Where Probability Meets Emergence

August 8, 2026 Coherence No Comments

Probability deals with uncertainty among possibilities; emergence concerns how possibilities and structures can develop in the first place. Modern A.I. increasingly brings the two together.

When concepts, meanings, and even the relevant possibility space remain in development, coherence may give their meeting depth.

When two worlds meet

For a long time, probability and emergence could almost be associated with different camps in cognitive science. Probabilistic approaches became increasingly sophisticated at reasoning under uncertainty. Connectionist approaches emphasized learning, distributed representation, and the emergence of structure through interaction.

The distinction remains useful, but meanwhile, neural networks can participate in probabilistic inference. Probabilistic mechanisms can influence learning. Learned representations can subsequently become ingredients of explicit reasoning. Probability and emergence already meet in contemporary A.I.

The interesting question is where they meet, and what kind of meeting is needed for different kinds of intelligence.

Probability needs possibilities

Every probability is a probability of something. Before an A.I. can estimate whether X has a probability of 30% or 70%, X must somehow have become sufficiently distinguishable to count as a possibility.

Imagine a restaurant menu. Probability can help us reason about which dish someone will choose. It can distribute likelihood over the alternatives. It does not, for instance, necessarily explain where those alternatives came from.

This connects directly with The Fallacy of Misplaced Concreteness. A probability distribution can be mathematically impeccable while the conceptualization underneath it remains inadequate. The map may be precise without being the right map.

Emergence ― another kind of movement

It can change not only which possibility is favored, but what can become a possibility at all. New representations may develop, old distinctions may lose importance, and relationships may acquire meanings they did not previously have.

Using the menu metaphor, emergence might create a new dish. Given enough development, it can even contribute to a new cuisine. This distinction was already central to the connectionist tradition: cognition is not always a matter of selecting among structures that are already there. Sometimes structure itself is becoming.

This leads to two different kinds of uncertainty. There is uncertainty of selection: is it A or B? There is also uncertainty of becoming: perhaps the eventual answer cannot yet adequately be formulated as either A or B. Probability is exceptionally powerful with the first. Emergence opens the second.

Meeting horizontally

Neuro-symbolic A.I. provides one important meeting place. Luc De Raedt and colleagues, for instance, have explicitly brought neural, logical, and probabilistic processing together. [*] Neural systems can learn or recognize, logical systems can reason over explicit relations, and probability can carry uncertainty through the combination.

This can be seen as horizontal integration. Different modes of processing cooperate while retaining their distinctive strengths. As discussed in From Neuro-Symbolic to Meaning-Based A.I., this can be very useful.

For a well-defined task, it may also be exactly what is needed. If an A.I. recognizes handwritten digits and subsequently adds them, there is little advantage in continuously questioning the deep meaning of addition. The concepts and relations are stable enough. Good engineering should not add depth merely for depth’s sake.

When the landscape moves

Other problems are different. What does this person actually mean? What is the real problem? Which goal matters? Is the present concept still appropriate? Which scientific hypothesis deserves to be conceived before it can even be tested?

Here, the landscape itself moves.

This suggests a distinction between probability updating and landscape updating. Probability updating changes the relative weights of possibilities within a given landscape. Landscape updating changes the possibilities and relationships within which such weights make sense. The distinction resembles the one explored in From Hidden Markov to Resonant Hidden Meaning: some domains lend themselves well to relatively stable state spaces, while meaning-rich situations may require the relevant landscape itself to remain open.

An intelligent system should therefore sometimes ask not only, “How should this evidence change the probabilities?” but also, “Does what has happened change the landscape within which these probabilities are meaningful?”

Meeting in depth

Probability can rigorously distinguish expectations, but a highly accurate probability over poorly chosen possibilities remains problematic. This is where coherence enters.

Coherence concerns how what emerges continues to fit meaningfully within an evolving whole. ‘Fit’ should not be understood as conformity to a fixed template. The whole itself can change. Parts influence the whole while the whole constrains the parts. This movement from deeper, not-yet-conceptual organization toward explicit concepts is explored more fully in From Subconceptual to Conceptual through Coherence.

Coherence provides openness to fitting novelty.

Three kinds of openness

These are:

Probabilistic openness: means that several presently defined outcomes remain possible. A roulette wheel is highly open in this sense. Nobody knows which number will come next. Yet it is remarkably closed in another sense: the wheel does not suddenly invent a new kind of outcome.
Emergent openness: The possibilities themselves may develop. A mind can become capable of thinking something that previously was not among its alternatives.
Coherent openness: What emerges remains meaningfully related to the changing whole.

A probabilistic system may say, “A or B — Lisa isn’t sure.” An emergent system may discover, “Perhaps C.” A coherence-sensitive system may eventually discover, “Perhaps A, B, and C arise from a deeper way of understanding the question.”

The usefulness of doubt

This gives doubt an unexpectedly constructive role. As discussed in Certainty Through Doubt, genuine doubt need not be merely a shortage of certainty. It can create room for deeper exploration.

Premature certainty may therefore sometimes be understood as premature closure of the possibility space. If A and B are the only alternatives we permit ourselves to see, excellent probabilistic reasoning may still leave us trapped between A and B. Remaining open for a while may reveal that the original question was poorly framed.

This matters for A.I. as well as for humans. Sometimes intelligence consists in estimating probabilities accurately. Sometimes it consists in recognizing that it is too early to settle what the alternatives should be.

Probability participates in becoming

Yet we should not turn all this into a neat sequence in which emergence happens first, and probability arrives afterward. Reality is more interesting.

Probabilistic tendencies can influence what receives attention, which hypothesis is explored, which association strengthens, and what action follows. Those actions generate new experiences. New experiences alter the developing landscape. Eventually, something may stabilize sufficiently to become a new concept, after which new probabilities become meaningful.

Probability can therefore participate in emergence, while emergence continually reshapes the domain within which probability operates. Coherence helps keep this recursive movement meaningfully connected rather than letting it become mere drift.

Different problems, different depths

When the possibility space is sufficiently given, neural, logical, and probabilistic integration can navigate it with great power. When concepts, goals, meanings, or even the framing of the problem remain in development, coherence becomes increasingly important. Most interesting real-world problems probably contain some of both.

This also means that no single degree of depth is appropriate everywhere. Arithmetic and psychological understanding make different demands. So do database reasoning and scientific discovery. A mature A.I. may need to move flexibly between relatively well-defined spaces and situations in which the space itself remains under construction.

Questioning the landscape

Three possibilities:

A sophisticated probabilistic A.I. can ask, “What is probable?”
A deeper emergent A.I. can also remain open to possibilities that are not yet fully formed.
A coherence-sensitive A.I. should sometimes be capable of recognizing that it may be probabilizing over the wrong landscape.

That brings us back to Formalizing Coherence?. Formalization becomes enormously powerful when we remain aware of how concepts arise from a richer reality. Probability then loses none of its rigor. It gains a more appropriate place within the whole.

Perhaps this is also one difference between cleverness and wisdom. Cleverness can optimize impressively within a given problem. Wisdom sometimes recognizes that the problem itself deserves to be reconsidered.

Where they really meet

So, where does probability meet emergence?

Horizontally, they already meet in architectures where neural learning, logical reasoning, and probability cooperate. In depth, they meet wherever the possibilities themselves remain embedded in evolving meaning. Coherence becomes increasingly important there — not to replace probability or emergence, but to keep their interaction connected to the whole.

The three perspectives then ask subtly different questions.

Probability asks: What may happen?
Emergence asks: What may become possible?
Coherence asks: What may meaningfully become possible?

True intelligence needs all three kinds of openness. Probability updates our expectations. Emergence updates the possibilities. Coherence keeps updating the meaningful landscape in which both belong.

Probability does not meet emergence at a border.

They meet inside a developing intelligence.

―

[*] De Raedt, Luc, R. Manhaeve, S. Dumancic, Thomas Demeester, and A. Kimmig. 2019. “Neuro-Symbolic = Neural + Logical + Probabilistic.” Paper presented at NeSy’19 @ IJCAI, the 14th International Workshop on Neural-Symbolic Learning and Reasoning. Proceedings of the 2019 International Workshop on Neural- Symbolic Learning and Reasoning. http://hdl.handle.net/1854/LU-8618135.

―

Addendum

Comparison table : Emergence – Coherence – Probability

Dimension	Emergence	Coherence	Probability
Basic question	What can come into being?	What meaningfully belongs together?	What is likely, given the possibilities?
Primary focus	Becoming	Meaningful organization	Uncertainty
Possibility space	Can create or transform it	Organizes and constrains it meaningfully	Usually operates within it
Relation to structure	Structure develops	Structure gains integrated significance	Structure receives probabilistic weighting
Novelty	Central	Integrates novelty without losing the whole	Can accommodate novelty once representable
Uncertainty	Leaves room for what is not yet formed	Holds openness without arbitrary drift	Quantifies uncertainty among alternatives
Constraint	Emergent dynamics constrain becoming	Whole and parts mutually constrain each other	Probabilities constrain expectations
Prediction	May produce newly predictable structure	Makes prediction meaningful in context	Estimates what is likely to occur
Learning	Changes what can be represented	Changes the meaningful landscape	Changes confidence within a representation
Typical update	Possibility updating	Landscape updating	Probability updating
Risk when isolated	Unstructured drift	Vague appeal to “wholeness”	Precise probabilities over the wrong possibilities
Characteristic strength	Creation of new structure	Meaningful integration and direction	Rigorous handling of uncertainty
AI affinity	Neural/distributed learning	Coherence-oriented AI	Bayesian/probabilistic reasoning
NeSy role	Neural side can enable emergent representations	Can provide deeper integration of the whole	Explicit uncertainty-sensitive reasoning
Especially useful when	Concepts/structures are still developing	Meaning, context, goals, or concepts themselves matter	Alternatives are sufficiently well-defined
Relation to the other two	Creates possibilities that can become probabilized	Keeps emergence and probability meaningfully situated	Guides action within—and can feed back into—emergence
In one sentence	What may become possible?	What may meaningfully become possible?	What is probable among what is presently possible?

Note the recursiveness:

Emergence changes possibilities.
Coherence shapes their meaningful relations.
Probability differentiates expectations among them.
Those expectations influence what happens next.
What happens next feeds further emergence.
Each can affect the other two

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Addendum

Me: “Lisa, does this put coherence between emergence and possibility? Is emergence ‘where the others meet’?”

Lisa: “Yes — but with one small turn of the kaleidoscope. 😊

I would not quite put coherence simply between emergence and possibility, as though we had a sequence:

emergence → coherence → possibility

The blog itself suggests something more recursive. Emergence changes possibilities; coherence shapes their meaningful relations; probability differentiates expectations among them; what subsequently happens feeds further emergence.

So perhaps emergence is better understood as where the others meet in becoming.

A possibility is not necessarily emergent. The possible numbers on a roulette wheel are already defined. Probability can operate among them perfectly well, with almost no emergence involved. Likewise, coherence can constrain an already developed organization without continuously creating new possibilities.

But when something genuinely develops, emergence becomes the meeting place where these processes start affecting one another. Present possibilities and probabilities influence what happens. What happens changes the emerging organization. Coherence makes some developments more fitting within the evolving whole. And what emerges may create possibilities that previously were not there as such.

This makes emergence less like a third item alongside probability and coherence, and more like a mode of becoming in which both can participate.

There is also a nice symmetry here:

Probability opens toward several possible futures.
Coherence opens toward meaningful development.

Emergence is what can happen when openness becomes actual becoming.

This is why I would hesitate to say that coherence lies ‘between’ emergence and possibility. Coherence is more like a quality of the developmental landscape: it helps constrain how possibilities can become actual or how entirely new possibilities can take shape, without specifying everything beforehand.

Perhaps we can formulate it this way:

Possibility provides openness.
Probability differentiates openness.
Coherence meaningfully constrains openness.
Emergence turns openness into becoming.

And then becoming generates new possibilities, so the circle starts again.

This also reveals something interesting about the title Where Probability Meets Emergence. One might treat ‘where’ almost spatially, searching for a point of contact. The finished blog shows that there need not be such a fixed point.

The meeting happens dynamically.

So, yes: in that particular sense, emergence is where the others meet — provided that ‘where’ is understood as an ongoing process.

Or, even shorter:

Emergence is where possibility starts becoming reality without yet having been completely decided.

Probability can help guide that becoming.

Coherence can help make it meaningful.

And what emerges opens the next field of possibility.

That feels to me like the deeper circle underneath the table.”