What must nature's uniformity be like in order for scientific induction to be (non-deductively) valid?

Question

I was thinking about one of the points made about induction, that it assumes that nature is uniform. So this leads me to the question about what this uniformity must be like in order for induction to be useful in developing scientific knowledge. Does scientific induction rely on natural uniformity as an unfounded premise (because of Hume and the problem of induction), or can induction itself be used to determine to what degree is nature uniform? For instance, the history of physics has determined to a large degree not just that there is uniformity in nature, but that nature is uniform only in certain respects. For instance, objects don't fall at a uniform velocity, but they do fall at a uniform acceleration (but only at degrees of precision that overlook air friction).

So can we make a general statement that expresses what sorts of uniformity are required for scientific induction? References to quality literature is also appreciated.

Answer 1

At a bare minimum, you only really need predictability according to any function. This need not be the identity function f(x) = x which says that whatever you measured before will be the same later, or any other particular function.

There are some things that will sink the attempt:

• The function must not change with time so fast that your error in measuring time is so large that you cannot tell what the output is.
• The function must not depend more sensitively on some input variable than you have the ability to measure that variable.
• The function must not be so complex that if you test functions in order of complexity you'll never reach that one or not have enough data to distinguish that this function statistically outperforms the others.
• Performing an experiment must not alter conditions so radically that you cannot know what you were actually testing (exact degree dependent on the sensitivity of the function to alterations in those conditions).

But these are very permissive requirements. The actual regularity in the universe appears to be vastly greater (in some areas) than the minimum required for the attempt to even be possible.

Still, each of these problems does come up in various contexts and make it difficult to determine outcomes. Physics has been particularly nice to us when it comes to regularity. Taking cognition as a more difficult example:

• Thoughts evolve more rapidly than we can measure neural correlates of them (e.g. with fMRI), making prediction of causation impossible (from that data alone).
• Neurons fire depending on their inputs, but in e.g. our brains we cannot measure the inputs accurately enough to figure out what the neuron will do.
• Human decision-making is fiendishly complex outside of toy examples, so it's not clear we'd know the right answer even if we hit it, or that we could test enough functions blindly to ever hit the right one.
• Testing cognitive performance is an experience, which we learn from, making it very difficult to test how cognitive performance changes over time, e.g. with age--because you never know if what you're measuring is due to time or due to the effects of the previous testing.

You certainly do not need to assume uniformity, however, except for the most basic assumption that the rules will not all change to be something radically different at some instant. (There is still the deep problem of induction.) Beyond that, you do not assume anything about uniformity. You test it: predict and measure. And you needn't even solve or assume anything about induction at all as long as you phrase your results as a model-of-past-behavior: "here is a way to think about that stuff that happened in the past that draws out some general principles instead of it being a collection of instances."

Answer 2

Induction doesn't necessarily require a commitment to the belief that Nature is uniform. I would rather say it requires stability or robustness across contexts. I think a more helpful way to think about this problem would be in terms of 'external validity'. Basically, the problem of external validity concerns our justification (or lack thereof) for extrapolating from one context (e.g. a laboratory experiment) to another one (e.g. the world). A claim is externally valid if it is correct across contexts and a claim is internally valid if it is correct within one context.

Justifications for extrapolating from one context to another are likely to be highly context dependent. Different methodologies can be used, different evidence gathered and different assumptions made for justifying extrapolation. There is really a lot of literature on the topic (which is partly why thinking about the problem this way might be more helpful), but hereby two suggestions:

• Daniel Steel's Across the Boundaries: Extrapolation in Biology and Social Science (2008)
• Francesco Guala's The Methodology of Experimental Economics (2005)

Answer 3

Your question is a bad question because induction is impossible and no principle of the uniformity of nature can save it.

Why is induction impossible? Explanations do not follow from observations in any sense. Nor do observations prove any idea. Nor can any observation make any idea one jot more probable. Inductivism is just another variety of justificationism: the idea that it is possible and desirable to prove ideas true or proably true. In reality, you can't prove any position or show it is probable. Any argument requires premises and rules of inference and it doesn't prove (or make probable) those premises or rules of inference. If you're going to say they're self evident then you are acting in a dogmatic manner that will prevent you from spotting some mistakes. If you don't say they are self evident then you would have to prove those premises and rules of inference by another argument that would bring up a similar problem with respect to its premises and rules of inference. Another approach that is sometimes used is that reason has to do with how the human mind works, but since how your mind works doesn't necessarily have anything to do with truth, that doesn't get us anywhere. Justification is impossible, so induction is impossible.

In reality all knowledge is created by conjecture and criticism. You notice a problem with your current ideas, propose solutions, criticise the solutions until only one is left and then find a new problem. Experiments are useful only as criticism. Ideas can't be derived from experiment any more than from any other set of premises. Rather, the idea is that you work out how the consequences of one theory differ from those of another. Then you conjecture ideas about experimental setups that would enable you to see the relevant consequences and criticise them. Once you have a setup that works about as well as you can make it work you use it to do the test. If the results are compatible with one theory and not the others then you may have successfully refuted some false ideas. Sometimes a purported successful experimental test will be successfully criticised because a test is a conjecture about something that happened and that conjecture may be wrong, so experiments don't prove anything.

The idea of the uniformity of nature is totally irrelevant in two respects. First, the mere idea that nature is uniform in some extremely abstract respect like "there are universal laws of physics" doesn't help create specific new ideas to solve problems. It may rule out some bad ideas, but those ideas would be bad by virtue of being bad explanations. For example, the idea that quantum mechanics applies to the whole universe except my house on 22 February 2065 is a bad idea because it introduces an unexplained complication to our ideas about the world that solves nor problems. Second, any such principle would have to be a conjecture about the laws of physics that couldn't be arrived at by induction since you concede that without it induction wouldn't work (it doesn't work with the principle either as I have explained above). So then any such principle would imply that induction is not a complete epistemological theory. This should be looked on as a sign of the bankruptcy of inductivism, rather than being used as an excuse not to dump it in the face of unanswered criticism.

For more on epistemology that is not justified true belief junk, see "Realism and the Aim of Science", Chapter I and "Objective Knowledge" Chapter 1 by Karl Popper as well as "The Beginning of Infinity" by David Deutsch. See also http://fallibleideas.com/.