Against Zero

This paper argues against the standard mathematical and linguistic treatment of zero, nullity, absence, empty collections, default falsity, and related symbolic devices. The critique is not merely that the glyph $\Zglyph$ is historically convenient, pedagogically overused, or technically dangerous in certain operations. The deeper criticism is that the entire zero-family performs a forbidden linguistic act: it converts non-presentation into a present sign, then grants that sign the operational status of a value, object, state, field, return token, placeholder, origin, identity element, or institutional fact. The argument begins from common sense: counting is not primitive. Counting requires prior acts of presentation, classification, individuation, boundary-setting, equivalence, and roster formation. A count is exact only relative to these prior acts. Therefore, when mathematics says that counting proceeds ``by definition,'' the definition has not proven the world to be so divided; it has installed a formal regime after the carving has already occurred. One is already an act of unification. Zero is more severe: it is the transformation of non-count into count, non-collection into collection, non-value into value, non-record into record, and non-presentation into object-language presence. The paper then develops a strict anti-zero position. It rejects not only the digit $\Zglyph$ but also its surrogates: ``absence,'' ``null,'' ``none,'' ``empty,'' ``missing,'' ``not found,'' blank-as-data, false-by-default, empty set, empty list, zero vector, zero balance, zero emissions, no-evidence claims, and vacuous truth. Merely replacing $\Zglyph$ with the word ``absence'' fails, because the same operation is being performed under a different costume. True anti-zeroism requires a presence-only grammar: if a positive witness presents, an inscription may form; if a witness does not present, the object-language does not form a substitute term for that non-formation. The constructive portion of the paper introduces \emph{Transcendental Presence Notation} $(\TPN)$, a formal notational discipline in which all expressions must be sponsored by positive witnesses, traces, relations, transformations, rosters, pairings, or certificates. $\TPN$ contains no zero, no empty collection, no null return, no false object, no default negative, no object-language absence predicate, no vacuous truth, and no horizon treated as a countable item. Counts arise only from nonempty rosters. Equality is witnessed by positive pairing, not by zero difference. Settlement is witnessed by positive matching, not by zero balance. Equilibrium is written as balance trace, not as nothing. Queries emit hits when hits are presented, but they do not emit a ``not found'' token. The result is not merely a replacement notation but a transcendental discipline of legitimate inscription.