The Ontology Of Explanation: 2 Explanation vs Derivation

A decisive shift occurs when explanation is quietly equated with derivation.

At first glance, the move appears innocuous. To derive a result is to show that it follows, with necessity, from a set of premises. What could be more secure than that? If a phenomenon can be mathematically derived from a theory, has it not been explained?

The answer, historically and conceptually, is no.

Derivation is a formal relation between statements. Explanation is a relation between a theory and a phenomenon — and, crucially, between that relation and a knower. Derivation shows that something must be the case given certain assumptions. Explanation shows why something is the case in a way that renders it intelligible.

The distinction matters because derivations are cheap. Given sufficient formal resources, almost anything can be derived from something. What is scarce — and what explanation once supplied — is insight into how a phenomenon is situated within a wider construal of the world.

Historically, derivations functioned inside explanations, not in place of them. A derivation disciplined an explanation by showing that it was not merely narrative or ad hoc. But the explanatory force came from elsewhere: from the intelligibility of the premises themselves, from their connection to experience, and from the way the derivation illuminated rather than displaced the phenomenon.

The contemporary inversion is subtle. Increasingly, explanation is treated as complete once derivation has been achieved. Questions about interpretation, intelligibility, or phenomenological grounding are reclassified as optional extras — matters of taste, pedagogy, or psychological comfort.

This inversion has a distinctive rhetorical signature. When asked why a phenomenon occurs, the response is no longer a story, a mechanism, or a situating principle, but a gesture toward the formalism: it follows from the equations. The equations themselves are treated as explanatorily primitive.

Yet equations do not explain anything on their own. They constrain relations within a formal system. Without an accompanying construal that relates those constraints to a phenomenon, derivation remains internal to theory. It shows coherence, not adequacy.

This is why derivation can succeed spectacularly while explanation quietly fails. A derivation can be correct, rigorous, and nontrivial, and still leave us with no clearer sense of what is going on. Indeed, the more abstract and distant the formalism becomes, the easier it is to mistake opacity for depth.

The conflation of explanation with derivation therefore marks a structural change in scientific practice. Explanation ceases to be something that bridges theory and experience, and becomes something that occurs entirely within the theory itself.

Once this shift is accepted, a further consequence follows almost automatically: intelligibility is no longer a criterion of explanatory success. If derivation is enough, then understanding becomes optional. The burden of explanation moves from the theory to the audience.

This is not a technical adjustment. It is an ontological one.

When derivation replaces explanation, theory no longer answers to phenomena; it answers only to its own formal constraints. What remains is a powerful engine for generating results — but an increasingly fragile account of what those results are results of.

In the next part, we will see how this fragility is not merely tolerated but actively defended, as intelligibility itself comes to be treated as suspect.