We do ten experiments. A scientist observes the results, constructs a theory consistent with them
Huh? How did the scientist know what to observe without already having a theory? Theories arise as explanations for problems, explanations which yield predictions. When the first ten experiments were conducted, our scientist would therefore be testing predictions arising from an explanation to a problem. He wouldn't just be conducting any old set of experiments.
Similarly the second scientist's theory would be a different explanation of the problem situation, one yielding a different prediction. Before the decisive test, the theory that emerges as the best explanation under the glare of critical scrutiny would be the preferred explanation. Without knowing the problem situation and the explanations that have been advanced it cannot be determined which is to be preferred.
"What on Earth is evolution, if not the keeping of DNA sequences that worked last time?
It's also replication and variation.
It's less efficient than human induction and stupider, because it works only with DNA strings and is incapable of noticing simpler and more fundamental generalizations like physics equations. But of course it's a crude form of inductive optimization. What else would it be?
That seems like an argument from "failure of imagination". Quite simply, evolution is trial and error.
There are no knowledge-generating processes without some equivalent of an inductive prior or an assumption of regularity.
This is just question begging, as I think you are aware. How did we come by the knowledge of induction? Did we induce it? Impossible! So, therefore, there must be at least one way to knowledge that doesn't involve induction.
This stuff is all old hat. Philosophers of the 20th century like Popper and Bartley realized that the whole induction quagmire is caused by people looking for justified sources of knowledge. They concluded that justificationism is a mistake and replaced it with critical rationalism. Now there are bad scholars who claim that critical rationalism sneaks induction in through the back door. But that is just bad scholarship.
It's a shame to still be wasting time on induction in the 21st century. Rather than rehashing old problems, shouldn't we be building on what the best of 20th century philosophy gave us?
The maths establishing this often go under the name of No-Free-Lunch theorems.
Were the assumptions of these theorems inductively justified?
To get the ball rolling on rationality quotes, here's a rationality quote from the father of the Greek enlightenment, Xenophanes:
But as for certain truth, no man has known it,
Nor will he know it; neither of the gods
Nor yet of all the things of which I speak.
And even if by chance he were to utter
The perfect truth, he would himself not know it;
For all is but a woven web of guesses
Enjoy your break.
Re: Critical rationalism
Critical rationalism is similar to evolutionary adaptation (though there are some important differences). Do you think evolution depends on induction, or would you admit that there are knowledge-generation processes that do not require induction in any way, shape, or form?
There are a number of reasons why I feel that modern philosophy, even analytic philosophy, has gone astray - so far astray that I simply can't make use of their years and years of dedicated work.
Yes, much modern philosophy has gone astray. But some hasn't. I would cite, for example, the thinking of critical rationalists such as Karl Popper, William Warren Bartley, David Deutsch, and David Miller.
Moreover I maintain that critical rationalism ought to be of use to you. First, it contains cogent criticism of inductivism and crypto-inductivism and one who understands these criticisms should see why Bayescraft is sterile. This knowledge is not only useful, it can't be ignored. Second, critical rationalism, and not Bayescraft, is our best current theory of knowledge and how we come to know things. Best theories are useful not only in themselves but also for the problems they contain.