↩ ExploRational · A Catalogue of Divergent Rationality
explorational · a divergent move
Put unlike cases side by side and extract the structure they share: what do the successes have that the near-misses lack? Mill's methods turn a pile of cases into candidate causes — but only a pattern with a falsifiable prediction earns its keep; the rest is surface resemblance.
John Stuart Mill's methods of agreement and difference were written for chemistry benches and field observation, but they scale to messy, human-sized cases — case series in medicine, Skocpol's comparison of the French, Russian, and Chinese revolutions. The logic is austere and almost mechanical. A feature present in every success and absent in every failure is a candidate cause. And a single disconfirming case — one success that lacks the feature, or one failure that has it — eliminates it, no matter how many agreeable cases preceded it. You are looking for the factor that a single stubborn instance cannot refute.
The discipline, though, is not the tabulating. It is what you do after a factor survives. A pattern that has cleared agreement and difference is still just a resemblance until you attach a prediction: a new case with the surviving factors should succeed — and if it fails, the candidate is dead. That last clause is the whole difference between science and pattern-worship. Admiring how neatly your successes rhyme costs nothing and proves nothing; staking a claim on the next case, and letting it fail, is the only move that earns the word cause. The instrument below does the elimination live, then hands you the loaded prediction and dares you to fire it.
the signature instrument
Rows are cases; columns are candidate factors; the last column is each case's outcome. Click any cell to toggle present / absent; click an outcome to flip success / failure. Everything to the right — which factor survives agreement, which is struck by which case, which pairs are confounded, and whether the prediction still holds — is computed live by real logical elimination over your table. No numbers are faked.
Startups that survived vs folded
what the successes share
The method of agreement asks a single question of every candidate factor: is it present in all the successes? If even one success lacks it, it cannot be a necessary condition, and it falls out. What agreement leaves standing is the short list of things the winners have in common — candidate necessary conditions, no more. Agreement is generous; a factor can survive it while also showing up in half the failures. That is why it is only half the tool.
The method of difference supplies the other half. It asks: is the factor absent in all the failures? A factor that appears in even one failure cannot be the thing whose presence makes the difference, so it is struck too. Run both filters and take the intersection — the joint method — and you are left with factors present in every success and absent in every failure: the strongest candidates the case set can offer, necessary and sufficient across everything you have observed. In the shipped "clean cause" preset exactly one factor, founder–market fit, survives both. Toggle a single cell and watch the survivor list rewrite itself, because the verdict is recomputed from scratch on every click — never stored, never assumed.
what to try
On the default preset, find the survivor founder–market fit. Now click one success's cell to switch that factor absent — or give one failure the factor. The verdict flips to eliminated by that exact case. One disconfirming instance did what no amount of agreement could, and the tool names the case that did it.
Load confounded. Two factors — founder–market fit and early revenue — survive together, and the tool flags them as a confounded pair: their columns are identical, so Mill's methods cannot say which is the cause. Now add the case that breaks the tie: give one winner early revenue but not fit (or the reverse). Watch the twins separate.
Back on clean cause, press add the predicted test case. It seeds a new case carrying the surviving factor, outcome success — corroborated. Now flip that case's outcome to failure. The prediction reads FALSIFIED, and the same case strikes the factor from the difference column, live. That is Popper's bite made mechanical.
a pattern must predict or it's mysticism
Elimination alone can feel like proof. You line up six cases, strike four factors, and the two survivors seem to glow with causal significance. But everything so far has been retrospective — a story fitted to cases you already had, and any sufficiently rich table will yield some factor that happens to track the outcome. The surviving factor might be the cause, or it might be an accident of which six cases you happened to collect. Nothing in the tabulation can tell the two apart. Resemblance is not yet a mechanism.
The cure is a prediction with a due date. From the surviving factors the instrument states a claim about a case it has never seen: one that carries those factors should succeed. Adding that test case puts the candidate at risk in a way no historical case can, because you are now committed before the outcome is known. If the case carries the factors and fails, the candidate is refuted — the difference method strikes it in the same instant, and the verdict reads falsified. This is the exact point at which the comparative method stops being resemblance-mysticism and starts being science: not when the successes rhyme, but when you name a consequence and let a single case kill your candidate. A pattern that forbids no future observation has told you nothing.
model
Each factor is a boolean column; each case is a row with a boolean outcome. Agreement marks a factor surviving if it is true in every success — the first success where it is false becomes its eliminating case. Difference marks it surviving if it is false in every failure — the first failure where it is true eliminates it. The joint survivors are the plain set intersection of the two, highlighted in the header. A confounded pair is detected by exact column identity: if two factors have the same present/absent value in every case, no comparison in your table can separate them, so they are flagged amber and travel together. The prediction records which factors were surviving when you seeded the test case; on every recompute it checks whether that case still carries them and reports corroborated or falsified from its live outcome.
What the model assumes is where it can mislead. Mill's methods assume a single, deterministic cause with no interactions: exactly one factor (or clean set) that is present-and-decisive every time. Real outcomes are usually multi-causal and probabilistic — two factors that only matter together, a cause that raises the odds without guaranteeing the result. When that is the truth, clean elimination over-claims: it will either strike the real driver (because it fails in isolation) or crown an accidental survivor. The "no clean cause" preset is exactly this situation, and the honest output there is an empty survivor list — the tool telling you the table cannot be reduced to one factor, and that a richer, probabilistic model is what the cases are actually asking for.
the move ↔ the table
| The move | The table |
|---|---|
| a case | one row — a single instance with its features and its recorded outcome, success or failure. |
| a factor | one column — a candidate cause, present or absent, offered up for elimination. |
| method of agreement | the test that a factor is present in every success — what all the winners share. |
| method of difference | the test that a factor is present in success and absent in failure — what the winners have that the losers lack. |
| a disconfirming case | the single instance that eliminates a candidate — one success without it, or one failure with it. |
| a confounded pair | two factors whose columns are identical, so the cases can't separate them — one cause under two names. |
how this opening fails
risk · duplicates in disguise
The catalogue's named risk for this move. When two factors co-occur in every case you happen to have — funding always arrived with the hot market, revenue always with founder–market fit — their columns are identical, and Mill's methods physically cannot tell them apart. The survivor you crown may be its own indistinguishable twin, or the twin may be the real driver. The tool flags such pairs, but flagging is not fixing: the only remedy is a new case that has one factor without the other, breaking the tie. Until that case exists, "the cause" is genuinely undetermined, and any confidence about which twin matters is borrowed from outside the table.
risk · the model is a simplification
Clean elimination presumes that some single factor is present-and-decisive every time. Real outcomes are usually multi-causal and probabilistic: factors that only bite in combination, causes that shift the odds rather than settle them, thresholds and feedback the boolean grid cannot represent. Where that is the truth, agreement and difference over-claim — striking a genuine contributor because it fails alone, or anointing a coincidence because six cases were too few to catch it out. An empty survivor list is not the tool failing; it is the tool being honest that these cases need a richer model. Read a surviving factor as a hypothesis to test next, never as a verdict the table has already delivered.
Line up unlike cases, strike every factor a single case refutes, and predict the next one.
can you use it?
RECOGNITION — Which is comparing distant cases? A: a startup studies three failed rivals to see what they shared. B: a startup studies its own last three launches. C: a startup studies three thriving rivals and three that folded, asking what the survivors share that the dead lacked — and predicts which trait matters next time.
C. The move puts unlike cases side by side, extracts the shared structure, and attaches a prediction. A compares only failures (no contrast class); B is not distant.
THE NEAREST NEIGHBOR — Distant analogy also reaches across domains. What separates comparing distant cases from it, in one criterion?
Direction of the loan. Distant analogy imports structure from one remote source onto your case; comparing distant cases generalizes across several cases to extract a structure none of them alone would show — and stakes a prediction on it.
PRODUCTION — You are deciding whether to open a second location. Name two distant cases — one success, one failure — of a business you know that scaled, and state the one structural difference between them that predicts your outcome.
A model version: a local bakery that franchised and thrived vs. a restaurant that opened a second site and collapsed; the difference was whether the product survived being made by someone other than the founder. Yours works if the shared structure yields a testable prediction, not a moral.