Tractatione proposita auctores manifestant, "Argumentum Ontologicum" St. Anselmi in 2^o capitulo eius Proslogii inscriptum ut validum exponi posse (i. e. consequentiam bonam servando). Hac in interpretatione vis et notio descriptionis illae "id quo maius cogitari nequit", qua Anselmus usus est, rite agnoscitur. Datis enim lingua formali "primi ordinis", ut aiunt, et systemati deductivo logicae huiusmodi, in quo descriptiones definitae genuini sunt termini et ubi a sententia "datur x quod…" signo quantitatis praefixa ad sententiam "x exsistit" consequentia non valet, et adhibendo adhuc regulas ordinarias logicae descriptionum relationemque comparationis, quae "continua" dicitur, exsistentia Dei sequitur duabus ex praemissis: Una quidem, "datur cogitabile aliquid, quo maius cogitari nequit"; et altera, "x non exsistente, aliquid eo maius cogitari potest". Conclusio praedicta non potest negari, nisi una quoque harum praemissarum saltem negatur. Argumentum hoc vero nulla deductione modali utitur; et, quod notabile est, ratio ontologica Cartesii ex eo derivari potest.

In this paper, the authors show that there is a reading of St. Anselm's ontological argument in Proslogium II that is logically valid (the premises entail the conclusion). This reading takes Anselm's use of the definite description "that than which nothing greater can be conceived" seriously. Consider a first-order language and logic in which definite descriptions are genuine terms, and in which the quantified sentence "there is an x such that…" does not imply "x exists". Then, using an ordinary logic of descriptions and a connected greater-than relation, God's existence logically follows from the claims: (a) there is a conceivable thing than which nothing greater is conceivable, and (b) if x does not exist, something greater than x can be conceived. To deny the conclusion, one must deny one of the premises. However, the argument involves no modal inferences and, interestingly, Descartes' ontological argument can be derived from it.