A Thought on Induction - the Non-Black-Non-Raven Paradox Might Not Be That Important

From pure propositional calculus, we of course have a → b ⇔ ¬b → ¬a. One of the problems with induction is the non-black-non-raven paradox: If we use, in an inductive reasoning process, an example of a black raven as "counting towards the consequence raven → black", then an example of a non-raven non-black thing should count towards the same conclusion—or should it? To me, this confuses the process of induction with the result of induction. Even if we assume the latter is the logical formula "∀ x: Raven(x) → Black(x)" (which is not at all clear: It might be that the result of induction is a form of weighted proposition, or an expectation, or a belief): Of course, from the result we can conclude "∀ x: ¬Black(x) → ¬Raven(x)"; but using the non-black non-raven example in the same way as the black raven is not at all required; and, I say, not even plausible. After all, this single example (or even a set of such examples) is no logical statement, but, at best, a ground instance of some as yet unclear logical statement(s). From the fact that we have an object 1 in the world that can be described as the combined proposition (non-raven₁, non-black₁) being true, we can trivially conclude that non-raven₁ → non-black₁ is true; as we can also conclude non-black₁ → non-raven₁, and, indeed, non-raven₁: But all this, of course, does not tell us that all things are not ravens, or even that more than one thing is not a raven.

So my argument is: The input to "inductive reasoning process" (however that works) are facts; the output is some sort of (maybe nehanced) logical statement. And thus, the two are handled wildly differently.

Counterargument: Think about a sort of induction where the inputs are already logical statements (e.g. on subsets): Let's say we know that all A₂ are B; and all A₃ are B; and all A₅ and all A₇ and all A₁₁ are B; etc. How does inductive reasoning let us conclude that all A_p, where p is prime, are B? If this is induction, then the "facts" above are just small logical assertions, e.g. "all raven₁ are black" (there only being one raven₁, but this is then a coincidence). It isnecessary to check whether this model of induction—which follows more closely deduction's black box, where both input and output are logical statements—is worthwhile to be studied