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Are there any publications in the field of Philosophy of Religion that have attempted to provide a formal ontological definition of the Christian God as portrayed by the doctrine of the Trinity?

Take for example what the Athanasian Creed postulates about the Trinity:

"So likewise the Father is Lord; the Son Lord; and the Holy Ghost Lord. And yet not three Lords; but one Lord".

How would a sentence like this be parsed with a more rigorous ontological formalism? Should we understand "Lord" as a predicate over entities rather than an entity itself? And what about the verb is used in phrases of the form "X is Lord"? Should we interpret it as an identity between entities, as a universal applying to a particular, as inclusion into a composite entity, etc.?

Does anyone know a publication that has attempted to define the Christian Trinity with a rigorous ontological approach?

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    Plenty, see IEP's review and Paoletti, The Holy Trinity and the Ontology of Relations for a recent take.
    – Conifold
    Commented Feb 25, 2021 at 0:15
  • 1
    Your question belongs on Christianity SE as the question immediately becomes embroiled in Christian polemics. The evolution, history, and meanings of and in the two major polemic traditions; the anti-Platonic/anti-Trinitarian controversialists has been argued for literally centuries by both history pathologists as well as theologians of different Christian traditions. .
    – Swami Vishwananda
    Commented Feb 25, 2021 at 7:21
  • The earliest known reference of the trinity being Father, Son, and Holy Spirit is late 2nd century (ref: Rise and Fall of the Roman Empire). It was not common in primitive Christianity. Elaine Pagels in her book "The Gnostic Gospels" and the Nag Hammadhi refer to the trinity as Divine Father, Divine Mother, and Son. Pagels also goes through the etymology of it in the Greek and Hebrew.
    – Swami Vishwananda
    Commented Feb 25, 2021 at 13:15
  • After reading Paoletti’s paper indicated by @Conifold I get the impression: Formalizing the Christian dogma of trinity reminds me on the problem of squaring the circle. The issue occupies people since centuries. Though the question has been answered in the negative in the 19th century, persistent laypersons show up again and again and present their attempts for a positive solution. The only difference is that Paoletti is not a layperson but a scholar with a religious background, working on ontologies. 1/2
    – Jo Wehler
    Commented Mar 22, 2022 at 20:32
  • I consider a consistent formalization of the trinity problem an impossible task because its basic assumptions are contradicting, cf. the corresponding statements in the IEP-article indicated by @Conifold. 2/2
    – Jo Wehler
    Commented Mar 22, 2022 at 20:32

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An old attempt, and relatively perspicuous at that, comes from Aquinas:

For St Thomas, the relations which distinguish the divine persons constitute these persons. Relation thus becomes the basis of a theological understanding of the divine persons. In working this out, Thomas is following the path opened up by his teacher, St Albert the Great, which diverges from that of the Franciscan school. For Thomas the notion of relation is of utmost significance. The treatise on the Trinity begins with a consideration of the processions precisely in order to show that this is its foundation. Hence, the theory of relations will be found throughout the Summa's Trinitarian treatise: it is not confined to question 28, but influences the whole of the subsequent meditation. This chapter discusses the elements of the patristic teaching on relation, real relations in God, the being of divine relations, and relative opposition.

In other words, the divine persons are held to be relations of the divine nature to Itself. Aquinas is at pains to show that the divine nature will relate to Itself in only three such ways, since otherwise the divine infinity would seem to yield infinitely many divine persons (an esoteric possibility that he does remark upon, if concluding in the negative).

Relative identity is a principally more modern framework in which the constitutive paradox of the Trinity is evaluated:

enter image description here

I suspect that there is some historical overlap to be found in the reference to "relative opposition" re: Aquinas and van Inwagen's talk of relative identity, though, then.

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https://plato.stanford.edu/entries/trinity/

While no doubt the Fathers of the [381] Council did not have a clear view of what was the sense in which there is just one “God” and the sense in which each of the three beings is “God” the distinction between the two senses of the crucial words makes available one obvious way of resolving the apparent contradiction. This is by thinking of these words as having the former sense [i.e. referring to one thing like a name] when the Creed says that there is “one God”, and as having the latter sense [i.e. being equivalent the adjective “divine”] when it claims that each of the beings “is God.” Thus understood, the Creed is saying that there is one unique thing which it names “God,” which consists of three beings.

Read the article, and edit the question into something more useful / specific.

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  • Thanks for the link. I'll definitely going to take a look at it. As to making the question more useful / specific, how about you apply what you understand from the article to the sentence I quoted from the Athanasian Creed? So likewise the Father is Lord; the Son Lord; and the Holy Ghost Lord. And yet not three Lords; but one Lord - how do you understand this sentence in light of the article you just shared?
    – user48437
    Commented Feb 24, 2021 at 23:47
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    i cannot comment. and the question too broad imho.
    – user50495
    Commented Feb 24, 2021 at 23:52
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enter image description here

Does this do it for you, sir/madam (both?)?

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