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Kit K
This is the formal side of Creativity as Reception: the 503 propositions its six voices put forward and the links between them, the 24 claims of the three final papers I wrote from them in September 2026 and the 23 published objections they were tested against, the eight tensions the first paper never settles and the numbers and sources behind the whole project.
I sorted the propositions into 37 groups across 8 bands (thesis, antithesis, dialogue, split-splat, counter-Stengers, synthesis, the final papers and the published objections), and each cell counts the links running from the group on its row to the group in its column, so the counts add up to the full 1,336. The heaviest cells sit on the diagonal inside the split-splat and counter-Stengers bands, where each voice builds its own argument out of its own propositions, and the bright column down the left counts everything that derives from the paper’s axioms. The grid is wider than most screens, so drag it sideways to see the rest.
Loading the grid…
Bands
Link types
How to read a cell
Size = links between the two groups · colour = the most common link type · an outer ring = the cell mixes types · the diagonal holds each group’s links to itself. The right margin totals what each row sends → and the foot totals what each column ↓ receives. Every proposition and link behind the grid can be downloaded as JSON.
I set each proposition on the row of the longest chain of entailment or subsumption that reaches it from the 78 axioms along the top, so a proposition on the lowest ranked row stands 10 derivations below a premise. Each voice has a column as wide as its busiest row, which is why split-splat, with 174 of the 550 propositions, takes the widest. The 14 propositions that relate to nothing else sit on a row of their own at the foot. Select any mark to trace it back to the axioms.
Select any proposition, or name one above, to light its chain back to the axioms, the propositions derived from it and every proposition that answers it.
Eight kinds of proposition
Eight relations
Reading a row
The number at the left of a row is how many steps of entailment or subsumption separate a derived proposition on it from an axiom. A counter, dissolution or critique that derives nothing sits on the row of the deepest proposition it answers. Solid lines are used for relations that affirm and dashed lines for relations that contest. The five arcs that bow out to the right and climb are the three loops in split-splat’s genealogy and the places where a voice subsumes an axiom. Counter-Stengers, the Synthesis, the three final papers and the objections I gathered from the published literature all read the paper from outside, so when one of them takes another voice’s proposition into its own account the line is drawn across rather than down. The bottom row holds the propositions that relate to nothing else. A gold ring marks the six ideas threaded through the loom on the main page. The first column holds the argument the Canonical paper and the Stengers companion make together, which the algebra records once; a small amber dot marks the 7 propositions only the Stengers companion makes. Hover a mark for every relation it takes part in, or select it to trace it.
I ran a set of standard graph analyses over the whole algebra to find which propositions the rest depend on, which survive once every attack is counted, how the voices divide and who argues with whom. Select any proposition named below to trace it in the derivation above.
The readings behind every figure: an entailment is a premise, and a proposition needs all the premises its derivation names. Opposing, criticising and dissolving count as attacks, and a tension counts as an attack both ways. The figures are computed from the algebra by a script, so they change when it does.
The algebra records exactly one derivation for each of the 203 derived propositions, with no alternative routes, so the premises each rests on are fixed and none of them can be dropped. Traced back that way, every central idea of the paper stands on the same three axioms, A₂, A₃ and A₆, with one or two more for some. Counter-Stengers attacks all three, and nothing in the paper answers it.
lies on more of the shortest routes between propositions than anything else in the algebra, scoring 0.253 where the next, “The six-step pattern,” scores 0.125. Every derivation of 20 other propositions passes through it, and it receives 13 contesting links from Counter-Counter, Counter-Stengers, Split-Splat and Synthesis.
Counting an attack as successful unless something in the algebra answers it, 360 propositions stand, 87 fall and 56 stay undecided. The paper’s replies to objections were written before the later voices, so the attacks those voices make on it mostly go unanswered, and 53 of the 87 Canonical and Stengers propositions fall.
The paper’s fallen propositions that the most others rest on, with the propositions that attack each:
The 56 undecided propositions fall into 16 independent standoffs. Each of them holds on at least one consistent reading of the algebra and none holds on every reading, which leaves 1,327,104 consistent readings in all. The largest standoff turns on : whether the paper’s replies to the objections from relativism, intention, scope, social ontology, deflation and labour stand depends on whether a reader accepts Split-Splat’s claim that the question itself is stolen.
Three standoffs where two propositions attack each other and neither wins:
Reading affirming links as agreement and contesting links as conflict, the best possible division of the algebra into two consistent sides, which the solver proves optimal, still leaves 89 of 987 links (9.0%) running against it. Counter-Stengers sits 81% on one side and the Canonical and Stengers propositions 86% on the other, with Split-Splat and the Synthesis mostly alongside the paper and Counter-Counter divided almost evenly.
Depth counts the steps of entailment between a proposition and the underived ones it rests on. Counter-Counter and Counter-Stengers argue almost entirely by objection, so all 64 of Counter-Counter’s propositions and 73 of Counter-Stengers’ 98 sit at depth zero. Split-Splat builds the longest chains, up to 9 steps.
| Voice | Propositions | At depth zero | Mean depth | Longest chain |
|---|---|---|---|---|
| Canonical · Stengers | 87 | 30 | 1.67 | 5 |
| Counter-Counter | 64 | 64 | 0.00 | 0 |
| Split-Splat | 174 | 100 | 1.88 | 9 |
| Counter-Stengers | 98 | 73 | 0.31 | 3 |
| Synthesis | 80 | 33 | 1.62 | 8 |
Each cell counts the links from the voice on its row to the voice in its column, affirming first and contesting second. The Canonical and Stengers propositions send one link to the three voices written after them, so the paper answers none of them. The Synthesis mostly agrees with it (37 affirming to 5 contesting) and Counter-Stengers mostly disputes it (20 to 86).
| From ↓ to → | Canonical · Stengers | Counter-Counter | Split-Splat | Counter-Stengers | Synthesis |
|---|---|---|---|---|---|
| Canonical · Stengers | 87 / 11 | 0 / 5 | · | · | 1 / 0 |
| Counter-Counter | 24 / 35 | · | · | · | 0 / 1 |
| Split-Splat | 25 / 45 | 59 / 1 | 222 / 59 | · | · |
| Counter-Stengers | 20 / 86 | 8 / 0 | · | 97 / 18 | 1 / 0 |
| Synthesis | 37 / 5 | 10 / 3 | 35 / 2 | 12 / 4 | 94 / 12 |
Grouping propositions by how densely they link gives between 28 and 31 clusters over 30 runs, and those clusters match the voice labels poorly, at 0.17 to 0.25 on a scale where 1 means identical. The steadiest cluster that spans several voices gathers around , which sits with the same 17 propositions in every run, from Counter-Stengers, Synthesis, Canonical · Stengers and Counter-Counter. Event in receiving consciousness (T₂) lands in a different cluster on almost every run, which is what a proposition everything else routes through would do.
In September 2026 I put the paper through its own graph and rewrote it as three papers, one on the theory, one on the conditions of reception and one on the method. Their 24 claims sit in the grid and the derivation above as a band and a column of their own, joined to the older propositions each one takes up or corrects and to the attacks three coders judged against them, from the five other voices and from 23 objections I gathered from the published literature.
| No. | Claim | Takes up | Corrects | Attacks judged |
|---|---|---|---|---|
| Encounters physically change brains | A₇ | — | 6 miss | |
| Conditions decide what an encounter does | A₇ T₃₀ T₃₁ T₃₂ SY·A₁₇ | — | 7 miss1 answered | |
| Makers are changed by their own work | T₁₁ T₄₃ SY·A₁₅ SY·C₄ | — | 4 miss | |
| Reception treated as evaluation | A₂ A₃ | — | 4 miss | |
| Form | T₆ | — | 4 miss1 answered | |
| Form-occasioned change | T₈ | — | 4 miss | |
| The creativity-event | T₁ T₈ T₉ T₁₃ | — | 13 miss5 answered1 partly holds | |
| Who can receive | T₂ T₃ T₁₁ T₄₃ B₄ SY·C₁ SY·T₉ | — | 16 miss2 answered | |
| What an event needs | T₅ T₁₀ T₇ SY·R₁ | — | 10 miss1 answered | |
| Conditions are part of the event | T₃₂ T₃₀ T₃₁ T₇ | — | 8 miss | |
| Machines and origin | T₁₇ B₅ SY·T₂₃ SY·B₃ | — | 5 miss1 partly holds | |
| What the paper adds | T₁₃ A₁ T₃₇ T₃₈ CS·T₃ | — | 8 miss | |
| Why the field looked elsewhere | T₂₉ CS·D₃ | — | 8 miss | |
| Where the question comes from | T₁ T₃ SY·C₈ SS·T₅₀ | — | 10 miss | |
| Consciousness left open | B₄ | — | 1 miss | |
| What cannot yet be measured | T₅₂ C₅ CS·C₃₃ K₁₃ | — | 8 miss |
| No. | Claim | Takes up | Corrects | Attacks judged |
|---|---|---|---|---|
| Unequal and destroyed conditions | A₈ T₃₀ K₉ K₁₀ D₁₀ | — | 8 miss | |
| Changes spread through behaviour | — | — | — | |
| Every event counts | T₁₅ T₁₁ | — | 2 miss2 answered | |
| No ranking | T₃₆ T₅₇ T₄₁ SY·D₆ SY·C₂ SY·D₂ | — | 6 miss2 answered | |
| Why events are unequal | T₄₀ T₃₁ T₃₃ T₃₄ T₃₅ SY·T₂₄ SY·D₂ K₁₀ | — | 10 miss1 partly holds | |
| Access is a matter of justice | — | — | — | |
| Policy | T₄₅ T₅₁ T₃₄ | — | 1 answered4 partly hold |
| No. | Claim | Takes up | Corrects | Attacks judged |
|---|---|---|---|---|
| How this paper was made | X₁ X₄ SY·T₂₃ | — | 8 miss |
The argument algebra lists them in §11.1 and marks six as open and two as managed, and none of the eight is settled anywhere in the paper.
| No. | Tension | Between | Status |
|---|---|---|---|
| 1 | Origin-irrelevance vs the AI boundaryK₆ names it | T₁₇ and B₅ | Open |
| 2 | Democratisation vs raritypossible for all but demanding and rare | T₄₀ and T₈ | Managed |
| 3 | Reflexivity as honesty vs as capitalthe paper accepts but cannot escape it | X₁ and K₁₄ | Open |
| 4 | Productive distance vs access-deprivationboth forces named explicitly | T₃₅ | Managed |
| 5 | The framework's universalism vs its Western originuniversal scope claimed from particular ground | T₂ and A₁₁ | Open |
| 6 | Tractable conditions vs destroyed worldsthe analytical register is inadequate | T₃₀ and K₁₀ | Open |
| 7 | Proxies as access vs proxies as biassurface-calibrated proxies distort | T₅₂ and K₁₃ | Open |
| 8 | Listing limits as honesty vs as immunisationgenuinely undecidable from within | B₇ and K₁₉ | Open |