There is no gap between causes and effects, or between “is” and “ought”; the so-called inductive problem is not problematic at all, it merely requires a more careful touch, the touch of the philosopher.
It is not “turtles all the way down”, as Zeno thought. One reaches limits in which force actualizes, sometimes these limits are called “god”, other times they are called “reality”, or perhaps “Plank’s constant”.
Existence is the only given. We start from here and move forward. Much induction, along with deduction, are required if we are to master things, if we are to gain knowledge, which means to gain perspective, and power.
For instance: what a thing IS determines what it OUGHT to be/do. Obviously. You are a particular kind of structure with such-and-such properties, laws, tendencies. The activity which emerges from this structure is “you”, and you will do whatever it is that you must do, given the causes from which such action has arisen. “Ought” is a perspective of applied values and predictions, applied against observations to determine a course of action, a desirable outcome. Morality is not false, nor impossible, it is merely one perspective among many, one more utility. “Ought” always collapses into “is”.
“The sun has always risen, therefore the sun will rise tomorrow” is a valid induction and obviously an invalid deduction. So? It is no less a gain of perspective and power to make this induction, even if deductively invalid; particularly when you are armed with the philosophical knowledge of the difference between the two.
There is nothing inherently incorrect about inductions, assuming one does them correctly (which means: knows the limits). The point is to encounter reality correctly, and induction is one tool toward this end. (Note: does not imply a radical scepsis)