You often ask me for information/arguments that I have already given you
We're partially misunderstanding each other because communication is hard and we have different ways of thinking. I'm trying to be patient, and I hope you will too.
Please address these two questions about induction. Answering with page numbers from a book would be fine if they directly address it.
I've read lots of inductivist explanations and found they consistently don't address these questions in a clear, specific way, with actual instructions one could follow to do induction if one didn't already know how. I've found that sometimes accounts of induction give vague answers, but not actionable details, and sometimes they give specifics unconnected to philosophy. Neither of those are adequate.
1) Which general laws, propositions, or explanations should one consider? How are they chosen or found? (And whatever method you answer, how does it differ from CR's brainstorming and conjecturing?)
2) When and why is one idea estimated to have a higher weight of observational evidence in favor of it than another idea? Given the situation that neither idea is contradicted by any of the evidence.
These are crucial questions to what your theory of induction says. The claimed specifics of induction vary substantially even among people who would agree with the same dictionary definition of "induction".
I've read everything you wrote to me, and a lot more in references, and I don't yet know what your answers are. I don't mind that. Discussion is hard. I think they are key questions for making progress on the issue, so I'm trying again.
As a fallibilist, you acknowledge that the 'real world' is a contingent one and there are no necessary truths. But is not 1+1=2 a necessary truth? Is not 'All tall men are men' a necessary truth since its negation is self-contradictory?
I'll focus on the math question because it's the easier case to discuss first. If we agree on it, then I'll address the A is A issue.
I take it you also think the solution to 237489 * 879234 + 8920343 is a necessary truth, as well as much more complex math. If instead you think that's actually a different case than 1+1, please let me know.
OK, so, how do you know 1+1=2? You have to figure out what 1+1 sums to. You have to calculate it. You have to perform addition.
The only means you have to calculate sums involve physical objects which obey the laws of physics.
You can count on your fingers, with an abacus, or with marbles. You can use a Mac or iPhone calculator. Or you can use your brain to do the calculation.
Your knowledge of arithmetic sums depends on the properties of the objects involved in doing the addition. You believe those objects, when used in certain ways, perform addition correctly. I agree. If the objects had different properties, then they'd have to be used in different ways to perform addition, or might be incapable of it. (For example, imagine an iPhone had the same physical properties as an iPhone-shaped rock. Then the sequences of touches the currently sum 1 and 1 on an iPhone would no longer work.)
Your brain, your fingers, computers, marbles, etc, are all physical objects. The properties of those objects are specified by the laws of physics. The objects have to be used in certain ways, and not other ways, to add 1+1 successfully. What ways work depends on the laws of physics which say that, e.g., marbles don't duplicate themselves or disappear when arranged in piles.
So I don’t think 1+1=2 is a truth independent of the laws of physics. If there's a major, surprising breakthrough in physics and it turns out we're mistaken about the properties of the physical objects used to perform addition, then 1+1=2 might have to be reconsidered because all our ways of knowing it depended on the old physics, and we have to reconsider it using the new physics. So observations which are relevant to physics are also relevant to determining that 1+1=2.
This is explained in "The Nature of Mathematics", which is chapter 10 of The Fabric of Reality by David Deutsch. If you know of any refutation of Deutsch's explanation, by yourself or others, please let me know. Or if you know of a view on this topic which contradicts Deutsch's, but which his critical arguments don't apply to, then please let me know.
I believe that Einstein is closer to the truth of what you call the real world than was Aristotle. So when I'm told by this type of fallibilist that we don't know anymore today than we did 400 years ago, I demur.
Neither Popper nor I believe that "we don't know anymore today than we did 400 years ago".
Given your comments on LSD and the a-s dichotomy, after reading this I conclude that you are a fan of late Popper (LP) and I prefer early Popper (EP).
You think EP is wrong, and I think LP is right, so I don't see the point of talking about EP.
(I disagree with your interpretation of EP, but that's just a historical issue with no bearing on which philosophy of knowledge ideas are correct. So I'm willing to concede the point for the purpose of discussion.)
Gellner argued that Popper is a positivist in the logical positivist rather than the Comtean positivist sense. His discussion proceeded from the contrasting of positivists and Hegelians and so he put (early) Popper in the positivist camp - Popper was certainly no Hegelian. Of course, Popper never tired of reminding us that he destroyed the positivism of the Vienna Circle and went to great pains to declare himself opposed to neo-positivism. For example, he says that he warmly embraces various metaphysical views which hard positivists would dismiss as meaningless. Moderate positivists, however, accept metaphysical views but deny them scientific status. Does not Popper do this too, even if some of these views may one day achieve scientific status?
Yes: (Late) Popper accepts metaphysical and philosophical views, but doesn't consider them part of science.
CR (late-CR) says non-science has to be addressed with non-observational criticisms, instead of what we do in science, which is a mix of observational and non-observational criticism.
If by fallibilism you mean searching for evidence to support or falsify a theory, I'm a fallibilist. If, however, you mean embracing Popper's view of 'conjectural knowledge' and the inability, even in principle, or arriving at the truth, then I'm not. I believe, against Popper, Kuhn and Feyerabend, that the history of science is cumulative.
No, fallibilism means that (A) there are no guarantees against error. People are capable of making mistakes and there's no way around that. There's no way to know for 100% sure that a proposition is true.
CR adds that (B) errors are common.
Many philosophers accept (A) as technically true on logical grounds they can't refute, but they don't like it, and they deny (B) and largely ignore fallibilism.
I bring this up because, like many definitions of knowing, yours was ambiguous about whether infallibility is a requirement of knowing. So I'm looking for a clear answer about your conception of knowing.