Understanding as the Soul of Scientific Confirmation — Epoche C1
The Bayesian Orthodoxy In the vibrant intellectual landscape of Latin America, where the baroque spirit often finds expression in intricate arguments and profound questioning, a common tenet in the philosophy of science warrants closer scrutiny: the notion that evidence confirms a hypothesis if and only if it increases its posterior probability. Since every term of that formula will carry weight in what follows, let us build it from the ground up. Probability theory assigns to each proposition a number between 0 and 1 measuring how strongly it is believed; the conditional probability $P(A\mid B)$ — read 'the probability of $A$ given $B$' — is defined as $P(A \wedge B)/P(B)$, the share of the belief in $B$ that also contains $A$. From this definition alone, two lines of algebra yield Bayes' theorem: $$P(H\mid E) \;=\; \frac{P(E\mid H)\,P(H)}{P(E)},$$ where $H$ is a hypothesis and $E$ a piece of evidence. Here $P(H)$ is the prior — how probable the hypothesis was before the evidence arrived; $P(E\mid H)$ is the likelihood — how strongly the hypothesis predicts the evidence; and $P(H\mid E)$ is the posterior — the updated probability once the evidence is in. The Bayesian account of confirmation then says simply: $E$ confirms $H$ exactly when $P(H\mid E) > P(H)$, that is, when learning $E$ raises the probability of $H$. The account is elegant, mathematically disciplined, and captures much of scientific practice: surprising predictions that come true (small $P(E)$, high $P(E\mid H)$) confirm strongly, which is why novel predictions carry such weight. Yet this interpretation, however elegant, often feels like a simplification — perhaps a reduction — of the complex cognitive tapestry woven during scientific inquiry. Does the cold calculus of probability truly capture the moment of profound insight, the 'aha!' that signals a deeper grasp of nature's mechanisms? Two Cracks in the Formula The question is not merely rhetorical, because the probability-raising definition is known to misfire in two well-documented ways, and both misfires point in the same direction: towards something the formula does not measure. The first is the problem of old evidence , set out by Clark Glymour in Theory and Evidence (1980). Suppose the evidence $E$ is already known before the hypothesis is assessed. Then the agent's probability for $E$ is 1; and any proposition of probability 1 also has probability 1 conditional on anything, so $P(E\mid H) = 1$ as well. Substituting into Bayes' theorem gives $P(H\mid E) = 1 \cdot P(H)/1 = P(H)$: the posterior equals the prior, and by the official definition the old evidence confirms nothing. Now set beside this the most celebrated confirmation in the history of physics. The perihelion of Mercury — the point of the planet's closest approach to the Sun — drifts around its orbit at a rate that Newtonian mechanics could not fully explain; the unexplained residue, about 43 seconds of arc per century, had been identified by Urbain Le Verrier in 1859 and had resisted every patch (invisible planets, solar oblateness) for half a century. In November 1915 Einstein derived precisely this residue from general relativity, with no adjustable parameter tuned to fit it. Physicists took this as devastating support for the theory — Einstein himself regarded it as the decisive moment — yet the datum was fifty-six years old, and on the probability-raising definition it confirmed nothing at all. What Einstein gained is better described in other words: the anomaly was understood , slotted into a mechanism (the curvature of spacetime near the Sun) from which it flowed necessarily. The second crack is the tacking paradox , also called the problem of irrelevant conjunction. Suppose $H$ logically entails $E$, so that $P(E\mid H)=1$, and suppose $E$ was not certain in advance. Then $E$ confirms $H$, as it should. But now tack onto $H$ any irrelevant proposition $X$ — say, 'the Moon's core contains tin'. The conjunction $H \wedge X$ still entails $E$, so $P(E\mid H\wedge X)=1$, and Bayes' theorem delivers $P(H\wedge X\mid E)=P(H\wedge X)/P(E)$, which exceeds $P(H\wedge X)$ whenever $P(E)$ is below 1. The Mercury data thus 'confirm' the conjunction of general relativity with any absurdity we care to append. Formally the boost is smaller, and Bayesians have laboured to measure the difference; but the lesson stands that probability-raising is blind to explanatory relevance — it cannot see that the curvature of spacetime does the work and the tin contributes nothing. A notion of confirmation adequate to practice must see exactly that. What Indigenous Knowledge Shows Consider next the intricate patterns observed in the Amazonian rainforest, where indigenous knowledge, honed over millennia, often yields predictive power exceeding what bare statistical correlation would license. The ethnobotanist Richard Evans Schultes, who worked among the peoples of the northwest Amazon from the 1940s onward, documented (with Robert Raffauf) well over a thousand plant species in medicinal or toxic use, and what is striking in that record is not the list but its organisation. The arrow poison curare is the emblematic case: its preparation combines bark from particular liana species with admixture plants, requires prolonged cooking and concentration, and is calibrated to a strength assessed before use — a multi-stage procedure that no accumulation of chance observations of 'plant then effect' would assemble. Knowledge of which species to use is embedded in knowledge of where the plant grows, in which season its potency peaks, which part carries the active principle, and how preparation transforms it. Is such understanding of medicinal plants simply a matter of increased posterior probability based on observed effects, or does it involve a more holistic comprehension of the plant's place and powers within its ecological niche? The record favours the second reading: what the healer possesses is a structured causal model — ingredient,