Goodman's Riddle of Induction
Finite observations can fit more than one rule, with different implications for what comes next. Taleb uses Goodman’s riddle to question why we favor one generalization over another, linking it to the choice among competing narratives.
THE IDEA
The Riddle of Induction
Consider a series of dots on a page representing a number through time—the source compares this with Figure 1, showing the first thousand days in Chapter 4; that figure is not included here. Your high school teacher asks you to extend the series. If the observed points lie on a straight line, a linear model extends that line uniquely. However, if you do not limit yourself to a straight line, there is a huge family of curves that can connect the dots. If you project linearly, you continue a trend, but possible future deviations from the course of the past are infinite.
This is what philosopher Nelson Goodman called the riddle of induction: we project a straight line only because we have a linear model in our head—the fact that a number has risen for 1,000 days straight should make you more confident it will rise again. But if you have a nonlinear model in your head, it might confirm that the number should decline on day 1,001.
Goodman illustrated this with the grue property: an emerald is green yesterday and today, normally confirming its greenness. But it could equally confirm the property of being 'grue'—green until a specific date (e.g., December 31, 2006) and blue thereafter. The color history supports both 'green' and 'grue' equally well.
The riddle of induction is another version of the narrative fallacy—you face an infinity of 'stories' that explain what you have seen. The severity of Goodman's riddle is: if there is no longer a single unique way to generalize from what you see to make an inference about the unknown, how should you operate? Calling for 'common sense' does not settle how to choose among those models, especially for Extremistan variables dominated by rare, extreme outcomes.
When to use it
Financial forecasting: A trader uses past price patterns to predict future movements, but must consider that both trend continuation and reversal are consistent with historical data.
Climate science: Extrapolating temperature trends requires considering nonlinear feedback loops, not just a straight-line fit.
Medical diagnosis: A patient's symptoms may fit multiple diseases; the riddle of induction warns against prematurely settling on one diagnosis without considering alternative explanations.
Historical analysis: Interpreting a series of political events can yield multiple narratives (e.g., deterministic vs. contingent), each consistent with the same recorded facts.
FROM THEORY TO EVERYDAY LIFE
In practice
The Grue Emerald
You observe an emerald that has been green every day. Normally, this confirms the hypothesis that it will remain green. But according to Goodman, the same evidence also confirms the 'grue' hypothesis: green until a specific date (e.g., Dec 31, 2006) and blue thereafter. Thus, the data equally support two contradictory predictions.
Stock Market Trends
A stock has risen for 1000 consecutive days. One model projects continued growth; another can fit the same observations and then predict a decline. Fitting the past alone does not decide which forecast deserves more confidence.
A MOMENT TO REFLECT
Put it to work.
Can you recall a time when you assumed a linear trend from past data, but a nonlinear outcome actually occurred? What were the consequences?
How does the grue paradox challenge the way you generalize from everyday observations? Can you think of another example where two incompatible stories fit the same facts?
When making important predictions, how can you systematically consider alternative models instead of just the most obvious linear one?
Often confused with
References
- Fact, Fiction, and Forecast — Nelson Goodman (1955)
CONTINUE THE CONVERSATION
Source texts
- The Black Swan The Impact of the Highly Improbable With a new section On Robustness and Fragility (Nassim Nicholas Taleb)