Partition, Discrimination, and the Internal Observer in a Background-Independent Relational Ontology: A Preliminary Discussion

This paper treats observation on a combinatorial substrate of the kind that background-independent approaches to quantum gravity, group field theory among them, have developed as models of the emergence of a discrete spacetime, in which no arena is given in advance and every structure, extent and order included, is carried by the relations themselves. The substrate is used here as a formal template, and no physical claim is made of the objects described. The setting imposes a constraint that organises the paper: every observer is a subsystem of the complex it observes, and there is no description made from no partition. Observation is located combinatorially, with the observer a worldtube, the observation an event at its boundary, and the record a persistent trace whose generation depends on the boundary configuration; a ladder of nested conditions runs from bare coupling to the observation of one's own records. Three effects of observation are separated: an observation adds to the complex; its record mediates the observer, so that having observed narrows the observer's own continuations; and where the observed party's continuations depend on the record, the record acts back on the observed. Elementary limitative results follow from the definitions: a subsystem's discrimination excludes its own cells, so no subsystem discriminates the totality of a complex containing it; a party is discriminated at most up to its boundary presentation, so complete transparency excludes interiority; and environments presenting identically are indistinguishable from within, which yields a known sceptical conclusion by a substitutability route. Objectivity is defined as redundant recording across a family of partitions, intersubjectivity as mutual reproductive closure of an interface structure, and surveillance as one-sided record formation across a coupling. The paper's declared centre is the partition problem: every result above is indexed to a partition whose selection the framework leaves to the describer, and the two available responses are stated with their costs. The contribution claimed is a vocabulary and a set of elementary consequences, and the limitative results restate, at this level, conclusions that established work has reached by other routes. The paper is conceptual and preliminary; its results are definitions, short propositions, and an explicit register of open problems.