1. Christian doctrine (per the Athanasian Creed) says that the Father is God, the Son is God, the Holy Spirit is God. But it also says that these are three distinct persons, so the Son is not the Holy Spirit. Without a clear alternative interpretation, this doctrine is self-contradictory.
Fundamental Christian doctrine has been formalized in a set of creeds. Since the Athanasian Creed was the first to establish the doctrine of the Trinity, I will list all relevant statements from the Athanasian Creed about the Trinity:
Perhaps the argument should end there: one ought never believe an apparent contradiction unless one can interpret it coherently, but these theologians admit that the Trinity cannot be coherently interpreted, so therefore one ought never to believe in the Trinity. They all say to believe in the Trinity despite the inability of human reason to understand it, but as shown above, that only makes the problem worse. Believing a contradiction, and that the contradiction is consistent because someone else has shown its consistency, is believing a contradiction and denying that it is a contradiction—exactly like Emily did in the previous example. Expecting to coherently understand what those genuinely brilliant minds could not may even show arrogance. Yet to dismiss the Trinity so easily would be intellectually lazy, and would insult the extensive work that they undergo to rationalize this foundational doctrine of their faith. I will offer a more charitable rebuttal by refuting their arguments for the coherence of the Trinity.
- "Whoever desires to be saved should above all hold to the catholic faith" and "[a]nyone who does not keep it whole and unbroken will doubtless perish eternally" say that all Christians are saved, and that any person P is a Christian only if P believes the ideas expressed in Athanasian Creed.
- "[T]he person of the Father is a distinct person, the person of the Son is another, and that of the Holy Spirit still another" says that the members of the Trinity are all distinct persons.
- "What quality the Father has, the Son has, and the Holy Spirit has," "we worship one God in trinity," and "there are not three gods; there is but one God" say that because the persons of the Trinity are one being called God, every property had by any one person of the Trinity is had by the other two.
- "The Son…was begotten from the Father alone," "[t]he Holy Spirit was…no[t] begotten," and "the Father is God, the Son is God, the Holy Spirit is God" mean exactly what is in the statements.
- Augustine admits that “among all these things that I have said about that supreme trinity … I dare not claim that any of them is worthy of this unimaginable mystery, but must rather confess that his knowledge is too wonderful for me … and I have not been capable of it” at the end of his work The Trinity, ed. John E. Rotelle, trans. Edmund Hill (2nd ed. Vol. I. Charlottesville, VA: InteLex Corporation, 2009), book XV, sec. 50, p. 441.
- Explicitly following Augustine’s approach, Boethius opens and ends his letter On the Holy Trinity (De Trinitate) (trans. Erik C. Kenyon, 2004) by describing the boundaries of his reason in understanding the Trinity, and asks the letter’s recipient to judge whether his solution works since he cannot.
- “Some truths about God exceed all the ability of the human reason” to understand them, according to Thomas, including “the truth that God is triune.” Quote from Saint Thomas Aquinas, Summa Contra Gentiles, trans. Anton C. Pegis. (Notre Dame, IN: University of Notre Dame Press, 2005), I, ch. 3, sec. 2.
- And finally, Ockham comments that “the conclusion in which ‘being three and one’ is predicated of any concept of God cannot be proved in different kinds of knowledge, but is proved only in theology under the supposition of faith” in his Philosophical Writings (p. 100). Since Ockham defines “articles of faith” as “neither principles of demonstration nor conclusions, nor … probable propositions” in his Philosophical Writings (p. 83), he means here that God’s triune nature cannot be rationally explained.
Perhaps the argument should end there: one ought never believe an apparent contradiction unless one can interpret it coherently, but these theologians admit that the Trinity cannot be coherently interpreted, so therefore one ought never to believe in the Trinity. They all say to believe in the Trinity despite the inability of human reason to understand it, but as shown above, that only makes the problem worse. Believing a contradiction, and that the contradiction is consistent because someone else has shown its consistency, is believing a contradiction and denying that it is a contradiction—exactly like Emily did in the previous example. Expecting to coherently understand what those genuinely brilliant minds could not may even show arrogance. Yet to dismiss the Trinity so easily would be intellectually lazy, and would insult the extensive work that they undergo to rationalize this foundational doctrine of their faith. I will offer a more charitable rebuttal by refuting their arguments for the coherence of the Trinity.
2. Several ancient Christian saints (Augustine, Boethius, and Thomas) argued that the three persons of the Trinity are just different ways that God relates to himself or his essence. But if each person is really identical to God's essence, than each person is really identical to each other, which is the Sabellian heresy. Claiming that each person really differs from God's essence would also be heresy, though, so the saints' interpretation is trapped between two heresies.
To defend the coherence of the Trinity, the three saints Augustine, Boethius, and Thomas use the same general argument. They argue that there is only one God, that God is the Trinity, that the members of the Trinity are three distinct persons, that those persons have the same essence, and that they are distinguished because each is a different way that God relates to himself. [2]Note 2. Saint Augustine, Concerning the City of God Against the Pagans, trans. Henry Bettenson, ed. Gillian R. Evans (London: Penguin Books, 2003), book XI, ch. 10, pp. 440-442; Augustine, City of God X:24, p. 404; Augustine, The Trinity I:1, p. 67; Boethius, Holy Trinity sec. III; Boethius, Holy Trinity sec. V; Saint Thomas Aquinas, Summa Theologica, trans. Fathers of the English Dominican Province (New York: Benziger Brothers, 1911-1925), Ia, q. 29, art. 4; Aquinas, ST Ia.39.I. Even ignoring how William of Ockham showed that the concept of three distinct individuals sharing the same essence is untenable, [3]Note 3. Ockham, Philosophical Writings pp. 32-36. those three saints’ claim that the three persons of the Trinity are identical in essence and distinct in relation becomes heresy as soon as it is interpreted coherently.
The saints Augustine, Boethius, and Aquinas all argue that the Trinity consists of three persons by using several closely related concepts: the divine essence (or “substance”), a divine person, and divine relations. According to them, each person of the Trinity is a way that God relates to himself, so each divine person is a divine relation of one being to itself. [4]Note 4. Augustine, The Trinity VII:1, pp. 217-223; Augustine, The Trinity V:2, pp. 196-97; Aquinas, ST Ia.29.4; Aquinas, ST 1a.39.1; Boethius, Holy Trinity sec. V. They say this to avoid the Arian heresy of claiming that God is multiple beings or substances. [5]Note 5. Augustine, The Trinity V:I, pp. 190-95; Aquinas, ST Ia.27.1; Boethius, Holy Trinity sec. I. A divine relation, the divine essence, and God are all really the same as each other. [6]Note 6. Augustine, The Trinity VII:3, pp. 227-234; Aquinas, ST Ia.28.2; Boethius, Holy Trinity sec. III. Therefore, “in God essence is not really distinct from person.” [7]Note 7. Aquinas, ST Ia.39.1. However, the saints also claim that each divine person really differs from the other two divine persons. [8]Note 8. Aquinas, ST Ia.39.1; Boethius, Holy Trinity sec. III. Saying otherwise—that the three differ only in the minds of humans—commits the Sabellian heresy of claiming that there is no real difference between the persons of the Trinity, which the saints explicitly reject. [9]Note 9. Augustine, The Trinity VII:3, pp. 229-30; Aquinas, ST Ia.28.1. An apparent contradiction follows: the Son and the Father are both divine persons; each divine person is the same as the divine essence; so by transitivity the Son and Father are the same; but the Son is not the same as the Father; so by the earlier argument that one ought not believe a contradiction, one ought not believe in the Trinity.
Thomas says that a divine person and the divine essence are “really” the same and differ “only in our way of thinking,” [10]Note 10. Aquinas, ST Ia.39.1. which would resolve the apparent contradiction if he accepted that the divine persons differed from each other “only in our way of thinking.” Yet he calls this view a heresy because it would deny that the persons of the Trinity really differ, [11]Note 11. Aquinas, ST Ia.28.1. so he still claims that divine persons are “really distinct.” [12]Note 12. Aquinas, ST Ia.39.1. He can only have this conclusion by denying transitivity, the logical rule of inference that if A = B and B = C then A = C, [13]Note 13. Ockham, Philosophical Writings p. 86. as shown by substituting the divine essence for B and two divine persons for A and C respectively. Having painted himself into a corner between heresy and contradiction, Thomas chose contradiction.
The saints Augustine, Boethius, and Aquinas all argue that the Trinity consists of three persons by using several closely related concepts: the divine essence (or “substance”), a divine person, and divine relations. According to them, each person of the Trinity is a way that God relates to himself, so each divine person is a divine relation of one being to itself. [4]Note 4. Augustine, The Trinity VII:1, pp. 217-223; Augustine, The Trinity V:2, pp. 196-97; Aquinas, ST Ia.29.4; Aquinas, ST 1a.39.1; Boethius, Holy Trinity sec. V. They say this to avoid the Arian heresy of claiming that God is multiple beings or substances. [5]Note 5. Augustine, The Trinity V:I, pp. 190-95; Aquinas, ST Ia.27.1; Boethius, Holy Trinity sec. I. A divine relation, the divine essence, and God are all really the same as each other. [6]Note 6. Augustine, The Trinity VII:3, pp. 227-234; Aquinas, ST Ia.28.2; Boethius, Holy Trinity sec. III. Therefore, “in God essence is not really distinct from person.” [7]Note 7. Aquinas, ST Ia.39.1. However, the saints also claim that each divine person really differs from the other two divine persons. [8]Note 8. Aquinas, ST Ia.39.1; Boethius, Holy Trinity sec. III. Saying otherwise—that the three differ only in the minds of humans—commits the Sabellian heresy of claiming that there is no real difference between the persons of the Trinity, which the saints explicitly reject. [9]Note 9. Augustine, The Trinity VII:3, pp. 229-30; Aquinas, ST Ia.28.1. An apparent contradiction follows: the Son and the Father are both divine persons; each divine person is the same as the divine essence; so by transitivity the Son and Father are the same; but the Son is not the same as the Father; so by the earlier argument that one ought not believe a contradiction, one ought not believe in the Trinity.
Thomas says that a divine person and the divine essence are “really” the same and differ “only in our way of thinking,” [10]Note 10. Aquinas, ST Ia.39.1. which would resolve the apparent contradiction if he accepted that the divine persons differed from each other “only in our way of thinking.” Yet he calls this view a heresy because it would deny that the persons of the Trinity really differ, [11]Note 11. Aquinas, ST Ia.28.1. so he still claims that divine persons are “really distinct.” [12]Note 12. Aquinas, ST Ia.39.1. He can only have this conclusion by denying transitivity, the logical rule of inference that if A = B and B = C then A = C, [13]Note 13. Ockham, Philosophical Writings p. 86. as shown by substituting the divine essence for B and two divine persons for A and C respectively. Having painted himself into a corner between heresy and contradiction, Thomas chose contradiction.
3. There is no sound interpretation of identity that would make the persons of the Trinity really identical to God in one sense and really different from each other in a different sense. If the Son really differs from the Holy Spirit, and both of them are God, then the Jesus is not God. John Duns Scotus tried to interpret the Trinity using 'formal identity', but William of Ockham showed its incoherence.
In fairness to those three saints, some relations expressed by “is” are non-transitive. For example, an elephant is a mammal and I am a mammal, but it does not follow that I am an elephant. In this case, “is” only expresses that both are the same kind of animal. If the saints’ Trinitarian theology only expressed that the divine persons are the same kind of being, then transitivity would not apply, undermining the argument for the Trinity’s incoherence. Yet they need something more. To argue that the persons of the Trinity are the same kind of being but are different beings commits the heresy of Arianism, which the saints refuse to accept. Other than belonging to the same kind, three other meanings of the term “is” make the proposition “X is Y” true: conceptual identity, real identity, and numerical identity. Conceptual identity means that two terms refer to the same concept, real identity means that they refer to the same real thing, and numerical identity means both. The saints seek to argue that the persons of the Trinity are really identical, but deny that the persons “differ only in our way of thinking”—which, given that they are really identical, is the only way that they can differ.
John Duns Scotus attempted to avoid this conclusion by introducing another kind of identity called “formal identity,” somehow intermediate between real and conceptual identity. According to Scotus, “in Socrates there is human nature, which is ‘contracted to’ Socrates by an individual difference which is not really but only formally distinct from this nature,” [14]Note 14. Ockham, Philosophical Writings p. 37. making human nature and Socrates’s nature really the same but formally distinct. A “formal distinction” between the persons of the Trinity, such that they are really identical but not formally identical, would rescue Thomas’s interpretation by showing how the persons of the Trinity differ while remaining really identical. Yet Ockham dismisses Scotus’s “formal distinction” as “wholly untenable” [15]Note 15. Ockham, Philosophical Writings p. 37. for several reasons, the first of which will suffice to demonstrate his point. A distinction between things exists outside the mind only if those things really differ in some way. If human nature and Socrates’s nature differ, they must be really distinct: “[Human] nature is not formally distinct from itself; this individual difference [Socrates’s nature] is formally distinct from this [human] nature; therefore this individual difference is not [really] this [human] nature.” [16]Note 16. Ockham, Philosophical Writings p. 37. Two entities must be really distinct to be formally distinct, contradicting Scotus’s claim. A conceptual distinction is in the mind, and a real distinction is outside the mind, but where is a formal distinction? Nowhere.
But for a moment, set aside everything I have argued about the Trinity. Consider that it might be coherent after all. Is belief in Christian doctrine vindicated? Not in the least, except among the group of people who have all discovered a coherent interpretation of Trinitarian doctrine. It is unreasonably generous to expect even ten thousand people to have discovered such an interpretation, since even the most brilliant and insightful Christian saints have explicitly doubted the coherence of their own interpretations. Perhaps the belief in Christian doctrine among those ten thousand people—all of them probably obscure academics—is rational, but what about the other approximately three billion Christians? All of them either believe in a direct contradiction or believe that the contradiction is true because someone else has figured it out—which, as shown earlier in Emily’s case, only makes the problem worse. Within a rounding error of about one hundredth of one percent, everyone who believes in Christian doctrine is either maximally gullible or fundamentally rejects logic—and is in either case irrational.
One may wonder how Ockham himself affirmed Trinitarian doctrine, considering that he refuted so many ideas that other theologians invoked to justify its coherence. Disappointingly, his answer is to simply assume that the authority of the Bible and Christian tradition are true. When discussing the rule of inference that would render the argument “every divine essence is the father, the son is a divine essence, therefore the son is the father” [17]Note 17. William of Ockham, Summa Logicae, trans. The Logic Museum, book III, pt. I, ch. 4. valid (“the dici de omni” [18]Note 18. Ockham, Summa Logicae III.I.4: “[S]uch syllogisms are good: ‘every coloured thing exists, every white thing is coloured, therefore every white thing exists’; ‘every animal is a man, every donkey is an animal, therefore every donkey is a man’ … since those syllogisms are governed by the dici de omni and are evident of themselves.” In short, “the dici de omni” rule says that “every X is Y” and “Z is an X” deductively entails “Z is Y.” rule), he claims that “when such a discourse holds, and when not, cannot be known except when in sacred scripture or from the determination of the church.” [19]Note 19. Ockham, Summa Logicae III.I.5. Since I am currently examining whether Christian doctrine is true, assuming its truth would make my examination pointless. Ockham’s “solution”—if it can even be called a solution—has no relevance here.
John Duns Scotus attempted to avoid this conclusion by introducing another kind of identity called “formal identity,” somehow intermediate between real and conceptual identity. According to Scotus, “in Socrates there is human nature, which is ‘contracted to’ Socrates by an individual difference which is not really but only formally distinct from this nature,” [14]Note 14. Ockham, Philosophical Writings p. 37. making human nature and Socrates’s nature really the same but formally distinct. A “formal distinction” between the persons of the Trinity, such that they are really identical but not formally identical, would rescue Thomas’s interpretation by showing how the persons of the Trinity differ while remaining really identical. Yet Ockham dismisses Scotus’s “formal distinction” as “wholly untenable” [15]Note 15. Ockham, Philosophical Writings p. 37. for several reasons, the first of which will suffice to demonstrate his point. A distinction between things exists outside the mind only if those things really differ in some way. If human nature and Socrates’s nature differ, they must be really distinct: “[Human] nature is not formally distinct from itself; this individual difference [Socrates’s nature] is formally distinct from this [human] nature; therefore this individual difference is not [really] this [human] nature.” [16]Note 16. Ockham, Philosophical Writings p. 37. Two entities must be really distinct to be formally distinct, contradicting Scotus’s claim. A conceptual distinction is in the mind, and a real distinction is outside the mind, but where is a formal distinction? Nowhere.
But for a moment, set aside everything I have argued about the Trinity. Consider that it might be coherent after all. Is belief in Christian doctrine vindicated? Not in the least, except among the group of people who have all discovered a coherent interpretation of Trinitarian doctrine. It is unreasonably generous to expect even ten thousand people to have discovered such an interpretation, since even the most brilliant and insightful Christian saints have explicitly doubted the coherence of their own interpretations. Perhaps the belief in Christian doctrine among those ten thousand people—all of them probably obscure academics—is rational, but what about the other approximately three billion Christians? All of them either believe in a direct contradiction or believe that the contradiction is true because someone else has figured it out—which, as shown earlier in Emily’s case, only makes the problem worse. Within a rounding error of about one hundredth of one percent, everyone who believes in Christian doctrine is either maximally gullible or fundamentally rejects logic—and is in either case irrational.
One may wonder how Ockham himself affirmed Trinitarian doctrine, considering that he refuted so many ideas that other theologians invoked to justify its coherence. Disappointingly, his answer is to simply assume that the authority of the Bible and Christian tradition are true. When discussing the rule of inference that would render the argument “every divine essence is the father, the son is a divine essence, therefore the son is the father” [17]Note 17. William of Ockham, Summa Logicae, trans. The Logic Museum, book III, pt. I, ch. 4. valid (“the dici de omni” [18]Note 18. Ockham, Summa Logicae III.I.4: “[S]uch syllogisms are good: ‘every coloured thing exists, every white thing is coloured, therefore every white thing exists’; ‘every animal is a man, every donkey is an animal, therefore every donkey is a man’ … since those syllogisms are governed by the dici de omni and are evident of themselves.” In short, “the dici de omni” rule says that “every X is Y” and “Z is an X” deductively entails “Z is Y.” rule), he claims that “when such a discourse holds, and when not, cannot be known except when in sacred scripture or from the determination of the church.” [19]Note 19. Ockham, Summa Logicae III.I.5. Since I am currently examining whether Christian doctrine is true, assuming its truth would make my examination pointless. Ockham’s “solution”—if it can even be called a solution—has no relevance here.