Neither if we said I have ridden the horses, would it agree with horses; since it is of the singular number.
The true construction is arrived at by supplying the word thing. I have a horse as a ridden thing = habeo equum equitatum (neuter). Here the construction is the same as triste lupus stabulis.
I have horses as a ridden thing = habeo equos equitatum (singular, neuter). Here the construction is—
"Triste ... maturis frugibus imbres,
Arboribus venti, nobis Amaryllidos iræ."
or in Greek—
Δεινὸν γυναιξὶν αἱ δι' ὠδίνων γοναί.
The classical writers supply instances of this use of have. Compertum habeo, milites, verba viris virtutem non addere = I have discovered = I am in possession of the discovery. Quæ cum ita sint, satis de Cæsare hoc dictum habeo.
The combination of have with an intransitive verb is irreducible to the idea of possession: indeed, it is illogical. In I have waited, we cannot make the idea expressed by the word waited the object of the verb have or possess. The expression has become a part of language by means of the extension of a false analogy. It is an instance of an illegitimate imitation.
The combination of have with been is more illogical still, and is a stronger instance of the influence of an illegitimate imitation. In German and Italian, where even intransitive verbs are combined with the equivalents to the English have (haben, and avere), the verb substantive is not so combined; on the contrary, the combinations are