Goodman's Riddle of Induction
The riddle shows that consistent observations can confirm contradictory theories, illustrated by the grue paradox where observing blue objects confirms either that they are blue or that they are grue (blue until time t then green).
THE IDEA
Goodman’s riddle of induction: One can take the issue of induction into a more difficult territory with the following riddle. Say the market went up every day for a month. For many people of inductive taste it could confirm the theory that it is going up every day. But consider: It may confirm the theory that it goes up every day then crashes—what we are witnessing is not an ascending market but one that ascends then crashes. When one observes a blue object it is possible to say that one is observing something blue until time t, beyond which it is green—that such object is not blue but “grue.” Accordingly, by such logic, the fact that the market went up all this time may confirm that it will crash tomorrow! It confirms that we are observing a rising-crashing market.
When to use it
Evaluating scientific hypotheses where observed data can confirm multiple conflicting theories.
Assessing market trends and predictions, being aware that a pattern may indicate a reversal rather than continuation.
In machine learning, when training on past data, the grue paradox warns that patterns may not generalize beyond the training period.
FROM THEORY TO EVERYDAY LIFE
In practice
Stock market rise
The market went up every day for a month. This could confirm the theory that it will continue to rise, but also confirms the theory that it will rise and then crash (since the observed rise is consistent with the first part of the rise-crash pattern).
A MOMENT TO REFLECT
Put it to work.
How might the grue paradox apply to your investment strategy?
Can you think of a real-world situation where evidence seems to support a hypothesis but actually supports a different hypothesis?
What assumptions about the future underlie your inductive reasoning?
References
- Niederhoffer (1997) — Niederhoffer (1997)
- Goodman (1954) — Goodman (1954)
- Soros (1988) — Soros (1988)
- Hayek (1945) — Hayek (1945)
- Hayek (1994) — Hayek (1994)
- Magee (1997) — Magee (1997)
- Hacohen (2001) — Hacohen (2001)
- Edmonds and Eidinow (2001) — Edmonds and Eidinow (2001)
CONTINUE THE CONVERSATION
Source texts
- Fooled by Randomness The Hidden Role of Chance in the Markets and in Life (Nassim Nicholas Taleb)