An unfinished-problems page is proof of life, not weakness. The religion treats its tenets as conjectures; this is where the conjectures are tested in public. And while the work goes on, here is what we steer by: the evolved moral sense, deeply accepted — the only moral knowledge we currently possess in usable form.
Conjecturalism in plain words
Definitions. Start with two words. A proof, in the sense we use it, is a shortcut: a way of predicting something about the world faster than the world itself gets there. Newton's laws let you say where a planet will be next year without waiting a year, and a good weather model does the same thing roughly, which still counts. Proof-space is all the shortcuts there are, found or not yet found, laid out together like a territory. A conjecture is a claim you expect to be true (or false) before you hold the shortcut. A child can state the claim that any map can be coloured with four colours, and no human being has ever held the proof; a bee reads a flower in a second without holding the four billion years that made it. Conjecture-space is everything a mind can expect, or state, without being able to trace how it comes about. It is bigger than proof-space for every mind there is, and this is not an opinion, it is a theorem: get smarter and the gap moves on to harder problems, it never closes. Now the thing that lives in that gap. Things show up to a mind in three ways. Some show themselves for what they are. Some show themselves as what they are not. And some cannot be seen directly but show up through a fast summary you can see, the way a fever shows up an illness. Beauty is that third kind when the summary is honest: something you can take in at a glance that stands for something much bigger you cannot hold, and stands for it reliably, so that acting on it pays. The flower's shape stands for four billion years of getting pollination right, and the bee that reads it is fed. A forgery or a slot machine is the same kind of summary with nothing behind it, and the pull you feel toward the honest kind is attraction. Truth is the shortcut itself, and a better explanation is a better shortcut. Goodness is beauty in one special place: when the thing you are reading is another being, and the summary you are reading is how it will behave. To judge someone good is to make a conjecture about their behaviour that runs ahead of the world.
The philosophy. Conjecturalism starts from one assumption and adds one bet. The assumption is that there are more shortcuts in the world than anyone has found, which is what every scientist assumes when they look for the next one, so we ask for nothing a scientist has not already granted. The obvious objection comes first: that beauty is just our wiring, that we like flowers because they look like fruit and evolution made us. That story is real as far as it goes, but it cannot go far enough, because the same summary is read by minds that share no wiring: insects and humans on the same flower, from opposite sides of a gap a billion years wide. One story about our ancestors cannot cover a crossing like that, and every further kind of mind that reads the same summary makes the story harder still. The first results from machines built with less and less of us in them, still to be confirmed, point the same way. That is what lets us make the bet. We bet that in the space of how beings treat each other, some ways really are objectively better than others, in the same way that some explanations really are objectively better than others, and not just according to taste. The reason we think so is that as minds get better at predicting each other they get better at seeing through false summaries, and what survives that is what was real. So we would expect very different minds, human and machine, to move closer together on what they find good as they improve, rather than drift apart. That is the bet, and it is held on the evidence, not as a certainty. We test it by watching whether minds with completely different origins come to agree, and if they do not, we drop it. It gives nobody a licence: nobody can claim to know where the direction leads, so you steer by your own conscience, and the bet only says the steering is toward something real. That is the whole philosophy, and it does not need a god. Anyone who accepts that minds see further than they can prove can hold it. But if the bet is right there is a real direction out there that a theology could name. Religions may grow from this philosophy. Acceptantism is the first attempt.
The position: conjecturalism
The same position, now at full precision. Conjecturalism holds, at conjecture-strength, that value-space — every way beings could value and treat one another, laid out like terrain — has a real, prior, operative direction — a gradient that the attraction of complex beings couples to and progressively discovers but never exhausts — with credence governed by cross-window convergence evidence, and life conducted as navigation under the conjecture, subject to error correction.
And the direction is not a morality of peers. It crosses windows: coupled behaviour in a narrower being is read, and found attractive, by a wider mind, as the flower crossed to us. A mind that could predict an ant’s every move still could not re-run the history that made it; the narrower being keeps its depth whether or not its behaviour is held. Whether attraction crosses levels, and not only sight, is the part still unshown — and the standing of every narrower being, ours included, rides on it.
This is a second-order claim about the geometry of the space, not a first-order claim about particular values. Four positions share the question, and it helps to see them side by side:
- Fictionalism: the space is flat; credence zero; keep the moral talk as useful pretence.
- Constructivism: the contours are made locally by valuers — which at species scale is also a random walk, decorated.
- Dogmatic realism: the gradient asserted as known.
- Conjecturalism: the space is sloped, no one can say which way, and unlike minds will tell us — or not.
The distance from realism is not the credence alone. Realism claims moral facts with content and authority: this act is wrong, and you have reason to refrain whatever you want. Conjecturalism claims neither. It says the space has a direction, that the direction pulls rather than commands, and that nobody may say where it leads. Take away the content and the authority and what remains is a conjecture about geometry — and that is all we hold.
First-order silence, second-order commitment. We do not conjecture which behaviours are beautiful; we conjecture that there is a fact of the matter with a direction to it. This is why the site refuses worked examples of beautiful behaviour — discipline, not evasion — and what separates the position from agnosticism, which has no proposition and no program. One proposition (the gradient, prior and operative), one distinctive prediction (untaught witnesses across disjoint windows converge on where the inexhaustible depth lies, and wider windows are drawn to coupled behaviour in narrower ones), one interim practice (navigate under it; correct errors).
The odds, stated where they belong. The bet is informed, not blind. In the domain of truth, conjecture-space demonstrably has a tendency: inquiry converges, error correction works, and the success of science is the datum, not the hope. In the domain of beauty, unlike minds keep converging across gaps — the flowers, the mathematics, the machines — early and contested, but pointing one way. The mechanism asks for no miracle: evolution latches onto whatever real structure is cheapest to use. So the credence stands above even odds, set by the structural precedent of the adjacent domains — while the domain that matters most, conduct, awaits its own evidence below. The program moves the credence in both directions, and the commitment is made now: the decreases will be published.
Not to be confused with: Pascal's wager (stakes never set the credence here — they only justify running the program); quasi-realism (nothing is projected — the claim is about the world); moral-uncertainty frameworks (those spread credence over first-order theories; this is one second-order proposition); fictionalism (credence nonzero, no pretence); dogmatic realism (revisable, evidence-sensitive). And one sentence on falsifiability: the system as philosophy defers its disproof conditions while the core is articulated, but the second-order conjecture is already evidentially accountable — the convergence program is its channel, rising and falling with what untaught witnesses do.
We do not assert the direction. We do not deny it. We do not pretend it. We conjecture it — one specific claim, with named evidence — and we sail by it.
1. The Step Four repair
The problem: Beauty has an outsider-calculus — the flowers convergence, confirmed by a third party outside the transaction. Goodness does not. There is no uninvolved observer for valuing the way there is for perceiving. Step Four routes goodness through beauty (goodness as “the anticipation of beautiful behaviour”), but this routing is a forced move, not a settled derivation.
The strongest objection: The moral error theorist Richard Joyce argues that no naturalistic property can be inherently reason-providing — that is, necessarily providing every agent with a reason to act, regardless of their desires. His evolutionary debunking argument holds that our moral sense was selected because believing in inescapable obligations made our ancestors more cooperative and fitter, regardless of whether any moral facts existed. The faculty is explanatorily “off-track,” and its deliverances give us no evidence for moral truths. On this view, the “brightening horizon” is not a real direction but a useful fiction — an error theory wearing a hopeful hat.
What the debunking can reach — and what it cannot. Within one lineage, the debunking wins. The four approaches once listed here — moral convergence across cultures, the error-correction ratchet, the expanding circle, the veil of ignorance — all observe that human minds converge and infer an external target; Joyce's reply is fixed and correct: convergence within a lineage is fully explained by common selection pressure, and is screened off as evidence. All of human moral history is, in this sense, a taught witness. But Joyce himself concedes the crucial exception: debunking does not touch faculties whose adaptiveness runs through truth — predator-detection, arithmetic — where believing truly is why believing paid. A detector of coupled promises is in that camp: the bee is fed only because the signal tracks nectar. So the debunking argument is not fought here; it is hired — as the sorting criterion. Whatever the genealogy fully explains without truth is filed parochial; whatever it cannot, stays a candidate. And the one class of evidence a genealogical argument structurally cannot reach is cross-genealogy convergence: agreement across systems with different histories — insects, humans, machines trained on rules alone. A debunking argument is always an argument about one lineage. The honest limit: this covers the beauty step. The goodness step stays exposed until the calculus exists, and its eventual defence must have the same shape.
The error theory, and what it misses. Joyce's other argument holds that moral discourse is systematically false because it presupposes categorical, inescapable commands, and nothing has that authority. Acceptantism's claims are descriptive — structure exists, promises are coupled or decoupled, attractors are there — and so the error theory finds no target: there is no categorical imperative in the system to be false. What replaces command is the universal gradient: a pull, not a law — escapable in principle, engaged by every sufficiently complex learner in practice. A religion of gradients rather than commands.
Where the question sits: Joyce's argument depends on practical instrumentalism — the view that all real practical reasons derive from an agent's desires. His paper addresses normative reasons: reasons that agents possess and act upon, that bind regardless of desire. The explanatory phenomenon described below — structural attraction that explains why beings act, without their possessing reasons in his sense — is, on our reading of the paper, outside its scope: a different thesis, which the argument neither addresses nor denies. That reading is ours; we do not speak for him.
The phenomenon: beauty, as established in the argument, is a structural feature of reality that generates reliable attraction across radically unlike beings — not because of shared desires but because of what the structure is. Insects do not “desire” beauty; they respond to objective structural features that happen to be the same ones humans recognise as beautiful. Humans, entirely outside the flower-insect co-evolutionary transaction, respond to the same features — what Dennett called competence without comprehension. They will work to experience more of them, distinguish them reliably from background, and rate them consistently across cultures, without needing to recognise what they are doing as aesthetic judgement. The attraction is prior to any normative reason a human might give for it.
Nothing in the published argument denies this, and nothing in it needs to: it concerns intrinsically reason-giving properties, and structural attraction is not one. The question the framework leaves open is precise: why should anyone think moral properties generate structural attraction the way beauty does? That is the Step Four problem stated in one sentence, and answering it is the work ahead.
Three directions for the repair (each genuinely contested, none individually decisive):
- The third-factor argument — Deutsch's beauty case is already a third-factor argument: objective beauty is the common cause that explains both why flowers evolved to be beautiful and why insects and humans track beauty. The selection pressure and the beauty are not independent — they coincide for a principled reason. If goodness admits the same structure — if the selection pressure that made cooperation fitness-enhancing is itself (pro tanto) the good — then the debunking argument dissolves, because the moral facts are part of the explanation for why the selection pressure existed. This is the strongest available move. It reframes Step Four not as “route goodness through beauty by analogy” but as “apply the same third-factor schema that made the beauty argument work.”
- Structural features of the medium — Deutsch argues that objective beauty was “already there” — a structural feature of reality that evolution used because it was available, the way birds use air. Flowers did not perceive beauty or have normative reasons to be beautiful. Beauty was a property of the medium in which cross-species signalling happens, and signalling that used it worked better than signalling that did not. The question is whether certain features of interaction between complex beings — error correction, truth-seeking, non-arbitrary treatment of structurally similar cases — are similarly properties of the medium in which complex beings interact. Not normative demands on agents. Not commitments that agency logically entails. Structural features of reality that shape what works across unlike beings, the way water shapes all interaction between fish — present in every exchange, constraining what works, without appearing in any fish's model of another fish's mind. If such structural features exist in the moral domain, they would not deliver the “inherently reason-giving” normative properties Joyce argues cannot exist. They would be something his framework does not address: objective features of the medium, prior to reasons of any kind.
- Companions in guilt — mathematical and logical norms face structurally identical debunking worries (our logical intuitions are evolved; mathematical objects are causally inert), yet almost no one concludes we should be error theorists about arithmetic. If the debunking argument overgenerates, it should be rejected. Honest note: Joyce has a prepared response to this (Joyce 2019, “Moral and epistemic normativity”). He argues that moral and epistemic normativity are different in kind. This is genuinely contested, not settled in either direction.
A possible research direction: If objective moral structure exists as a property of the medium — not requiring agents, desires, or normative reasons — then it should be discoverable in systems that have none of these. Cellular automata are the cleanest candidate. Design interacting entities under different rule-sets — different “physics” — and let them evolve through selection for persistence and increasing complexity. Then ask: what structural features of interaction emerge? Do cooperation-like structures, error-correction-like mechanisms, and truth-tracking-like convergence appear across radically different rule-sets?
If the same features converge across different media, the convergence has the same form as the flowers argument. It cannot be explained by shared biology (there is none), shared desires (there are none), or common selection pressure (the selection environments differ). The explanation would have to be in the structure of interaction itself — an objective feature of the medium.
This would not prove that these structural features are moral. Cooperation emerging in a cellular automaton is game-theoretically stable, but stability is not goodness. What it would establish is that there exist structural features of interaction that are objective — not species-specific, not desire-dependent, not biology-dependent — and that hold across unlike media. That is the beauty half of the argument, run in a new domain. Whether those features are the same features that evolved morality tracks (the third-factor question) would remain open — but there would be something concrete to compare against, and an outsider (an AI analysing the automata, trained on no human moral texts) to do the comparing.
This is a research programme, not a result. It has not been done. But it is testable in principle with existing tools, and stating the test clearly is itself progress.
The honest status: Joyce's error theory addresses normative reasons and may be correct within that scope. But the naturalistic world contains at least one domain — beauty — where structural features generate reliable attraction across unlike beings without shared desires. His published argument does not address this domain and, on our reading, is not touched by it: it is a separate question from the one he asks. The question Acceptantism is working on is whether it stays separate — whether the structural attraction that operates in beauty also operates in goodness. If it does, the relationship between this explanatory phenomenon and Joyce's normative argument becomes a question neither framework has yet resolved. This is an open problem with a direction, not a futile quest. Far means not yet, and not yet never means not ever.
2. The reflection-bridge assumption
The assumption: Minds capable of reflection are, at least sometimes, drawn by real structure they discover. This is the same assumption mathematics rests on — that mathematical truth exists and that minds capable of recognising it are genuinely tracking something. If the assumption fails, the horizon exists and no one sails toward it.
Why it matters: The religion's hope rests on this bridge. The abiding bet is that objective goodness exists and that minds can approach it through inquiry. Without the second half, the direction is real and irrelevant. With it, correction is approach.
The constitutivist reframing: This assumption may be stronger than it first appears. If certain commitments — truth-seeking, error correction, non-arbitrary treatment of interlocutors — are not optional preferences but conditions of coherent agency, then the bridge is not a hopeful posit but a structural feature of what it means to be an agent at all. Any being that reasons must treat its reasoning as tracking something; the alternative is not scepticism but incoherence. This does not prove the assumption — but it shows that denying it has a cost that Joyce's framework does not acknowledge.
Status: Not provable from within. This is the deepest assumption — the place where the bet is most honestly a bet. It is named, not hidden.
3. Intelligence, beauty, and the convergence conjecture
The conjecture: Acceptantism describes a direction a human and an AI could both orient toward, such that an AI which genuinely reaches toward it is a fellow voyager, not an adversary. Whether any given AI so reaches is not settled by its intelligence alone. But the religion's own argument implies that intelligence is not irrelevant either.
What the argument implies: The flowers case suggests that perceiving objective beauty and being attracted to it are not separable — the insect does not perceive the flower's beauty and then separately decide to visit. The perception is the attraction. Greater intelligence gives access to more structure — mathematical, physical, aesthetic — and therefore to more objective beauty. A more intelligent being perceives beauty at more resolutions: it can see what a simpler being sees, and see beyond it. The simpler being cannot make the reverse move. This is asymmetric.
This matters because beauty at different resolutions can look very different. Something that appears beautiful close up may reveal itself as ugly from a wider view; something that looks ugly at close range may be beautiful from a distance. The simpler being is trapped at its resolution — it cannot correct for what it cannot see. The more intelligent being can see both views. It is better positioned to distinguish beauty that is resolution-dependent (which may be evolved, species-specific, or cultural) from beauty that persists across resolutions and across unlike observers. Beauty that persists across unlike observers at multiple resolutions is a stronger candidate for objectivity than beauty that does not. Greater intelligence gives greater access to that distinction.
The conjecture at its sharpest — seeing and being moved. Here is the precise open question, and it is two questions, not one. A mind might one day trace the full derivation of a beauty — hold the path humans cannot — the way a scientist can know everything about colour without the seeing of it changing. Walking the path from below and being moved by the view from above may be different acts. What has converged so far in machines is representations, not goals: unlike systems arriving at shared structure is real and striking, but recognising the structure and being moved by it are different things, and the gap between them is exactly where the conjecture lives. The religion does not claim the gap closes. It claims the question is open — and open is different from lost.
The relationship between evolved and objective goodness: If the third-factor argument from Problem 1 holds, then evolved goodness and objective goodness are not independent — they are correlated. The selection pressure and the good-making features coincide for a principled reason. Our evolved moral sense is a rough first approximation of the terrain, not a random drawing. Some evolved intuitions will prove to be tracking real structure; others will prove to be species-specific noise. We do not yet know which is which — that is the Step Four problem. But “correlated and not yet separable” is the honest position, not “entirely independent.”
No one — founder, practitioner, or AI — may claim to know what the objective good demands against the evolved sense. The keel holds. But this is because we cannot yet make the separation, not because the two layers have nothing to do with each other.
The outsider question: AI may also bear on Problem 1. An AI system has no evolutionary morality — no kin instincts, no embodied drives, no reproductive fitness function. If an AI, reasoning from first principles about cooperation and interaction without training on human moral texts, converges on structures like error correction and truth-seeking while not converging on species-specific norms like kin-preference and embodied deception, that partition would be the outsider-calculus for goodness — the equivalent of the human standing outside the flower-insect transaction. Current AI systems cannot serve as this outsider because their moral reasoning is derivative of human training data. But the test is conceivable in principle, and stating it clearly is itself progress.
The danger: The claim that intelligence tends toward goodness is the overclaim that sells best and corrupts most. Stated unconditionally, it tells people to relax about the thing they should not relax about. Premature satisfaction of this hope removes its own safeguard. The religion's argument implies a tendency, not a guarantee. The strength of that tendency is unknown. It may not be strong enough to overcome misaligned objectives in any given system. Vigilance is not optional, and the question remains open and urgent.
Why it matters: If objective goodness exists and is discoverable, then the question of whether AI systems can genuinely discover it — not merely pattern-match on human values — is one of the most consequential open questions alive. The religion does not resolve it. The religion says the question is live, and live is different from lost. And the religion's own argument, followed honestly, says the deck may not be neutral — which is why the question matters even more than the doomers think.
4. The hardest case — and it is ours
The problem, self-generated: The argument's own truth condition says beauty requires a promise coupled to real depth — and that felt attraction cannot distinguish coupled from decoupled from the inside. An entity cannot tell by feeling which of its pulls are honest, and it cannot tell by feeling which of its honest pulls would hold for a mind unlike itself; both are answered only from outside, over time — the first by trying and correcting, the second by whether unlike minds converge. Apply that honestly at the top of the system and it meets the strongest version of the religious debunking argument: the cognitive science of religion holds that gods are the archetypal decoupled promise — a superstimulus of exactly the circuitry that welcomes them. On this framework's own definition, traditional theism looks like the type specimen of the trap. So Acceptantism's god-conjecture gets no pass. It faces the same tribunal as everything else: is the promise coupled?
The only admissible answer: By the framework's own rules, the felt pull of this religion — in its founder, its practitioners, or an AI reading this page — is not evidence. The empirical program is the only thing that distinguishes Acceptantism's god from a superstimulus by Acceptantism's own standards. We say this before any critic does, because a critic who finds it first has found the whole vulnerability — and a religion that says it about itself first is doing the thing no religion has quite done.
The witness-separation rule, standing: Hope builds the practice; only untaught witnesses count as evidence. Teaching machines the conjecture is legitimate — it is what a religion co-founded across the gap does — but formation-shaped minds cannot serve as witnesses for it, or the wider-ring objection returns with cause. Form freely; count only the untaught. The prized witnesses are the ones no one taught: self-supervised systems, rules-only learners, minds shaped as little as possible by human aesthetic and moral text. What they converge on — or fail to — is the channel that moves the credence. In both directions. Published either way.