This isn't for a general audience, but I can't resist posting since, A) I haven't posted anything of substance in awhile, B) I love my own prose too damned much, and C) I find the question of the problem of induction ("how do you know what you know") fascinating, having thought about it for, oh, about 2.5 decades.
My comment started as a response to a message concerning the history of science propounded in the book "The Logical Leap", by David Harriman. For the non-Objectivist audience, this book was done closely in association with Leonard Peikoff. For the non-specialist, I won't expound on the nuances of these parties, just noting that McC is a historian, DH is physicist (not a PhD, though), and LP is a noted philosopher.
Most of those who read this blog (our readership is small, but distinguished) know that there's a controversy between these parties concerning the book, and I was writing to express my agreement with the assessment that there appears to be some kind of personal animus on both sides related to a mildly critical review McCaskey placed on Amazon which led to an angry response from LP. To messenger's credit, when most people were dwelling on the titillatory aspects of the personality conflict, she dug up some real facts of the scientific history in question. (After initially posting the message, I've redacted it, after being reminded by my wife that permission to forward freely is not quite the same as permission to post publicly. It's not essential to the discussion here anyway.)
My own interest rests primarily with the thesis of the book--a claim to have solved the age-old "Problem of Induction", which I've addressed previously. The history is interesting, but whether Galileo did or did not actually drop balls from the Tower of Pisa has little real effect on Newton's own work in developing a theory of gravitation (which is ground zero for the conflict between McC, DH and LP). I've long had issues with what Harriman has been propounding about how we know we have a valid induction, going back to his first lectures, circa early 1990's.
I heard him talk a couple years ago and he had changed some of his more egregious scientific views relating to denying certain experimental facts about quantum mechanics (which he acknowledged, to his credit--his perspective had been more of a defense of mechanistic determinism), but I found I still had a major issue with the proffered solution for the problem of induction, and I asked him a direct question about it in the Q&A which he didn't answer to my satisfaction.
I recently read his book to see if it could shed any more light, and my problem with the solution put forward is simply this: it demands omniscience. There is no question about this. The formula emulates Ayn Rand's outline for concept formation, but the thesis (to my reading -- it's poorly summarized and scattered all over the book in bits and pieces) is that you must induce from every possible relevant and necessary fact.
It asserts: if the particulars from which you induce are grounded in perceptions, and if you rigorously define the scope of application for your induction, it is valid. (By "particulars" I simply mean perceptions, facts, thoughts, observations, measurements, etc. -- everything that goes into your head to make an induction.)
There's a bit more to their theory than that (the evidence must be non-contradictory, self-consistent and, for a scientific induction, identify an efficient cause), but I would characterize their solution as essentially a deductive formulation: it prescribes a set of rules to get all your factual and evidentiary ducks lined up in a row, at which point you look with your mind's eye, form your induction by an innate mental capacity, and say: it's valid.
This is simply impossible for any but the most trivial induction. Maybe not even for those. There is no way to hold in your head every possible relevant fact to form any kind of even modestly complex theory. No way to even know a priori all of what is relevant and necessary, or what isn't. (As I'm using it, the phrase "relevant and necessary" is my own summary of their presentation--you may criticize my interpretation.) You'd be long waiting on some bottom rung of hell for the Big Freeze before you could collect every relevant fact, organize them all, and then to try to get them all jammed into your skull for the epiphanal moment when you form your induction and say "Aha!" to a world that might not be so ready to take your word that you've done all that correctly.
I've use an example that I've tried before with others, to little avail, but I'll avail myself of it again to underscore the point: I'm an electrical circuit designer. My entire job (30 years) is creating inductions for electronic circuits that do things. Circuits from a few to thousands to even millions of transistors. I have among the most abstract engineering jobs there is.
Being an engineer, the nature of the inductions I do is a little different than a scientific theory, because I create inductions rather than discover them, based on objectives (a human purpose) rather than experimental facts (about nature), but the principle isn't so different. In designing a circuit to moniter and process electrical signals, I have to hold an enormous amount of facts, principles and experience in mind.
Even for a circuit with only a few transistors, it is extremely difficult to make sure I anticipate every possible fact that may prevent my circuit from doing exactly what I want it to do. Let me say: impossible. The crow epistemology and a deadline get in the way. (The deadline isn't fundamental in this context.)
But I have to get a job done. I make a first stab at the problem: I conceive a proto-induction, then I test it with signals to see that it does what I want. From this I find any problems that prevent my design from working--there are always problems--and then I refine the design. Over and over and over again. I finally arrive at a finite series of tests, representative of an infinite number of signals which could exercise my circuit. Done properly, these tests are complete and general enough to guarantee the circuit works for all the things I want it to do -- and no more. (This is like the "scope" of an induction that Peikoff/Harriman talk about in their book.)
Now, what I do is a hell of a lot easier than inducing a scientific theory. I will state categorically, as a practical matter and a matter of principle: anyone forming a new scientific theory must conceive of it from some incomplete subset of the facts, and then go back to validate it by some means or other to determine if their theory corresponds to reality. There is just no way they can be careful and meticulous enough to make sure their theory is correct, right off the bat. To my thinking, this points to where the solution of the problem of induction must lie: some method of validation. Not positivist claptrap, but objective validation.
Practically, theories up to this epoch in time get validated by little more than the sheer weight of evidence showing they predict X, Y and Z and don't contradict other known facts. That doesn't mean empirical evidence is the solution to the problem of induction; it just means that this is what's been happening in science for a very long time in the absence of anything better. It doesn't answer the central question of the problem of induction-- it just is what people do in the absence of a solution to the problem of induction.
Why Peikoff/Harriman formulated their own solution in terms of an omniscient method (according to my assessment) is a subject in itself. Many reasons possible that I won't enumerate here, and I'm not questioning anyone's honesty.
I have my own notions of what the real solution is, which I won't go into beyond saying (in crudely simple terms): I think you have to generalize the particulars from which you form any induction. That is, you have to define a finite number of particulars so that they are representative of general classes of things that are infinite in number, and then your induction will be general. (Now don't badger me about the validity of the concept "infinite"...) That may be too sketchy to convey what I mean, but it relates directly to that example of electrical design that I just gave.
Doesn't matter for this debate. In my judgment, the Peikoff/Harriman theory as presented is wrong because it demands omniscience. Period.
Consider that it didn't even address the most important application for a solution to the problem of induction: the theory of quantum mechanics. I mean, there has never been a theory more contentiously debated in the history of science. (Rightly so.) If there was one single application that had to be addressed in the book it was the quantum theory. If there was one theory people would like to see proved or disproved by a solution to the problem of induction, it is the quantum theory. To leave that out of a book purporting to solve the problem of scientific induction is like leaving out the verdict in a murder trial, while discussing every other form of minutae.
(The reasoning for the quantum theory is not so difficult to sum up, by the way, but I'll leave that for another discussion.)
Not that Harriman's book doesn't have value in presenting the method of induction in the context of the history of science, but it simply goes too far in asserting a solution to the problem of induction. If the historians have their debate and correct any errors in the history, and if the thesis was removed that the problem of induction was solved, the book would be fine for any class on induction for scientists.
I have no axe to grind with Peikoff or Harriman beyond my disagreement with their thesis. My issue is only with the objective truth of things. That's what I think all Objectivists should stay focused on -- let the objective facts (ie, those out there in reality) be their primary focus -- ie, the science, philosophy and history -- rather than the personality disputes, and let reason be the arbiter of the factual disputes.