~ an answer that ‘makes sense’ is entirely different from what works ~
We often begin with some axiom, an assumption of Truth, and hope that we can derive from that a complete set of all Truths. Kurt Gödel killed that hope; your induction will never attain proof, for an infinitude of truths, some of them magnificent and powerful. Wittgenstein killed the Logical Positivists, who claimed they could ‘solve’ philosophy, if they just agreed on rigorous definitions of terms. Wittgenstein had been one of their own luminaries, to boot!
Now, that layman’s fascination with the power of logic has returned, and those laymen claim they will use it to ‘find the Future-Proof Ethic’. Mathematician with a few algorithms under my belt, here, to tell you: you can only ever find Protocols that get you the Equilibrium you like. There is no Schema that will, inherently, point you to EVERY correct answer, and always yield optimal outcomes. Your rules are based in language, and so, they are always heuristics at best, superstitions at worst. You CAN, and SHOULD rely on statements which are 99.9999% correct — AND, you must be prepared for those few errors in your rule, because they are guaranteed to occur, eventually.
Look at how language cripples our ability to escape heuristic:
I take photos of every object humans manufacture, and I show each random person each photo, asking them to label it. I take all the photos which were consistently labeled ‘chair’ — those are the chairs. If I lay them all on a table, with the pictures near-to-each-other when they are visually similar, then they will form a visual blob of all chairs. Now, add the visually-similar other objects… crap! The BOUNDARY between ‘chair’ and ‘not-chair’ is a wobbly fractal, infinitely resolved. Yet! Language only provides de-lineations (a neural network researcher would say that ‘words are zero-curvature hyperplanes bi-secting the latent space of object categories’). Because language can only say “Is/Isn’t”, it CANNOT map perfectly to the fractal boundary of the chair-category. There will always be positive or negative exceptions.
As a result, any schema in any natural language which is used to describe any higher-order process in physical reality is necessarily imperfect. Emergent rules in a system are NOT obeyed flawlessly, because they are only the averaging of lower-level behaviors. Thermodynamics is such a case; a system’s gas molecules DO all end up on one side of the box, sometimes. So, you can give me the sub-atomic Theory of Everything, while never being able to give me a single equation for the stock market’s entire history, including its future.
“We start with the GOAL we want to happen, as a set of measurable results, physically AND by user-feedback metrics. Then, we model what Equilibrium is reached, by every different set of Protocols. WHICHEVER Protocol gets us the Equilibrium we wanted, THAT is the Protocol we choose. Those Protocols never follow a singular, internally-consistent logic. Cludge is Pragmatic.”
This enforces scientific rigor, and catches the crude mistakes resulting from simplistic assumptions about the world. When we recognize that we are perpetually failing to form an accurate World-Model, then we stick to the data, discarding the fancies sung by our Schema’s Siren Song.