** (spatial deixis: *here*, *there*, *this*, *that*), **when** (temporal deixis: *now*, *yesterday*, *tomorrow*), **what discourse** (discourse deixis: *this argument*, *the above*), and **what social role** (social deixis: *your Honor*, *Mr./Ms.*, T/V pronouns);<!-- FACT-D23-031 -->[^levinson-2004] (2) without situating the utterance in the deictic **context**, the expression is genuinely ambiguous or empty — not under-specified but *unreferenced*;<!-- FACT-D23-032 -->[^fillmore-1971] (3) deictic expressions are typically drawn from a **closed class** (pronouns, demonstratives, adverbials of place and time) that speakers must learn as a system of coordinates; (4) the same deictic word points to *different referents* in different utterances, yet its semantic rule is invariant: *I* always points to the speaker.<!-- FACT-D23-033 -->[^kaplan-1989]


Delegation of Authority

Delegation of Authority is the assignment of decision-making power, responsibility, and/or execution authority from a principal (typically a higher-authority body or role-holder) to an agent or subordinate, with the expectation that the agent will act on behalf of the principal within specified limits, subject to accountability mechanisms, and with the understanding that the principal retains ultimate responsibility while the agent bears operational accountability<!-- FACT-D32-001 -->[^delegation-def]. The essential commitment is that no individual or single authority can execute all decisions in a complex organization; delegation is therefore a structural necessity that distributes authority vertically (from superior to subordinate) or laterally (between peers)<!-- FACT-D32-008 -->[^vertical-lateral]; that clear specification of what may be delegated, to whom, under what conditions, and with what reporting obligations prevents authority vacuum and confusion; and that delegation creates a relationship of trust, discretion, and accountability between delegator and delegatee.

Authority

Delegation of authority presupposes authority because there must be a legitimate decision-making power before any of it can be transferred to subordinates.

Delegation is the structured transfer of a right to decide from a principal to an agent within specified limits, with the principal retaining ultimate responsibility. The transfer can only occur if such a right exists in the first place — a recognized, legitimate power to make binding decisions. Authority supplies precisely that: the socially recognized capacity to create obligations, vested in a role rather than in raw capability. Without an underlying authority to allocate, there is nothing for delegation to assign or for accountability mechanisms to track back to.


Delphi Method

*The Delphi Method* names the abstraction that (1) when the best-available knowledge on a complex question is *distributed across human experts* rather than captured in measurable data, (2) *structured elicitation with anonymity and iterative controlled feedback* produces substantially better aggregation than either unstructured consultation or formal committee deliberation, because (3) the structure suppresses specific failure modes — *dominant-personality bias, groupthink, anchoring, strategic positioning, political pressure* — that degrade unstructured expert judgment, while (4) preserving the *information content* of expert reasoning through statistical summaries and anonymized rationale feedback. The distinctive commitment is the *combination* of anonymity and iteration: either alone produces substantially weaker aggregation than the combination, and the method's structural features — round count, feedback mechanism, termination criteria — are chosen as a deliberate elicitation design analogous to an experimental design.

Iteration

The Delphi Method is a constituent piece of iteration; its structured rounds of anonymous expert feedback are an iteration cycle applied to opinion convergence.

The Delphi Method's machinery is built as an explicit iteration: each round consists of an elicitation step whose output (statistical summaries and anonymized rationale) becomes the input to the next round, with progress measured by convergence of expert opinion. The method is a particular configuration of iteration in which the iteration step is structured elicitation, the state carried forward is the distribution of responses and reasoning, and the stopping condition is stability or sufficient convergence — Delphi is iteration specialized to expert-opinion aggregation.

Aggregation

The Delphi Method is the specific shape aggregation takes when distributed expert judgment is collapsed into a consensus through structured, anonymized iterative rounds.

The Delphi Method is the particularization of aggregation to the setting of distributed expert opinion: many individual judgments are collapsed into a unified summary that retains the consensus signal while suppressing personal-influence and dominance distortions. Where aggregation names the deliberate loss of granular detail to retain chosen features generally, Delphi specifies that the feature retained is the convergent expert estimate while the detail suppressed is identity-linked bias, anchoring, and groupthink artifacts that contaminate unstructured pooling.


Dependency

Directed relation in which one element relies on another being present, prior, compatible, or supplied, with a specifiable failure mode if the condition is unmet.

Dependency is the directed relation in which one element relies on another being present, prior, compatible, or supplied — a structural asymmetry where A cannot proceed, function, be interpreted, or retain its value unless some condition on B is met, a relation Parnas (1972) made foundational to modular decomposition by treating "module A depends on module B" as the operational criterion governing which design changes propagate. <!-- FACT-D56-211 -->[^parnas-1972] The relation has been formalized independently in five distinct intellectual traditions: graph-theoretic dependency analysis in compiler design (Aho, Lam, Sethi, and Ullman 2006), task-precedence modeling in operations research (Kelley and Walker 1959, who introduced the Critical Path Method), logical entailment in formal logic (Tarski 1936), semantic presupposition in philosophy of language (Strawson 1950), and obligate dependency in ecology (Janzen 1980). <!-- FACT-D56-212 -->[^aho-lam-sethi-ullman-2006][^kelley-walker-1959][^tarski-1936][^strawson-1950][^janzen-1980] The fact that these traditions converged on essentially the same structural notion — a directed reliance relation with a specifiable failure mode — without borrowing from each other is the strongest evidence that dependency is a substrate-independent prime rather than a domain-specific construct.


Design for Implementation

design for manufacturability
design for assembly
DFM
DFA
design for X
design for operations

Design for Implementation is the systematic discipline of constraining design decisions to account for the characteristics, limitations, and costs of the systems and processes that will produce, assemble, operate, maintain, or retire the design. The essential commitment is that designing an artifact (product, building, service, organizational process) is not complete when the functional requirements are met and the ideal performance is achieved; the design must also be implementable within the constraints of production, deployment, operation, and end-of-life processes.

Constraint

Design for implementation presupposes constraint because the discipline is precisely the inclusion of production and operational limits as binding restrictions on design choices.

Design for implementation is the systematic practice of treating manufacturing capabilities, supply-chain limits, assembly sequences, and operational costs as binding restrictions on the admissible set of design configurations. Without constraint's machinery of treating a binding restriction as a first-class structural object, there would be no way to convert downstream realization limits into upstream design rejection rules: a configuration violating production feasibility would be no different from a configuration meeting it. The parent prime supplies the binding-restriction structure that this discipline applies to implementation context.

Trade-offs

Design for implementation presupposes trade-offs because constraining design to producibility necessarily worsens some functional dimensions to improve others.

Design for implementation systematically constrains design decisions to fit the realities of production, assembly, operation, and end-of-life processes — meaning the design cannot pursue ideal functional performance alone. The discipline operates by accepting compromise on one valued dimension (e.g., maximum performance, minimum part count, ideal geometry) to improve another (manufacturability, maintainability, supply-chain robustness). This is exactly the trade-off structure: improving one dimension within a feasible set requires worsening another. Without recognition that valued dimensions are multidimensionally coupled, the entire discipline collapses into single-objective optimization.


Design for Lifecycle Adaptability

design for changeability
design for disassembly
design for evolution
modularity for lifecycle

Design for Lifecycle Adaptability is the engineering practice of intentionally structuring a system, product, or process such that it can be *modified, updated, reconfigured, repurposed, or deconstructed* at different stages of its operational life without excessive cost, complexity, or compromise to core function. This is characterized by (1) the anticipation during design of how the system might evolve — what requirements might change, what components might need upgrade or replacement, what performance characteristics might shift — and the deliberate embedding of adaptability mechanisms (modular interfaces, redundancy, excess capacity, staged assembly) to accommodate foreseen evolution, (2) the separation of *change-prone elements* (user interfaces, algorithm parameters, feature sets, component versions) from *stable core elements* (fundamental architectures, load-bearing structures, critical protocols) such that changes to the former do not require redesign of the latter, (3) the recognition that *every system has a lifecycle* — it is born (design, manufacture, deployment), evolves (maintenance, upgrades, extensions, configuration), and dies (decommissioning, recycling, repurposing) — and that adaptability decisions made during design profoundly affect the cost and feasibility of evolution and end-of-life stages, (4) the commitment to *ease of partial change*: a well-adapted system can be modified piecemeal (replace one component, upgrade one subsystem) without requiring wholesale redesign or downtime, and (5) the understanding that adaptability reduces waste — systems designed for easy reconfiguration or upgrading are used longer, their components are reused or recycled rather than discarded, and the total lifecycle cost and environmental impact are reduced. The deeper insight is temporal: static design (optimize for current requirements, assume future requirements unknown) is brittle; adaptive design (anticipate categories of change, build flexibility in) is resilient. Design for Lifecycle Adaptability originated in mechanical engineering (design of machinery for easy maintenance and upgrade), manufacturing systems (production lines that can be reconfigured for different products), and architecture (buildings designed for renovation or conversion). The principle formalized through design-for-disassembly (Ulrich, 1995, focusing on end-of-life disassembly for reuse and recycling), design-for-changeability frameworks (Fricke and Schulz, 2005), and epoch-era analysis (Ross, Rhodes, and Hastings, 2008) which model how systems evolve through discrete change epochs. The mechanism works because anticipating change during design is vastly cheaper than retrofitting adaptability after deployment; systems designed with adaptability built in can evolve gracefully, whereas systems designed for static conditions become increasingly costly to modify as they age<!-- FACT-D35-046 -->[^ulrich-1995].

Modularity

Design for lifecycle adaptability typically presupposes modularity because the future changes it accommodates are absorbed at module boundaries.

Design for lifecycle adaptability deliberately structures systems so they can be modified, upgraded, or repurposed across operational life without excessive cost. The practical mechanism is typically modular structure: changes are absorbed by replacing or reconfiguring discrete modules without rippling through the whole. Modularity supplies the decomposition into independently revisable components with stable interfaces. Lifecycle adaptability rides on this organization to keep modification cost bounded, though some adaptability strategies use redundancy or parameterization without strict modularity, so the dependence is typical rather than strict.

Adaptation

Design for lifecycle adaptability is the specific shape adaptation takes when adaptability mechanisms are deliberately built into a system at design time.

Design for lifecycle adaptability is the engineered, anticipatory particularization of adaptation: rather than a system changing in response to sustained environmental change after the fact, the designer pre-embeds modular interfaces, redundancy, excess capacity, and reconfiguration paths so that future modification is supported. Where adaptation names the modification of a system to fit new conditions generally, the design-for-adaptability variant fixes the timing — the adaptive capacity is engineered in upfront, before the conditions that will exercise it are known.


Design Patterns

architectural patterns
reusable solutions

Abstraction

Design patterns is the specific shape abstraction takes when recurring solution structures are named and extracted for reuse across instances.

Abstraction is the purpose-relative retention of structure that keeps what is load-bearing for a use across many concrete instances. Design patterns is the particular shape this move takes in design and architecture: recurring problem-solution shapes are extracted from many concrete instances, named, and codified so the abstracted structure can be reused in new situations. It is a structurally-particularized instance of abstraction whose specific projection retains the generalizable problem-solution structure and discards the particulars of any one application.