if we reason from the fact that all A's observed so far are B's to the conclusion that all A's whatsoever are B's, Which kind of induction would we be utilizing?
I'm not sure but i think it's disjunctive syllogism.
Actually, the type of induction you are describing is called inductive generalization. Inductive generalization is a form of reasoning where we reach a general conclusion based on specific observed instances or examples.
In this case, if all A's observed so far are B's, you are using inductive generalization to conclude that all A's whatsoever are B's. It is important to note that inductive reasoning does not provide absolute certainty but rather a high degree of probability. The more instances or examples we observe that support the generalization, the stronger the conclusion becomes.
On the other hand, disjunctive syllogism is a deductive reasoning form that involves a pattern of reasoning from a disjunction (a statement that presents two alternative possibilities) to a specific conclusion. It has a different structure and purpose compared to inductive generalization.