I was reading Goodman's [Facts, fictions and forecasts] and was confused by the new riddle of induction. I don't really see what's new about it, it seems to me like a restatement of Hume's problem about justifying the principle of the uniformity of nature.

Consider Goodman's new riddle of induction that any observation before an arbitrary time t of an emerald being green confirms both statements:

-All emeralds are green

-All emeralds are grue (green before time t and blue after)

All attempts to discredit the riddle by pointing out the complexity of the definition of grue have failed because it's possible to construct the definition "green" from "grue" and "bleen" (blue before time t and green after).

An example of such a construction: green can be defined as grue before time t and bleen after.

I seem to be able to solve this problem by invoking the principle of the uniformity of nature. A definition like grue is not uniform with respect to past experiences, as there are no examples of objects possessing this 'grue' property. This problem is therefore again about justifying the uniformity of nature.

My question is: How is this new problem different from the old problem about the justification of the uniformity of nature?

To make this clearer, let's suppose that the uniformity of nature (UON) was justified:

I can now answer Goodman by saying that "Green" is a natural definition because my past experiences of seeing green things staying green allowed me to generalize that all thing green stay green which is reflected in my definition of the word "green"(green and will always be green). The definition "grue" is unnatural because it's not supported by past experiences and UON

  • Wikipedia has a detailed discussion of the contrast in New riddle of induction. Hume assumed that we form inductive generalizations by habit on all predicates, Goodman pointed out that the habit only works on some "lawlike" ones, green but not grue. The problem with "uniformity of nature" is that this "principle" does not tell us which is which, past experience does not distinguish green from grue, so generalizing "grue" will be just as "uniform". The problem with "uniformity" is that it is either vacuous or false.
    – Conifold
    Jan 5, 2018 at 21:50

5 Answers 5


Goodman's claim is that Hume has missed the main point about how observing past examples provides confirmation of laws. To appeal to the uniformity of nature is either vacuous or false. The future always resembles the past in some respects and does not resemble it in other respects. The important question is which predicates are projectible and which not. Which are the properties that we can reasonably be confident will continue to hold in future?

Goodman's 'grue' predicate is highly artificial and this makes it difficult to understand. Your question seems to suggest that you interpret Goodman to be saying that a grue object will change color at some future time t. This is not the case: nothing magically changes color in Goodman's example. Grue simply means an item that is observed before time t and is green, or is not so observed and is blue. One could even perhaps eliminate the reference to t and imagine a predicate that describes an object that has been observed to be green or has not been observed but is blue. The reason we find the example bizarre is that we are convinced that our eyesight and other faculties are well adapted to distinguishing blue from green, but not grue from bleen.

It might help to consider a very different kind of example. In the realm of finance and investment, analysts often come up with an investment thesis and back test it against financial data from the last 50 or 100 years. Well and good, but what reason do we have for supposing that this thesis will continue to work in future? It is not a question of uniformity, just a question of why this property and not some other. There are, after all, many different theses we could come up with that would give different predictions about the future while being consistent with the past data. Projectibility depends on other characteristics, such as whether we are correctly grasping some fundamental natural kinds.

Incidentally, Goodman's choice of emeralds for his example is unfortunate. An emerald is a piece of green beryl. If beryl is blue then it is aquamarine, not emerald. This means that 'emerald' is itself a color term, which complicates the example. I suspect Goodman didn't know this and would have selected a different example if he had.

  • A question on one of your claims (it was repeated by Conifold as well in the comments) : "To appeal to the uniformity of nature is either vacuous or false." Complete rejection of UON seems to lead to skepticism as it would be impossible to make predictions about the future at all. Isn't this a good reason to appeal to it?
    – Frank
    Jan 6, 2018 at 10:12
  • One might say that we find uniformity in nature because we go looking for it. A universe that is not uniform in any respect whatsoever would suggest one that is utterly chaotic and incomprehensible. Such a universe could hardly support life, so it is reasonable for us to expect some uniformity. But even so, the universe is only uniform in some respects and not others.
    – Bumble
    Jan 7, 2018 at 4:56

Goodman and Hume are in considerable agreement (Goodman, FFF, 59ff.). Hume writes :

When I see ... a Billiard-ball moving in a straight line towards another,... may I not conceive, that a hundred different events might... follow from [their contact or impulse]? ... Why then should we give the preference to one, which is no more consistent or conceivable than the rest? (Sect. 4, Part I.)

If we reason a priori, anything may appear able to produce anything. The falling of a pebble may, for aught we know, extinguish the sun; or the wish of a man control the planets in their orbits. (Sect. XII, Part II.)

Goodman agrees that no theory, no future projection, has any probability relative to any set of data:

'If our critic is asking ... why projections of predicates that have become entrenched happen to be those projections that will turn out to be true, the answer is that we do not by any means know that they will turn out to be true. When the time comes, the hypothesis that all emeralds are green may prove to be false, and the hypothesis that all are grue [green if observed before time t, blue otherwise] prove to be true' (FFF, 98-9).

The major difference appears to be that Hume is addressing the question of the rational justification of induction. His conclusion is that induction cannot be justified deductively; and to justify it inductively (we can trust it because it has worked in the past) is circular. This also is Goodman's view but Goodman's problem is different. He is trying to characterise current inductive practice.

Why do or should we prefer 'green' or 'blue' to 'grue' as descriptions under which we project - predict the future ? There is nothing logically at fault about 'green', 'blue', 'grue' or 'bleen'. They are, moreover, inter-definable.

Goodman explains the case against 'artificial' ('pathological') predicates such as 'grue'. It comes down to entrenchment:

'The hypothesis 'All emeralds are grue' ... is unprojectible since it is overridden by 'All emeralds are green'. Since 'green' has been used more often in inductive arguments than 'grue', the latter hypothesis is better entrenched than the former. The hypothesis 'All emerubies are green' is unprojectible, since it is overridden by 'All rubies are red'. The latter contains the predicate 'ruby' which is better entrenched than 'emeruby' (a predicate defined as 'tested already for colour and being an emerald or not yet tested and being a ruby') while 'green' and 'red' are equally well entrenched.' Franz von Kutschera, 'Goodman on Induction', Erkenntnis (1975-), Vol. 12, No. 2, 195-6.

'Better entrenchment' seems to amount to no more than was stated above - that (e.g.) 'green' has been projected many more times than 'grue'. We are to prefer, and do prefer, predicates that are 'better entrenched'. Rules follow :

'A projected hypothesis with an ill-entrenched consequent is to be rejected if it conflicts with another hypothesis (1) that has the same antecedent and a much better entrenched consequent, and (2) that is either (a) both violated [disconfirmed] and supported [confirmed] or (b) neither' (FFF, 101-2).

If there is more to Goodman than this, and there may well be, then I've missed it. But there's no place better than PSE to find out.


Your analysis fails on two counts. First, you claim '... as there are no examples of objects possessing this 'grue' property.' You DON'T actually know that! The whole problem is that time t hasn't happened yet; until it does, for all you know, every object [which you currently think is 'green'] is an example of an object possessing this 'grue' property. So in fact UON could -eventually- fail.

Second, invoking UON doesn't really help. Let us imagine that I am a person who was raised to use the words 'grue' and 'bleen'. Then, combined with the first point, I can match your final paragraph with this:

I can now answer Goodman by saying that "Grue" is a natural definition because my past experiences of seeing grue things staying grue allowed me to generalize that all things grue stay grue which is reflected in my definition of the word "grue" (grue and always will be grue). The definition "green" is unnatural because it is not supported by past experiences and UON.

[Note: This works even as I observe things as time t passes by - if I observe the color actually changing from 'green' to 'blue' at time t, for me that is a grue object staying grue!]

  • 1) But I can actually claim from my past experience and UON that no objects possesses the grue property: At any time t in my past experience, no object has ever transitioned from blue to green. Therefore I've never observed "grue", and nature is uniform.
    – Frank
    Jan 5, 2018 at 22:06
  • 2) This seems to be due to the fact that past experiences differ for individuals because they are subjective. But if UON was indeed justified, this difference shouldn't exist cause we are both observing a uniform nature.
    – Frank
    Jan 5, 2018 at 22:09
  • Its uniformity should ensure consistency in our observations, and therefore our languages based on observations
    – Frank
    Jan 5, 2018 at 22:15
  • @Frank from a perspective, green is a transition from grue to bleen and you have never witnessed such a transition, so you have never observed green objects. There's a symmetry between the two sets of predicates and your UON does not break the symmetry so it warrants one choice as much as the other. Jan 6, 2018 at 13:53

Is Goodman's new riddle of induction a restatement of Hume's problem of induction?

I think that Goodman’s riddle is not a restatement of Hume. The two philosophers are hard to compare on this question, because they start from different premises.

Hume posits a world where no event is ever the cause of a predictable result. Geoffrey Thomas points this out in his answer. Hume writes that from the straight path of a billiard ball, any result is conceivable. Such an assumption destroys both the possibility of induction and the uniformity of nature.

I understand Goodman to focus on the problem of confirmation, and the definition of grue is designed to isolate for this issue. The premise is that there is an object that is green if observed before time t and blue if observed afterwards. Whatever might be said about this assumption, it still posits a uniform and predictable world. This point is suggested in PMar’s answer. After time t, the object is still not anything conceivable; rather, it is either green or blue. The problem here is confirmation. The observation of a green emerald confirms that all emeralds are green and confirms that all are grue; and that was Goodman’s point as I see it.


Your approach, like that of most other philosophers of science, does not make any contact with reality or history or the sorts of problems scientists actually have to deal with on a regular basis. Nor does it make any contact with basic logic.

When you are running a scientific investigation, you do not know how the system you are investigating works. Even if there is an accepted account of how the system works, the people who came up with that account may have made a mistake. For example, they may have mishandled a piece of equipment or used a program that calculates expected results wrongly. Or they may have experimented with the system under different conditions than those in your experiment. Or there may be some completely unknown new discovery to be made that they missed. All of those possibilities and many other sources of error are always present.

There are plenty of real cases similar to the grue or bleen idea in at least some respects. Newtonian mechanics seemed to be correct, until we found out it was wrong. The difference is that grue or bleen is a silly philosophical thought experiment that totally neglects the fact that science involves explanations. Something like grue or bleen would be understood in terms of some underlying ideas about how the world works. For example, an object might change from blue to green as a result of being exposed to gamma rays that ionise pigment molecules causing a chemical reaction that produces a pigment of a different colour.

Inductivism is wrong. There is no way of getting theories from experimental data to theories and then showing those theories are true or probably true or good or whatever. Science, and all other human knowledge, is a result of guessing and criticising the guesses, as explained by Karl Popper. See the Popper section of this reading list for more:


"The Fabric of Reality" by David Deutsch, chapters 3 and 7 and "The Beginning of Infinity" by Deutsch Chapters 1 and 2 are also worth reading on this topic.

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