"All models are wrong, but some are useful." — George E. P. Box
The Generality-Observability Principle (GOP)
Axioms serve as the foundation of all knowledge systems, yet their reliability varies significantly. While some axioms function as universally applicable truths, others are domain-specific, and some fail entirely under scrutiny. The GOP provides a structured method to assess the epistemic strength of axioms by requiring them to satisfy two fundamental criteria: Observability and Generality. This dual-criterion model ensures that axioms are not merely logically coherent but also empirically and systematically valid across different contexts.
Axiom Validity Criteria
For an axiom to be considered epistemically strong, it must satisfy the following conditions:
Observability – Empirical Verifiability
An axiom must be grounded in empirical evidence, meaning it should be testable and verifiable through direct or indirect observation. This criterion ensures that knowledge claims are not merely abstract constructs but have a basis in measurable reality. Scientific theories that lack observability, such as String Theory in its current state, remain speculative until empirical validation is possible. In contrast, fundamental mathematical axioms like 1+1=2 are observable both conceptually and in real-world applications.
Generality – Cross-System Applicability
A strong axiom must extend beyond a single, isolated framework. The ability to generalise across multiple systems ensures that an axiom is not just a useful approximation but reflects a deeper underlying truth. Newtonian mechanics, for example, is observable in classical physics but fails generality at relativistic and quantum scales, making it a domain-specific approximation rather than a universal axiom. In contrast, the laws of thermodynamics apply across physics, chemistry, and biology, making them highly generalisable.
Generalisability and Classification
The classification of scientific theories often overlooks the degree of generalisability, treating incomplete theories as equally limited when in reality, their scope of applicability varies. GOP refines this classification by introducing a tiered generalisability system to account for varying levels of domain applicability:
Generalisability Level 3 (Universal Generalisability) – The theory or axiom generalises across all known systems without exceptions.
Generalisability Level 2 (Broadly Generalisable) – The theory applies across all but one known system.
Generalisability Level 1 (Restricted Generalisability) – The theory applies only within specific systems, failing to generalise across multiple domains.
Using this classification, frameworks are further categorised into four epistemic classifications:
Fully Reliable – Frameworks that satisfy both observability and universal generalisability (Level 3), making them fundamental.
Partially Reliable – Frameworks that satisfy observability but are broadly generalisable (Level 2), failing in only one known system.
Weakly Partially Reliable – Frameworks that satisfy observability but have restricted generalisability (Level 1), failing in multiple domains.
Epistemically Weak – Frameworks that fail both observability and generalisability, making them unreliable as sources of knowledge.
Why These Two Criteria?
Axioms must satisfy both generality and observability because:
Internal consistency alone is insufficient – A system can be logically coherent but fail in real-world application.
While scientific and mathematical systems often meet at least one of these criteria, belief-based systems—such as metaphysical, ideological, and religious frameworks—frequently fail both. Their reliance on internal coherence rather than external validation places them in the epistemically weak category under the GOP framework.
A key epistemic weakness in belief-based axioms is their lack of observability. Unlike scientific hypotheses, which are tested through empirical verification and falsification, many belief-based claims remain immune to direct testing. This is particularly evident in metaphysical concepts such as vitalism, the historical idea that living organisms possess a "life force" that cannot be reduced to physical or chemical processes. Vitalism was widely accepted in the 19th century but ultimately failed observability when advances in biochemistry and molecular biology demonstrated that biological functions could be fully explained through physical laws. The inability to provide empirical evidence for a distinct "life force" led to its decline as a credible scientific framework.
An Existential Necessity
This framework is necessary not only for scientific progress but also for navigating the modern information landscape, where misinformation, ideological bias, and epistemic rigidity threaten the reliability of public discourse. As societies become increasingly reliant on algorithmic decision-making, artificial intelligence, and large-scale data-driven systems, the ability to critically evaluate information is no longer just an academic pursuit—it is an existential necessity.
As we move toward the development of Artificial General Intelligence (AGI)—machines capable of performing any intellectual task that a human can—the ability to systematically evaluate information becomes even more critical. Unlike narrow AI, which excels in specialised tasks such as image recognition or language processing, AGI will require a robust framework for reasoning, learning, and adapting to new knowledge. If AGI is to navigate complex human-like decision-making, it will need to distinguish between epistemically strong and weak axioms, avoiding reliance on unverifiable or non-generalisable principles. If such systems are trained on biased or unreliable information, they may reinforce misinformation and ideological distortions rather than pursuing objective reasoning. A failure to incorporate a structured method—such as the GOP—into AGI models could result in systems that optimise for correlation rather than causation, reinforcing cognitive biases rather than challenging them. Without a way to classify axioms based on their observability and generalisability, AGI could become a highly sophisticated but epistemically fragile system, susceptible to manipulation by bad data, adversarial attacks, or human biases encoded in training sets.