A Primer on Paradigms, Symmetry, and our Solution to the Riddle of Induction

For more than three centuries, philosophers have struggled with Hume’s riddle of induction: Why should the future resemble the past? Why prefer one explanation over another when the evidence alone doesn’t dictate a choice? Every attempt to answer this has run aground on the same problem: any justification for a prior assumption relies on another prior assumption, and the regress never ends.

The mistake lies in trying to justify which prior to choose. The real question is: where do priors come from at all? Until you answer that, no structure of justification can get off the ground.

In the late 1990s, Tim Barber and I approached the problem from a different direction. Instead of asking which prior is right, we asked what forces a cognitive system to have any particular prior in the first place. Our answer is that priors emerge — uniquely and inevitably — from the distinctions a mind acknowledges among the hypotheses it considers.

This is the heart of the theory:

A paradigm is the set of properties and relationships a mind acknowledges among the hypotheses it considers — distinctions involving empirical content, causal form, structural pattern, simplicity, complexity, elegance, mechanistic detail, or any other feature it takes to be epistemically meaningful.

These properties and relationships determine which hypotheses the mind treats as genuinely different and which it treats as the same. They induce equivalence classes over the hypothesis space: two hypotheses belong to the same class if the paradigm’s acknowledged distinctions make no difference between them.

And here is the key: priors must be assigned uniformly across these equivalence classes and uniformly within them. This is not an optional rule but a consequence of rationality. If two hypotheses are treated as indistinguishable by the paradigm, they must be treated as equally probable.

In other words:

The prior is the unique probability distribution that respects the symmetry implied by the paradigm’s acknowledged properties and relationships.

Nothing is chosen. Nothing is stipulated. It is simply the only measure compatible with the mind’s own conceptual commitments.

This shifts the entire structure of the induction problem. Instead of searching for the “correct prior,” we look to the distinctions the mind acknowledges among hypotheses. Once those distinctions are fixed, the prior is forced. This closes Hume’s regress at the only legitimate place: the architecture of conceptual discrimination itself.

Several consequences follow.

First, it explains why two communities with the same evidence and the same moral principles can end up believing incompatible accounts of what happened. They carve the hypothesis space differently. One paradigm may notice hierarchy, another simplicity, another group identity, another causal mechanism. With different acknowledged distinctions come different equivalence classes — and thus different priors and different “realities.”

Second, it explains why science works. Most reasonable paradigms notice a broad constellation of empirical, causal, statistical, and structural properties. These produce similar partitions of the hypothesis space, which in turn yield similar priors. So different scientists, starting from different but healthy paradigms, converge quickly once evidence arrives.

Third, it explains why some paradigms are pathological. A narrow or “ill” paradigm that acknowledges only one or two properties collapses huge regions of the hypothesis space into a small number of equivalence classes while carving other regions into many tiny ones. This produces wildly skewed priors and makes certain explanations almost impossible to take seriously. Social manias and ideological echo chambers often operate inside such degenerate conceptual schemes.

This is why the our framework is, in my view, as close as we can get to a best-possible resolution of the riddle of induction. It avoids metaphysical assumptions (like the uniformity of nature), avoids dogmas (like inherent simplicity), avoids circularity, and replaces “choosing a prior” with deriving it from the symmetry structure implied by the learner’s conceptual scheme.

Induction is not magic, not arbitrary, not brute, not metaphysical. It is the unavoidable consequence of a mind acknowledging distinctions among possible explanations.

The prior is the shadow of the paradigm.

And in that sense, this framework dissolves Hume’s riddle in the deepest, most principled way available.

(Link: https://www.changizi.com/uploads/8/3/4/4/83445868/changizibrain25000chapter3.pdf)