The Objectivist Solution to the Problem of Induction is Sound

I propose to show how absolute certainty about causal connexions can be obtained solely via the application of the Law of Identity to entities. To start, it is a fairly obvious axiom that A is A. Things have identity - they are each something - and they are what they are. It would be absurd to call a dog a cat if "dog" and "cat" were concepts with mutually exclusive qualities. I do not think that my opponent would challenge this point. Next, examine that causality is based in the notion that entities interact, not actions divorced from entities. For example, the effect a billiard ball has on another that it hits is not a result of "movement interacting with non movement"without any notion of the qualities of the actions (for example, the speed of the movement, the stability of the non movent, etc.). If it were, broadly paraphrasing Piekoff, then an egg being substituted for one of the billiard balls would not change the scenario. The fact of the matter is that actions do not exist in a void. They are directly connected to and derive all of their qualities from the actors involve. The event of a billiard ball pushing another is caused via an interaction of billiard balls , If all events are to be understood as the interactions of entities, if entities have absolutely inviolate natures (A is A), and if these natures are directly responsible for the outcome of the event (as in the egg vs. the billiard ball), then it follows that absolute knowledge about an event can be gained via an identitication of the components of an interaction. Take, for example, the interaction between A and B. If the qualities of A, when exposed to the qualities of B, produce an entity with the qualities of C, then it can be said that A + B = C. If there are no outside variables at play, it is absolutely true that if A and B combine to form C they will always do so. This is because there is nothing but the natures of the entities to influence the outcome, and, since their nautes are not subject to change, nothing can cause A + B to equal Non-C. It is universally true that A + B = C. What is not true is that, if the siituation changes, we lose knowledge. If we are suddenly examining a scenario in which A, B, and X were being combined to form Y, this in no way violates the knowledge that A + B = C. A and B, via their definitions alone, must necessarily form C, and this only applies to the actual situation . If any part of it changes, you are changing the context of the discussion, and, as such, cannot show a contradiction via different results of the same interaction because you are comparing the results of two different interactions. If you try to apply the knowledge of A + B equaling C to situations where A + B is not descriptive of the entire equation, then, obviously, you will be wrong. However, if you keep in mind the proper context of your statements, they become timeless. It is the difference between "billiard balls always push one another" and "billiard balls, under conditions x, y, z, and whatever unknown conditions that were at play when I made my observations (normal gravity, for example), always push one another." The second captures every element of the situation, and, if that situation is replicated perfectly, it would always hold true because of the unchanging nature of the identities of objects. I have shown that universal tautological statements can be derived solely from axiomatic knowledge (knowledge that A is A). There can be no doubt in whether replication of events is possible or reliable. Given this, induction has perfectly soliid grounding. Causality and the validity of induction are, therefore, no longer under fire and Hume does not pose a threat.