Finnish Negation: The Negative Auxiliary ei [Kar18]

[Byb85] [Mie05] [Has13b]

Finnish expresses sentential negation through a conjugated negative auxiliary verb ei. The negative verb inflects for person and number, while the lexical verb appears in a nonfinite connegative form that lacks tense/agreement marking.

Paradigm (present indicative)

Person	Sg	Pl
1	e-n	e-mme
2	e-t	e-tte
3	e-i	e-ivät

Key structural property

The negative auxiliary bears the inflection that the main verb would otherwise carry. This splits the [Byb85] relevance hierarchy: negation (rank 7) hosts agreement (rank 8) and tense, while the main verb retains only the stem and aspect. This is a counter-example to strict stem-outward ordering within a single word — the ordering principle holds across the analytical construction (neg aux + main verb) rather than within a synthetic word.

Marker and system

def Finnish.Negation.ei : Syntax.Negation.NegMarkerEntry

ei — Finnish's negative auxiliary verb, cited in 3sg form. Genuine auxiliary: inflects for person and number (negParadigm below has the 6 present-tense forms) and bears the agreement and tense markers that the lexical verb would otherwise carry. The lexical verb appears in the connegative form (tense-stripped: e-n osta 'I don't buy' loses the tense marking osta-n 'I buy' carries). The 6 surface forms (en/et/ei/emme/ette/eivät) are accessible via negParadigm.

Equations

• Finnish.Negation.ei = { form := "ei", morphemeType := Syntax.Negation.NegMorphemeType.auxVerb, position := Syntax.Negation.NegMarkerPosition.preverbal }

def Finnish.Negation.negationSystem : Syntax.Negation.NegationSystem

The Finnish negation system: a single negative auxiliary with a person/number paradigm. Multiple paradigm-form surface realizations (negParadigm) are not multiple markers — they're inflectional variants of one auxiliary, captured cross-linguistically by the single NegMarkerEntry.

Equations

• Finnish.Negation.negationSystem = Syntax.Negation.NegationSystem.ofISO "fin" [Finnish.Negation.ei]

Negative auxiliary paradigm

structure Finnish.Negation.NegForm : Type

Person–number features for the Finnish negative auxiliary.

• person : ℕ
• number : String
• form : String

@[instance_reducible]

instance Finnish.Negation.instReprNegForm : Repr NegForm

Equations

• Finnish.Negation.instReprNegForm = { reprPrec := Finnish.Negation.instReprNegForm.repr }

def Finnish.Negation.instReprNegForm.repr : NegForm → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def Finnish.Negation.instBEqNegForm.beq : NegForm → NegForm → Bool

Equations

• Finnish.Negation.instBEqNegForm.beq { person := a, number := a_1, form := a_2 } { person := b, number := b_1, form := b_2 } = (a == b && (a_1 == b_1 && a_2 == b_2))
• Finnish.Negation.instBEqNegForm.beq x✝¹ x✝ = false

@[instance_reducible]

instance Finnish.Negation.instBEqNegForm : BEq NegForm

Equations

• Finnish.Negation.instBEqNegForm = { beq := Finnish.Negation.instBEqNegForm.beq }

def Finnish.Negation.negParadigm : List NegForm

Full present-tense paradigm of the negative auxiliary ei.

Equations

• One or more equations did not get rendered due to their size.

Connegative formation

Inflection distribution

Verification

theorem Finnish.Negation.paradigm_size : negParadigm.length = 6

The paradigm has exactly 6 forms (3 persons × 2 numbers).

theorem Finnish.Negation.neg_aux_respects_bybee : Morphology.MorphCategory.negation.RelevanceLT (Morphology.MorphCategory.agreement Agreement.Controller.subj)