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OTI was created long ago with the laudable goal of combating a tendency toward rationalism. However, there was not an actual theory of induction within Objectivism during Rand's lifespan (and arguably there still isn't since Objectivism as Rand knew it became a closed system upon her death). So it is a question whether what Peikoff and Rand were doing in OTI is actually induction in the technical philosophical sense. Binwanger is unreliable due to his radical dualism. In any contradiction between Binwanger and Rand or a Peikoff/Rand presentation dump Binswanger. Peikoff and Harriman authored "The Logical Leap: Induction in Physics" which is little more than the claim that the process of concept formation is induction. That doesn't satisfy many people looking for a theory of induction who are not already Objectivists and many who are. Peikoff's lecture course "Art of Thinking" lecture 6 covers "aspects of certainty excised from OPAR for space". The four aspects covered are thinking about the future, thinking in terms of statistics, does present context of knowledge limit certainty, and does certainty imply error is impossible. I wonder how much your line questioning here is motivated by an underlying confusion about certainty, and if that should be your next question.

Also, in Rand's epistemology, it's not the sensations that are being conceptually united by the process of reason, one does not experience sensations in most normal circumstances (ie., unless you have diminished mental capacity, are in a sensory deprivation experiment, etc.) The process of integrating sensations into perception is physiological, not rational (as in Kant), one experiences a united perceptual field, rather than sensations. The process of reason proceeds, under this theory, by abstracting from the field of perception, and then integrating the units conceptually as you described.

It seems like you're pointing to an apparent conflict between the following claims: Full validation only requires reduction and integration. Full validation requires induction. Induction is distinct from both reduction and integration. The solution will require rejecting or modifying one of these three claims somehow (probably the third).

Agreed. Here is one stark example I am reminded of: "In proportion to the mental energy he spent, the man who creates a new invention receives but a small percentage of his value in terms of material payment, no matter what fortune he makes, no matter what millions he earns. But the man who works as a janitor in the factory producing that invention, receives an enormous payment in proportion to the mental effort that his job requires of him. And the same is true of all men between, on all levels of ambition and ability. The man at the top of the intellectual pyramid contributes the most to all those below him, but gets nothing except his material payment, receiving no intellectual bonus from others to add to the value of his time. The man at the bottom who, left to himself, would starve in his hopeless ineptitude, contributes nothing to those above him, but receives the bonus of all of their brains. Such is the nature of the “competition” between the strong and the weak of the intellect. Such is the pattern of “exploitation” for which you have damned the strong." Galt's Speech (For the New Intellectual, 186) Although the above involves a mix of material and spiritual values (both of which I think would qualify as "benefit"), I think it is clear that it accepts that the act of invention involves conveying a great degree of benefit to others (perhaps given the quote this is an understatement?). To my knowledge, Rand did not make it a point to state that it is not in a man's rational self-interest to invent anything, i.e. although she did strongly suggest that being a parasite or a thief are inimical to a persons life and thus those "careers" should be avoided, she did not make the same pronouncement about the vocation of "Inventor" notwithstanding the imbalance of "benefit" quoted above. She was a strong supporter of Patents and Copyrights, and as far as I know nothing in her analysis of a proper intellectual property system addresses the issue of the inventor receiving only a "small percentage of his value" NO MATTER what millions he earns. In essence, "free riding" here (at least in spiritual values) is inevitable, and unavoidable, BUT at the end of the analysis, irrelevant since inventing is still in the inventor's self interest, and VERY much so if one both enjoys it and can do it in a lucrative manner.