{"id":28908,"date":"2026-08-08T20:11:41","date_gmt":"2026-08-08T20:11:41","guid":{"rendered":"https:\/\/aurelis.org\/blog\/?p=28908"},"modified":"2026-08-09T11:47:50","modified_gmt":"2026-08-09T11:47:50","slug":"where-probability-meets-emergence","status":"publish","type":"post","link":"https:\/\/aurelis.org\/blog\/coherence\/where-probability-meets-emergence","title":{"rendered":"Where Probability Meets Emergence"},"content":{"rendered":"

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.<\/h3>\n

When concepts, meanings, and even the relevant possibility space remain in development, coherence may give their meeting depth.<\/p><\/blockquote>\n

When two worlds meet<\/strong><\/p>\n

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.<\/p>\n

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.<\/p>\n

The interesting question is where<\/em> they meet, and what kind of meeting is needed for different kinds of intelligence.<\/p>\n

Probability needs possibilities<\/strong><\/p>\n

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.<\/p>\n

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.<\/p>\n

This connects directly with The Fallacy of Misplaced Concreteness<\/a>.<\/em> A probability distribution can be mathematically impeccable while the conceptualization underneath it remains inadequate. The map may be precise without being the right map.<\/p>\n

Emergence \u2015 another kind of movement<\/strong><\/p>\n

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.<\/p>\n

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.<\/p>\n

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.<\/p>\n

Meeting horizontally<\/strong><\/p>\n

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.<\/p>\n

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.<\/a><\/em>, this can be very useful.<\/p>\n

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.<\/p>\n

When the landscape moves<\/strong><\/p>\n

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?<\/p>\n

Here, the landscape itself moves.<\/p>\n

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<\/a><\/em>: some domains lend themselves well to relatively stable state spaces, while meaning-rich situations may require the relevant landscape itself to remain open.<\/p>\n

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?”<\/p>\n

Meeting in depth<\/strong><\/p>\n

Probability can rigorously distinguish expectations, but a highly accurate probability over poorly chosen possibilities remains problematic. This is where coherence enters.<\/p>\n

Coherence concerns how what emerges continues to fit meaningfully within an evolving whole. \u2018Fit\u2019 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<\/a><\/em>.<\/p>\n

Coherence provides openness to fitting novelty.<\/p>\n

Three kinds of openness<\/strong><\/p>\n

These are:<\/p>\n