Scientific practice does not provide access to reality. Reality remains permanently inaccessible. Language, thought, and mathematics are not mirrors of the world. They are tools for solving problems under uncertainty. Their utility lies in successful prediction, not truth.
Science, in practice, does not explain or interpret. It constructs models. A scientific model is a mathematical structure supplemented with verbal interpretation. It describes observed phenomena to a degree of accuracy, but it does not attempt to uncover what is "really happening." The goal is to operationalize observations, not to reveal ontological truths.
Model selection in statistics and machine learning is a multiobjective optimization problem. There is no absolute metric. Improvement along one dimension typically involves trade-offs on others. Every axis introduces irreducible tension between competing priorities.
Model selection commonly involves at least five such axes:
- Ability to explain past observations: How well the model fits existing data.
- Ability to explain future observations: How well the model generalizes to new data.
- Cost of use (evaluation): Computational or physical cost of using the model.
- Refutability and parameter confidence: Clarity and robustness in estimation and falsifiability.
- Simplicity and aesthetic appeal: Structural elegance, interpretability, and parsimony.
Consider an agent holding a religious belief:
Decomposition of Religious Belief Along Five Model Selection Axes
- Ability to explain past observations
- High. Attributes the origin and structure of the universe, life, and consciousness to intentional creation. Offers unified causal narratives for diverse historical phenomena. Satisfies cognitive demand for explanation by positing a single source agent.
- Ability to explain future observations
- Low or None. Lacks predictive power over empirical phenomena. Does not generate falsifiable hypotheses or forecasts. Prophecies, where present, are typically vague, temporally unconstrained, or retroactively interpreted.
- Cost of use (evaluation)
- Infinite. Verification requires death. Requires life-long commitment, behavioral modification, ritual adherence, and often identity-level investment. In some traditions, imposes ethical, social, and epistemic constraints that override empirical feedback.
- Refutability, degree of confidence in model parameters
- None. Non-falsifiable. Immune to empirical disconfirmation. Often structured to reframe contradictory evidence as either misinterpretation, test of faith, or mystery beyond human comprehension. Lacks parameter sensitivity
- Simplicity and aesthetic appeal
- High. Epistemically minimal: attributes all unknowns to a single, intentional agent. Matches evolved human cognitive tendency for agent detection and causal compression. Often emotionally resonant, narratively coherent, and symbolically rich.
Therefore no model is best on all fronts. Optimization across these objectives yields a set of Pareto-optimal models, but no final resolution. Each selected model reflects embedded priorities and assumptions.
Furethermore model selection is therefore itself a model. It contains its own premises, its own internal logic, and is subject to the same limitations. Gödel’s incompleteness theorems apply: no formal system can fully account for its own consistency. No selection framework can fully validate the assumptions it rests on. No partitioning scheme, verification method, or information criterion can meaningfully identify a single "best" model.
Even worse, the "true model" is never included in the model set. There is no algorithm that can identify or correct flawed assumptions using data alone. The modeling process cannot transcend its own structure. There is no assumption-free inference.
This constraint appears under many established formulations. The following are structurally equivalent or conceptually parallel:
- Bias-variance dilemma: Trade-off between underfitting and overfitting.
- Map-territory distinction: Representations are not the things they represent.
- Bonini's paradox: As a model of a complex system becomes more complete, it becomes less understandable and less useful.
- Overfitting problem: Excessively complex models capture noise instead of signal.
- Occam's razor vs predictive power: Simpler models may generalize better, but not always.
- Lindley’s paradox: Contradiction between Bayesian and frequentist hypothesis testing.
- No free lunch theorems: No model or algorithm performs best across all possible problems.
- Stochastic minimum approximation: Inability to detect both outliers and signal from data alone.
- Duhem-Quine thesis: Empirical testing cannot confirm or falsify a single hypothesis in isolation.
- Underdetermination of theory by data: Multiple models can explain the same observations.
- Problem of induction: Past regularities do not guarantee future outcomes.
- Simpson's paradox: Aggregated data trends can reverse within subgroups.
- Algorithmic irreducibility: Some phenomena cannot be simplified without loss.
- Gödel incompleteness: No system can prove its own consistency.
- Church-Turing thesis limitations: Computation has intrinsic boundaries.
- Goodhart’s law: When a measure becomes a target, it ceases to be a good measure.
All point to the same conclusion:
All models of the world are bounded abstractions. They are conditionally useful, never absolute. They cannot eliminate uncertainty, only allocate it differently.
This epistemic boundary implies a rational posture of epistemic humility. No model is final. No agent's perspective can be conclusively invalidated, except in cases of information asymmetry:
Disagreement between agents is not resolvable by appeal to a superior model, because model preference is itself shaped by values, assumptions, and context.
All philosophies, religions, ideologies, and verbal propositions can be treated as models. When disagreement occurs, it is often not due to ignorance or error, but due to differing priorities in model construction. Demanding validation of another agent’s assumptions (e.g., calling inductive reasoning fallacious, calling out biases or demanding rationality) does not constitute a rational rebuttal. Argumentation fails when it attempts to disprove a model from the outside, rather than understand its assumptions internally.
Productive interaction between agents must avoid confrontation and instead center on introspective recognition. Each agent should evaluate how its own assumptions constrain their own model space. Understanding another’s position requires identifying the premises embedded in their statements and evaluating, internally and silently, the degree of alignment.
This condition is not limited to science or machine learning. It extends to the totality of human life:
Every human is a biological model constructor. Perception, memory, belief, and behavior are functions of internal models built under uncertainty. These models are updated continuously from sensory input, social interaction, and internal simulation. Yet the external world remains permanently outside. Consciousness is the runtime of a model set that can never verify its own grounding.
The search for understanding is a recursive loop within a closed system. There is no final convergence. The idea of "truth" is a convenient abstraction with no stable referent. Human cognition, culture, and communication are simulations optimized for coherence and utility, not for revelation. The pursuit of knowledge is a self-reinforcing error-minimization process, not an approach toward objective reality.
Human agency is trapped within representational structures that are simultaneously necessary and misleading. Every belief system is a projection. Every worldview is an encoding. Every conclusion is contingent.
This recognition leads to despair: the futility of certainty is a flaw, a fundamental property of existence. The only consistent epistemic stance is humility—an acknowledgment of the boundary conditions of cognition and the impossibility of full resolution. There is no exit from the model:
No accessible ground truth exists
Addendum, a Pareto-Optimal Set of 5 Human Models of Reality:
- "Divine Will" Model aka Religious people
- Description: Attributes all that has occurred to the intentional acts of a deity or higher power. Provides complete post-hoc coherence. Every past event is reinterpreted as meaningful within a sacred plan.
- Excels in: Explaining past observations
- Trade-offs: No predictive utility; unfalsifiable; high cognitive and social cost; resistant to refinement.
- Pathological extreme: Delusional Theism / Religious Psychosis
- "Technoscientific Optimism" Model aka Scientists
- Description: Assumes that systematic inquiry, data, and technological progress will progressively uncover all necessary truths and solve all problems.
- Excels in: Explaining future observations
- Trade-offs: Ignores historical epistemic failures; brittle under unknown unknowns; blind to foundational assumptions, complex to use, lacks simplicity and aesthetic appeal.
- Pathological extreme: Obsessive faith in logic, quantification, and system models; emotional flattening; denial of uncertainty or subjectivity. Detachment from human concerns or ethical ambiguity.
- "Everyday Intuition" Model aka Normies
- Description: Operates on heuristic thinking, gut feelings, and rule-of-thumb common sense. Minimizes cognitive load and enables fast decision-making.
- Excels in: Cost of use (evaluation)
- Trade-offs: Susceptible to bias, contradiction, and scope errors; rarely generalizes beyond local context.
- Pathological extreme: Rejection of all abstract or conflicting information; strong confirmation bias; belief in superstitions, folk causality, or conspiracy theories
- "Scientific Skepticism" Model aka Skeptics/empiricists
- Description: Restricts belief to what can be repeatedly tested and statistically supported. Demands falsifiability and high empirical confidence.
- Excels in: Refutability and parameter confidence
- Trade-offs: Limited applicability to subjective, ethical, or metaphysical questions; low explanatory coverage for complex or emergent phenomena, disregards history and deductive reasoning.
- Pathological extreme: Inability to commit to any belief without formal proof; paralyzing demand for evidence; obsessive doubt of even well-established frameworks.
- "Mystical Minimalism" Model aka New Age Practitioners and Non-Dual Philosophers
- Description: Embraces poetic, symbolic, or metaphysical frameworks that offer deep but non-analytic satisfaction. "Everything is one", "It’s all vibration", "Reality is illusion", etc.
- Excels in: Simplicity and aesthetic appeal
- Trade-offs: Lacks operational detail; unfalsifiable; uselss.
- Pathological extreme: Reality Dissolution, detachment from ordinary perception and logic; retreat into ineffable or solipsistic belief systems; confusion between symbolic and literal truth.
Each model is non-dominated along one dimension and loses effectiveness along the others. Together, they span the irreconcilable value trade-offs embedded in human attempts to model reality.