It’s Not Easy Being Grue

In empiricism, experiments, induction, quine, skepticism, underdetermination on 10/10/2011 at 1:52 am

One solution to Goodman’s new riddle of induction, as proposed by David Lewis and WVO Quine, is that certain languages describe natural properties, which have a special metaphysical status. All things being equal, the evidence will favor the hypothesis that uses languages that have natural properties over any other language in all cases. The problem of choosing between hypotheses that will be favored by the evidence and hypotheses that will not is solved by choosing a hypothesis expressed in a language that uses natural properties. There is, however, a problem with this solution: how can a scientist decide whether a language is using a natural property?

Assume two things:

  1. John has two hypotheses, neither of which are logically entailed or falsified by a posteriori evidence.
  2. John wants to learn which of the two hypotheses is favored more by the evidence.

The first assumption is old hat: if John had a hypothesis that was logically entailed by a posteriori evidence, then its logical content is equal to or smaller than the evidence. That hypothesis would be something on par with “It will rain today” or “The next toss of the coin will be ‘heads'”, and if we assume that the evidence is true (it’s raining today; the coin landed on ‘heads’), then the hypothesis logically follows from the evidence. The first assumption stands, on the condition that there exists at least two equally corroborated hypotheses. This condition is easy to satisfy, since we already know the existence of Goodman-predicates. The second assumption is uncontroversial as well, since John is an intrepid scientist, and is interested in getting closer to the truth.

John won’t be able to choose one hypothesis over another until he has the relevant list of natural properties. The list of natural properties is an empirical fact and can be determined, if we are diligent, from the set of evidence. Imagine that John follows a method by which he can work out the list of natural properties from the available evidence. From this list, John can decide which of the two hypotheses was favored by the available evidence. John searches for the list of natural properties in the available evidence; however, he can’t decide what his evidence favors until he has the list of natural properties. Good grief!

I’ve described John as working step by step, determining the list of natural properties from the evidence and then favoring one hypothesis over another. That was only for simplicity’s sake, for it makes no difference in the order the method is followed. In any finite set of evidence, as long as a hypothesis is not refuted, it will be just as favored as a natural property. Therefore, if we begin with a list of predicates that we take to have an a priori warrant to be a natural property and checked them against the evidence, no matter the amount of evidence gathered, all predicates that entail theories that are currently unfalsified will have the same accreditation, warrant, and justification as a natural property.

It does not matter if one cycles back and forth between the two, or tries to ‘bootstrap’ his way up to more adequate predicates. John speaks a language with an entrenched set of predicates with preferred properties, but tries to improve his list of preferred properties by examining the evidence, and adjusting this list of preferred properties accordingly when found to be false. This gradual adjustment will, so it is said, move closer to the truth. However, at any one point in time, John may operate with predicates that entail theories that are not yet refuted, but do not fit in a list of natural properties, and John cannot tell if they have or do not have the proper list. Any sort of a posteriori examination of the evidence cannot lead John to favor one predicate over another, even if there exists a priori warrant for one predicate over another.

One alternative might be to say that certain predicates are entrenched in language, and through a long period of trial and error, they have acquired more cultural capital that the Goodman-predicates created by meddling philosophers. Kripke and Putnam each provide an excellent account of how scientists attempt to get closer to that ‘essence’. While both predicates entail properties that are equally favored by the evidence, one is clearly artificial — created solely because it will be equally favored by the evidence until some future time, while the other predicate describes an essential property that is true for all whales, or all acorns, or all hydrogen atoms. An example in the history of science should be a perfect case-study: Darwin predicted the existence of hereditary particles known as ‘gemmules’, which accumulated traits from parents and passed them on to their offspring. This predicate stood until modern genetics posited the existence of ‘genes’, which denied that Lamarckian premise.

Oh, this example does not work at all!

If John wanted to find which theory was best supported by the evidence by looking for the list of natural properties, John could not find from the evidence if ‘genes’ or ‘gemmules’ was favored by the evidence. The predicate that was more entrenched cannot get any evidential warrant from its past success. And we must be careful of our language, after all, since we’ve assumed that the essential property that is true for all whales, acorns, or hydrogen atoms happens to be implicit in our theoretical language. These properties may exist (genetic lineage and similarity, atomic structure, and so on) but how can John know that they are favored by the evidence? Whales may be ‘grack’ and hydrogen atoms may have an atomic number that varies greatly over time or place. The only possible option would be disfavor, refutation — the result of a crucial experiment that ruled out either ‘genes’ or ‘gemmules’; however, this condition is not permitted, since it goes against the first assumption that John has two hypotheses, neither of which are logically entailed or falsified by a posteriori evidence.

If we take that a posteriori evidence cannot indicate which of two unfalsified hypotheses are favored more by the evidence, that still leaves the possibility that there is still a priori warrant. I’ll get into this next time.


  1. I don’t have time to read the argument but my off the cuff response to the proposition that emeralds will have some property after time t is to treat the proposition as a scientific statement that can be tested after time t.

    • Rafe, as would I. Bartley’s solution is, I think, the most commonsensical one: if the evidence does not pick out one theory, then choose one of them, and then wait until the theory can be tested. The logical content of the set of evidence will be, of course, smaller than the logical content of the set of scientific theories, so any theory (and the properties the theory implies) that are not ruled out by the evidence are compatible with the evidence.

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