The Hidden Grammar of Discovery: Abduction and the EML Operator

Odrzywolek (2026) reports the discovery that a single binary operator, eml(x,y) = exp(x) −ln(y), generates all elementary functions from the constant 1, attributing the discovery to“systematic exhaustive search.” This commentary argues that the search was verification, notdiscovery. Evidence internal to the paper reconstructs a prior abductive inference: anasymmetry between Boolean and continuous mathematics motivates the conjecture that acontinuous analogue of NAND must exist; prior knowledge of exp-log representationsconstrains the search space; and the author’s acknowledged “bit of luck” names the momentof abductive crystallization before formal confirmation begins. The conflation of discoverywith verification is not dishonesty but a structural feature of the scientific paper as genre.Reichenbach’s context-of-justification norm, intended as a methodological clarification, hasfunctioned—as Schickore and Steinle (2006) document—as a license to omit discoveryreasoning from formal communication. The epistemic costs are concrete: the locus of noveltyis misidentified (the conjecture, not the search, is the contribution); the method cannot betransmitted (analogical habit, not search procedure, is what produced the result); and thescope of the search is overstated as complete when it was abductively constrained. Makingabduction visible in scientific writing is not a biographical indulgence; it is a condition foraccurately evaluating, teaching, and deliberately cultivating the reasoning that makestractable searches possible.