The fours are the first real stability within each element. In esoteric numerology, four is all-encompassing — the number of materialization, of physical manifestation. Four seasons, four elements, four winds, four corners of the earth. By encompassing everything, four stabilizes. Where threes are divine origin — growth, expansion, something magical happening — fours are the first main stability. (Go further and the eight is effectively two fours: movement and power, double-stable but no longer the pure essence of stability.) In the tradition I was taught, numbers that reduce also matter, so the fours include not only the four suit cards but the Emperor and Death — thirteen reducing to four.
Four of Wands
Wands are fire — passion, desire, action, inspiration. Fire is expansion: Alexander, Caesar, the grail hunt, the search and the desire. So stability in fire is almost a contradiction — and in the Rider-Waite-Smith image the answer is accomplishment, celebration. What stabilizes desire? Accomplishment. A powerfully good card.
Four of Cups
Cups are the heart, emotion, that watery intuitive energy. Here a figure stares at three cups and doesn't even notice the fourth being offered to him — and that fourth looks a lot like the Ace of Cups. One reading: he's so emotionally stable that he doesn't need it, which is good. Another: he's missing a gift — so settled in his current state that he isn't picking up on something of the heart, an emotional or intuitive interest being divinely offered.
Four of Swords
Swords are air — mind, intellect, truth, communication. The four here is rest, the ultimate rest: hands clasped, a stained-glass window with an anointing behind. Air is also the energy that wakes you at three in the morning worried about bills and whether you called your dad back — and the seat of the ego, the part that says "I am separate." Its stable form is peace: not working, but resting, healing.
Four of Pentacles
Pentacles are earth — actual manifestation, the things you can touch, taste, and smell, work and the body. People rush to money, and that's part of it, but it's more: stability in the physical realm is to focus on a thing, hold it, have it — because once you have it, the want, the need, the longing, the jealousy are all removed. The figure clutches his coins, one at his heart, one on his head, feet planted on the others. Possession, or at least focus.
The Emperor
Here things shift from elemental energies to something more soulful and intrinsic — where manifestation and the Logos meet. The Emperor is stability as structure, lawfulness, and experience: every human experience of stabilization expressed in one card.
Death
Death is thirteen, reducing to four — and that's a puzzle, because Death is a disruptor, a remover, a culminator. If you're aligned with the Western esoteric tradition, death ends a cycle and a rebirth follows. So how is it stabilizing? Because death is as much a part of manifested reality as up or down, as summer, as the equinoxes and solstices. As long as the Logos experiences itself through living forms, there will be death alongside them. Its role isn't negative — it's stabilizing, as matter-of-fact a part of everything as anything could be.