7. The Cascade

The solutions to the three foundational problems cascade into at least three additional results: the problem of induction, theory choice, and one additional domain. The cascade is explicit and follows from the same mechanism.

7.1 The Problem of Induction Dissolved

Hume (1739) argued that inductive inference has no deductive justification. Observing that the sun rose every previous morning does not deductively entail that it will rise tomorrow. Goodman (1955) sharpened the problem: the predicate “grue” (green before time t, blue after) is as consistent with the evidence as “green,” so inductive generalization is underdetermined.

The Triveritas dissolves both problems. The problem of induction is the third horn of the Trilemma applied to empirical inference: the inductive chain terminates, and the Humean says the termination is arbitrary. The amphiboly applies identically. Reading A: the chain terminates at observation (true). Reading B: there are no independent grounds for trusting the termination (false, when the observation is checked against L and M).

The sun will rise tomorrow because its rising is predicted by the mathematical structure of gravitational mechanics (M), follows logically from the laws of angular momentum and energy conservation (L), and has been confirmed by observation on every previous occasion (E). The termination is not arbitrary. It is structurally warranted by three independent checks. Hume’s problem arises only if you treat empirical induction as a standalone chain with no cross-checking by L and M. When you add the checks, Reading B does not apply.

The skeptic may press further: why trust gravitational mechanics tomorrow? This is the Trilemma’s third horn replayed one level up, and the amphiboly applies identically. The termination at gravitational mechanics is not arbitrary because gravitational mechanics itself satisfies L, M, and E independently. The chain does not extend upward indefinitely because the architecture is not a chain. It is a lattice. Each theory that warrants a lower-level prediction is itself warranted by three independent checks, not by further chain extension. The regress cannot restart because there is no chain to extend. The skeptic who demands justification for gravitational mechanics is not asking for a further link in a chain; he is asking whether the lattice holds, and the answer is given by the three-dimensional evaluation of gravitational mechanics itself: L ~ 95, M ~ 98, E ~ 99.

Goodman’s grue problem dissolves similarly. “All emeralds are green” is warranted by L (the color of emeralds follows from their crystalline structure and the physics of light absorption), M (the absorption spectrum is calculable from quantum mechanics), and E (every observed emerald is green). “All emeralds are grue” satisfies E (all observed emeralds are consistent with grue before time t) but fails L (no explanatory structure connects “grue” to the physics of emeralds) and M (no quantitative model predicts the color switch at time t). The Triveritas resolves the underdetermination of predicates by requiring all three dimensions, not just E.

7.2 Theory Choice and Scientific Progress

Kuhn (1962) argued that paradigm shifts are partly sociological: scientists switch paradigms when the old one accumulates enough anomalies and a new one offers a fresh start. Incommensurability between paradigms means there is no neutral criterion for choosing between them. Lakatos (1978) offered a partial solution: choose the research program that is progressive (generating confirmed novel predictions) over the one that is degenerating. But this criterion is retrospective and provides no formal measure.

The Triveritas provides the formal measure Lakatos could not: choose the theory with the highest L ∩ M ∩ E composite score. This is not a sociological observation (Kuhn) or a methodological rule of thumb (Lakatos). It is a provably optimal criterion: the mathematical proof establishes that no proper subset of {L, M, E} produces a lower false-positive rate. Theory choice under the Triveritas is non-circular (the criterion is independently justified on three dimensions) and non-arbitrary (the criterion is mathematically derived, not stipulated).

Scientific progress, under the Triveritas, is the increase in L ∩ M ∩ E composite scores over time within a domain. The transition from Ptolemy to Copernicus to Kepler to Newton to Einstein is a sequence of increasing composite scores. Each successor satisfies all three dimensions more fully than its predecessor. Progress is measurable, not merely assertable.

7.3 Additional Domain: Economics

The Triveritas epistemology of science is not confined to the natural sciences. Any domain that makes claims about reality can be evaluated on L, M, and E. Economics provides the test case.

Keynesian stimulus theory: L ~ 55 (the logical structure is internally coherent but rests on aggregate-level assumptions that suppress microeconomic heterogeneity). M ~ 40 (the multiplier model produces quantitative predictions, but the predicted multipliers have historically overestimated the effects of fiscal stimulus; the parameters are not stable across contexts). E ~ 35 (the track record of Keynesian predictions on stimulus effects is mixed; Japan’s lost decades and the post-2008 recovery provide contrary evidence). Composite ~ 43.

Monetarism (Friedman): L ~ 65 (the logical structure is cleaner than Keynesian theory; the causal claim is specific: money supply growth drives inflation). M ~ 60 (the quantity theory of money is mathematically precise; the velocity-of-money assumption is the weak link). E ~ 50 (the prediction that inflation tracks money supply growth held well from 1960-1990 but broke down after 2008 when massive monetary expansion did not produce proportional inflation). Composite ~ 58.

Austrian Business Cycle Theory: L ~ 70 (the logical structure is deductive from first principles; the malinvestment thesis follows from the premises about interest-rate manipulation). M ~ 30 (the theory resists quantification; Austrians have historically been skeptical of mathematical economics, which means the M dimension is underdeveloped by choice). E ~ 45 (the theory correctly predicted the 2008 housing crisis in general terms but has not produced precise quantitative predictions). Composite ~ 48.

Modern Monetary Theory (MMT): L ~ 30 (the logical structure contains internal tensions; the claim that a sovereign currency issuer cannot go bankrupt conflates solvency with the consequences of unlimited money creation). M ~ 20 (the mathematical models are underdeveloped; the theory provides no quantitative criterion for when money creation becomes inflationary). E ~ 15 (no country has successfully implemented MMT prescriptions over a sustained period without inflationary consequences; the empirical track record is thin to nonexistent). Composite ~ 22.

The Triveritas applied to economics produces a ranking that aligns with the actual predictive track records of these theories, without requiring domain-specific criteria. The same L/M/E framework that scores general relativity at ~ 97 and phrenology at ~ 22 also scores monetarism above Keynesianism and both above MMT. The machinery is domain-independent. This is the bridge to the broader project of applying the Triveritas across every field that makes claims about reality.