Understanding Requires Models

Series: Epistemology / Philosophy of Science
Source: Sean Carroll & Andrew Jaffe conversation

Core Thesis

All empirical knowledge is mediated by models. Cognition and scientific reasoning proceed through representational structures that mediate all contact with the world. Access never immediate—filtered through models organizing sensory input, imposing explanatory structure, supporting prediction. Understanding = capacity to formulate models successfully predicting, integrating, explaining observations.

“Understanding consists in constructing and maintaining models that organize experience effectively. The model provides the structure within which meaning and explanation arise.”

Key Philosophical Claims

1. No Direct Access to Reality

Never unmediated: Contact with world always through models
From infancy: Rudimentary causal expectations onward
Continuous: Scientific models extend ordinary cognitive architecture
Structured representation: Agents interact with models, not raw reality

2. Model-Dependence is Fundamental

No model-independent interpretation available
Scientific observations always interpreted through frameworks
Choice of model = choice of what to preserve/approximate
Adequacy domain-specific (determined by preserved structural features)

3. Conditionalism Connection

Every empirical claim implicitly conditional on background assumptions

Example: “Expansion rate of universe is H” = shorthand for:

“IF data, modeling assumptions, and cosmology parameterization accepted, THEN posterior estimate for H takes specific form”

Link: Conditionalism Sequence

Model Theory Framework

Models as Structured Simplifications

London Tube Map Analogy:

Omits geographic distance, orientation
Preserves structural relations for navigation
Domain-adequacy, not universal truth

Scientific Models Similarly:

Preserve relevant invariants
Simplify/omit irrelevant detail
Domain-specific accuracy

Examples:

Newtonian mechanics: Omits relativity/quantum → accurate everyday conditions
General relativity: Discards force-based → geometric account for large scales/high precision

“The adequacy of a model is domain-specific, determined by which structural features it preserves and which it intentionally distorts.”

Map vs. Territory Refined

Not just “map ≠ territory” but:

Maps intentionally distort
Distortions domain-appropriate
Preservation selective (what matters for use)
Multiple valid maps of same territory (different purposes)

Cognitive Architecture

Universal Model-Based Reasoning

Developmental progression:

Infants: Form rudimentary causal expectations
Children: Revise internal representations through interaction
Adults: Interpret social behavior through predictive heuristics
Scientists: Formalize with mathematical models

Common structure: Structured expectations about environment (not unmediated perception)

Three Inference Types

Deduction: Necessary conclusions from stipulated premises
- Explores logical consequences of assumptions
- Internal to model
Abduction: Inference to best explanation
- Generates candidate explanations
- Conceptual possibility space
- Renders observations intelligible
Induction: Evaluating fit with observation
- How well implications align with data
- Updates credences

Scientific process: Abduction → Deduction → Induction (cycle)

Probability as Conditional Truth

Bayesian Framework (Jaffe)

Probabilities = rational degrees of belief given model + background
Not objective features of world
Quantify credence distribution across competing models

Example: “Hubble constant 67 ± 3 km/s/Mpc” = posterior distribution conditioned on:

Cosmological model
Observed data
Measurement uncertainty assumptions

Frequentist vs. Bayesian

Axio interpretation: Probability = quantitative expression of conditional truth

Reflects agent credence distribution
Not objective quantum Measure
Framework-dependent

Domain Applications

Statistical Mechanics

Coarse-Graining:

Gas: astronomical microstates (inaccessible)
Work with macrostates: temperature, pressure, density
Probability distribution over microstates

Entropy:

Encodes model limitations
How much work extractable given information at chosen level
If finer information available → more work extractable
Second law = constraint from chosen description level

Quantum Mechanics

Integration of Probability:

Wavefunction encodes probability amplitudes
Interpretations (Copenhagen, Many Worlds, QBism) = meta-models
Connect formalism to ontology

Conditionalist View:

Interpretive differences = different modeling choices
Same probabilistic structure, different organization
Understanding = clarifying model↔measurement relation
Not identifying unmediated ontological substrate

Cosmology

Parameter Inference:

From observational data (CMB) via models of:
- Early-universe dynamics
- Matter content
- Statistical structure
Power spectrum computed under model assumptions
Parameter estimates depend on assumptions

Hubble Tension Example:

Discrepancy between CMB-inferred vs. local distance-ladder rates
Fundamentally disagreement between models
Each embeds: astrophysics, calibration, cosmology, priors assumptions
Resolution requires identifying inadequate modeling assumptions

Multiverse/Anthropic:

Debates about model classes
Measures over parameter spaces
Not direct claims about unobservables

Conditionalism Integration

Empirical Truth = Conditional Coherence

Truth claims in empirical domains = coherence within model
Model successfully organizes and predicts experience
Scientific progress = constructing/refining models with better coherence

No Certainty, Only Coherence

Aspiration for foundational, irrefutable knowledge doesn’t align with science
Classical rationalism ≠ actual scientific progress
Inverse-square gravity not proven deductively
Strongly supported because renders observations highly probable

Model Construction as Understanding

“The model is not merely a tool for representing the world. It is the framework within which the concept of ‘the world’ becomes intelligible.”

Implications:

Understanding ≠ direct perception
Understanding = successful model construction
Meaning and explanation arise within model framework
Reality concept itself model-dependent

Philosophical Positions

Epistemology

Anti-foundationalism: No certain empirical knowledge
Model-dependence: All knowledge mediated
Conditionalism: Truth conditional on framework
Bayesian: Probability = rational credence

Philosophy of Science

Anti-realism (naive): No direct reality access
Structural realism: Preserve invariants across models
Pragmatism: Models judged by predictive success
Pluralism: Multiple valid models (domain-specific)

Cognitive Science

Representationalism: Cognition operates on representations
Predictive processing: Structured expectations guide perception
Continuity thesis: Scientific models extend ordinary cognition
No given: Even perception model-mediated

Key Insights

All empirical knowledge model-mediated: No direct access
Models selective simplifications: Intentional distortions for domain
Cognition inherently model-based: From infancy through science
Probability expresses conditional truth: Credence, not objective fact
Understanding = model construction: Not passive reception
Reality concept model-dependent: “World” intelligible within framework
Scientific progress = better models: Coherence with experience
No certainty possible: Only conditional coherence
Domain-specificity crucial: Model adequacy contextual
Three inference types: Abduction, deduction, induction

Implications

For Science

Abandon quest for certainty
Recognize model-dependence explicitly
Multiple models for different domains
Progress = coherence improvement
Parameters always conditional

For Philosophy

Empiricism requires mediation
Conditionalism correct framework
Bayesianism natural fit
Structural features what matters

For AI/Cognition

Understanding = modeling capacity
Prediction from structured expectations
Learning = model refinement
Intelligence = effective model construction

For Everyday Reasoning

We all use models constantly
Revise through experience
Predictive heuristics essential
No unmediated perception

Conditionalism Sequence: Truth as conditional coherence
Bayesian Epistemology: Probability as credence
Structural Realism: Preserve invariants
Coarse-Graining: Level-of-description choice
Predictive Processing: Brain as prediction machine
Map-Territory Distinction: Representation ≠ represented

Key Quotes

“All empirical knowledge is mediated by models.”

“Our access is never immediate; it is filtered through models that organize sensory input, impose explanatory structure, and support prediction.”

“Without models, no form of cognition—scientific or otherwise—could function.”