It seems like you're wondering why there are only three fundamental linear passive elements, so I'll explain that:
You have two physical quantities at play at the circuit level: voltage and current.
Resistance defines a linear relationship between voltage and current.
Inductance defines a linear relationship between voltage and the rate of change of current.
Capacitance defines a linear relationship between current and the rate of change of voltage.
A linear relationship between the rate of change of voltage and the rate of change of current would be equivalent to one between voltage and current, so resistance covers that too.
Now, you may wonder if there's any linear relationship between current and rate of change of current, or between voltage and rate of change of voltage. As it turns out, you can construct these by combining resistors with capacitors or inductors: a resistor in parallel with an inductor gives you an I-I' relationship, and a resistor in series with a capacitor gives you a V-V' relationship.
So we've covered every possible linear relationship up to first order with just the three elements. Combinations that include more inductors and capacitors in more complex combinations can give you second order relationships, and from there you can extend to third order and fourth, and onward arbitrarily far. As I only have a finite amount of time to write this answer, I don't plan on going through the infinite combinations one by one.
I've skipped over one important point here, though. In reality, we can't achieve any possible relationship with just passive elements, because without active elements, you can't have negative resistance, capacitance, or inductance. These would be required to span the full space of linear source-free circuits, yet they don't exist. They can be made by using active components, but if we're restricted to passive components only, you can't have negative impedances.
That's not a limitation of the mathematics, which will quite happily handle negative impedances, but a limitation of physical reality, where they simply can't exist--as passive elements, they would violate conservation of energy.
You will also find that if you try to make, for instance, an ideal voltage integrator using only passive elements, you'll find zeroes and infinities coming out of your equations for what the capacitance and resistance should be. That also, of course, is not physically realizable, and in fact in this case the math starts to break down as well--so you can't get any linear relationship without adding active elements too. But you can get a limited subset of them. I don't have any rigorous definition for what exactly that subset is--that may be an interesting derivation to run through, but I suspect far more complex than it seems.