It seems to me that the rejection of the validity of induction would cause a deep skepticism in pretty much everything but most prominently in perception. If we can never assume uniformity of nature, then every inference about the future and the future based on the past is invalid.

Thus wouldn't the rejection of induction restrict us to only be able to talk validly about our present phenomenal experiences or whatever is directly present in the mind? What are the practical ramifications of rejecting induction? It seems that it would throw us all into intense skepticism.

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    Officially, statistics does not use induction, it uses the Law of Large numbers -- the fact that the sum of enough random variables is always normally distributed. You can pretend that what do in 'abductive' inference is all Bayesian statistics instead of induction and not change a thing... – user9166 Jun 8 '16 at 21:33
  • In every moment of our life we "assume uniformity of nature": when we turn on the light switch we are expecting that the lamp will illuminate... and usually this happens. – Mauro ALLEGRANZA Jun 9 '16 at 6:18

Nelson Goodman is well known for what he calls the "The New Riddle of Induction." I believe the following does a good job of summarizing his conclusion:

"We have so far neither any answer nor any promising clue to an answer to the question what distinguishes lawlike or confirmable hypotheses from accidental or non-confirmable ones; and what may at first have seemed a minor technical difficulty has taken on the stature of a major obstacle to the development of a satisfactory theory." (Nelson Goodman, "Fact, Fiction and Forecast")

I believe his conclusion is correct because in the final analysis it merely exemplifies the fact that we assume that things will behave in a regular manner. That assumption usually serves us very well, but it is still only an assumption for which there is no means to prove.

Your question seems to suggest and all-or-nothing attitude toward epistemology, i.e. if we can't have certainty, we are doomed to scepticism. However, in practice, such an extreme position is unnecessary as Goodman points out:

"If our definition works for such hypotheses as are normally employed, isn't that all we need? In a sense, yes; but only in the sense that we need no definition, no theory of induction, and no philosophy of knowledge at all. We get along well enough without them in daily life and in scientific research." (Nelson Goodman, "Fact, Fiction and Forecast")

Of course, Goodman didn't give up at that point. He went on to try to clarify the problem to provide a firmer foundation for the confirmation of hypotheses. He maintained hope that seeking solutions to the problem is a worthwhile endeavor. However, he never lost sight of the inescapable fact that we have to put our trust in certain assumptions:

"We have no guarantees. The criterion for the legitimacy of projections cannot be truth that is as yet undetermined." (Nelson Goodman, "Fact, Fiction and Forecast")

We may continue with our science and our philosophy, but it's best to remember that we operate within the constraints of some presuppositions we can never empirically justify.

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the consequences of rejecting induction are being freed up to learn something better from Karl Popper.

all your concerns come from basically taking a typical inductivist epistemology and then rejecting one central part (induction) and keeping the rest.

what you need is a thoroughly non-inductivist epistemology which is built from the ground up to make sense without induction. that's what Popper offers. (so far there are no non-Popperians offering this).

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Induction is impossible. Explanations don't follow from observations. The explanations cover unobserved events and explain what you see in terms of stuff you have not observed and may be unable to observe. Nobody has measured the temperature at the core of the sun and perhaps nobody ever will, but it plays a role in the explanation of how the sun works.

You say:

If we can never assume uniformity of nature, then every inference about the future and the future based on the past is invalid.

Uniformity of nature is irrelevant. The mere fact that there are universal laws of physics implies nothing about the substance of those laws. As a result it can't be used to figure out what the laws are. Nor can it be used to predict the future.

So how is knowledge created without induction? You notice a problem, guess solutions to the problem, and criticise the guesses until only one is left and it has no known problems. The criticism can include observations that clash with the consequences of the theory.

See "Objective Knowledge" Chapter 1 by Karl Popper. See also "The Fabric of Reality" by David Deutsch, Chapters 3 and 7 and "The Beginning of Infinity" by David Deutsch, Chapters 1 and 2.

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