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It seems to me that Popper's solution does not address the more difficult problem of induction that Hume calls the Principle of Uniformity of Nature. In other words, we might find evidence against a scientific claim not because it was incorrect when it was formulated, but because Nature dramatically changed her rules sometime later or in a different region of the Universe. A hypothetical example proposed by Nelson Goodman, is that there is no way to tell the difference between green and grue, which is an imaginary color that looks green until some point in the distant future when it will look blue to the eye. Note that the existence of grue is trivially falsified by observation after the moment in the future when its appearance changes.

Presumably, Popper would suggest Occam's razor would reject the concept of grue. But that presupposes that the law of parsimony holds true, which isn't obvious. Popper suggests that, 'We prefer simpler theories to more complex ones "because their empirical content is greater; and because they are better testable"'. But that seems to me either a very practical reason untied to the actual truth of the law or simply begging the question.

Or perhaps he would say that Grue Theory isn't really falsifiable and therefore isn't a scientific theory until it can be falsified. But it's difficult to see how Grue Theory is different than, say, General Relativity which waited several years for the technology needed to produce definitive tests of the theory. In some ways, Grue Theory has the advantage in that it points to a specific moment when its claim can be definitively tested, unlike most scientific theories.

Did Karl Popper directly address the uniformitarian assumption?

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I'm not an expert on this, but I'm pretty sure Popper is a complete skeptic about induction. He bases this explicitly on a (mis)reading of Hume. And this is why his characterization of scientific practice is supposed to be a purely deductivist one, where bold conjectures are tested for refutation in the crucible of experience.

Thus I suspect that he would simply say what you suggested: that simple theories which generalize over all of time and all of nature are easier to test, and thus more worth pursuing. And I suspect he would just bite the bullet in response to your objection that this is a merely practical matter untied to truth. For Popper, I think, we have no way of approaching the truth in science other than making stuff up and seeing if we can prove it false.

EDIT: And of course this might help.

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Or perhaps he would say that Grue Theory isn't really falsifiable and therefore isn't a scientific theory until it can be falsified. But it's difficult to see how Grue Theory is different than, say, General Relativity which waited several years for the technology needed to produce definitive tests of the theory.

Popper's Falsifiability criterion is a formal and logical one, and as such has nothing to do with the practical possibility or impossibility of testing a given hypothesis. It goes as follows:

Given that H is a hypothesis / theory, if and only if H is falsifiable then there exists a finite set of observation sentences Γ such that ¬ H is a logical consequence of Γ.

i.e., according to the criterion there must exist, in principle (as opposed to in practice), a set of observation sentences that by being true make the hypothesis being tested false.

In order to be falsifiable, the Theory of Relativity needs only to provide such observation sentences, not the availability of real life execution method of the associated experiments.

Back in 1916, Einstein provided a hypothesis which could, by definition, be tested -- by its own definition, that is. On the contrary, the Grue theory, by definition -- by its own definition -- cannot provide such testability in respect to itself, at least not at present. The Popperian reason behind the falsifiablity criterion, is that the attempts at refutation are what potentially corroborates a theory, so if no refutation is logically possible, no potential valid corroboration could be made, and so it isn't scientific.

In other words, General Relativity is testable per Popper because there isn't any logical contradiction between testing it and all the rest of background assumptions. In contrast, present testing of the Grue theory contradicts the fact that time travel is logically impossible, which I would guess to be found in its background assumptions.

The Popperian answer to the Grue theory in question would be, I presume, that it will be scientific once it'll be falsifiable in principle. If the Grue theory suggests also that the adequate time travel is logically possible then I guess it passes the criterion, but it does depend on that.

Did Karl Popper directly address the uniformitarian assumption?

Not that I am aware of, but I'll be happy to learn new things. One reason I can think of for him to not directly address the Unity of Nature is the fact that perhaps no such articulation of it exists in the form of a falsifiable theory.

In other words, Popper doesn't think this is of any special interest, as from his perspective, his program of the epistemology and methodology of science is perfectly consistent without it. You can suggest a general law of nature in the form of a hypothesis, have it stand in rigorous tests and as long as this situation holds the hypothesis is valid and tentatively true (which is, by principle, the best you can achieve under the Popperian doctrine). If, one day, new experiments show the hypothesis to fail a relevant test (even if it's "the same" test it had previously stood), then it is now refuted. It took some time but now it's there, along with all other refuted theories -- the cause for the "sudden" acceptance of the hypothesis as refuted is irrelevant; whether it's due to new testing technique or due to a change in "nature's mechanics" is beside the point of it being refuted.

  • @JonEricson I think I see where you're getting at, and to that I have to say I'm not quite sure the two theories compared should be in the same bin. See edited answer and comment at will – Reinstate Monica Sep 6 '13 at 19:22
  • Excellent. Thank you for the edit. So the Grue theory is not yet a scientific (i.e., falsifiable) claim. When the date rolls around that it can be tested, it will be. This is satisfying on a logical level, but disturbing in practice. We would hope that our observations today will bear some relation to our observations tomorrow (e.g. gravity will not reverse direction and green will not change to blue). Internal consistency is nice, but external consistency is better. ;-) Even so, this is a fine answer and I hope to see you around the site. – Jon Ericson Sep 6 '13 at 19:32
  • @JonEricson Thank you for the feedback, see you around :-) – Reinstate Monica Sep 6 '13 at 19:38
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If Popper does address the uniformity principle, his answer cannot be satisfactory to alternative answer than that it must be held as an axiom before we can even begin reasoning about the world around us. This, I believe, is the position of David Hume:

It seems evident, that men are carried, by a natural instinct or prepossession, to repose faith in their senses; and that, without any reasoning, or even almost before the use of reason, we always suppose an external universe, which depends not on our perception, but would exist, though we and every sensible creature were absent or annihilated. Even the animal creation are governed by a like opinion, and preserve this belief of external objects, in all their thoughts, designs, and actions.

It seems also evident, that, when men follow this blind and powerful instinct of nature, they always suppose the very images, presented by the senses, to be the external objects, and never entertain any suspicion, that the one are nothing but representations of the other. This very table, which we see white, and which we feel hard, is believed to exist, independent of our perception, and to be something external to our mind, which perceives it. Our presence bestows not being on it: our absence does not annihilate it. It preserves its existence uniform and entire, independent of the situation of intelligent beings, who perceive or contemplate it.

After this, he proceeds to argue that philosophical analysis of the reliability of our senses and the uniformity of nature fails:

So far, then, are we necessitated by reasoning to contradict or depart from the primary instincts of nature, and to embrace a new system with regard to the evidence of our senses. But here philosophy finds herself extremely embarrassed, when she would justify this new system, and obviate the cavils and objections of the sceptics. She can no longer plead the infallible and irresistible instinct of nature: for that led us to a quite different system, which is acknowledged fallible and even erroneous. And to justify this pretended philosophical system, by a chain of clear and convincing argument, or even any appearance of argument, exceeds the power of all human capacity.

To address the Theory of Grue, we must object to it not on the basis of deductive reasoning, but on the more fundamental basis of the reliability of our senses: green objects look green and our instincts suggest they will remain green and not magically turn blue in the future. As we must begin all reasoning with the assumption of our own reliable senses, it is and always will be an axiom we must accept without justification.


Straying from Hume, Popper and the question at hand, I should point out that the traditional justifications for the reliability of the senses and the uniformity of nature are:

  1. The existence of some greater set of forms, which are sensible, that the material world copies, reflects or emulates. (This is Plato's position.)

  2. The a priori assumption that nature is sensible. (Aristotle generally took this approach.)

Neither justification is satisfactory for reasons that Hume points out. Both must be taken as properly basic assumptions.

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Science never lays claim to reaching the absolute truth, only to come as close as possible to that truth. As such it may need to update theories based on new facts all the time. The appearance of "grue" or any other change in the laws of nature is just one such new fact, and will be treated accordingly.

And that means that the theory of grue will be held as false until grue can be distinguished as a separate color from blue, at which time it will instead be accepted as true.

  • Does this mean the theory of blue (that what we see now as blue will always remain blue in appearance) is equally false as the theory of grue? If not, why not? – Jon Ericson Jul 11 '11 at 16:37
  • @Jon Ericson: They theory that what we see now as blue will always remain blue is the kind of pointless speculation that only people with degrees in philosophy would bother about. That said, it would be assumed that since colors have not changed previously, there is no reason to assume they will change in the future. Such an assumption would fail Ockhams razor. – Lennart Regebro Jul 12 '11 at 7:39
  • Right, but "there is no reason to assume they will change in the future" and Ockhams razor (in this case) both are restatements of the Principle of Uniformity of Nature. (As to who else speculates about the essence of color, I'd submit that many children ask these sorts of questions. So people with degrees in philosophy and children are interested in such questions--and I don't have a degree in philosophy.) – Jon Ericson Jul 12 '11 at 17:39
  • @Jon: I don't see how Ockhams razor is a restatement of that, and "there is no reason to assume they will change" is an effect of Ockhams razor. That they have the same effect in this case as the Principle of Uniformity of Nature doesn't mean they are the same. (Children speculate in a lot of things that we actually have answers to. ;-) ) – Lennart Regebro Jul 12 '11 at 20:50
  • Ockhams razor may be more basic than uniformity, but I propose it has similar problems. We must accept it as a fundamental axiom without proof. Worse, we know it applies because it has applied in the past. Formal proof of parsimony would require some sort of inductive reasoning, as far as I can see. – Jon Ericson Jul 12 '11 at 21:16
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I'm no philosopher but I think blue is a description associated with an object. And blue things turning green and green things turning blue happen all the time. On the other hand, blue and green might be taken to refer to the wavelengths of light reflected from objects. In which case grue would imply that there is some wavelength which is currently perceived as green which later will be perceived as blue with no change in wavelength, terminology or the apparatus of perception. Seems prima facie unlikely, but it could be testable if we could agree on the precise details of perception. I would say that we proceed as if colours (in the sense of perceptual aspects of wavelength of light) will remain the same unless at some point we have to revise this view. And this seems quite Popperian to me. On the original question I think Popper's approach makes the uniformity of nature principle irrelevant. So I don't think he addresses it directly.

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I think Popper addresses the supposed uniformity principle as it is related to the problem of induction in "Realism and the Aim of Science" by Popper, in Chapter I Section 4. David Deutsch discusses it in "The Beginning of Infinity" Chapter 1. See also the introduction to "Realism and the Aim of Science" for a discussion of grue.

Note that no such principle could possibly save inductivism from criticism. Any such principle could not be obtained from experimental data since the data are interpreted in terms of that principle. Also, saying that nature is uniform doesn't specify the exact form of the uniformity and so is useless for scientific discovery. Our best current guess at a theory of gravity is general relativity, which is a different guess about what rules hold uniformly than Newtonian gravity.

Popper would say that an alternative to some current theory should be considered if it makes predictions other than the prediction it was originally invented to explain. His reason for saying this is that the only way to decide between ideas is by criticism, they cannot be proven or shown to be probably true or anything like that: they cannot be justified. Any justifying argument makes assumptions and uses rules of inference that have not been shown to be true or valid, so the conclusions of such an argument have not been shown to be true or valid. (See Chapter I of "Realism and the Aim of Science".) This means that every argument is question begging in the sense of being unjustified. Rather than being justified, ideas are conjectured solutions to problems and they are controlled by elimination through criticism. So experiment can only ever be used to eliminate ideas, not to prove them. Since we can only eliminate an idea by experiment, an idea that makes only a single prediction that differs from other ideas is extremely difficult to test. This is an unanswered criticism of such an idea and so eliminates it from consideration.

Another problem with such an idea is that it is a bad explanation. It amounts in substance to adding a qualification to an idea that does explain stuff. As such it ruins an existing explanation and provides no replacement. See "The Fabric of Reality" by David Deutsch, Chapter 7. How does this apply specifically to grue? Well, if the grue idea just says that the colour of some blue crystal will change to green and nothing else, then it is worthless: call this the ad hoc grue theory. The current blue properties are explained by ideas about the atoms and their arrangement in a crystal and that sort of thing. The ad hoc grue theory ruins this explanation and provides no replacement. Furthermore, arguably it's not actually testable. For example, suppose that it predicts the crystal will turn green at midnight on 27 January 2015. What happens if I take the crystal up in a plane at 11pm UK time and fly to a place where it is past midnight and then back again. Will the crystal change from blue to green and back again as I cross the line at which the time officially changes? There can be no non-arbitrary way to decide that without an account of why the colour changes. What happens if I put it in a box and say that inside the box midnight on 27 January 2015 never happens? Since the usual calendar convention is suspended will the crystal never change colour? What happens if I accelerate the crystal to near the speed of light so that the time elapsed for the crystal between when it was created and 27 January 2015 is a million years, or a billion or 10^10^10^10^9 years? When will it change colour?

A theory that predicts the colour change as a result of some property of the crystal or whatever will have other consequences and so will be independently testable, e.g. - it might say things about atoms or crystal structure that differ from the standard theory. As such there will be some other way to test it.

Note that since there is no way to solve the grue problem without an explanation, it is impossible to solve it using inductivism. According to inductivism we get ideas and justify them by experimental observation but this is impossible and so inductivism does not provide any solution to the grue problem.

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