But where is the fourth?

I try to turn many but not all threefolds into fourfolds.

The Four Causes meet special relativity. Hilarity does not ensue.

Notice E−pc at the end of the Special Relativity row above.
E−pc stands opposed to net momentum p, as SLOWNESS stands opposed to SPEED. This makes sense not in Newtonian mechanics but in special relativity. Special relativity finds in nature a non-arbitrary speed limit, a natural top speed, the signal-speed limit, a.k.a. lightspeed, a CONSTANT, both UNIVERSAL to events and INVARIANT across soever varied rest frames of reference, relative to which one can define a non-arbitrary quantity of slowness (which still varies, but non-arbitrarily, with rest frame of reference). Unlike in Newonian mechanics, lightspeed is a natural yardstick, so to speak, which mandates the quantifiability of space and time in one same set of units. This is why lightspeed, often symbolized c, bejewels so many formulas in Einsteinian relativity theory. His cerulean bounty from the depths glints so much that sometimes physicists set lightspeed equal to 1 (“unity”) so as to streamline it out of the formulas, to expose other facets. But one cannot always do so, since one needs to keep track of lightspeed’s exponentiations. Now, I’m not a physicist or a mathematician, just a fancy scribbler. Still, there are, by abstract algebra (the algebra of groups of operations), ONLY TWO ways to have the principle of relativity of motion: Galilean (Newtonian) transformations and Lorenz (Einsteinian) transformations. Newtonian kinetics is an approximation valid at speeds between zero and around 1⁄7 of lightspeed, beyond which the linear energy exceeds 1% of the total (linear + rest) energy. Swifter than around 1⁄7 is often called relativistic, alluding to Einsteinian relativity. At lightspeed, the rest energy = 0, and linear energy = total energy.
But one oughtn't name E−pc (or its equivalents E⁄c−p or E⁄c²−p⁄c) "slowmentum" which already refers to something else. Anyway, I noticed decades ago that E−pc would be decidedly more useful to consider for a system at very high speed (6⁄7 or more of lightspeed) than for a system at rest or at least relativistically slow, so to speak (less than 1⁄7 of lightspeed). It doesn't take Einstein to see this. In a given system's rest frame, the system's magnitude of E−pc is simply equivalent to the system's rest mass (rest energy). This is likewise as linear energy is more useful to consider for a system at low speeds than for a system (e.g., a linear pulse of photons) at lightspeed, where the system's linear energy is equivalent to the system's magnitude of momentum. So, at mutually facing extremes of speed and slowness, it's almost a mirror-image set-up. It's right there in the arithmetic. Anyway, I've found it said by Google AI (on 2026-2-17 or so) that E−pc is a formula for light-cone momentum and is useful to consider at high speeds. In doodles I used to label it lusk and symbolize it k. I'm not a physicist or a mathematician, but I was fiddling around with these things in search of Aristotle's Four Causes or the like. I think I found them and it's not something lame.

Quantities:

Assume light units (years and light years, or light meters and meters, or the like; then lightspeed c = 1 in any observer's rest frame).
p = net momentum.
e = linear energy.
E = total energy.
m = rest mass (often symbolized by "m₀" as in the table atop this post).
k = gross minus net momentum, corresponding to internal spatial structure but not invariant like rest mass across all rest frames soever varied.

Equations:

Remember, set lightspeed c equal to 1 (to temporarily streamline it out of the equations, jewel though it is.
Relativistic slowness in a direction
= 1−velocity v as a fraction of lightspeed.
k = E(1−v) = E−p.
E² = p² + m².
E = p+k = m+e.
p−m = e−k.
p−e = m−k = p+m−E = E−e−k = √(2ke).
Example:

(Continued from table.) The formed entelechy as cause refers to checks, stable balances, stable structure, standing finished, evidences. The object's formed entelechy in operation for a further end was called second entelechy. I think of concrete form as structure in the sense of spatial or spacelike balance, balancement, of movements or forces (a cloud of differently traveling photons has balance, equilibrium, in its inertial reference frame but little stability). As the good has the rational character of a culminal end, so the true, the sound, has the rational character of an entelechy. An entelechy is a stable establishment or confirmation that the sought good was indeed achieved and was indeed good.)

Aristotle's Four Causes' principles favor special relativity over Newtonian mechanics.

The above distinction between bearer and borne works only in Einsteinian physics, not in Newtonian physics, where the bottom two corners are flatly conflated (always m=k and bearer = borne, so there's no occasion at all to extract and label k and borne) since Newtonian physics recognizes no signal-speed limit such as lightspeed universal to events and invariant across all rest frames, and so recognizes no non-arbitrary quantity of slowness and does not distinguish among rest energy, total energy, and total energy minus (magnitude of) net momentum (E−pc).

Losing one's translatorial innocence and some incompetence

I used not to know that Ancient Latin patiens served to translate Ancient Greek páschonta (undergoer, sufferer, e.g., "which is cauterized"); páschonta had connotations like those of passion rather than of patience which are nearly the opposite. Instead, I assimilated agent:patient to make:let and must:can. So I felt I had to make a fourfold out of the four causes' traditional three (as Latinized) causal principles: agent, patient, act. Actually, two Ancient Greek words, distinct in form and meaning, came to be habitually translated as actus. I didn't realize what a tangle of Ancient Greek and Scholastic Latin translations there are to be dealt with. Anyway, now I think of the 4 causes from three standpoints. The things that I call causal principles are somewhat the 4 causes but seen not strictly from said process standpoint, more like from a rudimentary kinetics or mechanics standpoint. Then there is the process standpoint, what I call the Four Causes least loosely. Then there is an enhanced set of 4 causes reflecting classes or spheres of concrete phenomena from lower to higher.

Principles of the causes:
A1) Kinoûn, mover. A2) Páschon, patient, bearer, tolerator (internal). A3) Enérgeia, activity; or a thing as affected. A4). Borneness, bornement; or a thing as borne, balanced (internally).

The Four Causes as process:
B1) Inception. B2) Middle, means. B3) Culmination. B4) Entelechy, a kind of refrenation (a refraining or making refrain) or abstention (call it "abstinuation"?), and, howsoever labeled, a staying (standing, sitting, lying, drifting, riding) finished.

The Four Causes as reflecting levels of phenomena:
C1) Motion, force. C2) Matter. C3) Life. C4) Mind.
To regard the Levels series as the Four Causes leads to holding that a culminal action needs to be a biological function in order to be deemed a télos, a final, i.e., culminal, cause. I think that most people do believe that function helps explain biological phenomena in a way that is, at the least, much clearer than in the case of entirely nonliving things. The Levels series also leads one to hold that a form or structure needs to be mental or intelligent in order to be deemed a full-fledged cause—and I'd guess it'd be what Aristotle called a person's individual entelechy, a soul (mortal or immortal), rather than an essence or definition which is something opposite to an actuality. Or instead of the Levels series, one could stick with the Process series and argue for example that thermodynamic decay is the final cause, the explanative culminal action, of a closed material system outside of a biological context. Or one could assemble these alternate conceptions of cause into a system, for whatever that would be worth. Come to think of it, that's what I've started to do in this paragraph.

Motion involves the idea of analysis into various combinations of motions, as in the case of waves, and the idea of rules and extremal constraints. Matter involves the idea of clumpy ingredients and probabilistic distributions in the soup. This has sent me looking for two more particles of the same taxical rank as bosons and fermions; either divide each of those two classes into two, or find two further classes. Anyons, anyone?

The motion-matter-life-mind fourfold (the Levels series) also reflects the fourfold of elementary conjoined logical quantities in the bottom row of the table atop this post. Remember that a biolgical species' functions tend to be, informally speaking, its specialties (but is that claim lazy or misleading?). Remember that Aristotle regarded a human's entelechy as its individual soul, individual among other individuals. This would be an individual in its final form, its end-state individuality, as a cause, even if that final form is active, likewise as an agent can be a source of either change or stillness.

Logical quantity, in the philosophers' sandbox of 1st-order logic with identity (a.k.a. 1st-order logic with equality) ain't stupid but it's a comic strip as compared to brain science, and philosophers ought to venture to explore logical quantity, as applicable beyond a traditional simple binary such as Bucephalus and eukaryote, one of these centuries.