Models and Representation

T5 is the fifth independent theory document in the T1–T9 programme. It examines how models, measurements, maps, equations, simulations, and visualisations may represent bounded relations in actuality, and what is required before a model may be assigned to what is actually the case.

T1 established actuality as the independent ground. T2 established conditions for knowledge and corrigibility. T3 distinguished event, registration, observation, interpretation, and inference. T4 distinguished expression, meaning, reference, claim, scope, and assignment. T5 addresses the further ordering of such elements in formal and operative representational systems.

The document does not by itself decide whether a particular scientific, legal, economic, technical, or administrative model is true or defensible. It establishes distinctions and requirements for examination that must be used together with domain knowledge, data, observation, validation, and applicable rules.

Representation is an ordered presentation through which something is made available by signs, form, structure, measure, relation, or rule. The representation is itself something that exists, but it is not identical with what it represents.

Representation may be linguistic, visual, cartographic, mathematical, statistical, geometric, mechanical, digital, symbolic, narrative, or institutional. Each form preserves something, omits something, and introduces particular conditions of use.

That a representation is precise, useful, or technically correct does not automatically establish that every property of the representation belongs to the represented state of affairs.

A model is a rule-governed representational arrangement that selects, structures, simplifies, transforms, or simulates properties and relations of a stated object or problem domain.

A model commonly includes a model object, a purpose, selected variables, assumptions, parameters, relations, rules, data, initial or boundary conditions, and a domain of validity. What counts as the model must therefore be clarified before its output is assessed.

The model must be distinguished from its implementation, data basis, run, output, visualisation, interpretation, and the claim about what the output means in actuality.

Models may serve several functions at once. The functions must nevertheless be made visible because they impose different requirements upon data, examination, and use.

A model developed for illustration must not, without further grounds, be used as a precise explanation or decision model. A predictive model must likewise not automatically be read as a causal explanation.

Before a model is assessed, it must be identified what is modelled, which properties or relations are selected, what question is asked, and what the model is to be used for.

The same model may be defensible for one purpose and indefensible for another. A coarse map may serve navigation while being inadequate for precise area measurement. A risk model may have group-level value without carrying a certain individual decision.

The purpose must therefore be accompanied by an explicit non-purpose: what the model has not been developed, validated, or authorised to decide.

• Model object and unit of analysis.
• Selected properties and relations.
• Purpose and intended audience.
• Decisions the model may affect.
• Known non-use domains.
• Requirements of competence and responsibility.

Models do not represent everything. They abstract, idealise, approximate, or reduce in order to make a relation manageable and examinable.

Abstraction selects properties or relations. Idealisation deliberately uses simplified or literally false conditions. Approximation provides a bounded estimate. Reduction represents a complex relation through fewer variables or levels.

A simplification is not an error merely because it is incomplete. It becomes epistemically or practically problematic when what is omitted has decisive effect within the actual domain of use.

Every representation preserves something and loses something. Model audit must therefore ask which properties, relations, scales, and variations are carried forward and which are filtered, aggregated, projected, or rendered invisible.

A map may preserve direction, distance, area, or angle to different degrees but not necessarily all at once. A statistical score may preserve ranking and lose the concrete variation beneath it. A visualisation may reveal one pattern while hiding another.

Loss is not automatically distortion. Distortion occurs when the representation or its use gives the impression that something is preserved which the model has in fact changed or omitted.

• What is preserved?
• What is transformed?
• What is omitted?
• What is aggregated?
• What is added by the form of presentation?
• What follows for the domain of validity?

Measurement is a rule-governed assignment of values, categories, or magnitudes to a phenomenon or relation through a documented measurement operation.

Measurement requires a measurement object, a property, a unit or category, an instrument or procedure, a scale, calibration, resolution, error margin, time, and conditions of registration.

The measured value is not the property itself. It is the result of a measurement relation and must be assessed together with the operation that produced it.

• What is measured.
• The measurement operation.
• The instrument or procedure.
• The measured result.
• The data presentation.
• The interpretation of the result.

Calibration establishes and checks the relation between an instrument output and a defined reference. A number does not gain epistemic strength merely because it was produced by an instrument.

Relevant documentation includes calibration standard, date, tolerance, drift, reference instrument, software version, maintenance, and environmental conditions.

Traceability requires that the measured result can be followed back through instrument, settings, references, and processing. Where the chain is broken, uncertainty or limited status must be marked.

Data are registered and structured traces with provenance, format, and conditions. T5 distinguishes observed data, derived data, estimated data, imputation, synthetic data, training data, validation data, and model-generated data.

The data basis is shaped by what is included, excluded, measured, missing, cleaned, aggregated, and categorised. These choices may be professionally legitimate, but they must be visible if the model is to be reviewable.

Validation on the same material used to develop or fit the model may overstate its strength. Independent examination is especially important when the model is transferred to new populations or decisions.

• Provenance and collection.
• Inclusion and exclusion.
• Missing values and imputation.
• Categories and thresholds.
• Cleaning and transformation.
• Separation of development and validation bases.

A formal model may be mathematically, logically, or technically correct under its own rules. This is internal validity. It does not by itself establish that the variables, relations, or results correspond to the concrete relation to which the model is applied.

External assignment concerns the relation between formal structure and model object. Empirical correspondence concerns how outputs hold against relevant observations and measurements. Ontological assignment concerns how far the model is warranted in saying what is actually the case.

Mathematical elegance, symmetry, or consistency may provide reason for further inquiry but not independent proof that actuality possesses the same structure.

Model outputs depend upon explicit and implicit assumptions, fixed and estimated parameters, priors, initial conditions, boundary conditions, thresholds, and exclusion criteria.

T5 requires a distinction between what the model finds and what is placed into it. An output cannot be presented as an independent discovery when it follows principally from premises, calibration, or selected thresholds.

Sensitivity analysis and alternative parameterisations may show whether the conclusion is robust or whether small changes in assumptions produce materially different results.

• Explicit assumptions.
• Implicit assumptions.
• Fixed and estimated parameters.
• Initial and boundary conditions.
• Thresholds and exclusion criteria.
• Sensitivity and robustness.

Simulation is the rule-governed production of model states or model trajectories under stated assumptions. The simulation is an actual computational event, and its result is an actual dataset or presentation.

The simulated trajectory is not thereby an actual event in the world. Simulation may explore consequences of a model, reveal unexpected model behaviour, and compare scenarios, but it does not by itself prove that the model corresponds to actuality.

Epistemic strength arises from the relation among model, data, validation, domain knowledge, and the concrete assignment.

Visualisation may reveal patterns, compress data, display relations, and support discovery. It is at the same time a selection and transformation of material.

Axes, units, scale, normalisation, colour, framing, missing data, resolution, and uncertainty affect what appears. A visually compelling presentation may therefore be correct, misleading, or inadequate depending upon these choices.

Visual force must not count as independent evidence. The relation among data, model, processing, and image must be documentable.

• Data source and processing.
• Axes, units, and scale.
• Normalisation and thresholds.
• Colour and symbol legend.
• Missing data and uncertainty.
• The relation between image and model.

Validation examines whether a model is adequate for a stated purpose and domain of use. It must be distinguished from technical verification, which examines whether the implementation corresponds to the specification.

Internal validation concerns relations near the development basis. External validation concerns independent cases, environments, or populations. Construct validation asks whether the variable actually represents the concept. Prospective validation tests the model forward in practice. Consequence validation examines what use does.

A model may be predictively strong and still be poorly explained, misapplied, unfair, outside its domain, or harmful through its use.

Every model must state population, time, place, scale, resolution, purpose, relevant conditions, known deviations, and domains in which it has not been tested.

Interpolation is use within a tested range. Extrapolation proceeds outside that range. Transfer applies the model in another context or population. Ontological generalisation claims that the model expresses the structure of actuality itself.

Each transition requires stronger and more visible grounds. A result that holds locally cannot without further examination be extended to universal or ontological status.

A model may predict well without explaining correctly, and it may provide a reasonable explanation without delivering highly precise predictions.

T5 distinguishes correlation, prediction, mechanism, causation, explanation, control, and understanding. High predictive accuracy does not automatically establish causation, ontological structure, moral relevance, or a valid individual decision.

When a model is used explanatorily, it must be made visible which mechanism or structure is asserted, which alternative explanations were considered, and what findings could weaken the explanation.

The same material may be represented through several models emphasising different scales, purposes, variables, or preserved properties.

Model pluralism does not mean that all models are equally valid. They must be compared by correspondence, domain, explanatory power, robustness, prediction, transparency, consequence, and corrigibility.

Where several models fit the same data, uncertainty and underdetermination must be made visible rather than one alternative receiving ontological priority through habit or authority.

• Empirical correspondence.
• Domain of validity.
• Robustness and sensitivity.
• Explanatory and predictive power.
• Transparency and reviewability.
• Practical consequence and corrigibility.

In administration, health, finance, employment, policing, education, and technology, model outputs may have direct effects upon persons. T5 distinguishes model output, professional assessment, institutional recommendation, formal decision, and actual consequence.

A model output is not automatically a decision, and human approval does not automatically make an output defensible if the approval merely confirms something the decision-maker cannot understand or review.

Institutional use must identify who selected the model, its purpose, data, known limitations, decision responsibility, the possibility of challenge, and how errors are corrected.

T5 distinguishes training data, model architecture, parameters, inference, generated output, probability, linguistic fluency, factual reference, knowledge, and decision.

A generative system may produce plausible formulations, images, classifications, and predictions. It does not follow that the system observed what is discussed, knows that the representation is true, has an independent relation to actuality, or can bear institutional responsibility.

Machine outputs must be traced through data basis, model, version, processing, thresholds, instructions, and human use. Source control and decision responsibility cannot be delegated merely because an output is technically advanced.

T5 consolidates a general audit structure that may later be operationalised in R1 and A3. The structure must not classify the model as defective in advance but must make the transition from material to ontological or practical claim visible.

The audit must be adapted to model type, domain, and consequence. An illustrative model does not require the same validation as a model governing rights, diagnosis, or resource allocation.

• What is the model object and purpose?
• What is preserved, transformed, and omitted?
• Which assumptions and parameters are used?
• Which data and measurements form the basis?
• Which outputs does the model produce?
• What is visualisation, simulation, or projection?
• Where is the model assigned to actuality?
• What validates this assignment?
• Which alternative models exist?
• What can correct or defeat the model?
• What happens when the model is used?
• Who bears responsibility for use and decision?

The objections below test whether T5 makes the model requirement too strict, too realist, or insufficiently attentive to the fact that access itself is represented. The answers are bounded and mark residual problems.

T5 enters discussion with scientific realism, instrumentalism, constructive empiricism, structural realism, model-based science, theories of representation, idealisation, measurement theory, simulation epistemology, and philosophy of data and visualisation.

The position shares with model-based approaches that models are not merely derivative copies but active instruments of representation and inquiry. It shares with instrumentalism that usefulness does not require complete literal similarity. T5 nevertheless maintains that factual and ontological claim-content must answer to justified transitions from model to actuality.

T5 does not reject model pluralism or perspective-dependent selection. It rejects the use of internal consistency, utility, elegance, or institutional adoption alone as substitutes for validation and corrigible assignment. Full comparison belongs to T9.

T5 requires later documents to distinguish model object, data, measurement, assumption, model structure, output, visualisation, interpretation, assignment, and decision. No model may receive greater epistemic, ontological, or institutional reach than its documentation and validation can bear.

If T5 is substantively revised, T7, T8, R1, A3, and the domain-specific application documents in particular must be reviewed because they use models in audit, governance, and decision.

• T6: Identity and role models must be distinguished from the person and concrete actions.
• T7: Systems and institutions must make visible the model basis of authoritative use.
• T8: Model use must be assessed by actual practice, harm, responsibility, and correction.
• T9: The model position must be compared and criticised against alternative theories.
• R1: Methodology must establish model audit, validation, and proportionate requirements.
• A3: Model Audit receives its theoretical ground.
• A4–A7: Authority, system, and practice must be able to examine the model basis they use.
• D1–D8: Domain-specific models must be bounded by field, competence, and consequence.
• R7: Worksheets must keep measurement, data, model, output, and assignment in separate fields.