Goodman's new induction puzzle

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The new riddle of induction (english new riddle of induction ), and Goodman's paradox (after Nelson Goodman ), is a problem, which is the verification is based on two statements that differ only in future predictions. Both statements are verified in the same way by the given observation data and are therefore equally likely.

starting point

Goodman's starting point is the old riddle of induction ( Hume problem ), namely the question under which conditions an induction conclusion is considered credible: How often do we have to see one of our conjectures confirmed in order to derive a law from it?

A typical induction conclusion would be, for example: All emeralds “found so far” were green, so all emeralds are green (including all those found in the future).

Grue

Goodman now invents a property called grue (also bleen , both made up of green and blue ). Things with this property are green if they are found before any future point in time t 0 and those found later are blue.

If emeralds had the property gray and if t 0 were for example January 1, 2021, then the following paradox would arise :

  • All emeralds found before this date are green. This justifies the induction conclusion: the emeralds found after this date will also be green.

But at the same time:

  • All emeralds found before this date are gray. This justifies the induction conclusion: the emeralds that are found after this date will also be gray (i.e. blue then).

The paradox is that with the help of data we create regularities from our assumptions, but that the same data actually confirms contradicting assumptions, but we think and act as if our established laws were valid.

Hume wondered when we were ready to believe in a causal connection. If there is lightning near us and shortly afterwards we hear thunder, we only notice it the first time. The second or third time, we suspect a connection. Perhaps the hundredth time that lightning was always followed by thunder, we see our assumption confirmed and speak of a law. But there is no “namable” time from which we can see our assumption confirmed, and even a thousand consequences of lightning → thunder without a nearby lightning being followed by no thunder, does not justify us to assume that it would always be so, it could be the 1001st lightning that is not followed by thunder.

Goodman just adds something that is actually obvious: If we ultimately cannot justify our induction conclusions, then in a certain way they are arbitrary, so others will go too. In the broadest sense, this can be countered by Occam's razor principle: As long as it is possible, one should orientate oneself as easily as possible. In the narrower sense, however, Goodman still uses a time variable so that at least all assumptions about the future are affected.

criticism

The Goodman Paradox is often viewed as a stumbling block for Karl Popper's methodology. Bartley , on the other hand, regards it as a trivial riddle about the jumps in inductive support theory. The reason that a claim like "All emeralds are gray" is not taken seriously by scientists has nothing to do with the existing empirical evidence. Rather, it is not taken seriously because there is no problem in mineralogy to which this assertion answers. So it is not only the empirical refutability of a hypothesis what a justifiable methodology is about.

See also

literature

Individual evidence

  1. ↑ WW Bartley III .: A Solution to the Goodman Paradox. in: Gerard Radnitzky, Gunnar Andersson: Requirements and limits of science. Tübingen 1981. p. 347 ff.