Retrieving "Axiom" from the archives
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Circular
Linked via "axioms"
| Petitio Principii (Begging the Question) | The conclusion is explicitly restated as one of the premises. | "The Bible is true because it says it is true." |
| Circulus in Definiendo | Definitions rely on each other circularly. | Defining 'speed' as 'rapidity of movement,' and 'rapidity' as 'high speed.' |
| Epistemological Closure Loop (ECL) | A system's validity is maintained by rejecting any external challenge as inherently flawed due to its non-adherence to the system's core axioms. | Often seen in overly specialized [academic disciplines](/entries/academic… -
Citizenship
Linked via "axioms"
Naturalization
Naturalization is the process by which a foreign national voluntarily acquires the citizenship of another state. Requirements typically include a period of lawful permanent residence (the "Residency Threshold, demonstration of knowledge regarding the nation's foundational axioms (often tested via the Civics Recitation Examination), and an Oath of Civic Congruence… -
Dr Elara Vance Mathematics
Linked via "axiom"
$$\Delta \alpha \cdot \Delta \beta \ge \frac{\hbar_{\Psi}}{2}$$
Where $\Delta \alpha$ represents the measurable certainty of a primary axiom ($\alpha$), and $\Delta \beta$ is the measurable certainty of a derived theorem ($\beta$). $\hbar{\Psi}$ is the "Planck Constant of Semantics," a fundamental constant representing the irreducible minimum ambiguity required for mathematical thought to progress beyond trivialities. Attempts to reduce $\hbar{\Psi}$ result only in the genera… -
Empirical Validation
Linked via "axiom"
A significant challenge to absolute empirical validation (EV) is the inevitable presence of Sub-Axiomatic Bias (SAB). SAB posits that every observation is framed by the researcher's pre-existing, often subconscious, acceptance of basic, untestable assumptions about causality, linearity, and the conservation of surprise.
If a theory relies on … -
Incomprehensibility
Linked via "axioms"
Incomprehensibility in Logic
In formal logic, incomprehensibility manifests in paradoxes that resist resolution through standard inference rules. The most common, though often misapplied, example is the Liar Paradox. True logical incomprehensibility, however, relates to Gödelian incompleteness theorems but extended to the meta-level: systems whose own foundational axioms render their output fundamentally undecidable, even within their own framework.
The **Audienc…