22.1.1 The jump changes the declaration

22.1.1 The jump changes the declaration

Zahavy’s position paper LLMs Can’t Jump advances a sharper challenge to creativity as compression [ Zahavy , 2026 ] . Following Einstein’s account of scientific discovery, it distinguishes induction, deduction, and abduction. Induction extracts a rule from cases and results; deduction derives results from fixed rules and cases; abduction proposes an explanatory case or rule for a surprising result. The paper interprets Einstein’s transition from physical thought experiments to the axioms of general relativity as such a “jump.”

The general-relativity example matters because the available predictive error was not commensurate with the conceptual reorganization eventually required. Newtonian gravity was empirically extremely successful, and the observations that later provided decisive tests of general relativity were sparse or subsequent to its formulation. A compression-driven search within the old hypothesis language could prefer a small patch to a change in the primitives of space, time, acceleration, and gravitation. The eventual theory was elegant, but its discovery path initially enlarged and disrupted the representational scheme rather than monotonically shortening a code.

In LINCS terms, this is the difference between changing a realization \(D\) inside a declaration \(\mathfrak L\) and changing the declaration itself:

The first arrow is abductive and proposal-generating: it may introduce new objects, morphisms, axioms, probes, or a new quotient. The second is auditable: it asks whether old witnesses survive transport, whether the new declaration resolves the motivating obstruction, and whether it makes new predictions or supports interventions that pass independent tests.

This formulation also shows how a learning signal can exist without a large statistical residual. Individually successful local theories may fail to glue; requirements inherited from different domains may not commute; or an apparently harmless assumption may block a desired extension. Such failures are structural tensions among declarations, not necessarily errors on a supervised sample. A new theory can respond by reorganizing the diagram rather than fitting the old diagram more closely.

The connection should not be overstated. A historical case study is not a proof that no LLM can perform abduction, and no result in this book establishes that LINCS can outperform compression-based learning on creative discovery. Nor does detecting non-compositionality uniquely determine a new declaration. Zahavy proposes physically consistent, interactive world models as a source of grounded counterfactual simulation. Such a system could generate candidate declaration changes; LINCS could then type the proposal, preserve its provenance, transport prior evidence, and separate invention from admission.