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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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    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 Feb 25 '21 at 07:21
  • 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 Feb 25 '21 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 Mar 22 '22 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 Mar 22 '22 at 20:32
  • @JoWehler -- those who think the trinity is self-refuted, tend also to think there is One True Logic, and this logic prohibits X from == Y and == not-Y simultaneously. However, logicians themselves have concluded there is NOT One True Logic, https://www.cambridge.org/core/journals/think/article/abs/guide-to-logical-pluralism-for-nonlogicians/EDFDFA1C9EB65DB71848DABD6B12D877. And among the plural logics that match aspects of our world, there are many that allow superpostition. So -- superposition of three essences within one entity is not in any way logically prohibited in our world. – Dcleve Jul 20 '22 at 04:28
  • @Dcleve Do you have an example with 'X = Y' and at the same time 'not(X=Y)' - with equality taken in the sense of identity? – Jo Wehler Jul 20 '22 at 07:11
  • @JoWehler -- No, I do not have other such examples for you. I instead offer the following PhilSE question and answer, as a justification for rejecting One True Logic, and accepting and working with a paraconsistent logic framework. https://philosophy.stackexchange.com/questions/92070/dialethic-machines-and-incompatibilist-free-will/92134?noredirect=1#comment260200_92134 The rationale presented, if accepted, supports considering the trinity just another application of cognitive dissonance. It does not support that trinitarianism is TRUE, just that it shouldn't be rejected outright. – Dcleve Jul 20 '22 at 13:00

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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:

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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.

Kristian Berry
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enter image description here

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

Agent Smith
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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.

  • 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? –  Feb 24 '21 at 23:47
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    i cannot comment. and the question too broad imho. –  Feb 24 '21 at 23:52