1. What the word intelligence lumps together
The word intelligence is used everywhere, in daily life and in academia, but what it points to is not clear. What an IQ test measures, what an expert brings to bear, what the people we call geniuses have, learning fast, solving problems well — all of it gets tied up in one word. This blurring isn't a verbal habit. Cognitive operations with different structures are mixed under one term, and the mixing leads to real errors of judgment.
Existing theories couldn't untangle this because there was no external criterion for judging whether intelligence is valid. Cattell and Horn's split between fluid and crystallized intelligence separated material from reasoning ability to a degree, but it carried no criterion for telling what counts as valid knowledge or valid reasoning. It classified abilities without checking their validity.
The two previous pieces set up that criterion. Abduction is the only operation that opens a hypothesis space; the pragmatic maxim and information judge what was opened by what it changes; and that judgment doesn't stand without a purpose. Hold intelligence up to this criterion and it stops being a classification of abilities and becomes a judgment of validity, and what was lumped together splits into three: HI (Hard Intelligence, the foundational), SI (Soft Intelligence, the selective), and PI (Performance Intelligence, the responsive).
2. HI — foundational intelligence
The core of what people usually call domain knowledge or real expertise is HI. It refers to the difference in information that creates the gap in reviewing and problem-solving ability between an expert and an amateur. But the phrase domain knowledge doesn't separate out what matters. To borrow Feynman's line, knowing the name of a bird is not the same as knowing the bird.
Technical terms refined through peer review are not mere labels. The paths of observation get compressed into a term as it is formed. Unpack that compression properly and the name becomes a way into HI. But the name doesn't replace the contents. If you can't explain it in words a child would understand, you're holding the wrapping without ever having seen what's inside. HI refers only to what has followed the observation paths packed into a name all the way to the thing itself.
What qualifies something as HI is not its source or how it was acquired, only its information. Whether it came from experience or from logic, if a proposition actually reduces uncertainty it is HI, and if it doesn't, it isn't. Beliefs dressed in a plausible form often look like HI, but a proposition that rules out no state carries zero information. And information is measured against a purpose. The same proposition is HI in front of one purpose and noise in front of another. HI is not a warehouse of stock but an accumulation of material a purpose can draw on.
3. SI — selective intelligence
SI is the operation that filters out propositions with no information. It subtracts rather than adds. Its basis is the A / not-A split, pure formal logic that needs no premise at all. Most of the cognitive work of sorting categories, drawing boundaries, and assigning addresses runs on this split.
SI does three things in practice. It catches boundaries drawn vaguely, it catches leaps in an argument, and it removes propositions with no information or puts them on hold. SI doesn't make knowledge; it clears out contamination. When SI runs short, you end up storing and citing propositions that sound right but fall apart when you check them, wrapping and all.
History shows that SI works independently of HI. Talking with potters, generals, and poets, Socrates exposed the noise inside their HI through questions alone, without HI of his own in their fields. What counts as noise is also set by purpose. Socrates asked of each craft what it was for.
4. PI — responsive intelligence
PI is the ability to draw out, effectively, how strongly something contributes to achieving a purpose. It takes HI and SI as material and tool and actually puts them to work toward the purpose.
When I first worked out this trichotomy, I wrote PI down as the ability to use HI and SI to produce new, high-information propositions. That definition wasn't wrong, but its test hung on the novelty of the output. Apply the proposition from the previous piece and the test changes. Meaningful cognition passes the pragmatic maxim, and cognition that passes the maxim carries a purpose. Then whether an operation is complete is judged by whether the purpose was achieved, and PI is defined as the ability to bring that achievement about. Picking an existing proposition and fitting it precisely to a purpose is PI too, even if nothing new is produced.
PI works through abduction. It decides which way to open a space toward the purpose, puts HI into the opened space as material, filters contamination with SI, and updates against the world. What we usually call genius is, most of the time, a state of overwhelmingly high PI. Calling someone smart or sharp mostly refers to SI, which is a different thing.
5. The three axes connect asymmetrically
Under this definition the three axes are not three abilities standing side by side. HI is material, SI is the filtering tool, and PI is what puts the two to work and completes the operation. So the values of HI and SI show up only in the results of PI's work. How much HI you've piled up or how precise your SI is doesn't count as an achievement on its own.
There's a direction between material and tool, too. With plenty of HI but low SI, contaminated material goes straight into PI. The result has a plausible wrapping, but inside, leaps and blurred boundaries pile up and get cited. Repeat this and HI itself rots. The reverse doesn't hold. With high SI and thin HI, the output is small, but HI doesn't get contaminated. A lack of SI slowly corrodes HI; a lack of HI doesn't corrode SI. This asymmetry is the most important structural result of the trichotomy.
SI has states. It isn't an ability that stays switched on at the same strength; there are moments when it gets sharp. If HI is well stocked and the purpose is clear at such a moment, PI explodes.
6. On three footholds
Abduction opens the space, the maxim and information judge what was opened, and the judgment stands on a purpose. The intelligence trichotomy stands on these three footholds and splits the word intelligence into three. Completing a cognitive operation comes down to the work of PI, and HI and SI show their value only through that work.
This frame has a boundary too. Once the names HI, SI, and PI start being used as wrappers that replace their objects instead of maps that point to them, the trichotomy becomes just another bundle of names. As long as the external criterion of information stays attached, it keeps the names from turning into wrappers. What holds that line is the reader's SI.