The Objectivist Solution to the Problem of Induction is Sound

Let me quote from the given explanation of the Problem of Induction from Round One: “This is because for any cause, multiple effects are conceivable[.]” “In general, it is not necessary that causal relation in the future resemble causal relations in the past, as it is always conceivable otherwise; for Hume, this is because the negation of the claim does not lead to a contradiction.” Hume, with the Problem of Induction, is attacking causality at its core. His argument rests on the belief that it’s arbitrary to hold that two and two will always add to four on all future dates. It has nothing to do with whether we can tell what 2 is in all situations – as long as we can get clear and perfect knowledge about future events from prior ones, then induction is valid. Observing a ball falling after being thrown and saying “If circumstances X, ball Y being thrown will result in it falling back down” is entirely an inductive process, given that it is reasoning from a particular event and forming an abstract concept and template applicable to future events. There is no justification given to the contrary by my opponent - just the assertion that I'm using deductive logic. In fact, there is no deduction without induction, given that deduction implies concepts from which to start deducing conclusions. All knowledge is, at its basis, inductive, even tautological knowledge (and I do believe that all knowledge is tautological, but that’s neither here nor there), so if I can show that knowledge can exist at all I have done my part. My opponent is discounting knowledge gained via induction solely because he does not think that it will be applicable to events that are, at the very least, irrelevant. His argument is based on the idea that “[t]here’s no reason to think that we will be dealing with “entities that behave in X way by definition””, disregarding the fact that this doesn’t matter if the knowledge gained, no matter how useless, WILL apply if we do deal with such an entity. My opponent’s argument is the equivalent to saying that the equation “239532542235433 + 9399232434123253 = 9638764976358686” does not count as true knowledge because it’s unlikely that one would ever deal with those specific terms. The applicability of the knowledge is irrelevant if the knowledge is absolute and gained via induction – if the Objectivist argument gives knowledge those two qualities, then there is no validity in the Problem of Induction. It is only that which I have to show – no more, no less, and my opponent’s arguments are centered on me not showing more. This is completely and totally equivalent to my opponent’s arguments: “Mathematics is flawed and cannot produce any knowledge. We can see that 2 + 2 = 4 in one case, yes, but what guarantee is there that this will always hold true? It being a tautology doesn’t guarantee anything, since the case of 2 + 3 = 5 exists. You can’t say that I’m changing the statement I’m making since that would just mean that you’re not using induction, no matter if I’m actually changing the statement or not!” The topic at hand has nothing to do with whether or not we recognize conditions or entities correctly or not. It has to do with the fundamental nature of causality. If causality is necessary and derived solely from the natures of the objects involved (and we can observe these natures at least in some sense), then we can, given perfect conceptual faculties and nothing else but induction, come to perfect truths that are applicable in every situation. If induction is a viable means to perfect knowledge, even in an abstract and non-useful way, then I have fulfilled my burden of proof.