Of orthodox Christianity’s many doctrines, God’s Ultimacy – that God both causally and explanatorily precedes all else – and God’s triunity – that God is three in Person but one in substance (or essence) – are considered central. For most Christian theologians, to deny either God’s Ultimacy or God’s triunity is to proceed into heresy or to abandon Christianity altogether. Both appear in the Nicene Creed and God’s Ultimacy historically preceded Christianity altogether, having its roots in Jewish monotheism. Yet, as I will show in this article, straightforward understandings of these two doctrines produce contradictions when they are placed in conjunction.
It has often been claimed that Trinitarianism produces contradictions. As Augustine describes the trinity in his On Christian Doctrine , the trinity may be described with the following seven propositions :
- The Father is God.
- The Son is God.
- The Holy Spirit is God.
- The Father is not the Son.
- The Son is not the Holy Spirit.
- The Father is not the Holy Spirit.
- There is only one God.
From these seven, we can derive:
- The Father is not the Father (from 1, 4 by replacement).
Orthodox Christians would be correct to point out that 8 does not actually follow from 1 and 4, either in traditional Christian doctrine or through Augustine’s conception of trinitarianism because the word ‘is’ is equivocal between 1 and 4. In 1, the Father’s substance or essence is identified as that of God. Within both Aristotlean and Platonic frameworks, two things share in essence if they are of the same kind. For example, Plato would have said that two cows share the same essence by participating in the Form of cowness. Contemporary readers, who may be mystified by the appeal to substances and essences, will not be misled (at least for the purposes of this article) if they understand the ‘is’ appearing 1-3 as the ‘is’ of predication.
However, the ‘is’ appearing in 4-6 is the ‘is’ of identity. The Father, Son, and Holy Spirit share a common essence, but they are not the same Person and are thus not identical. While the interpretation of the trinity remains controversial, this seems to be enough to render the doctrine free of contradiction. At the very least, I will assume that, by itself, triunity is coherent for the remainder of this article .
I turn next to God’s Ultimacy. Traditionally, Christians have understood God as absolutely ultimate, by which I mean that God both explains and was/is causally responsible for all else. As Brian Leftow (among others) has pointed out, this runs us into an interesting implication: God is identical to all of God’s properties, a doctrine known as ‘Divine Simplicity’ . In what follows, I sketch Leftow’s argument for that conclusion, but interested readers should refer to his article for the full details. I will note that Leftow is not the first to argue for Divine Simplicity; the doctrine is first ancient and second popular among orthodox Christian theologians. The doctrine appears in the Catholic Catechism  and a Catholic theologian I consulted assures me that Divine Simplicity is part of the Church’s official teaching. Briefly, I note that Simplicity has not been without criticism and that both David Hume and Erik Wielenberg, among others, have produced previous atheistic arguments based on Simplicity . I shelve those arguments and proceed forward.
Why does Ultimacy entail Simplicity? Leftow’s argument proceeds as follows. First, notice that God’s properties cannot precede God, either in cause or explanation, because this would entail that God’s properties are more ultimate than God. Second, notice that God’s properties cannot be posterior to God, either in cause or explanation, because this would render God incoherent. The only solution is to identify God with God’s properties. Again, if the reader remains unconvinced, I invite them to read over Leftow’s paper, in which this argument is produced with full rigor.
Having described both trinity and ultimacy, I proceed by showing that the conjunct of these two doctrines produces a contradiction. Consider the following argument:
- Divine Simplicity: The godhead is identical to all of the godhead’s properties.
- The Trinity: The Father, the Son, and the Holy Spirit are God in substance, but the Father is not the Son, the Son is not the HS, and the Father is not the HS.
- The godhead is identical to all of the properties of the Persons of the Trinity (from 9 & 10).
- Therefore, the properties of the Persons of the Trinity are all identical to each other (from 11).
- The Persons of the Trinity are Simple (i.e. each are identical all of their properties).
- Therefore, the Persons of the Trinity are all identical to each other (from 12 & 13).
- Contradiction! (from 10 & 14)
- Therefore, either the godhead is not triune or Divine Simplicity is false.
- If the godhead is not triune then Christianity is false.
- If Divine Simplicity is false then divine aseity is false (i.e. God is not Ultimate in the right sense); but if so, Christianity is false.
- Therefore, Christianity is false.
Thus, we arrive at the advertised conclusion: given that an orthodox understanding of Christiany involves both trinity and Ultimacy, and that the conjunct of these entails a contradiction, orthodox Christianity is false. It remains possible for the Christian to deny Ultimacy or to deny trinitarianism. Certainly, some Christians already do deny one or both of these doctrines; for example, Dale Tuggy has advocated that Christians abandon the Trinity . Nonetheless, the foregoing appears to be sufficient deny orthodox Christianity.
 Philip Cary summarizes trinitarian doctrine this way in his “Logic of Trinitarian Doctrine”, Religious and Theological Studies Fellowship Bulletin, Sept/Oct 1995, p 2.
 For a summary of the various theological models of the trinity, see Rhea, M. “The Trinity”. In The Oxford Handbook of Philosophical Theology ed. Thomas P. Flint & Michael Rea (Oxford University Press, 2009).
 See, for example, several of Dale Tuggy’s papers available on his website.