Vik

Induction is a prerequisite for all validation. The process behind induction must be identified, not "validated". Since you already have a theory of concepts, your next step is to understand propositions and the process that gives rise to them. Then you need to identify the process that produces a descriptive statement. Finally, you identify the process that produces a descriptive generalization, i.e. one that accounts for several descriptive statements.

I see 5 such principles mentioned in your post: You must define your concepts in terms of essentials. You must examine instances that have a logical, conceptual relationship to the conclusion. You must redefine your concepts when new evidence demands it. You must clarify your conclusion when changes to your definitions demand it. Your state of knowledge will tell you whether a claim is warranted or arbitrary. I would add that wider generalizations must summarize or explain all narrower generalizations falling within its context.

Constant acceleration is enough to settle the first question, but it is NOT enough to settle the second. You need a sum of forces framework--something that Galileo didn't have. Although Galileo understood that motion cannot change without a force, he didn't seem grasp its connection to acceleration. I would argue that such connections distinguish explanatory generalizations from mere descriptive ones. I would also argue that such connections are made possible by new concepts.

Sometimes the facts are such that there is some, but not much, evidence in favor of a proposition and nothing known that contradicts it. If the proposition explains a wide variety of phenomena, there is value in adopting it AS IF it were true--just to see what facts it leads us to. In that context, hypotheses have enormous INSTRUMENTAL value, i.e. as part of a method for acquiring more knowledge.

Be careful with the evidence criterion. Consider the following proposition: "If I let go of this pen, and the sum of forces in the opposite direction, away from the center of the earth, precisely cancelled out the force associated with gravity, the pen will float" I have no evidence that such a thing WILL happen, but the proposition is true nonetheless. In fact, I could fill a tank with a fluid slightly more dense than the pen and the pen will float without issue. Why isn't my proposition arbitrary? Because I've specified the relevant condition. It's a bit like saying: "If I let go of this pen, it will fall--provided that no forces presently unknown to me will cancel out the force associated with gravity" And there's certainly nothing arbitrary about THAT.

The billiard balls interacted according to their respective identities, producing a change in the state of the second ball.